Homeschool Math Blog

2012-01-28T17:13:00.002-04:00

Bon from Math is not a four-letter word made this little counting song, sung to the tune of "Twinkle Twinkle Little Star". Hope your little ones enjoy it!

Three-day sale for Math Mammoth

2012-01-24T08:37:00.004-04:00

SORRY I forgot to post it here (I just sent this to my email list).

For January 23-25, get 23% off of all Math Mammoth downloads & CDs
at Kagi store.

Use the coupon code THREEDAYS.

Go to http://www.mathmammoth.com first, then find the links to
Kagi's order pages. OR, use these direct links:

~ Light Blue series (complete curriculum)
https://store.kagi.com/cgi-bin/store.cgi?storeID=5KN_LIVE&page=Math_Mammoth_LightBlue_Series

~ Blue series
https://store.kagi.com/cgi-bin/store.cgi?storeID=5KN_LIVE

~ Golden and Green Series
https://store.kagi.com/cgi-bin/store.cgi?storeID=5KN_LIVE&page=MathMammoth_Workbooks

~ Make It Real Learning workbooks
https://store.kagi.com/cgi-bin/store.cgi?storeID=5KN_LIVE&page=Make_It_Real_Learning

~ Bundles (CDs or downloads)
https://store.kagi.com/cgi-bin/store.cgi?storeID=5KN_LIVE&page=Math_Mammoth_Packages

THREE DAYS ONLY!

Triangle puzzle - equal areas

2012-01-23T12:11:00.000-04:00

I hope Pat doesn't mind that I copied the image from his blog... He posted this triangle puzzle on his blog and I thought you might enjoy it, too!

Basically, we have a triangle DFE inside a rectangle, dividing the rectangle into various triangles. And, the three areas of fainter color are equal. That is, the area of the triangle DAE = area of the triangle EBF = area of the triangle FCD. (Notice the image is not drawn to scale at all.)

And, we're asked to solve the RATIOS AE : EB and BF : FC.

I'll post a solution later.

Versa Ruler

2012-01-23T11:20:00.000-04:00

Well, this IS something different! A physical ruler that can draw shapes with any angle measure you want.

Unfortunately it's not yet in production. In fact, the project is needing funding... but very interesting! Please read more at

Rule Like Never Before! NEW Shape-making Versa Ruler

This ruler give you accurate measurements for every side and angle. You can connect sides to form angles, which scale and skew smoothly, and you can lock angles and sides. Cool!

Vi Hart and mathematical doodling

2012-01-21T08:59:00.000-04:00

I just learned about Vi Hart's "doodling in math class" videos (hat tip goes to Fawn Nguyen).

Vi calls herself mathemusician - and definitely, she's a talented and smart gal! I'm sure you'll enjoy her videos (as long as you can follow her super fast speeaking). Here are some that I enjoyed:

Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]

Here's a link to learn more about Fibonacci numbers in nature, so you can read about it at a slow pace : )

Binary Hand Dance was pretty cool too!

Her series of "mathematical doodling" videos have become somewhat of a viral success. Here's one more:

Doodling in Math Class: Infinity Elephants

Math teachers are at play again

2012-01-20T20:32:00.001-04:00

Denise's done a beautiful job with the current Math Teachers at Play carnival number 46, lots to read and explore and see... head on over!

Compound interest

2012-01-09T23:57:00.003-04:00

Photo courtesy of Mooster

Someone sent me in a question concerning compound interest...

Please send me the formula for compound interest and explain line by line.

p(1 + rate)³

What does the 1 stand for and must you add it to the rate of say 10%?

100(1+10)^{3 years} = ???

Obviously I am looking for a basic course?

The formula that this person is using is correct... the formula for compound interest is

A = p(1 + r)^t

but this formula doesn't give us the amount of interest -- it gives us the amount of money you would withdraw after t years.In the formula, p is the original principal, r is the interest rate, and t is the time in years.

However, we cannot put the interest rate in as he did. If r = 10%, then r = 0.1 must be used in this formula. In other words, FIRST convert your percentage into a decimal.

For example, if the principal is $5000 and r = 10% = 0.1, then we get

A = $5000 × 1.1^t

The number 1 in the formula p(1 + r)^t doesn't stand for anything by itself. It comes from using the distributive property in simplifying p + pr into p(1 + r).

Which, p + pr is the principal + interest earned after one year; that is what you could withdraw after one year.

BUT if you don't withdraw it, but leave it all to earn more interest, then that becomes your "new" principal, and the year after that you will have that times 1 + r.

Basically, this is how compound interest works:

After year 1: You have p + pr which is p(1 + r). Notice that your original principal got multiplied by (1 + r). If you leave this on the account to earn more interest, then next year you have that amount times (1 + r).

After year 2: you have p(1 + r)(1 + r). If you leave this on the account to earn more interest, then next year you have that amount times (1 + r).

After year 3: you have p(1 + r)(1 + r)(1 + r). Let's simplify this using an exponent: You have p(1 + r)³

After year 4: you have p(1 + r)⁴

And so on. After year t, you have p(1 + r)^t.
Hope this helps some!

Math Mammoth & Common Core Standards - announcement

2012-01-02T10:48:00.002-04:00

I will be aligning Math Mammoth to the Common Core standards. This might take me half a year. Thus far it looks like just minor changes for grades 1-5, and a bit more changes for grade 6.

Nearly all US states (only 5 or 6 haven't) either have adopted or will adopt the Common Core standards, so this means that Math Mammoth will probably be aligned to YOUR state's standards as well!

Actually, Math Mammoth is even now fairly well aligned to the Common Core standards. Common Core standards are based on having a few "focus" areas for each grade level (instead of the "inch deep and mile wide" curriculum so prevalent in the past), and Math Mammoth being a mastery-based program has always had similar basic focus areas for each grade.

Math Mammoth books and their origin - video

2011-12-27T16:37:00.001-04:00

Here's a little 2-minute video of me talking about Math Mammoth books, their origin, and also featuring "Mathy" the mammoth. : )

Fraction videos, part 2

2011-12-26T17:09:00.003-04:00

I have created a set of 11 fraction videos that cover simplifying fractions, multiplying fractions by whole numbers, multiplying fractions by fractions, multiplying mixed numbers, fraction multiplication and area, simplify before multiplying, dividing fractions, ratios, and converting fractions to decimals.

That's a good bunch of fraction arithmetic!

You can use these fraction videos to supplement Math Mammoth Fractions 2 book, or Math Mammoth Grade 5-B complete curriculum. Pre-service or working teachers could use these as lesson plans for fraction topics. Students can of course learn as well, because the videos are meant for both students and teachers.

The other "half" of fraction arithmetic is on this page--9 videos.

These two pages have a total of 20 videos - over 3 hours of fraction instruction, for free. It would fill a DVD... but I've uploaded them to Youtube for everyone to enjoy and benefit from.

Area & perimeter activities - a teacher's experience with Math Mammoth

2011-12-20T10:42:00.000-04:00

Ms. Pineda used two lessons from my book Mamut Matemáticas Geometría inicial with her bilingual class. Below is her lesson plan, and some reflections. I asked her some questions.

How did the children like the activities?

The worksheets were a great guide for them because they kept them focused, and the amount of , "What do I do?" questions were very minimal.They seemed comfortable referring back to the worksheets for definitions and examples. I also noticed there was a lot less hand-raising.

How did you like using Math Mammoth materials?

It definitely made my job easier, because I did not have to continue going back to each group to explain what are or perimeter were. The definition was in front of them along with examples.

How many class periods did you use them?
It took us two 45-minute periods to complete all the activities. The students were so engaged they did not want to quit.

Did you use both English and Spanish, or only Spanish worksheets?
I only used the Spanish versions, but I plan on assigning the English for homework when we return in January.

Did you give them any homework?
They were able to keep their booklets in their math folder in order to refer to them in the future. They will usually go back and complete any unfinished assignments.

LESSON PLANS & PICTURES

AREA

Area and Perimeter Activities
Ms. Pineda, 3rd Grade Bilingual Teacher

Objective: Measure the area of geometric shapes using square units.

Materials: Comenzando con área worksheet (a lesson from Mamut Matemáticas Geometría inicial),, attribute blocks, ¼ - ½ inch graphing paper, pencil, mini booklet made from manila paper, markers or crayons.

Procedures:

Use the worksheet to discuss how area is calculated.
Trace a shape using your pencil.
Count the whole squares by writing the numbers.
Combine two halves to make a whole square.
If one of your shapes crosses four squares, combine them to make a whole.

Once you have calculated the area of each shape. You may color it and glue it in your mini booklet.

PERIMETER

Objective: Measure the perimeter of geometric shapes in inches.

Materials: Perímetro worksheet (a lesson from Mamut Matemáticas Geometría inicial), attribute blocks, pencil, ruler, mini booklet made from manila paper, markers, and crayons.

Procedures:

Use the worksheet to discuss how perimeter is calculated.
Trace a shape on your booklet using your pencil.
Measure each side of the shape in inches.
Add the lengths to find the perimeter of each shape.
Combine two halves (½ + ½ = 1)to make a whole inch.
Trace the edges of each shape with a marker and color the area with a crayon.

Perímetro = 2 + 2 + 1 + 1 + ½ + ½ = 7

MathMammoth.com new home page design

2011-11-29T07:45:00.001-04:00

I've given the home page at www.mathmammoth.com a "lift" (new design)... go check it out, see if you like it!

Currclick Cyber Monday freebies

2011-11-28T12:39:00.001-04:00

Currclick has 8 + 2 freebies just for today (Cyber Monday)!
One of them is a physics book... I'm downloading it right now.

Happy Thanksgiving!

2011-11-24T12:35:00.001-04:00

Happy Thanksgiving!

Last year my kids learned this silly rhyme

A turkey is a silly bird
whose head goes wobble wobble
It only knows this one word
gobble gobble gobble!

Here's a video of kids shouting it...

Remember also Math Mammoth Thanksgiving sale... all my products are 25% off at Kagi store. See my website for details.

And happy Thanksgiving!

Math Mammoth reviews galore

2011-11-22T13:14:00.001-04:00

Click here to read a bunch of recent Math Mammoth reviews, by TOS review crew.

A few highlights:

TOS Review: Math Mammoth from Miscellaneous Musings
"My daughter took a break from her other math curriculum and began focusing just on fractions with the Math Mammoth blue series which includes explanations. About three weeks later she was able to test out of an entire text on fractions"

Review: Math Mammoth from Footprints in the Butter
"And I started this school year completely stressed about what to do with math.So finding out I'd be reviewing Math Mammoth again this year was a gift from God."

Math Mammoth -- A TOS Crew Review from Mountaineer Country
"Do you know what my daughter said to me? She said, rather matter-of-factly, “Why haven’t we been doing this all along? I love this math.”

TOS Review Math Mammoth from Circling Through This Life
"She really enjoys it. She calls it her “Elephant Math” and insists that Manny, her woolly mammoth do math with her. "
This review has a cute picture of a stuffed mammoth next to the girl's math work!

Math Mammoth~ TOS Review from Adventures in Unsell Land!
"We have used quite a few various math programs through the years between our 6 children and I have never seen one that is as strong on the mental math as Math Mammoth is. It's my favorite aspect of this program."

Math, it’s a Mammoth responsibility from A Teaching Heart
"It is suggested that you introduce multiplication before division, but other than that, you can proceed through the lessons as you wish. I find that mixing up the learning of multiplication with other math concepts gives Hunter’s brain a chance to process and retain facts. So we will be jumping around the books all year."

More reviews here!

Class Dismissed - a film about homeschooling

2011-11-19T10:13:00.001-04:00

I'm just spreading the word on an upcoming film about homeschooling. The movie is called Class Dismissed.

It does sound interesting, though I cannot be sure what all it will include.

The website says:

QUOTE
Class Dismissed will be the first full-length documentary devoted to exploring homeschooling as a viable alternative to traditional schooling.

As homeschoolers ourselves, we are constantly reminded by the degree to which the public misperceptions of homeschooling are far removed from reality. With this documentary we hope to both educate the general public as well as inspire the existing homeschool community.

