Category Archives: Thoughts on Learning

Algebraic Thinking


One of the most exciting things for 5th grade students is learning about algebra. They have been anticipating this subject for some time. What’s interesting is that they have been working with abstract mathematics forever, but it just isn’t often called algebra.

When we ask: 5 x 5 = ?, this could be written 5 * 5 = X sometime early on in elementary school. This introduction to variables can be a huge stumbling block for many students. It’s really important to get comfortable with variables in mathematics early on. We can make this problem slightly more difficult by asking it another way.

5 * X = 25 or finally 5X = 25 – now we’re doing simple algebra.

This week we have been looking at systems of equations and solving for all of the variables. These are wonderful problems that help students get familiar with variables in equations.

Here is a sampling of some of the problems we have worked on. Feel free to create some on your own. As long as you have a unique equation for each variable, there will be one and only one answer.

A + B + C = 36

A + A + B = 26

B + B + B = 18

The next problem we tried was

2A + B + C = 48

A + B + C = 40

2B + A = 18

At least one class tried this one

2/5A + B = 17

A + B = 20

And most challengingly some attempted the following

2A + B + C = 30

A + 2B + C = 35

A + B + 2C = 37


Wow! Stanford Online Class for Kids

Check out this amazing opportunity! This would be a wonderful thing to do with your child. Professor Jo Boaler is an exceptional mathematics educator and is offering this class for free. Class starts in late May or early June and can be completed at your own pace at any time through December 2014. This could be your summer math plan…

About This Course

How to Learn Math is a class for learners of all levels of mathematics. It combines really important information on the brain and learning with new evidence on the best ways to approach and learn math effectively. Many people have had negative experiences with math, and end up disliking math or failing. This class will give learners of math the information they need to become powerful math learners, it will correct any misconceptions they have about what math is, and it will teach them about their own potential to succeed and the strategies needed to approach math effectively. If you have had past negative experiences with math this will help change your relationship to one that is positive and powerful.

Adding with Fractions

We’re back at it with fractions!

Students should know how to:

  • compare any two fractions (<, >, =)
  • justify why they compare them that way (they have codes)
  • come up with equivalent fractions
  • create a double number line
  • fill in a rate table
  • divide whole numbers by fractions
  • multiply with fractions less than 1

Now we are using our understanding to add and subtract fractions. The essential first step to adding or subtracting fractions is working with equal sized pieces (common denominator). Some of this we can do mentally, like adding half and quarter, some we need to write out.

Talk to your child about the Land Sections problem!

The work right now revolves around continuing to make sense of working with fractions. If you talk with your child about math, ask them why things work, and how they know. When they can explain the why, they have really understood the material.