📊Lesson 3.7 Outline- Graphing Area Models (Two-Digit X Two-Digit) (For Teacher- Do Not Publish)
Lesson 3.7
For full lesson outline please see Advantage Math Lesson 3.7.
Standards:
4.NBT.5- Use strategies based on place value and the properties of operations to multiply a whole number of up to four digits by a one-digit whole number, and multiply two, two-digit numbers.
Objectives:
Math Objective: Students will be able to construct a two-digit by two-digit area model to model multiplication.
Language Objective: Students will discuss and work with a partner to create an area model with graph paper.
Vertical Alignment:
3.OA.7.B- Know from memory all products of two one-digit numbers
4.NBT.5- Use strategies based on place value and the properties of operations to multiply a whole number of up to four digits by a one-digit whole number, and multiply two, two-digit numbers.
5.NBT.5- Fluently multiply multi-digit whole numbers using the standard algorithm
Common Misconceptions:
None noted in Advantage Math Lesson 3.7
Lesson Outline:
🚀Launch A(in class or remote)
You may want to insert a video into the launch to show how a graph paper can represent a multiplication equation.
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Students will solve a simple multiplication equation, 5 X 7, using the graph paper to see if the product and the visual representation on the graph paper match.
- Questions you could ask:
- When might solving an equation like this become unreasonable?
- Vocabulary words: No new vocabulary words.
🤔 Download 🤔Explore A(in class or remote)
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Students are solving the equation and are asked to model their work on a graph paper.
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Questions you could ask:
- Did you use expanded form for each factor?
- How many sections did you color in?
- What was challenging about this?
- How might this be useful to solving equations with two-digit by two-digit factors?
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Questions you could ask:
🤔 Download 🤔Explore B(in class or remote)
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Students are solving another equation and are asked to model their work on a graph paper.
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Questions you could ask:
- Was this problem more challenging?
- Why is it important to use expanded form when solving?
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Questions you could ask:
đź’¬Discuss A (in class or remote)
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Question to use in your discussion:
- What value is there in writing or drawing the steps to solve a two-digit X two-digit multiplication equation?
- How might this help other students in your classroom?
Additional Resources:
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Differentiation (in class or remote)
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Challenge: Have the students use the commutative property to create a 31 Ă— 15 array. They should be prepared to discuss the four sections and how they are similar to the 15 Ă— 31 area model?
- Ways to make remote:
- Students can do this challenge on their own and submit their work and thoughts.
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Struggling : students who are struggling, place them in a small group where the base-ten blocks can be combined into a large quantity. Present an expression where students fill the area model in with base-ten blocks before drawing it on graph paper. Some students need more time going from the concrete to pictorial. With large numbers, they can’t just “imagine” the blocks, they must actually see them. Be less concerned about students writing the equations until they understand how to section the array
- Ways to make remote:
- Have students join you in an online meeting format (Zoom or Teams) and do the exact same activity. They might not have the place value disks, but you can show them yours to discuss.
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Challenge: Have the students use the commutative property to create a 31 Ă— 15 array. They should be prepared to discuss the four sections and how they are similar to the 15 Ă— 31 area model?
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Lesson Extension (in class):
- Instead of graph paper, students could use the floor and base ten blocks to create an area model.