Class Dismissed will focus on the topic of education, specifically the validity of homeschooling as an alternative to the industrial school model. Framed within the historical context of traditional schooling, and particularly at a time when education across the nation is in a state of crisis, the film will examine the numerous approaches to home learning, exploring both its history and recent growth. UNQUOTE

Take a look: Class Dismissed.
Also... the filmmakers are having a fund raiser right now — the campaign ends in 22 days.

A teacher's experience with Math Mammoth Geometry 1

2011-11-11T12:12:00.001-04:00

I intend to publish several of these "stories" or "reports" from teachers who have been using Math Mammoth. Here's the first one, from Megan in Belgium. She used some lessons from my Math Mammoth Geometry 1 book.

Presentationof the Class and the School

I am a1^st,5^thand 6^thgrade teacher in south Belgium. My school is what we call an“immersive school”. The students are taught in French, theirmother tongue, 14 periods a week. During the other 10 periods eachweek, class is given in English – the students are “immersed”in the language from the age of 5 and learn to speak this language ina very natural manner.

Becauseof these awkward hours, we teachers “share” the classes. In orderto have a full schedule, I give class in English 10 hours a week in5^thgrade, 10 hours a week in 6^thgrade and 4 hours a week in 1^stgrade. We also split the subjects between French and English – andGeometry is one of the subjects seen in English.

Now,the immersive program is not without its downfalls, one of whichbeing that we must consecrate two times as many periods per week onLanguage Arts, as we have both the French and the English language toteach. As a result, we have less time to teach everything else.

I amalso a first-year teacher, thrown into this system with no life-linesto cling to! I was searching desperately for a guide, something tohelp me, but also for something that would help my studentsunderstand this subject that is such a part of our everyday lives,yet seemingly so abstract. When I saw Maria Miller’s offer – one“free” e-book in exchange for a report of my experiences – Icouldn’t turn it up! So, without further ado, here is what I haveto say about Math Mammoth.

Session1

Istarted the year teaching lines and angles to both the 5th and 6thgraders. Most of the 5^thgraders did poorly on the test and some of the 6^thgraders needed a refresher course.

Forthe 5^thgraders, I dove right into the Geometry 1 Elementary Math book inorder to review the different lines and angles, as well as how todraw them (chapters Lines, Rays andAngles and DrawingRight Angles). I did not print out andphotocopy the pages exactly as they were, I chose instead to pick andchoose the exercises I found most appropriate for my students at themoment. I must say though, I felt no need to modify any of theproblems, as I usually do with workbooks.

Thereaction from my students was a good one, especially concerning theterm ray.Most of them had such a hard time remembering what a ray is and theimage of the sun and its rays was just the trick they needed! Theirresults were very satisfactory – though they all had a hard timewith the construction of the squares and the rectangles! I don’tthink they’ve passed a lot of time on that as of yet, and I hope itis a point that MM covers more thoroughly later on in the program.All in all, the weaknesses I noticed from the test have now beenovercome, except for one or two exceptions of course.

Agreat point about these exercises is that I could let most of theclass work independently while I spent a bit more time helping theslower/weaker students. Everything is very clearly explained and easyto follow and understand, even for 5^thgraders whose native language is not English.

Forone of my 6^thgraders, I started him off with the chapters MeasuringAngles and DrawingAngles as I noticed he had difficultiesusing his protractor. Once again, I did not give him all the pages inthese chapters, nor did I alter anything. (As a side note, it isquite nice to have such a great bank of problems at the ready – Iusually spend more time perfecting my worksheets than the childrenspend working on them!) He whizzed through the exercises and trulysurprised me with his improvement. It’s as if a light bulb went offin his head. I don’t know if it’s because of the book’sexplanations or not, but I’m glad it happened! He’s now at thesame level as the others.

Myother 6^thgraders did not receive sheets from this book during this period.

Sessions2 and 3

Forthis work period, I combined the chapters Measuring Angles and DrawingAngles for the 5^thgraders. I let several children do some examples on the board andthen students worked quietly on the worksheets (which, again, I didnot modify, save the page-layout). They finished these quickly,though that was because of laziness from most of them. They wereconvinced that the angle was still alright; even it was a few degreesoff! The papers were returned to them the next day and the redoneangles were more than acceptable.

I amnot sure about this, but I am getting the impression that Belgianstudents see certain geometry concepts earlier than their Americancompatriots. I am not saying that these concepts are known andmastered by Belgian children (far from it! :p), but they do have somebases to work from. I have yet to explain a point starting from zeroknowledge, though the book sometimes seems to suggest that theconcept is completely new.

Nevertheless,the MM book is so clearly laid out and the explanations are soconcise and understandable that I feel more confident myself inexplaining the different concepts to my students. Also, it is a loteasier for students to look at a piece of paper right in front ofthem and follow along with the pictures than just doing the exampleson the board alone. The drawn protractors act as a sort of teacher’saide – I don’t have to walk around to verify that each child hasplaced their protractor how they should because they can clearly seehow the protractor is supposed to be on their paper.

Also,it was very practical as I make sure to have the papers for the nextlesson printed out for my “ace” students that always finish wellbefore the others. Because of their clarity, these students can oftenget right to work without any additional explanations.

The6^thgraders are busy doing precision drills and going over drawing basicgeometric shapes (I’m surprised at how many of them have a hardtime drawing a square!), though I am not using MM for their work.

Session4

Thissession was dedicated to the EstimateAngles chapter in MM. This was a breezefor my 5^thgraders – much to my surprise! We started the lesson out by doing afew examples “in real life” using chalk on the playground outsideand our giant chalkboard protractor. Walking the lines and making theturns themselves really helped them understand what the directionsmeant when they said “turn 45° to the left”.

I mustadmit though, the last exercise had everyone baffled! I still don’tknow what the secret message is (I could look at the answer key, butwhere is the fun in that?)! Nevertheless, the children enjoyed trying to figure it out, andthen trying to find where they went wrong in their drawings. Itbecame a very rich activity in which the children analyzed and foundtheir own errors, as well as the errors of others.

Sessions5 and 6

Weworked on the chapter Parallel andPerpendicular Lines for these last twosessions. These concepts had already been touched upon in theearlier chapters, so it was more of an in-depth review than a newconcept for them. This really helped set things straight in theirheads and served as a great closing lesson for the first part of theschool year, before leaving for a week of vacation. Most of the workduring these two sessions was done individually while I worked with afew children in need of an extra boost.

Evaluations

Iincluded three evaluations in this first part of the MM curriculum:one on Lines, Rays and Angles;another on Measuring, Drawing and Estimating Angles; and the last one onParallel and Perpendicular Lines.These were tests that I created myself, based on the concepts coveredin the MM chapters.

Inever had more than three or four students out of twenty fail thetests, but these are also the students who present very importantweaknesses in nearly every subject matter. The other results weremore than satisfactory and provided for a very impressive firstreport card. (As a first-year teacher, I was very proud to have beenable to show the parents that their children had indeed learnedsomething with me.)

Continuation

I planon using MM for the rest of the year with my 5^thgraders, while adding my own touches. We’re going to start with thetriangles, but before using MM, I would like to use a more activeapproach for the discovery of the different types (let them createthe different triangles themselves, for example).

FinalWord

I findMM to be very complete, though a bit traditional. Perfect forhomeschooling parents who have little or no pedagogic experience, butI think it could benefit from the addition of a few hands-ondiscovery sessions. (Though I do believe that Maria speaks of acurriculum that shows how math is useful in everyday life… thiscould also be very interesting for a hands-on approach…) I have noproblem with the hands-on approach, but I was rather blocked by thetheory part of the geometry… MM is my perfect complement! I wouldhave been very lost this year if not for this amazing find.

Iwould like to thank Maria for this wonderful opportunity, apologizefor the absence of photos (I always get so caught up in my lessonsand with my students that the camera stays inactive on my desk!) andI do hope that my words and my experiences can help convince othersof MM’s wonderful structure, clarity and presentation.

Click the link to read more about the book Math Mammoth Geometry 1 and to see its FREE sample pages!

A free math assessment test

2011-11-09T07:21:00.001-04:00

LexxLearn is a new company and is offering a free math assessment test online. It's currently based on Massachusetts standards but is surely useful if you need to benchmark your student, wherever you live.

The grade levels offered are from grade 3 through grade 10. Each grade level test has about 35 questions.

You will need to supply your email address and create a password, which will then allow you to come back and continue the test at a later time.

Basics of percent of change - with videos

2011-11-06T08:05:00.001-04:00

The two videos below have to do with basics of percent of change, where you are given the initial and final quantities, and you have to calculate the the percent of change (percent change, percentage change).

The main formula I use is to calculate the DIFFERENCE in the quantities divided by the original quantity. Then this fraction is written as a decimal, and as a percent.

In the second video, I solve two word problems that involve percentage change - one having to do with percentage increase in area, and another where the price of a washer is discounted by 10%, then by another 10%, and we are asked the total discount percentage--yet the PRICE of the washer is NOT given!

Teachers - feel free to use these problems in your teaching!

I have recently been making lots of videos, aiming to produce full playlists for certain topics such as percent, decimals, and fractions. I also have many older videos on various topics. Click the image on the left to see my Youtube channel and see what I have uploaded thus far.

Winning the lottery with math?

2011-11-04T13:01:00.000-04:00

An article that might interest some of you... it talks about 15 mathematicians who used their knowledge of mathematics and statistics to be able to win in lotteries, blackjack, roulette, and other games that should be based on pure chance.

15 Brilliant Math Geeks Who Outsmarted the System

Some did nothing illegal and simply used their knowledge to their own advantage, others used their math skills to cheat and lie their way into millions, and some figured out a system just for the fun of it.

What fraction of the elephants is blue?

2011-11-02T17:00:00.000-04:00

Someone sent me a nice word problem to solve:

Image courtesy of Wednesday Elf - Mountainside Crochet

Bob went to the zoo last week and was captivated by the lovely baby elephants. Some were pink and some were blue. When he counted the elephants, he found that the number of pink elephants was 2 1/2 times the number of blue elephants. What fraction of the elephants was blue?

First of all, think: which ones are less, blue or pink? Clearly, the blue ones are less. Make those kind represented by ONE BLOCK or one unit.

So, let's let the BLUE elephants to be |----| (one block).

Then, the pink ones would be |----|----|--| (2 1/2 times as many)

Now, to get the fraction asked, I could use those little dashed lines in my blocks... See, I made each block have 4 little dashes ---- and the half-block has two.

So, the Blue elephants are "four dashes" and the pink ones are "ten dashes". I know that in reality we don't know how many blue or pink elephants there are, but this won't matter if we only want to know what FRACTION or what PART of the elephants are blue. So we might as well assign some quantities here that fit the problem.

From this, we can write the fraction. Blue elephants are 4, total elephants are 14, so 4/14 of the elephants are blue. This simplifies to 2/7.

You can also get the same answer this way: blue elephants are 1 block, and there are a total of 3 1/2 blocks of elephants. The fraction is 1 / (3 1/2) which is equivalent to 2/7 (multiply both numerator and denominator by 2).

Tiling word problem

2011-10-27T15:54:00.002-04:00

Someone sent me this problem to solve, so here goes:

Photo courtesy of Brajeshwar

Square polystyrene tiles, 50 cm by 50 cm, are used to cover the ceiling of a classroom measuring 7.4 m by 4.5 m

1. Find the number of tiles that are needed.

2. Find the total cost if one tile costs $130.

Now, consider the room that is 7.4 m by 4.5 m. The tiles will not fit exactly along the 7.4-meter side, so we will need to cut some of the tiles. So we might as well consider it to be 7.5-meter side for the purpose of figuring how many tiles we need.

Along the 7.5 meter side we would need 15 tiles, each 0.5 m. Why? Because 0.5 fits into 7.5 exactly 15 times. It's essentially a division problem... 7.5 ÷ 0.5 but you can solve it mentally by thinking that each meter takes 2 tiles, so 7.5 meters takes 7.5 x 2 = 15 tiles.

Similarly, along the 4.5 meter side you would need 9 tiles, each 0.5 m.

Therefore in total we need 15 x 9 = 135 tiles. Some of those will need cut!

