LESSON PLAN

Change in Quantity: Pictorial and Symbolic

Apothem Team

Grade 2 · Number

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Consolidate

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

Show a ten-frame with 7 counters. Write 7 + ? = 10. How many empty spaces? (3.) So 7 + 3 = 10. Now show a double ten-frame with 14 counters. Write 14 + ? = 20. (6 empty.) This visual-to-symbolic connection is the entire lesson in miniature.

Explore

Change problem cards: each card shows a situation with one quantity unknown. Students must: (1) draw the ten-frame or number line showing the situation, (2) write the equation with a box for the unknown, (3) solve by examining the visual model. Three card types for each structure.

Consolidate

Practice

Students solve 6 change problems (2 of each type), showing the visual model and the equation for each. Exit ticket: draw a ten-frame and write an equation to show 8 + ? = 15.

Exit ticket

Students solve 6 change problems (2 of each type), showing the visual model and the equation for each. Exit ticket: draw a ten-frame and write an equation to show 8 + ? = 15.

TIP The box or n is just a name for the number we are finding. Always ask: what number makes this equation true? This phrasing keeps the focus on meaning rather than procedure.

WORKED EXAMPLES

Write and solve: I had 28 stickers. After giving some away I have 13. How many did I give away?

This is a change-unknown problem: 28 - ? = 13. Or equivalently: 13 + ? = 28. Adding up from 13 to 28: jump 7 to 20, jump 8 to 28. Total: 15. Check: 28 - 15 = 13.

A student writes 6 + 4 = 10 + 3 = 13 for the problem 6 + 7 = ?. What is wrong?

This is a chain equation error: 6 + 4 = 10 is true, but 10 is not equal to 10 + 3. The equals sign should only connect two expressions with the same value. The correct recording: 6 + 7 = 6 + 4 + 3 = 10 + 3 = 13, written as separate steps, not a chain.

MATERIALS

•Ten-frames

•Hundred charts

•Open number lines

•Change problem cards

•Student whiteboards

WATCH FOR

!Chain equation errors (6+4=10+3=13) are extremely common and extremely important to address. The equals sign means balance, not therefore.

!Students may solve by counting all from 1 rather than using the visual model. Redirect by requiring them to show the ten-frame or number line before computing.