Lesson objective: Understand that the meaning of addition and subtraction do not change, no matter which tool we are using.

Students bring prior knowledge of the meaning of addition and subtraction as "add to/take from" and "put together/take apart" from their work in K.OA.A and 1.OA.1 as they work with solving addition and subtraction problems using a variety of tools. This prior knowledge is extended to include that the meaining of addition and subtraction do not change, no matter which tool is used as students solve a "put together/take apart" situations using two different tools and compare their math thinking and answers. A conceptual challenge students may encounter is thinking that different tools will calculate different answers.

The concept is developed through work with various tools such as concrete objects, linking cubes, arithmetic racks, ten frames, number bonds, and number lines, which provide a concrete and/or pictorial representation of adding and subtracting.

This work helps students deepen their understanding of operations, because they make connections from the concrete to pictorial to symbolic equations as they articulate the meaning of addition and subtraction.

Students engage in Mathematical Practice MP.3 (Construct viable arguments and critique the reasoning of others) as they explain how their tool shows adding as "put together" or subtracting as "take apart" and how that connects to an equation. Students also engage in MP.8 (Look for and express regularity in repeated reasoning) as they notice that the sum or difference remains the same regardless of the tool and/or strategy used.

**Key vocabulary:**

- equation
- tools
- math thinking

**Special materials needed:**

A variety of tools to allow students to represent the meanings of addition and subtraction as an action: Suggested tools:

- ten frames
- linking cubes
- number lines
- number racks
- base ten blocks
- counters