The cost will be 135 x $130 = $17,550. This would be expensive tiling... but I realize the person sending the question might have used some other kind of money units (not US dollars)!

Math Teachers at Play

2011-10-23T14:58:00.000-04:00

The most recent edition of Math Teachers at Play is now up at Maths Insider... beautiful and inspiring! Go take a look and enjoy!

Free kindergarten math ebook

2011-10-21T12:34:00.002-04:00

Renee from SchoolSparks.com is offering a totally free ebook for kindergarten math! It basically is a worksheets collection for K, colorful and beautiful.

The book covers number recognition, counting, patterns, sorting and classifying, and an introduction to graphs, and has 53 pages.

In addition to this very nice e-book, Renee also has hundreds of free kindergarten worksheets for parents and teachers to download and use at home or in the classroom.

Kakuro - cross-sums puzzle

2011-10-19T18:42:00.002-04:00

Kakuro is a numeric crossword puzzle that uses sums.

You fill in the white space using digits 1 to 9. The little numbers indicate what the sum of the neighboring row or column of blocks should be. You cannot use the same digit twice in any sum, so for example 12 cannot be 4 + 4 + 4.

It is considered more challenging than Sudoku, but just as addictive to its fans!

I find it gives nice simple addition practice for elementary school kids, yet is fun. You can play some Kakuro games online here. Here's another site.

This game is immensely popular in Japan, according to Wikipedia.

Free book - Geometry in Art

2011-10-14T18:55:00.000-04:00

I was told about this free download of the book Geometry in Art, by Hilton Andrade de Mello.

On the page, you need to scroll down to the words "free downloading".

This book is a basic introduction to geometry in art, with topics such as polygons, spirals, polyhedrons, tessellations, perspective, the golden ratio, symmetry, geometry and symbolism, and geometry and informatics. It has lots of illustrations and artwork by various artists, and can serve as a nice introduction for anyone who hasn't studied these topics before.

Currclick 50% off sale

2011-10-08T10:48:00.002-04:00

Currclick Affiliate Appreciation Weekend, 50% OFF sale is going on for just 2 more days. Over 4,000 titles are discounted by 50% OFF!

Just use the coupon code "appreciate" at check-out!

Click to start browsing now!

Mowing the lawn - mathematically

2011-10-05T10:56:00.001-04:00

Mowing the lawn is a oh-so familiar task to many of us. Now here's an article that approaches the problem of pushing the lawnmower the shortest distance possible mathematically.

A Victa-ry for mathematics

I'm sure you'll enjoy it! I did!

Yummy Math - real-life math activities

2011-09-26T09:07:00.000-04:00

Featuring...

Yummy Math

We provide teachers and students with mathematics relevant to our world today …

Yummy Math is actually a fantastic website. It has real-life math activities (as PDF and Doc files) that are free. The solutions, however, are only available to subscribers.

Recent topics include Starbucks, light bulbs, NFL, the U.S. Open, Labor Day, hurricanes, earthquakes, cheesy goldfish, going back to school, the hot summer, cost of diapers, or even the rescue of Chilean miners, etc. etc.

You can find real-world math activities that relate to social studies, earth science, food, entertainment, sports, holidays etc. I really like this site. The activities are well-planned and so varied!

Perennial Math - math competition

2011-09-23T23:41:00.001-04:00

Perennial Math is a new mathematics competition for students in grades 4-8. I thought some of you would be interested in it! What follows is their information that I have copied.

Your students can participate at either a team level or individual student level by registering on www.perennialmath.com. Don't worry if you cannot access the internet, you can always print and administer the tests to log in your students' scores later.

The competition consists of 5 tests each year (November-March). Each test contains 5 questions that get progressively harder. The tests must be completed in 30 minutes.

All students receive a certificate of participation and your team winner will receive a gold medal. Additional awards include plaques for teams who score in the top 10% and dog tags for each student who scores in the top 10% at each grade level. Students who get a perfect score on the test-and exceptional teams can have their name scrolling on our wall of fame.

Math in the real world

2011-09-23T23:30:00.001-04:00

I've put together a page of web resources about math in the real world. These include a website with movies that show how algebra is used in real life, a site with multimedia explorations, information about careers that require mathematics, sites with activity worksheets with real-life data, and some articles. Enjoy!

Math Mammoth for school teachers

2011-09-23T09:56:00.000-04:00

Hello!
This is a special offer I'm extending to school teachers, all around the world!

This is your chance to get Math Mammoth downloadable books for free, in exchange for making a PRESENTATION.

Here's how this thing works:

Contact me and I will send you Math Mammoth materials on a certain topic, such as basic addition or division facts or fraction addition, etc. Nearly any topic in grades 1-7.
Document (photos and/or videos) your class using the materials, and write up a "report" or a presentation, showcasing what you did, how the students liked it, and so on. It could be of a single teaching session, or it could cover a longer period of time. You could include student responses & comments, an example lesson plan, etc. Be creative...
Send me your presentation. I'll look it over. Depending on the quality and extent of your presentation, you'll then get MORE materials -- several books, or the whole Light Blue Series download, or the All Inclusive download.
I'll post your presentation on my blog for others to see! This will help and inspire others, when we share ideas of how to use Math Mammoth!

Sincerely,
Maria Miller

Math Teachers at Play

2011-09-17T18:20:00.000-04:00

Go on to enjoy the latest Math Teachers at Play blog carnival! Bon has created quite a funny "love" story about two people who have a kid... and all the math is somewhere in between!

Giveaways!

2011-09-15T10:39:00.002-04:00

I will be giving away FIVE copies of UberSmart Math Facts software to five lucky winners!

At the same time... if you don't win, David from UberSmart Software is graciously offering a BIG 40% DISCOUNT on his math facts software! The normal price is $24.95, but you can get it now for $14.97.

Click this link to take advantage of this discount.

You can also read my review.

And to boot, I will add to the giveaway THREE copies of Math Mammoth Blue Series CD (or download, if you prefer). Value: $100.

This giveaway is now closed. As usual, I got over 160 responders super quick. The 40% off discount is still valid though!

This giveaway is open to everybody, no matter where you live on this planet.

The giveaway runs till I have at least 160 participants. This will give you a 1 in 20 chance of winning. I will then choose the eight winners using the random number generator at Random.org.

Blogging as an Educational Activity

2011-09-14T22:30:00.000-04:00

Students who have trouble learning certain material by traditional methods may benefit from a lesson designed around blogging. You may increase a student’s attention in a particular subject or lesson plan with blogging because it has the draw of being an online activity. In fact, with proper boundaries and rules set out, blogging can serve as a constructive and worthwhile educational activity. Plus, working on a computer may distract your student from the fact that they’re doing something educational!

The setup for an educational blog couldn’t be easier: create a blog using a free service like Blogger or Wordpress, following their user-friendly instructions. Restrict full access to the teacher and change the blog’s settings so that students can sign on as users who can only post and view blog entries. From there it’s up to you to decide how best to start a student blogging for educational purposes. Below are a few ideas for possible educational blogging activities.

Writing Exercises
Your student could compose writing exercises to be submitted as posts to your blog. These exercises could vary from practice in formal/informal writing styles to lessons in basic syntax and grammar. The blog could substitute as your student’s workbook whereby it becomes an interactive space for all their writing assignments. And these assignments don’t have to exclude traditionally non-writing courses; you can have your student draft or solve math/science problems on their blog post as well. A blog’s greatest asset is its endless versatility.

Use blogging as a means to reinvigorate your student’s interest in a subject that they may not otherwise take to. In the case of writing, think of blogging as a way to disarm your students who show a strong aversion to the subject by presenting it in a different context.

Research Project

If you want to make the blogging experience more comprehensive, you could have your students use it as a place to document a research project. Basic research projects are a fun exercise for younger students because it helps them grasp how concepts they learn in class relate to the real world. You could assign a topic to your student—say covering a current event or the researching of key term in a lesson—and instruct them to post their findings about the topic on the blog. Encourage the student to elaborate on their findings in their blog post. If they find an interesting news article about their topic—details about a newly discovered star, for example—have them write a brief synopsis of the article and write about how it relates to the lesson that they’re researching. If the student protests the amount of writing, remind them that research projects are all about tying your findings back to the original topic.

Journaling

You could also design the blog as a space for journaling. If need be, adjust the privacy settings on your blog to ensure that it’s a safe space for your student to journal. The student could write reflections on their daily school activities or simply maintain a diary-style account of whatever interests them. Emphasize to the student that the blog/journal is their own project where they have the freedom to write about anything. Unless they write about questionable content, refrain from offering any major criticism on their journal entries. Blogging as a journaling activity can serve as a constructive creative outlet for your student; it fosters expression in a way that could warm students up to the writing process. Hindering that expression could discourage them from further writing.

Author Bio:
This is a guest post by Nadia Jones who blogs at online college about education, college, student, teacher, money saving, movie related topics. You can reach her at nadia.jones5 @ gmail.com.

Fun and practice with Roman Numerals

2011-09-13T23:40:00.000-04:00

Someone asked me recently whether I include Roman Numerals in Math Mammoth. Yes, I do... they are in the 3rd grade materials, but the section is not extensive.

For some extra fun, learning, and practice with them, check out these web resources:

Roman Numeras Tutorial
Good explanations of how numbers are formed using Roman Numerals, such as when to "add" or "subtract" the symbols. The page allows interactivity where the student can self-check his/her understanding.

Roman Matching Game
Drag the Roman numerals to the corresponding Arabic numerals. If you win the next game will be faster. See if you can beat the clock!

Roman Numerals Worksheets
Generate worksheets for converting Roman numerals to normal (Arabic) ones, or normal numbers to Roman numerals, or do easy addition and subtraction problems with Roman numerals.

Roman Numerals Dot-to-Dots
Some dot-to-dot worksheets with animal themes that use Roman Numerals.

Roman Numerals - Wikipedia
An article explaining the usage, origin, and a chart of Roman numerals.

Quia: Easy Roman Numerals
Translate Roman numerals into Arabic (covers I, V, and X only). Matching game, concentration, or word search.

Roman Numerals - A Maths Webquest
A set of web pages where you can learn all about roman numerals: how they originated, how to read & write the numerals, and places we still use the Roman number system today.

Roman Sequence Game
See how fast you can put these Roman numerals in the correct sequence.

Times Tales DVD giveaway

2011-09-05T17:55:00.002-04:00

Folks at Triggery Memory Systems are generously offering THREE copies of their new Times Tales DVD program for me to give away (for free!). Everyone is welcome to participate, no matter where you live on this planet. Shipping outside US will be by USPS First Class Mail.

This Giveaway is now closed!

The winners are:

Wes Ryan, Virginia,

Eileen Flater, Iowa, and

Erica Potter, Ohio.

Congratulations!

Winners are chosen randomly using the random number generator at Random.org. The giveaway will run UNTIL I have at least 150 responses, or till September 12, whichever comes first.

What is Times Tales?

Times Tales is a mnemonic-based program for learning multiplication and division tables. It uses simple stories to provide students with a "memory peg", allowing them to quickly
recall the facts.

CapJaxMathFax and UberSmart Math Facts programs

2011-08-30T09:39:00.003-04:00

I had the chance to look into two math facts practice programs, titled CapJaxMathFax and UberSmart Math Facts. Both programs drill math facts and keep track of your progress.

My testing "girl" liked them both just fine. Her focus definitely was on getting the percentages on the progress chart to go up (in both programs)!

CapJaxMathFax

Here's a screen of CapJaxMathFax showing a math problem to solve. It alternates the dot and cross symbols for multiplication. It also alternates showing the problems vertically or horizontally. The vertical line is my cursor blinking in the empty space.

If you answer correctly and in less than 3 seconds, it shows you the word "SUPER". Then you get the next fact by pressing "ENTER."

Personally I would have liked a little clearer workspace, but all these colors, buttons, text, etc. on the screen seemingly didn't bother my daughter.

Here is where you select what operation you want to practice, how long, etc. The "word problems" aren't really word problems, but just math facts with words instead of with symbols.

In CapJaxMathFax, you can either practice, or build your ratings. Ratings can be built when you can get "SUPER" answers—those where you answer in 3 seconds or less.

