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 compare numbers in a way that makes sense to them. Students can use physical objects or make drawings to represent each number (MP5), and match or count to compare. Students can also use their knowledge of the count sequence and understanding that each successive number refers to a quantity that is one more to compare the numbers. In the synthesis students describe how creating representations of numbers helps to compare numbers.
Action and Expression: Internalize Executive Functions.
After students decide which manipulative they will use for the activity, invite students to plan a strategy for how they will use their manipulatives to determine which number is more. If students choose to use counters, give them access to 5-frames to help with the counting.
Supports accessibility for: Visual-Spatial Processing, Conceptual Processing, Organization
Required Materials
Materials to Gather
Connecting cubes or counters
Launch
Groups of 2
Give students access to connecting cubes or counters.
“Work with your partner to figure out which number is more. Circle the number that is more.”
Activity
5 minutes: partner work time
Monitor for students who create representations of the numbers using cubes or a drawing and use these representations to compare.
Monitor for students who counted to figure out which number is more.
Student Facing
Circle the number that is more.
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Student Response
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Advancing Student Thinking
If students circle the number that is less instead of the number that is more, consider asking:
“What do you know about these two numbers? What are you trying to figure out?“
“How can you use the cubes to show each number? How can the cubes help you figure out which number is more?“
Activity Synthesis
Invite previously selected students to share the representations they made and how they used them to figure out which number is more.
“How did counting out the groups of objects or drawing pictures help you figure out which number is more?”
Invite previously selected students to share how counting helped them compare the numbers.
“We know 8 is more than 5. Compare these numbers using ‘less’.”


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