LESSON PLAN

Introduction to Equal Groups and Multiplication

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

Put 3 groups of 4 cubes on the board (separated). How many altogether? Students count. Can you add them without counting all? 4 + 4 + 4 = 12. How about skip-counting? 4, 8, 12. All three methods give 12. What is the pattern?

Explore

Array construction: each pair receives a number (e.g., 12) and must find all the arrays that make that total. 12 = 1x12 = 2x6 = 3x4 = 4x3 = 6x2 = 12x1. Draw each on grid paper. How many arrays did you find? What do you notice about 3x4 and 4x3?

Consolidate

Practice

Students create arrays for 6 different products, record them as equal groups, addition sentences, and arrays. Exit ticket: draw an array for 4 groups of 3 and write the addition sentence.

Exit ticket

Students create arrays for 6 different products, record them as equal groups, addition sentences, and arrays. Exit ticket: draw an array for 4 groups of 3 and write the addition sentence.

TIP Do not rush to the times sign. Let students become fluent with equal groups language (3 groups of 4) before introducing 3 x 4. The language carries the meaning the symbol needs.

WORKED EXAMPLES

How many wheels on 4 bicycles? Show with a drawing and an addition sentence.

Each bicycle has 2 wheels: 4 groups of 2. Addition: 2 + 2 + 2 + 2 = 8. Array: 4 rows of 2 dots. Skip-count: 2, 4, 6, 8. Answer: 8 wheels. All four representations agree.

A student draws a 3x4 array and a 4x3 array and says they are different multiplications. How do you respond?

They have different row and column arrangements, but the total is the same: both equal 12. Rotate one array 90 degrees: it becomes the other. This is commutativity: the order of multiplication does not change the product.

MATERIALS

•Linking cubes for grouping

•Grid paper for drawing arrays

•Equal-groups recording sheets

•Skip-counting strips

•Counters in groups

WATCH FOR

!Students may count the rows and columns rather than the total objects. Clarify: the rows and columns tell you how to group; the product is the total number of objects.

!Students may not see skip-counting as related to multiplication. Ask explicitly: when you skip-count by 3 to find the total of 5 groups of 3, what operation are you doing?