You start off with ratings of 0 in each math type. Your ratings climb as you work through each building level in the math skill types (+, -, x, ÷).

Here are my ratings after playing for a little while:

And this is the general progress chart:

The software has a free evaluation version that you can download here. Website: www.CapJax.com. The price for the software is $59.96.

UberSmart Math Facts

UberSmart Math Facts had a cleaner interface that I liked better, but it has less options. The math facts were shown as flash cards. You get a progress chart, but there aren't any "ratings" as in CapJaxMathFax.

There are three ways to practice. The first one is to View Flash Cards. The second one is to View Flash Cards and check the Beat the Clock checkbox. The third one is to take a Test. The first, "View Flash Cards" option, simply shows you the flash card and you just think the answer in your mind, and you can have the program show you the answer.

"Beat the Clock" is the main way to practice (this won't affect your progress chart). When you check this box, the flash cards become interactive and you must enter an answer before the computer answers it for you. If you enter the wrong answer, or the computer answers before you do, the correct answer is shown and that fact is moved to the end of the set, so you need to answer it again. The facts you didn't get are repeated in the set until you get them correct.

Once you think you're ready, you can take a "test". The results from tests will be shown in your progress chart. This is how you set up the practicing using the "test" option:

Here, I would like to see an option to select several tables for a test, such as 4s, 8s, and 9s. Currently it has an option for choosing one table at a time, or all of them.

This is how the flashcards look like in the test.

If you miss some facts in a test, the program will tell you what you missed after the test, and show you the correct answers.

After missing or answering slowly some facts in a particular test, such as in the 4s for multiplication, if you go to the "View Flash Cards" for that same kind of practice, you have the option of doing a "focused" viewing of flash cards. This makes the program only show you flash cards of the problems you missed or were slow in answering in the "test".

And lastly, here's the progress chart. Your goal is to get to 100%, and if you are not only 100% correct but also fast enough, it shows a neat star in the chart!

My "guinea pig" daughter was plenty motivated by trying to get the progress chart go up to 100%! (And that's how it should be, by the way... that the student would be internally motivated to learn something for the learning's sake.)

You can download a free 30-day trial of UberSmart Math Facts here.

The main website is Mathfacts.ubersmartsoftware.com/mathfacts.php. The software costs $24.95.

The main feature I'd like to see in these two programs is being more adaptive so that the program would drill those facts much more (not just one extra time) that the child has trouble with. I've seen how Math Rider does that (which I have also reviewed).

I would definitely recommend using something computerized to help children master their math facts. My children have enjoyed trying out many different programs and systems, and I feel it has been quite helpful. BUT not at first--only AFTER they have understood the concepts and the patterns in them!

I also recommend you use the free trials to check and see what program your child likes best.

My new percent lessons

2011-08-26T14:52:00.001-04:00

Need help with teaching percent-related topics? Or need help studying them? Check out these new lessons of mine -- with videos!
Click on the links to read the lessons. You can watch the videos here or on the lesson pages.

1. Percent - the concept and how to change fractions to percents.

2. Percentage of a number using mental math
For example, how to find 70% of 5,000 or similar problems.

3. Percentage of a number using decimals
The same as above, but this time we use a calculator & decimals,
not mental math.

4. "What percentage..." / "How many percent...?"
How to solve word problems that ask for the percentage.

Hating math?

2011-08-25T17:22:00.000-04:00

About this thing where people say, "I hate math", or "I'm not good at math", or "I never understood math", or similar things. It's well-known that in the U.S. at least, people seem to be able to say such things with ease -- it is totally acceptable socially -- but no one readily admits similar things about their reading abilities!

I just read two interesting posts by Bon from Math is Not a Four-Letter Word that deal with this topic... They can HELP you or others you know overcome this line of thinking.

How to Get People to Stop Saying "I Hate Math"

How to Quit Saying "I Hate Math"

You might also be interested in an old blogpost of mine: Developing a Positive Attitude (towards math).

Solar panels in a TREE model & Fibonacci numbers

2011-08-19T13:02:00.000-04:00

Did you know tree branches and leaves in a plant rotate around the trunk in a pattern based on Fibonacci numbers? That maximises the amount of sunlight that the leaves get, because it minimizes how much the upper level branches or leaves shade the lower ones.

Well, a 13-year old student has now built a "tree model" with solar panels and proven that it collects MORE sunlight than a flat array of solar panels! The article has lots of photos to show his experiments.

Giveaway of 3 copies of Math Dictionary for Kids

2011-08-11T12:49:00.003-04:00

PRUFROCK PRESS INC. is graciously donating THREE copies of their
Math Dictionary for Kids: (Grades 4-9) to be given away to my blog readers! (Only U.S. and Canada addresses, please.)

This dictionary has been recently updated and is now in full color!

Go check how it looks like inside At Amazon:

If you want to take part in the giveaway, leave a comment here, AND email me so I'll have your email address to contact you if you win.

I will run this until August 21 OR until I get 100 entries, whichever happens first. And it's only for U.S. and Canada addresses.

COMMENTS ARE CLOSED NOW... I GOT MORE THAN 100 in record time.

The WINNERS are RJC, Sheri R, and mommygirl @ HCA. THANKS EVERYONE!

AND, not only that, but Denise also has a math book giveaway at her blog... hers are for TWO books: Keith Devlin’s new e-book, Leonardo and Steve: The Young Genius Who Beat Apple to Market by 800 Years, and his latest print book, The Man of Numbers: Fibonacci’s Arithmetic Revolution. She said the number of entries was LOW, thus far. Go take part!

Math Mammoth sales in August 2011

2011-08-02T19:33:00.000-04:00

Homeschool Buyers Co-op group buy is live at
www.homeschoolbuyersco-op.org/math-mammoth

You can get Math Mammoth bundles for up to 50% off! (The discount level depends on the number of purchasers.) This is the best deal on the planet!
Currclick will have an August sale on lots of stuff starting TOMORROW AUGUST 3, including Math Mammoth books (but not bundles... they don't have a way to automatically include bundles in their sales). Math Mammoth 25% OFF! The sale runs till August 24.
http://www.currclick.com/index.php?filters=0_0&manufacturers_id=108
Concurrently I'll run the same sale at Kagi--25% off of all my books, including the CDs and bundles. Use coupon code AUGUSTSALE at Kagi checkout. Starts NOW (August 2) and runs till August 24.

Go to www.mathmammoth.com first, then find the links to Kagi's order pages. Or use these direct links:

See me stomp on a rocket (plus a free science resource)

2011-07-28T11:54:00.000-04:00

I have something a bit different to share with you today.
Supercharged Science (the science curriculum by Aurora Lipper) is giving away a neat product for free this week.

You can get a free copy here.

It's really good stuff. My daughter and me just looked at it today (Wednesday) afternoon, and we decided to do the first experiment in it (Stomp Rocket). Daddy got excited too, so we got it done in record time.

It was fun! We all stomped on the bottle, and up went the blue rocket, maybe 40-50 feet high. It was just really cool. The girls stomped on it many, many times to make it go. In fact, here are a few pictures...

OK I'm looking at my rocket & launcher and soon ready to stomp:

I stomped on it!

It went up!

Rocket up on the sky:

It's just awesome how Aurora Lipper (the founder of this science program) gives back to the community with her free products, teleclasses, and such. And my readers know how I try to do the same with my math stuff... provide free math worksheets, articles, videos, etc. for everyone to use.

Anyway, be sure to get your free copy of this science education program before the offer goes away. Get it from here:

www.sciencelearningspace.com/members/go.php?r=3095&i=l38

--

Article: education in Finland

2011-07-21T18:52:00.002-04:00

I'm not writing about this to lift myself up, no. It was an interesting read to me, of course, since I grew up in Finland, and I thought maybe some of you find it interesting as well. I never knew back then that the educational system was one of the top-notch in the whole world, but of course I am thankful!

Anyhow, the article mentions how there is no nation-wide testing. Well, there are national "matriculation" exams in the end of high school and for 9th grade, at the end of comprehensive school.

And it's true that teaching is a highly respected occupation there, which in turn attracts top-notch students to become teachers. BTW I have always felt that the MAIN problem with mathematics education in the U.S. goes back to the teachers, and not to the curriculum.

How Finland became an education leader

Another one on similar lines: West Virginia learns Finland's "most honorable profession": Teacher

I also found this article on CNN, that kind of ties in:
Why one good teacher quit. A high school math teacher is quitting and going into nursing because she can't make a living, and nurses make $20,000 more a year than she does.

How Khan Academy is changing education

2011-07-18T19:14:00.000-04:00

My hubby found this article about Khan Academy, and I think you'll find it interesting. It features this certain teacher's 5th grade classroom that is "flipped" or "inverted" -- kids listen to the teaching videos from Khan Academy at home, and do "homework" (math problems) at school.

How Khan Academy Is Changing the Rules of Education

Carnival time...

2011-07-16T09:54:00.000-04:00

Math Teachers at Play carnival is posted at Math Mama Writes blog. And it's not just for "math teachers" -- the carnival has lots of posts for elementary math, puzzles, teaching ideas, free downloads, etc. which are of interest for ALL homeschoolers and for parents who are helping children in math.

See, if you teach math at your house, you need to see yourself as a "math teacher!"

Using Math Mammoth in California

2011-07-02T13:42:00.003-04:00

I have prepared a document to help Californian parents and teachers who want to use Math Mammoth:

How to use Math Mammoth to meet California standards. As it turns out, Math Mammoth actually fares fairly well against California's mathematics standards. The table in the article lists the topics that are missing from each grade level in Math Mammoth, and resources to cover those topics.

Math museum

2011-06-28T17:40:00.000-04:00

Two articles that are probably of interest to my blog readers:

1) There will be a math museum open in Manhattan, New York, in 2012. New York Times has an interesting article about it! The museum is titled MoMath and its website is at momath.org . (Currently there are zero math museums in the United States). I hope it well!

2) 15 interesting facts about the history of homeschooling was an interesting read as well... such as when it was illegal, there's a college designed for homeschooled students (opened in 2000), how 1983 tax laws increased homeschooling etc.

Problem solving videos--bar/block model

2011-06-24T19:43:00.000-04:00

These videos show you examples of how to use the bar or block model in solving math word problems. The examples are all about 5th grade level. Enjoy! I hope they are of help!

First I solve the following word problem using a bar model (Singapore math style), taken from Math Mammoth grade 5 curriculum: Brenda and Lily shared the cost of a $11.70 lunch so that Brenda paid two times as much as Lily. Find their shares.

Next problem is this: One rake is $5.60 more than the other, and together they cost $22.70. How much does the cheaper rake cost?

And lastly, John spent 3/10 of his money, and had $45.57 left. How much did he have initially?

Order of operations and "bubbles"

2011-06-20T23:41:00.000-04:00

Or you could call it a "cloud" or "balloon", instead of a "bubble". Anyhow, the idea is simple: in a given math problem with many operations, have the child encircle in a bubble/cloud/balloon the operation to be done first. He/she can use colored pencils or crayons for more fun.

I just had this idea when my 2nd daughter was studying order of operations in addition and subtraction... that is, problems with many additions and subtractions, including parenthesis, things like

100 + 20 − (50 + 10)

or
20 − 8 − 6 vs. 20 − (8 − 6)

(Those are found in Math Mammoth grade 3 curriculum.)

So what we did was write some of the problems from the book on the whiteboard and she "bubbled" or drew bubbles around the operation to be done first. Well, her bubbles look like ovals, but she was thinking of them as bubbles--and that made it fun for her!

Click to enlarge

Then we did another fun thing, which is that she made me a difficult math problem with lots of additions and subtractions. It's seen in the bottom on the board. Then I solved it... and the answer turned out negative! Making problems for mom is always fun for little ones.

The same idea will of course work if you are dealing with multiplication and division as well.

Math Teachers at Play carnival #39

2011-06-19T18:40:00.000-04:00

The carnival is posted at Denise's blog... she's illustrated it beautifully with pictures and witty math jokes.. and lots to read and enjoy. Head on over!

Currclick back-to-the-beach freebies

2011-06-15T08:02:00.000-04:00

Currclick has a fun scavenger hunt going on again. You look for eight hidden sea creatures somewhere on the site to discover eight freebies.

