Representing Elementary Examples

What do you want your representation to show?

Say, “Build 17 and 29 and add them together. One ten and two tens make three tens or 30. Now, 7 ones and 9 ones is 16 ones. Can we regroup these into a ten? If we regroup that ten over to the tens column, we have four tens or 40. 40 and 6 ones make 46.” A mental model is built for this part of the traditional algorithm:

Young learners need to understand and develop confidence with representing an amount in a wide variety of ways.

Invite children to show 6 in different ways.

Which representation of 6 is the best way to show that 6 is an even number?

Which representation was the best way to show that 6 is greater than 5?¹

Using concrete materials and pictures to combine and separate numbers helps learners develop a mental representation on which they can hang their understanding of traditional symbolic algorithms.

For example, you can play with base ten materials to experiment with and encourage regrouping. When using these materials, be sure to emphasize an important rule: whenever there are ten of any kind of block, you must regroup. That connects this concrete or pictorial play as an appropriate mental model for traditional numeric algorithms.²(Battista, 2012, p. 60)

¹Adapted from: Small, M. (2010). Big Ideas from Dr. Small: Creating a Comfort Zone for Teaching Mathematics Grades Kindergarten – 3. Toronto: Nelson Education Ltd p. 24.

²Battista, M., 2012. Cognition-Based Assessment & Teaching of Addition and Subtraction: Building on Students’ Reasoning (Cognition-Based Assessment and Teaching). Portsmouth, NH: Heineman, p.60.