The document explores various models of addition and subtraction in a classroom setting, prompting open-ended questions for group discussions. It covers concepts such as the need for a set model of subtraction, the properties of addition, and different subtraction models, asking for insights on their utility and implications for teaching. Overall, it emphasizes the importance of understanding these mathematical concepts to enhance algebraic thinking.

1. ADDITION AND
SUBTRACTION
MODELS
Classroom exploration open-ended questions for
groups to explore

2. Set Model of Addition
■ Why isn’t there a set model of subtraction? If there was, what would it look like?

3. Number Line Model of Addition
■ Are the arrows necessary? Is there any reason to include them for addition?What
about other operations?

4. Commutative and Associative Properties
of Additions
■ The commutative property of addition is represented in two different models below.
■ Try to create a similar model for the associative property given below.
– “If a, b, and c are any whole numbers, then (a+b) + c = a + (b+c).”

5. Making 10 Addition Strategy
■ Describe why the strategy illustrated below could be useful.

6. Take-Away Model of Subtraction
■ When would the model shown below be useful?

7. Missing Addends Model
■ How can the models shown be useful for algebraic thinking?

8. Comparison Model of Subtraction
■ What are the merits of this model? At what age level would you recommend this?

9. Number Line Measurement Model of
Subtraction
■ Are the arrows necessary for this model?Would they continue to work for negative
values?