Then they also have lots of items on 40% off!

Beth's bookshelf

2011-06-05T20:39:00.000-04:00

A new blog I just found about children's books that teach math concepts, and she's having a giveaway of a fraction book RIGHT NOW! Hurry!

Beth's Bookshelf

Her blog looks neat! Last week's postings all have to do with fractions and what kind of children's books can be used to teach fractions. Thumbs up, Beth!

Tux Math - review

2011-05-26T18:21:00.002-04:00

You may have never heard of Tux Math, but among Linux users it's a fairly well-known children's arcade game for math facts practice.

My girls remembered about it just lately and have had somewhat of a frenzy of practice sessions with it. It's simple, free, yet fun. So I decided to give you, my readers, a quick review of it.

You "shoot" meteorites that are falling down by answering math problems (type the problem's answer and press Enter/Return). If you can't answer one, the meteorite does some damage to one of the penguin's igloo. Then after enough damage, the penguin in that igloo leaves (walks away).

But, once you answer a red "fiery" question that falls down real quick, you can get a cloud that comes and fixes the igloo. Then your penguin comes back! I think that's so cute!! You can only lose if all your penguins go away.

The background is always an image from space.

The options include any of the four operations, or have them mixed. You can practice specific times tables for example, which is good for my younger daughter at this time. As you go along in a game, then the questions start coming down quicker. At first they come down quite slow.

There's a training section, and there's a section where it gives you random questions. In that one, you play as long as you want, and when you stop, it'll tell you if you are in the top ten highest scores for you. If so, then you go in the "hall of fame."

Once you finish any particular type of problems (for ex. addition 0-5 or multiplication by 4), the star for that turns glowing yellow, and that's what my kids are after--they want to turn all those stars yellow. That's only in the training part, though. In the training part you have to answer a certain amount of questions.

You can make as many new "accounts" as you want and fill the "hall of fame" with you and your various nicknames.

It's just simple free game for math practice; there are no special features such as reports or training the facts you answer wrong.

Tux Math, or Tux of Math Command is software that is available as a free download for Windows, Mac, and Linux. Download it here.

Win a free calculator

2011-05-19T09:09:00.000-04:00

CalculateWhat.com is running a summer calculator giveaway. The prize is a brand new TI-83 Plus graphing calculator, a $99.99 value! Also, the second runner up will get a $25 Amazon Gift Card.

Note... This is not my giveaway... I just want to pass the word. Please read the contest rules and enter at CalculateWhat/contest. Essentially they want you to link to one of their online calculator pages to enter the contest.

Review: CAMS & STAMS books from Curriculum Associates

2011-05-03T19:56:00.000-04:00

I have just finished my review of CAMS & STAMS books from Curriculum Associates... It is a series of assessment books, student worktexts, and teacher guides for struggling students that presents each math topic in a highly scaffolded manner.

These books are supplemental to any basal math curriculum, and have been specifically designed to support struggling students. Each level consists of:

a student book (consumable worktext) with instruction and exercises. This is the heart of the program, and always covers the most important topics of the grade level, as given in the NCTM Focal Points and Connections.
A test booklet, which contains a pretest, a postest, and four "benchmark" tests. The benchmark tests are to be used to monitor student progress throughout the year.
A very detailed teacher guide for the student text, and another, much thinner teacher guide for the assessment booklet.

Read the review!

A woman without hands - inspiring!

2011-04-28T17:11:00.000-04:00

An inspiring slideshow about Jessica Cox - a woman born without hands. She even learned to fly!

Jessica cox english.pps

A new template

2011-04-22T17:20:00.002-04:00

Hope you like it! I just chose one that Blogger offers. They sure have improved their templates in the last few years because when I signed up with Blogger years ago, the templates were kind of lame... much better now.

How to help a student with a fraction word problem

2011-04-22T12:00:00.000-04:00

Today, my daughter had to tackle this word problem in her 5th grade Math Mammoth (lesson Multiply Mixed Numbers):

The square on the right measures 10 in. × 10 in. and
the rectangle inside it measures 6 7/8 in. × 3 1/2 in.
How many square inches is the colored area?

This requires the student to

multiply mixed numbers,
subtract mixed numbers,
understand about area, and
understand how to find the "colored" area by subtraction of areas.

So it is a multi-step word problem.

She didn't understand it, she said. My first "help" was this:
"Let's say we change those fractions to whole numbers 6 and 3. Can you mark those in the image? Would you be able to solve the problem now?"

The strategy I used is:
If you can't solve the problem at hand, change it and make it easier. Then try to solve the easier problem.

She was able to mark 6 and 3 on the sides of the rectangle (that is inside the square). But she said she couldn't solve it. She said it's not possible to find the area of the colored area!

Then I asked her, "Is there anything you CAN find? Is there anything you CAN solve using this information?"

And this is another great strategy in solving any problem (whether math or not): If you can't find the answer to the question in the problem, solve what you CAN solve. That might lead you to find the answer to your question somewhere along the way!

I said, "Well, we CAN find the area of the square. It is 100 square inches. We CAN find the area of the rectangle inside it."

THEN immediately after I said that, she saw it: "OHH! SUBTRACT!" And on she went to multiply the mixed numbers in the problem. So the story had a happy ending!

Here's the complete solution:

First multiply the mixed numbers 6 7/8 and 3 1/2 to find the area of the rectangle. Keep in mind they need to be changed into fractions before multiplying.

6 7/8 × 3 1/2 = 55/8 × 7/2
= 385 / 16 square inches

Change this into a mixed number. Here one needs to use long division to divide 385 ÷ 16 = 24 R1. This tells us the whole number part is 24. The remainder,1, tells us how many 16th parts are "left over."

So, 385 / 16 = 24 1/16 square inches. So this is the area of the rectangle.

Now, the area of the surrounding square is simply 10 in x 10 in. = 100 square inches.

And lastly, the area of the colored area is found by subtracting 100 − 24 1/16 = 75 15/16 square inches.

Decimals videos

2011-04-21T16:17:00.001-04:00

Here are some of my recent additions to Math Mammoth Youtube channel.
- videos about decimal arithmetic.

Add and subtract decimals
I explain the main principle in adding or subtracting decimals: we can add or subtract "as if" there was no decimal point IF the decimals have the same kind of parts--either tenths, hundredths, or thousandths. Many students have a misconception of thinking of the "part" after the decimal point as "plain numbers." Such students will calculate 0.7 + 0.05 = 0.12, which is wrong, and I explain why in the video.

Multiply decimals by whole numbers
I explain how to multiply decimals by whole numbers: think of your decimal as so many "tenths", "hundredths", or "thousandths", and simply multiply as if there was no decimal point. Compare to multiplying so many "apples". For example, 5 x 0.06 is five copies of six "hundredths". Multiply 5 x 6 = 30. The answer has to be 30 hundredths (hundredths corresponding to apples), or 0.30, which simplifies to 0.3.

Divide decimals using mental math
I explain two basic situations where you can use mental math to divide decimals: 1) Think of "stuff" (which is tenths, hundredths, or thousandths) shared evenly between so many people; OR 2) Think how many times the divisor fits into the dividend.

Long division with decimals
When the dividend is a decimal, and the divisor is a whole number, long division is easy: just divide as if there was no decimal point, and then put a decimal point in the answer in the same place as it is in the dividend. I also show an example where we add decimal zeros to the dividend, in order to get an even division. Lastly I show how the fraction 3/7 is converted into a decimal using long division.

Green tea word problem

2011-04-17T08:22:00.000-04:00

Photo credit: leojmelsrub

Ahmed sent me in this kind of word problem:

A tea producer want to market mixed green tea leaves at $14 per pound. how many pounds of high mountain green tea leaves worth $20 per pound must be mixed with 90 pounds of regular green tea leaved worth $10 per pound?

I have solve many problems like this one on my blog, but it never hurts to solve some more. This can be solved with algebra, using a chart. I've done that before for similar problems... so if you are reading this, and you feel a bit "rusty" in this area, try to make the chart yourself first, before you read further!

For the chart, we also need to choose a variable or several. In this case it is easy: the unknown is obviously what is asked, or the amount of high mountain green tea. Note also that the cost is always the price per pound times the amount.

mountain green   regular green  the mixture
 tea leaves  tea leaves
--------------------------------------------------------------------------
amount |   x   90   90 + x
--------------------------------------------------------------------------
cost   |  20x   $900   14(90 + x)
--------------------------------------------------------------------------

The chart is ready. Its purpose is to help us write an EQUATION of some sort which will solve x.

So where can we find something equals something? It comes from the cost. The COST of mountain green tea + the COST of regular green tea = COST of the mixture.

20x + 900 = 14(90 + x)

20x + 900 = 1260 + 14x

6x = 360

x = 60

Now, let's check. That's always the last step in solving equations.

We need 60 pounds of mountain green tea leaves mixed with 90 pounds of regular green tea leaves. The mixture will weigh 150 pounds. The cost of mountain green tea leaves will be $1200, the cost of regular green tea will be $900, and the total cost will be $2100. Calculating cost per pound: $2100 / 150 lb = $14 per pound, so it checks.

Math vocabulary resource

2011-04-14T11:46:00.000-04:00

Would you like to help children with their math vocabulary? SpellingCity has built a resource to address this: Math vocabulary spelling lists.

If you don't know SpellingCity, no matter what kind of spelling list you use, you can always practice the words in many ways: either just simple practice AND with several different games: MatchIt Sentences, Which Word (find which word correctly completes the sentence), sentence unscramble, hang mouse, word search, word unscramble, etc. Can't even list them all.

So it is definitely a very comprehensive math vocabulary resource!

Two problems about fractional parts

2011-04-13T21:55:00.000-04:00

I have 2 questions on fractions which I can't solve.

There were 3/5 as many adults as children on a bus. At the next bus stop, 6 adults and 6 children boarded the bus. As a result, there were 2/3 as many adults as children on the bus. How many people were on the bus at first?

A solution using bar diagrams (Singapore style):

children |----|----|----|----|----|

adults   |----|----|----|

Then we have:

children |----|----|----|----|----| +6

adults   |----|----|----| +6

Here look at the difference of children and adults. There are two "blocks" more children than adults. We know the number of adults is 2/3 of the number of children... therefore the DIFFERENCE of two blocks must be 1/3 of the children.

Now look:

children |----|----|----|----|----| +6

Two of those blocks is 1/3 of the total... the other two blocks is another 1/3 of the total... so |----| +6 or one block and 6 must be 1/3 of the total.
This means the +6 must be one block. Or, one block = 6. This now solves the problem, because originally we had 8 "blocks" of people, or 48 people.

Solution with algebra:
Let c be the number of children at first. There were (3/5)c adults at first.

Then 6 more adults and 6 more children come in, so now we have c + 6 children, and (3/5)c + 6 adults.

Now, the amount of adults = (2/3) of the amount of children.

(3/5)c + 6 = (2/3)(c + 6)

As this equation has fractions, let's multiply both sides by 15 to start.

9c + 90 = 10(c + 6)

9c + 90 = 10c + 60

30 = c

There were 30 children and 18 adults at first, or 48 total people.

2/5 of the counters in a box were red and the rest were blue. After putting another 48 blue counters into a box, 3/4 of the counters were blue. How many counters were in the box at first?

A solution using bar diagrams (Singapore style):

blue |----|----|----|

red  |----|----|

Then:

blue |----|----|----| + 48

red  |----|----|

...and now 3/4 of the counters are blue. So, |----|----| (the red ones) or two blocks is 1/4 of the counters. Therefore there are a total of 8 blocks of counters. but I drew five blocks and 48. So, 48 must be worth three "blocks", or one block is 16.

At first we had five "blocks" of counters, or 5 x 16 = 80 counters.

CHECK:
80 counters... 32 red and 48 blue.
Add 48 blue. Now we have 32 red and 96 blue, a total of 128.
Reds are 32/128 = 8/32 = 1/4. That checks.

A solution using algebra:
At first, we have (2/5)c counters red and (3/5)c counters blue. ONce we hadd 48 blue counters, we have (2/5)c red counters and (3/5)c + 48 blue counters, and c + 48 total counters. It says now 3/4 of the counters are blue. We write that as an equation:

(3/4) of all counters = number of blue counters

(3/4)(c + 48) = (3/5)c + 48 Multiply this by 20.

