Illustrative Mathematics | v.360 Curriculum

Problem 1

4.NBT.A.1

Pre-unit

Han says that the value of the 7 in 735,208 is 10 times the value of the 7 in 137,342. Do you agree with Han? Explain or show your reasoning.

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Problem 2

4.NBT.B.5

Pre-unit

Find the value of each product. Explain or show your reasoning.

\(27 \times 53\)
\(518 \times 6\)

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Problem 3

4.NBT.B.6

Pre-unit

Find the value of \(7,\!518 \div 6\). Explain or show your reasoning.

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Problem 4

5.MD.C.5

Pre-unit

What is the volume of this rectangular prism? Explain or show your reasoning.

Rectangular prism. 40 by sixty by eighty centimeters.

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Problem 5

5.NF.B.3

Pre-unit

2 diagrams of equal length. 5 equal parts, 1 part shaded. Total length, 1.

How does the drawing show \(2 \div 5\)? Explain or show your reasoning.
How does the drawing show \(\frac{2}{5}\)? Explain or show your reasoning.

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Problem 6

ForLesson 1: Estimate and Find Products

Find the value of each product. Explain or show your reasoning.

\(100 \times 50\)
\(120 \times 50\)
\(127 \times 50\)

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Problem 7

ForLesson 2: Partial Products in Diagrams

Complete the diagrams. Use each diagram to find the value of \(253 \times 31\).

Diagram, rectangle partitioned vertically and horizontally into 6 rectangles. — A

Diagram, rectangle partitioned horizontally into 2 rectangles. Top rectangle, vertical side, 30, horizontal side, two hundred fifty three. Bottom rectangle, vertical side, 1. — B

How are the strategies alike? How are they different?

Problem 8

ForLesson 3: Partial Products in Algorithms

Find the value of \(315 \times 43\), using partial products.

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Problem 9

ForLesson 4: Standard Algorithm: One-digit and Multi-digit Numbers, with Composing

Find the value of \(16,\!452 \times 6\). Use the standard algorithm.

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Problem 10

ForLesson 5: Standard Algorithm: Multi-digit Numbers, without Composing

Find the value of \(322 \times 41\). Use the standard algorithm.

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Problem 11

ForLesson 6: Standard Algorithm: Multi-digit Numbers, with Composing

Find the value of \(562 \times 34\). Use the standard algorithm.

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Problem 12

ForLesson 7: Build Multiplication Fluency

Andre is playing Greatest Product. He says the greatest product to make in the game is \(987 \times 65\). Do you agree? Explain or show your reasoning.

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Problem 13

ForLesson 7: Build Multiplication Fluency

Use the digits 1, 2, 3, 4, and 5 to make a product with a value close to 8,000.

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Problem 14

ForLesson 8: The Birds

The recommended side lengths for a birdhouse for a yellow-bellied sapsucker are 13 centimeters by 13 centimeters for the floor and a height of from 31 centimeters to 38 centimeters. What are the least and greatest volumes for this birdhouse? Explain or show your reasoning.

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Problem 15

Exploration

Jada remembers that the partial-products algorithm can go from left to right or from right to left. She wonders if the standard algorithm also can go in either direction.

Calculate \(418 \times 53\), using partial products right to left and left to right.
Calculate \(418 \times 53\), with the standard algorithm. What happens if you try to make the calculation from left to right?

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Problem 16

Exploration

Clare has a strategy for multiplying a number by 99. To find \(648 \times 99\), she calculates \(648 \times 100\) and then subtracts \(648\).

Use Clare's strategy to calculate \(648 \times 99\).
Use the standard algorithm to calculate \(648 \times 99\).
Which strategy do you prefer? Explain your reasoning.

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Multi-digit Multiplication Using the Standard Algorithm

Practice

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Problem 10

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Problem 13

Problem 14

Problem 15

Problem 16