Fishtank Learning

3rd Grade Math
Unit 3: Multiplication and Division, Part 2
Lesson 1

Objective

Study commutativity to find known facts of 6, 7, 8, and 9.

Anchor Tasks - Problem 1

Katia and Gerard are stocking shelves at the grocery store. Katia stocks 3 shelves with 7 boxes of cereal on each shelf. Gerard stocks 7 shelves with 3 boxes of cereal on each shelf.

Katia says they put the same number of cereal boxes on each shelf. Gerard says they didn’t, since they stocked a different number of boxes on each of a different number of shelves. Who do you agree with, Katia or Gerard? Explain.

Guiding Questions

Do you agree with Katia or Gerard? Why?
What could you have drawn to support your argument?
Write an equation that represents your argument.
If you know the value of 8 fours, do you know the value of 4 eights? Why?
Recall that the idea that we can multiply two numbers in any order and get the same product is called the commutative property.

Notes

Have students discuss their reasoning with each other, encouraging them to use a representation to defend their reasoning (MP.3). Students will likely draw an array for this problem, since that is the representation encouraged by the problem context and the model used to demonstrate the commutative property in Unit 2. But, they could also use a tape diagram to support their answer. Both possible models are shown below:

Anchor Tasks - Problem 2

Fill in the facts you know on the multiplication table below.

×	1	2	3	4	5	6	7	8	9	10
1
2
3
4
5
6
7
8
9
10

Guiding Questions

The multiplication table is a way to organize the multiplication facts. Each square contains the product of the factors that correspond with its row and column. (Point to the square that corresponds with the fact $$7\times3$$.) What are the two factors that correspond with this square? What is their product? Where should we write that product?
Based on Anchor Task #1, we know that there is another square where the product is 18. Find that square and fill it in.
What other facts can we fill in based on ones we already know from Unit 2?
What do you notice about the facts we already know? What do you notice about the ones we don’t know?
Once we learn $$6\times9$$, will we also know the fact for $$9\times6$$? Why?
How many total facts do we still have to learn if we eliminate the "repeat" facts due to the commutative property, or the property that switching the order of the factors doesn't change the value of the multiplication expression?

Notes

Students should have a personal copy of the multiplication table. If you already provide printed copies of Anchor Tasks, that will suffice. Otherwise you can provide students with a copy of a Blank Multiplication Table.
Have students hold onto their multiplication tables. They will fill in the remaining facts as they learn them later in the unit.

Anchor Tasks - Problem 3

Solve.

a. $$4 \times 8 =a $$

b. $$18 = b \times 6$$

c. $$c= 35 \div 7$$

d. $$9 = 18 \div d$$

Guiding Questions

I don’t know how to count by 8. What can I do instead to solve Part (a)?
For Part (b), can you think of what number times 6 has a product of 18?
How can the relationship between multiplication and division help you to solve Part (b)?
Part (d) is difficult because it is an unknown divisor. How did you solve?
If I can’t think of a corresponding 2, 3, 4, 5, or 10 fact and didn’t have my multiplication table in front of me, what strategies can I always rely on to solve multiplication and division problems?

Problem Set

View Problem Set

Discussion of Problem Set

What multiplication equations did you write for #1? What other equations can you write that are represented by this array?
How did you to solve the equations in #4? Were there any for which the commutative property, or switching the order of the factors, helped you?
What did you notice in the multiplication table in #6? Why does that pattern exist?

Target Task - Problem 1

Fill in the blanks to write two different equations that represent the array below.

Target Task - Problem 2

Sunni wants to solve the problem below.

4 × 6 = ?

Explain how she can use the fact that 6 × 4 = 24 to help her solve.

Word Problem

Wolfe and Amit go apple picking. They represent the number of apples they each picked in the picture graph below. How many total apples did they pick?

Fishtank Learning

3rd Grade MathUnit 3: Multiplication and Division, Part 2Lesson 1

Objective

Anchor Tasks - Problem 1

Anchor Tasks - Problem 2

Anchor Tasks - Problem 3

Problem Set

Target Task - Problem 1

Target Task - Problem 2

Word Problem

3rd Grade Math
Unit 3: Multiplication and Division, Part 2
Lesson 1