15(c + 48) = 12c + 960

15c + 720 = 12c + 960

3c = 240

c = 80

There were originally 80 counters.

Metal brainteasers

2011-03-30T11:15:00.002-04:00

Monkey Pod games produces high-quality, yet affordable wooden and metal brain teasers and puzzles. I got to review their Metal Brain Teasers Gift Set II. It has four things in it.

These were lots of fun to try to figure out. There's a double horseshoe with a ring that I was able to figure out eventually. This set of two pins was the easiest to solve:

The other two were harder (free the heart, and separate the two M-shapes). My hubby spent quite a while with the M-shapes but eventually got the solution for that one from their website.

Like I've said before, they make excellent gifts. This set comes in a nice wooden box but you could, if you wanted to, split the gifts and give just one brainteaser to three different children—or adults.

They also sell two other metal brainteaser sets:

Monkey Pod Games also has tons of wooden puzzles and brainteasers, some of them less than $10. Check them out! Hey, I got to playing around with Blogger's Amazon tool and found some images for you real quick... click for more info.

Math Teachers at Play #36

2011-03-29T23:07:00.002-04:00

I'm terribly sorry I forgot to mention Math Teachers at Play carnival this last time it was published (which is over a week ago). I noticed it in the morning, was gone for part of the day, and then forgot about it. The carnival looks great and is filled with lots of nice posts about all sorts of things, related to mathematics... please go check it out, and enjoy!

Math Teachers at Play carnival #36

Math genius at age 12

2011-03-28T22:11:00.000-04:00

Some of you might enjoy reading this article... a 12-year old boy (Jacob Barnett) is about done studying college-level studies in astrophysics and they want him to start doing research. He's also mildly autistic.

Genius at work: 12-year-old is studying at IUPUI

IUPUI is interested in him moving from the classroom into a funded researcher's position.
"We have told him that after this semester . . . enough of the book work. You are here to do some science," said IUPUI physics Professor John Ross, who vows to help find some grant funding to support Jake and his work.

Conceptua Fractions free tools

2011-03-22T15:45:00.001-04:00

I've heard a lot of good things about the free fraction tools at Conceptua Fractions. They are interactive online tools that use visual models to teach all fraction operations. They have a tool for identifying fractions, another for equivalent fractions, another for adding fractions with like denominators, another for adding with unlike denominators, and so on.

These tools exceed anything I've seen in the past... truly comprehensive and excellent. They always include several different visual models, and you can switch between them in an instant... the pie, a bar, a rectangle, a number line, or a dot model. You hover over the area to see the slider, and then you can drag it to partition your model into however many parts you want (well, up to 90 or 100 or so). Then you color or uncolor the parts with a single click inside the parts.

I want to mention that these tools are meant for the teacher, to illustrate the concepts. You would best use these tools when teaching the concepts, whether in whole-class instruction, in a homeschool, or in tutoring. They do have a few example problems, just a few of various kinds, to show what you can do with the student(s), but they don't provide quizzes or a slew of ready-made problems for the student to complete.

Ok, enough talking. Go try them out -- they're free. For each tool, it's maybe easiest to first look at the sample problems or watch the video that shows how to use it. Then you can go experiment with the tool itself. Lessons plans are also provided.

Free money worksheets

2011-03-18T06:14:00.000-04:00

I'm glad to announce these additions to the worksheet generators at HomeschoolMath.net. Use them to generate customizable free worksheets for counting coins and bills.

US money worksheets (cents & dollars)
Canadian money worksheets (cents & dollars)
Australian money worksheets (cents & dollars)
South African money worksheets (cents & rand)

I have two more coming up... British and European.

A homeschooler wins Intel's competition

2011-03-16T20:45:00.000-04:00

Just an interesting tidbit... 17-year-old Evan O’Dorney has won the first prize of $100K in The Intel Science Talent Search 2011 competition. He is and has been homeschooled. His entry to the competition had to do with math.

...he compared two ways to estimate the square root of an integer. Evan discovered precisely when the faster way would work. As a byproduct of Evan's research he solved other equations useful for encrypting data.

Read the details

One-minute cool math video

2011-03-16T06:45:00.000-04:00

This is a cool 'n' short math video (HT Denise) from a math blog Love 4 Math. My kids laughed... good fun! Good job!

Math Mammoth placement advice

2011-03-15T14:34:00.000-04:00

As you may know, I provide placement tests for Math Mammoth. These tests are end-of-year or exit tests for a given grade. They will work, whether you're planning to place the child in the grade-level series (Light Blue), or to use the topical books (Blue).

Many people don't know what to do if their child doesn't totally "flunk" the test but almost passes, or if their child does well in other areas, but misses the problems in some particular topic, such as fractions or multiplication. On that page, I provide advice for these situations.

Recently I also added suggestions as to what to do if the student does well in other areas, but can't do the word problems in the test.

I also provide personal guidance to anyone who sends in the test results. Over the years, I've done quite a bit of that type of "counseling". So your child's case, however "disastrous" it might be, is probably not unique.

Plenty of people write to me how their child "bombed" the test, or is many grade levels behind, and they need to know what to do. Nearly universally I can find a solution using my Blue Series books as supplements.

So, don't hesitate to contact me about the placement, if you need help.

Measuring obesity with BAI

2011-03-14T13:03:00.000-04:00

I'm not real super interested in obesity or calculations of people's weights, fat levels etc. but I ran across something half interesting that might be of interest to you.

It is a new way to measure obesity or if a person is underweight, normal weight, or overweight -- and it doesn't even use your weight in the calculation!

Murray has blogged about it at New measure of obesity – body adiposity index (BAI)

He also made a calculator for it that compares your "results" as far as BMI and this new index, BAI.

This new index uses your height and a measurement around the hips, and it's still somewhat experimental in the fact that it hasn't been thorougly tested in all races.

The formula is

  hip (cm)
-------------   −  18
[height(m)]^1.5

The resulting number should be a close estimate to your body fat percentage.

Just for the record, or if you are curious, I am of normal weight, and supposedly have about 29% body fat according to that calculation. Which, 29% body fat sounds high but it seems to be perfectly normal for females. It makes me think of this age-old saying "Human body is 70% water." That just can't be, not for females anyway. I would be 70% water, 29% fat, and 1% all the other stuff...???

Ok, upon checking I find that indeed, the human body is NOT 70% water. Females average 55% water and males 60% water, but obese people may only be 45% water.

A problem with a chord: find the radius

2011-03-08T20:07:00.000-04:00

Today I had the opportunity to solve a real math problem involving a circle and a chord of known length in it. I had to find the radius. It wasn't a textbook problem or a puzzle on some website, but a math problem I needed to solve for my own needs.

For a tiny while I thought I could find the answer online, but I didn't, so I'm writing it out in case someone else needs it -- they should be able to find this solution by searching the Internet.

I wanted to make a kind of "moon-sliver shapes" in CorelDraw, to use as watermarks in my new books. I have the height and the width of the "sliver".

Here's the problem mathematically:
I have a chord of a circle, 17 mm in length in my example, and the other distance marked in the image is 5 mm. I need to find the radius of the circle, AND the angle measure of the arc of the circle that makes the sliver's rounded part.

At first, like I said, I searched around if there was some theorem or formula that would tell me what I needed directly. I didn't find any, but I did realize that I can use this theorem to solve my problem:

If two chords intersect, the product of the segments of one chord equals the product of the segments of the other chord (see proof).

My problem looks like this:

My chord intersects the diameter of the circle, which is a chord too. The two parts of the first cord are 8.5 and 8.5, and the two parts of the other are 5 and d − 5. Thus I get the equation

5(d − 5) = 8.5²

From this it is quick to solve that d = 19.45. Then, the radius is of course half that, or 9.725.

On to the second part of my problem: to find the angle measure.

In this picture, I have a right triangle. I can therefore find the unknown angle α by using simple trigonometry, in this case the tangent.

The length 4.725 comes from the fact that the radius is 9.725, and then I subtract 5 from that.

The equation is tan α = 8.5/4.725, from which α ≈ 60.931°. The actual angle I want is double that, or about 121.862°.

I had to repeat this calculation several times for slivers of different "heights." (Or, actually I let Excel calculate the rest. Oh, how I love Excel!)

Here's one of the final pictures I made for my book:

Lulu sale again

2011-03-04T09:47:00.000-04:00

Lulu has a 20% off sale again... so you can use it to purchase Math Mammoth printed books.

20% off any book order
Enter code: GIANT305

Enter coupon code GIANT305 at checkout and receive 20% off your book order. The maximum savings for this offer is $100. Sorry, but this offer is only valid in US dollars and cannot be applied to previous orders. You can only use this code once per account, and unfortunately you can't use this coupon in combination with other coupon codes. This great offer expires on March 7, 2011 at 11:59 PM, so don't miss out! While very unlikely, we do reserve the right to change or revoke this offer at anytime, and of course we cannot offer this coupon where it is against the law to do so.

See the offer details online

The value of manipulatives

2011-03-03T07:26:00.000-04:00

(Note: I'm "resurrecting" an old post, with added information and a video. The topic is still very much valid.)

Manipulatives are IN, in math education. But do they TRULY facilitate learning to such an extent as people promoting them claim?

The entry at Text Savvy, Hands-on, Brains-Off, explains some of the pitfalls in manipulative use. Very enlightening!

Quoting from an article at Education Week (Studies Find That Use of Learning Toys Can Backfire):

In a similar series of experiments at the elementary-school level, the researchers found that children taught to do two-digit subtraction by the traditional written method performed just as well as children who used a commercially available set of manipulatives made up of individual blocks that could be interlocked to form units of 10.

Later on, though, the children who used the toys had trouble transferring their knowledge to paper-and-pencil representations. Mr. Uttal and his colleagues also found that the hands-on lessons took three times as long as the traditional teaching methods did.

The video below also illustrates how manipulative use can lead to problems.

The girl solves an addition problem involving thousands by drawing thousand-blocks, hundred-sheets, etc. on the board, taking 8 minutes. Then she says that at home she has been taught to stack the numbers and add. She solves it that way, too, taking 1 minute. But she gets two different answers.

(Hat tip to Denise)

Clearly, manipulatives aren't the best way to solve such problems, and children shouldn't be led to believe so. Not that this girl believed that way... she seems to understand which way is easier and quicker.

My take is that manipulatives aren't the ultimate answer to math teaching.

They're a reasonable starting point. But children should NOT be taught to rely on them. Children need to be taught and shown how to transfer all of that concrete play into the abstract.

In my books, I often instruct concepts with pictures, which essentially take the place of manipulatives. Then the student does a bunch of problems that have the same pictorial representation in them, including having to draw those same pictorial models to illustrate the math problems. THEN after that, the student goes on to totally abstract representation.

Here's one example from my book Add & Subtract 2-B: Adding with Whole Tens. The student first adds using the pictorial model, and then with numbers only.

I don't know if that approach suffers from the drawbacks mentioned in the article above. I hope not; from the feedback I get, it seems to work well.

Seniors & juniors algebra word problem

2011-02-25T18:51:00.000-04:00

Here's a word problem that someone sent me recently:

The total number of girls in the combined junior and senior classes is equal to the number of boys in those two classes. If the senior class has 400 students and the junior class has 300 students, and if the ratio of boys to girls in the senior class is 5:3, what is the ratio of boys to girls in junior class?

This problem gives a lot of information, and it sounds like it can be solved many different ways. But the first task is to notice what we are given and what we are asked.

We are asked about a ratio.
We're given one ratio, and all kinds of totals. There are boys and girls, senior and junior classes. In other words, there are four groups: senior boys, senior girls, junior boys and junior boys.

This sounds like it can be solved by setting up some equations and using algebra.

To start, you could for example notice the two facts given about the senior class: The senior class has 400 students and the ratio of boys to girls is 5:3.

From this it is easy to solve the number of boys and girls in the senior class.
The ratio 5:3 means 5/8 of them are boys and 3/8 of them are girls. Now, 5/8 of 400 is 250, and 3/8 of it is 150.

