As a parent, one of the many hats you wear is homework helper.  Sometimes this interaction goes smoothly, other times it does not.

Recently, there was an excellent Washington Post article about why it’s difficult to help your child with their math homework. The article offers a list of essential questions, from Christopher Danielson’s Common Core for Math for Parents for Dummies, to ask during moments of math homework frustration.

1. “Why?” and “How do you know?”
2. “What if?”
3. “Is it good enough?”
4. “Does this make sense?”
5. “What’s going on here?”

However, there are times when my second grader refuses to entertain my questions. I get the “Just tell me if I’m right!” plea. At these times, I find it best to step away from the worksheet he is working on and try to talk about the math he’s struggling with using a different medium. For example, when talking about subtraction with regrouping, we like to use these Magnetic Base Ten Pieces (white board not included). [Also, here is an app, Number Pieces, where students can demonstrate their thought processes by manipulating the virtual base ten blocks.]

A different medium might be a manipulative like pattern blocks or fraction strips, a household object with particular geometric properties, kitchen measuring cups, or a book. Recently we used this week’s magical math book to work through some fraction frustration.

The Book

Amazing Visual Math is a pop-up book that encourages children to interact with mathematical concepts through folding, unfolding, flipping, and tab-pulling. Amazing Visual Math was edited by Jolyon Goddard and published by DK publishing in 2014. Alison Gardner, the designer and paper engineer, created interesting foldables on each page.

The book is a mathematical reference book that explores different concepts from the first years of school (K-2). The sixteen colorful pages are full of different mathematical representations children can manipulate. There are mathematical facts and questions on each spread.

The Math

The different mathematical concepts presented in the book include 2D and 3D geometric shapes, addition and subtraction, an introduction to multiplication and division, and fractions.

There are different representations for each mathematical idea: fraction strips, arrays, number line models (they call it a number ladder), and nets that fold into three-dimensional shapes.

The Magic

My children have enjoyed flipping through the pages of this book for the past couple months. Lately, they’ve really been into origami and enjoyed these orgami-like pages the most.  They WOWed and OMGed as they unfolded and folded shapes into other shapes.

This book has been helpful to have around during homework time as well. A couple weeks ago, this book provided insight into my son’s beginning ideas about fractions. There was a question on Liam’s 2nd grade homework that asked to compare the fractions, 1/2 and 3/4. Liam was adamant that 1/2 was larger than 3/4. I was having trouble making sense of why he was thinking this and he wasn’t in the mood for any of my questions.  I decided to switch gears and pulled out Amazing Math Visuals. We started by exploring the fraction strip page below.

He identified 3/4 and 1/2 using the strips, but still maintained that 1/2 was larger and wasn’t budging.

We switched to a different representation, the fraction circle (see below). While working with the circle, it became clear to me why he thought 1/2 was bigger. In this continuous model,  Liam could pull the tab to change from 1/2 to 3/4 with the yellow portion growing on the same referent whole (the circle) for both fractions. Using this model, Liam reasoned that 3/4 of the circle was more than 1/2 circle.

 

I asked:

Can you explain why here  (fraction circle) you say 3/4 is larger and here (fraction strips) you say 3/4 is smaller than 1/2?

Liam explained using the fraction strips that 1/2 was bigger than 3/4 because “it has bigger pieces.”  He had been reasoning about the size of the pieces instead of the portion of the whole each fraction represented.  I shared with him how glad I was to understand his thinking and suggested that we make our own fraction strips and chat a bit more about fractions.

We made a set of fractions strips similar to the one in the book (here is basic template similar to what we used). Folding 1/2s, 1/4s, 1/8s is pretty simple since it involves halving the strip some number of times. 1/3s, 1/5s, 1/6, 1/7s, 1/9, 1/10s are a bit trickier.  Here is a video from Mashup Math describing how to make your own fractions strips.

Creating and using mathematical representations is an important part of mathematical communication. Amazing Visual Math provides a variety of representations for children to explore and is a great resource to have on hand during homework time or anytime.

We will be back in two weeks with more math book magic, this time from our second guest blogger, educator Simon Gregg (@Simon_Gregg).

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Thanks and see you in two weeks!  #mathbookmagic