standard_description: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: Narrative
The purpose of this activity is for students to determine whether a situation is about an unknown number of groups or an unknown number of objects in each group. After sorting the situations, students write a division expression to represent each situation. The fact that the structure of the expressions is the same for representing an unknown number of groups or an unknown number of objects in each group further emphasizes that division expressions can be interpreted two ways. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).
As students explain their reasoning around the unknown in the situation, encourage students to describe how they would start to solve the problem to make it clear what is unknown in the situation.
MLR8 Discussion Supports.
Synthesis. Display a sentence frame to support whole-class discussion: “We noticed _____ so we . . . .”
Advances: Speaking, Representing
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce the remaining cards once students have completed their initial set of matches.
Supports accessibility for: Organization, Attention
Required Materials
Materials to Copy
Card Sort: All About Bugs
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Display the image.
“We are going to work with some situations involving insects. Insects are a type of bug. These are all insects.”
“What are some parts of the insects we could count?” (legs, eyes, wings, antennae, body segments)
If needed, clarify what antennae are.
Distribute one set of pre-cut cards to each group of students.
Activity
“In this activity, you will sort some cards into categories of your choosing. When you sort the situations, you should work with your partner to come up with categories.”
5 minutes: partner work time
Select groups to share their categories and how they sorted their cards.
Choose as many different types of categories as time allows, but ensure that one set of categories distinguishes between “how many groups?” and “how many in each group?” problems.
If no students sorted the cards by type of division situation, give them a minute to do so, and then discuss how they know which type of division each situation represents.
“Now work with your partner to sort your cards by ‘how many groups?’ and ‘how many in each group?’ problems.”
“Once you have sorted your cards, write a division expression to represent each situation.”
5 minutes: partner work time
Student Facing
[IMG]
Your teacher will give you a set of cards that show situations. Sort the cards into 2 categories of your choosing. Be prepared to explain the meaning of your categories.
A. Mole crickets have special legs for digging. Ten special legs belong to 5 mole crickets. How many special legs does each mole cricket have?
B. A beetle has a pair of antennae for sensing heat, touch, smell, and more. If there are 8 antennae, how many beetles are there?
\(\phantom{00}\)
C. Fourteen antennae belong to a group of bees. If each bee has 2 antennae, how many bees are there?
D. There are 12 wings. If each dragonfly has 4 wings, how many dragonflies are there?
\(\phantom{00}\)
E. Thirty legs belong to 5 ants. If all the ants have the same number of legs, how many legs does each ant have?
F. There are 50 spots on 5 butterflies. If each butterfly has the same number of spots, how many spots does each butterfly have?
Write a division expression to represent each situation. Be ready to explain your reasoning.
Student Response
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Activity Synthesis
Invite students to share the expression for each situation.
Consider asking:
“What does each number represent in the expression?”
“Where do you see the number of groups in the expression?”
“Where do you see the number of objects in each group in the expression?”


aligns: no