Homeschool Math Blog

I've written a review of IXL.com (from "I excel"). It is an online math practice system - would be perfect for those of you who want your kids to have something for the summer months. IXL has unlimited questions on hundreds of math topics and a comprehensive reporting system. Their pricing is $9.95 per month for 1st child and only $2 for the next child. Read my review here .

I'm sure youngsters will like this card "game"! I'm going to try it with mine. Actually it's not really a game, but a fun way for kids to write some of their own math problems using a deck of cards. She even provides a free printout: Little Blue School: Math Card Game for Addition, Subtraction, Multiplication, Division HT: This week's Carnival of Homeschooling

Question: ...have an other question about using your worksheets for my daughter. She is six years old - home schooled. Currently, we are using Addition & Subtraction 2 She is able to add and subtract any numbers from 1 to 100 but when I try to explain "complete the ten" concept, she doesn't like thinking about it. She would rather solve 9+6 by counting on the finger 6 after 9 ... . She complains that I have to first subtract then add to make 10. My question is: Should I let her complete the exercises without making her think in this manner? It is important that she understands the IDEA in completing the ten. I gather that she does indeed understand the idea, but doesn't want to do it, since you'd have to both subtract and add, right? She just likes to do one operation, not two? The adding though, is really easy, because you add 10 + 5 or 10 + 7 or something to ten. If she's counting with fingers, she's not yet seeing the easiness of this adding. It...

I received recently the book Arithmetic for Parents. A book for Grownups about Children's Mathematics by Ron Aharoni. I think this book is exceptionally good, and very worthwhile to read if you're a teacher OR a parent. Ron Aharoni was like many: he thought he could easily teach elementary school mathematics because he knew college level math and beyond (he was teaching math in a university). But... he was in for a big surprise when he entered the fourth, fifth, and first grade classes in a backward town in northern Israel, in 2000. One surprise he had was that... ...he did NOT know how to teach elementary mathematics, in spite of his knowledge of university level math. For example, during his first lessons, he took children outside to measure shadows of trees and buildings, and then also to measure the children and their own shadows. The idea was to use the ratio of a child's shadow to his height in order to find the height of a tree or a building He a...

A geometry question from a visitor: 1. How much time should be invested teaching geometry at an elementary level? 2. How much time is actually dedicated towards geometry in a tradicional textbook Your guidance will be extremely appreciated! During elementary mathematics, geometry plays more of a sideline role at first. It is intimately tied with measuring topics - and really, the word "geometry" means "measuring the earth", the science to measure the land. The goal of elementary geometry seems to be that the student be able to find perimeters, areas, and volumes of common two and three dimensional shapes. I would add to that the goal that the student can understand and form abstract definitions, distinguish between necessary and sufficient conditions for a concept, and understand relationships between different shapes before entering 10th grade. (I've written about that before in the article Why is high school geometry difficult? . According to the Curriculum...

With my dd, I've had her study addition and subtraction lately, and fact families, practicing the connection between addition and subtraction. But she's young. So I know games go over well. To illustrate the fact families better, I made math "rods" out of cardboard - you know, all different lengths. She really liked them. But I got quite a surprise at her reaction to my made-on-the-spot Addition Surprise game... I took three of those rods, so that two of them sum up to the third, and used the two to cover the third. I held them up and said there was a "surprise number" behind. She saw the numbers on the two rods, added them, and told me the answer. I just said something like, "Ta da ta daa!!!" and uncovered the one on the bottom for her to grab. She just giggled and giggled, and absolutely loved it. Such a little thing to us adults - such an impact on a little one. Amazon actually sells cuisenaire rods , too, so here's a pic if you don't k...

Resources These are some of the links I've added to my site recently. Maybe there's some that interest you. Mathopenref.com Free online textbook for high school geometry; not finished. GapMinder Visualizing human development trends (such as poverty, health, gaps, income on a global scale) via stunning, interactive statistical graphs. This is an interactive, dynamic tool and not just static graphs. Download the software or the reports for free. How to write proofs A 12-part tutorial on proof writing. Includes direct proof, proof by contradiction, proof by contrapositive, mathematical induction, if and only if, and proof strategies. Money Math Crystal clear tutorial on interest. Graph Mole A fun game about plotting points in coordinate plane. Plot points before the mole eats the vegetables. All sorts of sites to explore! But if those didn't fit your bill, if you're in need of a game or tutorial about specific math topic, check my link lists of online math resources; they...