So seniors are solved... now to juniors. Let

B1 = boys in junior class
G1 = girls in junior class.

The first sentence of the problem gives us an equation:
G1 + 150 = B1 + 250

We also now that G1 + B1 = 300.

So let's solve this system of two equations:
G1 + 150 = B1 + 250
G1 + B1 = 300

I can subtract the bottom one from the top one to get:

150 - B1 = B1 - 50

200 = 2B1
B1 = 100

Since the total was 300, then G1 is 200.
And now the ratio of boys to girls, it is 100:200 or 1:2. All done!

You could also use straightforward algebra and set up four equations originally, using B1, G1, B2, and G2 for the numbers of boys and girls in junior and senior classes. You would get these four equations:

G1 + G2 = B1 + B2
B2 + G2 = 400
B1 + G1 = 300
B2/G2 = 5/3

And from these four you can solve all four unknowns, and then get the ratio of boys to girls in the junior class.

Chess games into piano music?

2011-02-24T11:45:00.000-04:00

I thought some of you might get a kick out of this...
As chess players know, the squares on a chess board are numbered this way:

And this happens to be the same notation as is used in music for notes (A, B, C, D, etc.), the numbers denoting how high the particular note is (in which octave).

So someone came up with the idea of "translating" chess games into music! Here's the link: Chess Music. Provided are three mp3's to listen to as examples of some famous chess games translated into piano music using this method. Kind of funny/interesting. Check also these free online piano lessons (very basic) if you need some.

Lulu birthday - coupon 20% off for MM printed copies

2011-02-17T13:30:00.000-04:00

I'll just copy it from Lulu's email to me.. You could use these coupons to purchase Math Mammoth PRINTED versions at a discount.

Enter coupon code HAPPY305 at checkout at LULU and receive 20% off your order. The maximum savings for this offer is $100.

Enter coupon code BIRTHDAY305 at checkout and receive 25% off your order of $500 or more. The maximum savings for this offer is $500.

These great offers expire on February 21, 2011 at 11:59 PM.

Purchase Math Mammoth books at Lulu from this link.

Sorry, but these offers are only valid in US dollars and cannot be applied to previous orders. You can only use these codes once per account, and unfortunately you can't use these coupons in combination with other coupon codes. These great offers expire on February 21, 2011 at 11:59 PM, so don't miss out! While very unlikely, we do reserve the right to change or revoke this offer at anytime, and of course we cannot offer this coupon where it is against the law to do so.

You can see this offer online here.

World Math Day

2011-02-15T12:45:00.000-04:00

World Math Day is coming soon, on March 1, 2011. You need to register beforehand, before February 28.

(Since math is spelled in two different ways (math or maths) around the world, they even have two different websites, www.worldmathday.com and www.worldmathsday.com, but both are the same thing.)

What is World Math Day?

It's a fun worldwide event where students from across the globe compete against each other in answering math facts.

Students play at home and at school against other students around the world in live games of mental arithmetic. Each game lasts for 60 seconds and students can play up to 100 games, earning points for their personal tally. Students can play beyond 100 games during the event, but points will only count to the World Maths Day Mathometer, not their personal point score. The students who answer the most questions correctly appear on the Hall of Fame. There are 5 different levels of play, 20 games on each level.

Schools, students, and homeschoolers can all participate! Just remember to register first. After registering, you can practice on the website before the actual contest day.

A magazine for homeschooled girls

2011-02-11T16:37:00.000-04:00

Just passing on a link of a new magazine specifically for homeschooled girls:

Back-to-Homeschool

My daughter liked the first issue... Go check it out!

They would also like submissions. For example you could send in your daughter's writing assignments or something like that.

Silly graphs (GraphJam)

2011-02-10T08:48:00.000-04:00

Just got some good laughs reading the blogpost at SquareCircleZ about funny graphs from GraphJam. Go take a look!

(The GraphJam site itself is not always family-friendly, but the blogpost I'm linking to is fine.)

A percentage problem

2011-02-06T18:56:00.000-04:00

Can you help me solve this question?

Jayne is given £5 for her birthday.
She spends 30% of it.
How much of her birthday money does she spend?

And... Is my method correct for this question?
100-30=70
70/5=14
1.40

No, the asker's method is not correct. In fact, it looks to me like she is randomly doing operations with numbers...

To find 30% of something, one MENTAL MATH method that I like is to first find 10% of that something.

Now, 10% of something is of course 1/10 of it. And to find 1/10 of it, just divide that by 10.

So, we divide £5 by 10 to find 1/10 of £5. It is £0.50. That's 10% of the total. And 30% of the total is three times as much, or £1.50.

So Jayne spent £1.50.

See also this video that explains how to find percentages using mental math:

Math Mammoth Light Blue Series bundles for grades 1-3 and 4-6

2011-02-05T13:45:00.000-04:00

Now you can purchase Math Mammoth Light Blue series as a bundle for grades 1-3, or for grades 4-6, for a discounted price of $64.

Previously I've had available a bundle for all six grades (and still do), but now you can just grab either the three lower elementary or the three upper elementary grade levels with the same 33% discount.

Please see the order page here.

Decimals videos: tenths, hundredths & thousandths

2011-01-30T20:53:00.000-04:00

I have now been able to get back to shooting videos after a long break. These three videos (titled Tenths, Hundredths, and Thousandths) deal with what decimals are (they're fractions!) and in that sense are tied together.

The first video explains about decimal numbers with one decimal digit (tenths) using fractions and a number line. I also include some easy addition problems.

In the second video below, I explain decimals with two decimal digits—or hundredths—using fractions and a number line. Also included an explanation of why you can "tag" or "add" zeros to the end of a decimal and its value does not change.

Lastly, I explain decimals with three decimal digits—or thousandths—using fractions and a number line. Then I show examples of converting fractions to decimals and vice versa.

Mastermind game giveaway

2011-01-21T08:39:00.002-04:00

First of all... Math Teachers at Play 34 is online... go check out the posts!

Then... I'm doing a giveaway again... one of you, my readers, can be a lucky one to win a free Mastermind board game!

Update: The winner is now chosen, the third commenter below, named Äiti. This went quick!!!!!! Comments are therefore closed.

The lady who contacted me about it said that many of today's adults actually KNOW the game from their childhood, but don't know it's still available.

I haven't played it as a child, but a few years ago I found Mastermind online (on several math games websites), and I found I like it!

This is how Mastermind works:
You need to guess the "secret code" of colored pegs: both the color and the order they are in. You make a guess, and your opponent (or computer) tells you some clues. A black clue means you got one peg the right color AND in the right position, whereas a white clue means you got a peg with right color in the wrong position.

It's basically a logic game... you need to think logically about your guesses and the given clues.

Go play it online here (against the computer) at National Library of Virtual Manipulatives. This version is nice, as it allows you to limit the number of colors, which is helpful for new players or small children.

How to take part?
Simply leave a comment to this blogpost. Follow my blog and once you see I've chosen the winner, the winner needs to contact me with their contact and shipping info. This giveaway runs until I have 10 comments OR January 31, whichever happens first.

Which operation should you use in word problems?

2011-01-17T19:45:00.000-04:00

I was asked just recently about word problems and WHAT operation to use in them.

Can you put a better explanation of when to use addition, subtraction, multiplication, and division, because my son is having a hard time understanding.

Many children have the same problem, and I have written about it in the past as well. In a nutshell, I feel the MAIN reason students have trouble is the way word problems are presented (or not presented) in math books.

Typically (and I still see this approach), when a lesson in a math book is on some operation, then the word problems in that lesson are typically solved using that particular operation. So, any intelligent kid who notices this pattern won't take time to decipher what the problem says, but will just take the two numbers that appear in the problem, and apply the operation that the lesson is about!

(For example, if the lesson is on subtraction, then the word problems are solved using subtraction.)

I have tried to AVOID this in my books from the start, and I think all other math curricula should follow suit, that whenever there are word problems to solve, that the operation or operations used to solve it SHOULD vary within the problem set.

Even in first grade addition, you can make two kinds of problems:

"Ann had seven marbles, and Mary had two. How many marbles do they have together?" SOLUTION: 7 + 2 = 9

OR

"Ann has seven marbles, but today she only found two. How many are missing?" SOLUTION: Think 2 + ___ = 7, or two and how many more makes seven?

So, starting in 1st grade, the word problems should never be such that they always involve the same operation. Then in 2nd grade, the word problems should proceed to easy 2-step problems.

When multiplication is introduced in 3rd grade, the word problems should be in two different ways so the child cannot automatically multiply the numbers in the problem, but has to think. For example:

Mary saw 12 duck legs. How many ducks were there?

OR

Grandma has 12 ducks, and each wore two blue ribbons. How many ribbons could you see when looking at all the ducks?

Now, recently I had an idea for help for all these elementary students that have trouble figuring out which operation to use. I THINK it might work fairly well, but I'd like to have your input on it.

Suppose we have a student in 3rd or 4th grade who can't do word problems. What if we used the word problems in Ray's Arithmetic with him/her, starting from the beginning?

Ray's is known to be full of word problems, starting from the simplest. It sort of uses word problems to teach arithmetic. It is an old book, and therefore it is available FREE online. See the links on the left for viewing it online or downloading.

See for example the word problems on page 26.

You can also purchase Ray's as printed books.

What do you think? Could Ray's get such students up to speed with word problems?

Free music appreciation lessons

2011-01-15T13:39:00.000-04:00

Just wanted to share with you a link to some free lessons on famous classical composers:
Famous composers - free online music appreciation lessons

For each lesson there's a picture of the composer, an easy reading about his life, and then several pieces of music, both videos and audios to listen to. They should work alright as music appreciation lessons for elementary school.

Games for order of operations

2011-01-05T21:31:00.001-04:00

Photo courtesy of minibe09

If your student or child needs more practice with order of operations, here are some online games for that. These shouldn't include integers, but just the four operations (addition, subtraction, multiplication, division) and parenthesis.

Most kids just love using games and interactive quizzes for practice instead of worksheets. Have fun!

Choose Math Operation
Choose the mathematical operation(s) so that the number sentence is true. Practice the role of zero and one in basic operations or operations with negative numbers. This helps develop number sense and logical thinking.
www.homeschoolmath.net/operation-game.php

Division and Order of operations and

Division and Addition - Order of Operations
Two mystery picture games.
www.dositey.com/2008/math/m/mystery2MD.htm
www.dositey.com/2008/math/m/mystery2AD.htm

Order of Operations Quiz
A 10-question online quiz that includes two different operations and possibly parenthesis in each question. You can also modify the quiz parameters yourself.
www.thatquiz.org/tq-1/?-j8f-la

The Order of Operations Millionaire
Answer multiple-choice questions that have to do with the order of operations, and win a million. It can be played alone or in two teams.
www.math-play.com/Order-of-Operations-Millionaire/order-of-operations-millionaire.html

Exploring Order of Operations (Object Interactive)
The program shows an expression, and you click on the correct operation (either +, —, ×, ÷ or exponent) to be done first. The program then solves that operation, and you click on the next operation to be performed, etc., until it is solved. Lastly, the resource includes a game where you click on the falling blocks in the order that order of operations would dictate.
www.learnalberta.ca/content/mejhm/html/object_interactives/order_of_operations/use_it.html

Order of Operations Practice
A simple online quiz of 10 questions that use parenthesis and the four operations.
www.onlinemathlearning.com/order-of-operations-practice.html

Quick Calculate
Practice your arithmetic of all four operations plus order of operations.
themathgames.com/arithmetic-games/addition-subtraction-multiplication-division/quick-calculate-game.php

Review of Math Rider software

2010-12-29T22:39:00.002-04:00

If your children like horses, they might fall in love with Math Rider game!

Math Rider is a "math facts" software game; that is, it specifically trains and practices the basic addition, subtraction, multiplication, and division facts.

Some special features include:

Each player has their own "account" in the game, and Math Rider is adaptive in that it trains those facts more that the child misses. I feel this is a great and important feature. More on that below...
I also really liked the statistics. You can see a color-coded chart that shows what facts the child has mastered, what s/he has some trouble with, and what s/he has lots of trouble with. Also, after each ride, the game shows you a bar chart with a bar for each fact in that ride. The taller the bar, the longer the child took to solve the fact.

