Homeschool Math Blog

There are now three new books available in the Blue Series. They are all for grades 5-6. The material for these books came from the Light Blue 5th and 6th grade curricula. Please click on the links to learn more and see samples. Math Mammoth The Four Operations (with a Touch of Algebra) The main topics studied in this book are simple equations, expressions that involve a variable, the order of operations, long multiplication, long division, and graphing simple linear functions. The idea is not to practice each of the four operations separately, but rather to see how they are used together in solving problems and in simple equations. We are trying to develop student's algebraic thinking. Many of the ideas in this chapter are preparing them for algebra in advance. Math Mammoth Ratios & Proportions & Problem Solving This worktext concentrates, first of all, on two important concepts: ratios and proportions, and then on problem solving. First, we study thoroughly the concept of...

Updated! There are some marbles in Box A and Box B. If 50 marbles from Box A and 25 from Box B are removed each time, there will be 600 marbles left in Box A when all marbles are removed from Box B. If 25 marbles from Box A and 50 marbles from Box B are removed each time, there will be 1800 marbles left in Box A when all marbles are removed from Box B. How many marbles are there in each box? Again, this is from Singapore and teachers have told students not to use algebra to solve this question. However, any form of heuristic tools are allowed to facilitate the students in solving the questions. I'd like to point out that I feel it's a good problem, but students might benefit from some "preparation". You could set up a preparation problem like this: Jar A has 100 marbles and jar B has 40 marbles. You will start removing marbles one by one from jar A, but by 2's from jar B. How many marbles are left in jar A when jar B is empty? What if you remove 2 marbles at a tim...

I downloaded the "balance" worksheet freebie , and daughter liked it. We homeschool and she would be in fifth grade this year if she were in public school. ... My question is about the balance worksheets - where would there be more of that? Stuff that does groundwork for algebraic thinking? It's not just balance problems that prepare a child for algebra. These are important factors also: a good number sense (e.g. mental math) understanding of the four basic operations, for example how the opposite operations work. Another example: understanding that a division with remainder such as 50 ÷ 6 = 8 R2 is "turned around" with multiplication and addition: 8 × 6 + 2 = 50. a good command of fraction and decimal operations. Understanding the close connection between fractions and division. understanding the concepts of ratio and percent. You can also simply write her more problems with an unknown. For example: Write 7 + x = 28 and similar ones, like 12 + x = 99 and ...

Today I have a "goodie" for you all: a free download of some pan balance (or scales) problems where children solve for the unknown: Just right click on the link and "save" it to your own computer: Balance Problems (a PDF). This lesson is also included in my book Math Mammoth Multiplication 2 and in Math Mammoth Grade 4 Complete Worktext (A part). The problems look kind of like this: These can help children avoid the common misconception that equality or the equal sign "=' is an an operation. It is not; it is a relationship. You see: many students view "=" as "find the answer operator", so that "3 + 4 = ?" means "Find what 3 + 4 is," and "3 + 4 = 7" means that when you add 3 and 4, you get 7. To students with this operator-view of equality, a sentence like "11 = 4 + 7" or "9 + 5 = 2 × 7;" makes no sense. You might also find these resources useful: Balance word problems from ...

I haven't blogged for a while but I've been thinking about this topic for a little while now. It is your multiplication algorithm, also called long multiplication, or multiplying in columns. I also happen to be writing a lesson about it for my upcoming LightBlue series 4th grade book . The standard multiplication algorithm is not awfully difficult to learn. Yet, some books advocate using so-called lattice multiplication instead. I assume it is because the standard method is perceived as being more difficult. But let's look at it in detail. Before teaching the standard algorithm, consider explaining to the students multiplying in parts , a.k.a. partial products algorithm in detail: To multiply 7 × 84, break 84 into 80 and 4 (its tens and ones). Then multiply those parts separately, and lastly add. So we calculate the partial products first: 7 × 80 = 560 and 7 × 4 = 28. Then we add them: 560 + 28 = 588. If you practice that for one whole lesson before embarking on the actual...

If you're interested in Singapore math's word problems, and how their bar diagrams work, check out this blog entry by Denise at Let's Play Math: Pre-algebra problem solving: 3rd grade She goes through a bunch of word problems from Singapore Math 3-A book, and explains both a solution based on algebraic thinking, and a solution with bar diagrams. It's good reading for all of us who teach, actually.

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