This topic is often not understood real well by teachers or students. But we want them to learn, not only the rule, but also the meaning. These ideas can help you to explain and understand division of fractions: 1) The rule of "invert and multiply" applies to division in general - not just to division of fractions. It is a general principle. For example: 20 ÷ 4 I can invert and multiply: 20 × 1/4 = 5. With whole numbers, division can be thought of as making equal parts. When you divide something by 7, you're dividing it into 7 parts, so might as well just take 1/7 part - multiply by 1/7. You can always change division into multiplication with this principle: 18 ÷ 2.51 = 18 × 1/2.51 2) Think of fraction division this way: how many times does the divisor fit into the dividend? You can use this to judge the reasonableness of your answer. For example consider 1 3/5 ÷ 2/3. Clearly 2/3 can fit into 1 3/5 more than two times. 1 3/5 ÷ 2/3 = 8/5 × 2/3 =...

So today I experimented, and gave my daughter a problem 15 + 25 for starters, to see what she'd do. 1 5 + 2 5 3  10 She promptly wrote down 3 and 10. Then she looked at the numbers, kind of wondering, saying "It's ten three." I asked her how would we say the number, pointing with my finger and making a sweeping motion from 3 towards 10, and then she said, "Thirty-ten." I said yes, it's thirty-ten, but we say it differently normally. Then I asked her to find it out using abacus. She easily found it was 40. Then we erased her numbers and wrote in 40. She did two more similar problems on her own, first adding tens, then ones (as her custom seems to be), and then erasing the numbers and changing them to the right result. She seemed very happy for being able to understand the gimmick. So we did all that without discussing 'carrying' or putting little number 1 up on top, or anything. I figure next time I'll try a problem where the ones add up t...

Just today I made my dd some more math problems with adding 2-digit numbers - the easy type where you don't have to carry. She's getting it now pretty good. I always talk about adding so many tens to so many tens so she won't forget it's about adding tens and adding ones. Somehow she's doing the tens first, then the ones, and she tends to say, after adding tens: 52 + 37 8   "Oh, it's going to be eighty-something." You know, that's the way many people add numbers mentally: 52 + 37, we add tens first and get 80. Then add ones. Even with 46 + 36, you probably add tens first and get 70, then add ones and go over to 82. So a thought hit my mind: one day I will present to her a problem where the ones make a ten, such as 26 + 34 Is she going to get an answer fifty-ten? Well, that's what it is, basically. We just need to recognize that's not the normal way of saying it but that we need to add that ten to the fifty so it becomes sixty. Anyway, I r...

Recently I've been writing worksheets for fourth grade... Later this year, I will make this collection available for whoever wishes to buy it. But for now, it's a work in progress. One topic I was pondering a lot was whether to include problems such as 15 + x = 30 into the worksheets. Or, 234 + x = 700 or x + 1,923 = 5,000. I hope you get the idea; in elementary books you often see these kind of missing addend problems with a little box: 15 + = 30 or 234 + = 700 or + 1,923 = 5,000. Well, I decided for the x over the box! I don't think solving missing addend problems with subtraction is too difficult to learn on fourth grade; after all, students have been working with addition and subtraction connection from 1st grade on, right? In my own old schoolbooks I actually see x from 3rd grade on. I made several problems with charts such as Write a missing addend sentence and a subtraction sentence to solve it. 1,500 |------------|-----| x 346 Hopeful...

I was updating my Division 1 ebook and thought I'd share a lesson idea. Have you ever tried this kind of exercise when studying remainder in division? 1 ÷ 3 = 0, R 1 2 ÷ 3 = 0, R 2 3 ÷ 3 = __, R __ 4 ÷ 3 = __, R __ 5 ÷ 3 = __, R __ 6 ÷ 3 = __, R __ 7 ÷ 3 = __, R __ 8 ÷ 3 = __, R __ 9 ÷ 3 = __, R __ 10 ÷ 3 = __, R __ 11 ÷ 3 = __, R __ 12 ÷ 3 = __, R __ 13 ÷ 3 = __, R __ 14 ÷ 3 = __, R __ 15 ÷ 3 = __, R __ 16 ÷ 3 = __, R __ 17 ÷ 3 = __, R __ 18 ÷ 3 = __, R __ 19 ÷ 3 = __, R __ 20 ÷ 3 = __, R __ 21 ÷ 3 = __, R __ 22 ÷ 3 = __, R __ 23 ÷ 3 = __, R __ 24 ÷ 3 = __, R __ 25 ÷ 3 = __, R __ 26 ÷ 3 = __, R __ 27 ÷ 3 = __, R __ You should do it with different divisors, and ask the student(s) to find a pattern. Do you know it? Tags: math , elementary , lesson

I've embarked on a new project in making worksheet collections for each grade from 3rd through 8th. While doing that, I had to generate images of clock faces, and so I decided to just use a few hours to make a worksheet generator at the same time. So if you're interested, click here to make clock worksheets . It's pretty simple, just two things you can do: either the student has to read the analog clock, or draw hands on it when time is given in digital form.

