Rewriting Equalities to Build Numeracy - Part 2

In our last post, we wrote about the work of Dr. Barbara Dougherty, the Director of the Curriculum Research and Development Group at the University of Hawaii. Dr. Dougherty's work emphasizes the importance of of instilling a solid sense of numeracy (being able to reason with numbers and other mathematical concepts) and operations (recognition of the relationships among addition, subtraction, multiplication, and division) to provide students with a true understanding of math.

One way to do this is to teach students to "Rewrite Equalities", a process that begins with understanding the meaning of = .

How do we do this?

Step 1: Establish an understanding of =

= does not represent “the answer” (as most kids think it does). It means that whatever is on one side has the same value as whatever is on the other side.

This seems simple, but it’s a big intellectual leap for kids. One of the biggest revelations will probably be the insight that it’s possible to have multiple numbers on each side of the =.

Try modeling this with manipulatives and sticky notes. Start with this:

  

Then show students that you can also do this:

Or this:

Or even this:

In all of the examples above, there are still a total of seven pennies on each side of the =. Challenge them to build their own models.

Step 2: Entry-Level Equalities

When it’s time to move from manipulatives to numbers, the teacher should demonstrate how to rewrite an equality in a few different ways. Begin by writing and explaining a series like this:

3 + 5 = 8

8 = 3 + 5

8 = 4 + 4

7 + 1 = 8

Now, invite students to take over with their own ideas. How many can they come up with? 

The student who remembers the commutative property doubles the number of expressions s/he can write, but don’t tell them this! Wait for someone to figure it out.

In my classroom, after they’ve worked for a while, students pick their two favorite expressions to write on the board and explain to the class.

Questions to Push Thinking:

• Can you rewrite the equality using a different operator, like a subtraction sign?
• Can you rewrite the equality by putting two or more numbers on each side of the equal sign?
• Can you rewrite the expression using decimals or fractions? What about negative numbers?

Step 3: More Advanced Equalities: Focusing on Operations

Challenge students to rewrite an equality using only the numbers in the inequality. They may use any operators and any format they’d like.

So a simple expression like this:

4 + 6 = 10

could be rewritten like this:

10 – 6 = 4

A more complex expression, like this:

3 x 4 x 2 = 24

could be rewritten like this:

2÷24 = 4 x 3

Students will notice that more complicated expressions can be rewritten in more ways.

I’m my classroom, we’ve learned that there is tremendous power in simple activities and procedures. I hope other educators find this activity to be as valuable as we have!