Here is the home screen. Click to enlarge.

The gameplay is centered around "quests". The player sets up a "quest" by choosing which operation to practice, and on which level. From there, the game first shows a storyline for a few screens.

Then starts the practice, in which a horse jumps a hurdle every time you solve a math fact correctly. If you answer wrong, the horse doesn't whinny but snorts, and you might have time to correct your answer. If you don't, or if you can't answer a problem at all, the horse stops at the hurdle and tells you the answer, and walks through the hurdle instead of jumping it.

The program adapts the problems as you go. The problems you miss or are slow at keep appearing more often than others. The speed adapts, too. If you are fast in answering, the problems appear faster and the horse rides faster, and vice versa.

These rides are 30 problems "long." After a ride of 30 problems, you can check your progress on the "quest" on a map. The backgrounds and hurdles on these rides vary as you proceed and travel through different landscapes. Completing the quest takes several of these 30-fact rides. Once you complete the quest, you are shown several more screens of the storyline to learn how it ends, and you get a special reward item.

The storylines include for example a sick mother, for whom you need to find a special flower, or you find a magical gem that a wizard tells you keeps darkness away, and you have to deliver the gem to the elven city. On the advanced level, you get to rescue a princess.

Personally I didn't care for the wizard/magic story, but you can easily fast forward through these short stories

You can read more about the game play on the Math Rider site.

The motivational reward items include points you get from riding, and the animated items you get from completing quests (flowers, flags, a castle, etc.). Additionally, the program tracks the "mastery" level of each operation and shows that in the animated items.

This is how the statistics looks like:

Both of my girls liked the game really well. They played and played and had to be dragged away from the computer!

My 5th grader already knows the basic facts pretty well, so for her the game was mostly fun with a little bit of review. She liked the changing backgrounds and the music. I really liked the music too (you can turn it off if you don't).

My 2nd grader just did addition and subtraction, and I feel the game did some good in helping her get speedier with her facts. They both liked best the different animated reward items you get when you finish the quests, such as flowers and flags.

It could be improved by adding more storylines. Right now, there is one story for any of the "easy" levels, no matter what the operation, and similarly for the other levels.

Also, I personally feel that children would benefit a lot from practicing the addition and multiplication facts using missing addends and factors (practicing "in reverse"). For example, in multiplication, the game could use 5 x ___ = 25, and in addition, it could use 6 + ___ = 13 types of problems.

I feel the game is well done and serves very well the purpose of practicing math facts and getting "up to speed" with them. The adaptive features work well and really help the mastery to come to pass.

Of course there are so many different games and ways to practice math facts that it's hard to choose! I hope my review helps you in deciding if this game would be for you. I can definitely recommend it for what it does.

Website: MathRider.com Price: $37.

Disclosure: I was given a copy of Math Rider software for free but did not receive any other compensation.

Fraction of a fraction word problem

2010-12-06T18:07:00.000-04:00

A problem about fraction of a fraction...

The sixth-graders have a fundraieser. They raise enough money to reach 7/8 of their goal. Nikki raises 3/4 of this money. What fraction of the goal does Nikki raise?

The picture below shows first of all 7/8. Nikki raises 3/4 of this goal. We need to find 3/4 of 7/8.

It's not easy to directly see what is 3/4 of 7/8. So to do that, I divide each 1/8 piece into four pieces, and then color three of the four. That way I color 3/4 of each of the seven eighths.

Of course, those tiny pieces are now 1/32 parts. I have colored 3 x 7 = 21 of them. So, the colored part represents the fraction 21/32.

This problem is also simple to solve without a picture, if you understand what is asked. To find 3/4 of 7/8, you simply multiply those two fractions. The word "of" translates into MULTIPLICATION in fraction math!

 3       7      21
---  x  --- =  ----
 4       8      32

A book on education crisis

2010-12-04T11:39:00.001-04:00

I'm just passing on a link that some of you might enjoy (or be sad about). I found it interesting -- a math teacher (Larry Zafran) telling his story of teaching math in an inner city high school in New York in the early 2000s. It appears not much was able to be done but to try to survive and get through the day while presenting the official curriculum topics in class, at least on the board.

http://www.larryzafran.com/education-crisis-book.htm

Math Mammoth Thanksgiving Sale

2010-11-23T17:40:00.000-04:00

Math Mammoth Thanksgiving sale is already in full swing... You'll get 20% off of all the downloads and CDs sold at Kagi store.

To take advantage of this offer, enter the coupon code THANK2010 at checkout.

Enter the coupon code on the shopping cart page (not the first order page). Coupon valid till November 29, 2010, only at Kagi store. Not applicable to printed copies.

Order pages:

Notation for solving equations

2010-11-21T13:09:00.001-04:00

I just found this via Math Teachers at Play...

Carolin's Notation for Solving Equations

Carolin is a student from Germany. I just wanted to note that that is exactly how I was taught (in Finland) to note what is done to each side of the equation, and I really like the notation. I don't know if it's used in all Europe...

Basically, you note in "the right side margin" what you're going to do to both sides of the equation in your next step. The "margin" is made by writing a vertical line to the far right of your actual equation solving process.


6x - 5 = 2x      | -2x

4x - 5 = 0       | +5

    4x = 5       | ÷4

     x = 5/4

I just wanted to pass this on in case some of you who are teaching how to solve equations find it useful with students.

Math Mammoth Statistics & Probability

2010-11-19T13:15:00.000-04:00

Math Mammoth Statistics & Probability is now available -- and it's the last book I'm intending for the Math Mammoth Blue Series. So the Blue Series is now complete!

Price: $5.30 (download), $10.30 (printed)

This book starts with the easiest topics, such as reading different graphs. These lessons are meant for 5th grade. Some are useful even in earlier grades. Then we study histograms and various kinds of line graphs, including how to draw them.

The next section deals with mean, median, and mode—the three measures of central tendency—how to use them, and how these concepts relate to line and bar graphs.

To create circle graphs, the student needs to calculate percentages, and it is assumed here that the student has already mastered how to calculate those. The lesson on data analysis presents various types of graphs for students to read, and reviews some other percent-related topics.

Then students learn how to make stem-and-leaf plots. Stem-and-leaf plots are simple plots that can be used with 15-100 data items. They are not often seen in media because you cannot use them with large amounts of data.

We study range as a simple measure of variance.

Probability is a topic that in the past was only taught in high school—for example, I personally encountered it the first time in 12th grade. However, in recent years it has “crept” down the grade levels and many states require probability topics even in elementary school.

We start with the concept of simple (classic) probability, and then expand into probability involving two events. This is all that is needful to master at this point (middle school). The exercises involve tree diagrams, dice, flipping coins, picking marbles, spinning spinners, and probability involving statistics, which are the usual types of situations in the study of probability.

See the free sample lessons (PDF) under the cover image on the book's page.

Two algebra 1 word problems (systems of linear equations)

2010-11-15T11:09:00.002-04:00

Here are two problems for you to solve... OR to learn from me when I solve them. Both problems are for algebra 1, and use a system of 2 linear equations.

By the way, the comments have some wonderful ideas for solving these mentally, without using algebra. So please read them too!

Problem: John bought red pens for $4 apiece and blue pens for $2.80 apiece. If John purchased a total of 24 pens for $84, how many red pens did he purchase?

Solution: This is a typical problem that will have two variables and two equations.

Let r be the amount of red pens he buys, and b be the amount of blue pens he buys.

We get our first equation from this sentence: "He bought a total of 24 pens." So, r + b = 24.

We get the second equation from the fact that his total purchases were worth $84, and red pens cost $4, and blue pens cost $2.80

4r + 2.8b = 84

Now, just solve this system of two equations using your preferred method.

r + b = 24
4r + 2.8b = 84

I will multiply the top equation by -4, then add the two equations.

-4r - 4b = -96
4r + 2.8b = 84
-------------------
-1.2b = -12
From this, b = 10.

Then since r + b = 24, r must be 14.

Problem: In a group of 60 workers, the average salary is $80 a day per worker. If some of the workers earn $75 a day and all the rest earn $100 a day, how many workers earn $75 a day?

Solution: To get started, first find out what are the unknowns. In this case, there are two. Some workers earn $75 a day, and some earn $100 (two quantities).

Let A = workers who earn $75 a day.
Let B = workers who earn $100 a day.

We need to have both variables when building the equations, even though the problem only asks for A.

THEN we need to somehow use the information given to build two equations. That is because to solve for two unknowns, you need two equations.

Well, there are 60 workers, so our first equation is pretty easy: A + B = 60.

Now, the first sentence may throw you off... but actually, the concept of average is not coming into the picture very much. The info in the first sentence is ONLY used to find out one useful fact: that the group of workers earns 60 x $80 = $4,800 in TOTAL each day. We use that to build our second equation, which has to do with the total earnings:

75A + 100B = 4,800

Now we have our two linear equations, and all that remains is to solve the system using any standard technique.

A + B = 60
75A + 100B = 4,800

Multiply the top equation by -100, and then add the two equations together:

-100A - 100B = -6000
75A + 100B = 4,800
-----------------------------
-25A = -1,200
A = 48

Then, B must be 12.

Check: 48 x $75 + 12 x $100 = $4,800. It checks.

Work & workers word problem

2010-11-11T12:48:00.002-04:00

Here's another one of those job / workers word problems (inverse or direct variation). Try and see if you can solve it using the "table" method instead of equations:

A certain job can be done by 18 clerks in 26 days. How many clerks are needed to perform the job in 12 days?

Again, we can set up a table and reason this out. Initially set it up like this:

jobs | clerks | days
--------------------------
  1  |  18    |  26
--------------------------
  1  |        |  
--------------------------
  1  |   ?    |  12

Then think of the "days" column. We want to "go" from 26 to 12. You could use a proportion here... or first figure out how many clerks are needed to do this job in 2 days, and then from that go to 12 days.

If 18 clerks do it in 26 days, then how many clerks would do it in 2 days... which is 1/13 the amount of time.... so we need 13 times as many clerks.
13 x 18 = 234 clerks are needed.

jobs | clerks | days
--------------------------
  1  |  18    |  26
--------------------------
  1  |  234  |   2  
--------------------------
  1  |   ?    |  12

Now, if 234 clerks do it in 2 days, how many clerks would do it in 12 days? Now, the time increases 6-fold, so we need only 1/6 as many workers.

234 / 6 = 39.

So 39 clerks are needed.

Simplify a ratio problem, for your entertainment :)

2010-11-11T12:09:00.003-04:00

Simplify the ratio 186:403. The answer is 6:13. How do we get it?

To simplify ratios (or fractions), we need to find COMMON FACTORS of the two numbers. So, one way to do it is to first find the GCF (Greatest Common Factor) of 186 and 403. Then divide 186 and 403 by it.

Alternatively, just find ANY factor of 186 and 403, and divide both by it, to simplify the ratio somewhat, and to get started. Then repeat the process.

Okay, 403 is not divisible by 2, 3, 4, 5, 6. This I know by divisibility tests. Maybe it's divisible by 7... need to try (calculator). No, it isn't.

Maybe by 11? No.

Maybe by 13? YES. My calculator helps. 403 = 13 x 31. I happen to know both of these are primes, so therefore 403 doesn't have any other factors.

Then 186.... is it divisible by 13 or 31?
By 13, no.
By 31, YES! 186 = 31 x 6

So since 186 = 6 x 31 and 403 = 13 x 31, then the ratio 186:403 simplifies to 6:13. Clearly that's as far as we can get, as it's simplified to the lowest terms.

Free online quizzes & tests, middle & high school math

2010-11-05T13:03:00.001-04:00

I just stumbled onto a pretty neat resource for all math teachers (parents too). It is Glencoe's Online Study Tools. What they have is online, multiple-choice tests, quizzes, and standardized test practices, for ALL middle and high school topics.

They are randomly generated so you can get as many different quizzes as you like.

Just choose any state you wish (it doesn't matter), then a book or course (such as algebra or geometry), and then you'll see the list of topics. In other words, you don't have to own the book in order to do the quizzes and tests.