Sums with 8 Well today's post will not contain any deep mathematical insights... Just two pics of the things we're doing at our house. We're studying simple addition facts. I just keep writing problems in her notebook. Have a happy weekend! Sums with 6

This morning, my baby found a set of addition flashcards I had bought at some yardsale, and scattered them on the floor. While picking them up, I was lamenting in my mind the fact how they are not usable with my other daughter. The set has 32 cards so obviously it doesn't cover all basic addition facts. It seems to have just random ones, such as 7 + 6 = __ or 8 + 4 = __ or 2 + __ = 2 or 1 + __ = 5 all mixed together. But what I'd want for right now is those cards only where the sum is five: 0 + __ = 5 and 5 + __ = 5 1 + __ = 5 and 4 + __ = 5 2 + __ = 5 and 3 + __ = 5 That's the approach I have used in my ebook Addition 1 : to practice the facts in small groups, grouping them by the sum. First you could study those facts where the sum is 4, then those with sum 5, and so on. That would make more of a logical approach to all this fact practicing. You know, everybody understands that you're supposed to memorize multiplication tables by the tables and not by 'all at once...

Today we went to town, for most of the day. At one point I noticed I was walking on hexagonal tiles, and I noted that to my daughter. From then on, we just kept looking around at store floors, walls, the sidewalk to find various tiling patterns. Most of them were either simple squares, or were using rectangular tiles, but with rectangle-shape tiles people had made all sorts of different designs or patterns. In some, the tiling combined two different shapes. She especially enjoyed seeing the 'artistic' ones (not true mathematical tilings) where people just had put all sorts of broken tile pieces in a cement. I guess that was our math lesson of the day. Made the long walking around town go quicker for her, for sure! Tags: elementary , math , geometry , lesson

One day last week we went to Time4Learning with my daughter again and she did an activity where the cartoon character was making jumps on the number line. She didn't quite get it when the guy in the activity jumped 10 jumps forward or backwards, so the next day we studied "adding 10 more to a number" with the help of a 100-chart. ( Click here to go to a bigger printable version ) I just colored a number on the chart, and then we jumped together 10 jumps forward, on the chart. Then she colored the 'landing' number. After a few of those, she was able to guess where she'd land. We also wrote the corresponding number sentences in her notebook. Actually I wanted to show the same thing on our abacus, but it's broken right now (needs glued). And, with my 10-bags (I've made those by putting 10 marbles into small bags) - but I couldn't find those since they're put away somewhere so the baby can't get to them. But maybe it was enough for her for th...

I have a dear friend who is not computer oriented (she said herself). She said one time she went online to find a game to reinforce some math concept for her son but couldn't find anything she liked. Either they were too repetitive, or too difficult to figure out, or something. So she just gave up, and "did things her way". Which, her way of teaching math is one-one-one teaching, and then she often writes problems for her son in a notebook. Upon seeing how her son solves the problem, she writes the next one. It might be going a little further in the topic, or it might be practicing a different aspect of the topic. I sincerely admire that! It's like writing a perfectly tailored math curriculum on the spot. (I often write problems for my daughter, too, in her notebook.) ------------------------------------------------ We have computer games, card games, flashcards, textbooks, workbooks, online lessons, manipulatives - but I think the most essential part of any math cur...

This weekend I was working with one of my ebooks, writing more content for it. I thought I'd share one of the problems I was putting in it. When you're first studying numbers in the 100,000's and millions, have the child use an encyclopedia or internet to find information such as: Population in the Northeastern states land area of the various Midwest states the amount of distinct animal species in the 7 continents number of newborn babies annually in European countries some astronomical distances ...or something similar. You could try tie it in with something you're studying in other school subjects. This way, using real data, it is not just some old made-up math textbook problem. THEN, the child is to organize the info in ascending or descending order. This lets them practice reading and writing big numbers plus comparing them. It is sort of a hands-on exercise and ties mathematics in with real world: how math is not just for school but is somethin...

Recently I added another math curriculum to the list of math curricula; it's called RightStart Mathematics. They are using a little different abacus from the usual to help children visualize numbers: the abacus has five beads one color, and the next five another color. Their idea is that using such abacus, children will eventually learn to recognize the amounts on abacus with a single glance, without counting the beads. They will then form a mental image and learn to 'see' seven as five and two. After checking their website, just a few days later, when checking dead links, I stumbled upon this same abacus in electronic form on another website. (However you can only do a few things with the applet, so it's not nearly as good as a real physical abacus.) This Ten frame tool uses a similar idea - kids are supposed to recognize amounts 0-10 visually, without counting. Obviously another tool for this is just a die, or dice. Great ideas, great tools.