Section A: Practice Problems Multi-digit Multiplication Using the Standard Algorithm

Section Summary

Details

In this unit we found products of a three-digit number and a two-digit number. We first

represented the products with diagrams that help us break down the product by place value.

This diagram breaks up the product $412 \times 32$ by place value. If we find and add up all of the partial products, we will get the product of $412 \times 32$ .

Diagram, rectangle partitioned vertically and horizontally into 6 rectangles.

Then we learned a new algorithm to multiply numbers, the standard algorithm for multiplication.

We can see the partial products are organized in a different way. 824 represents the partial product for 2 \times 412 and 12,360 represents the partial product for 30 \times 412.

We noticed that sometimes we need to compose a new unit when we use the standard algorithm, and we represent that unit with notation. Sometimes, we may have to compose more than one new unit.

The 1 above the 1 in 216 represents the ten from the product $3 \times 6$ and the 2 represents 2 hundreds from the product $40 \times 6$ .

Problem 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.

Problem 2 (Pre-Unit)

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

$27 \times 53$
$518 \times 6$

Problem 3 (Pre-Unit)

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

Problem 4 (Pre-Unit)

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

Rectangular prism. 40 by sixty by eighty centimeters.

Problem 5 (Pre-Unit)

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

Explain or show how the drawing shows $2 \div 5$ .
Explain or show how the drawing shows $\frac{2}{5}$ .

Problem 6 (Lesson 1)

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

$100 \times 50$
$120 \times 50$
$127 \times 50$

Problem 7 (Lesson 2)

Complete the diagrams and use each of them to find $253 \times 31$ .

How are the strategies the same? How are they different?

Problem 8 (Lesson 3)

Find $315 \times 43$ using partial products.

Problem 9 (Lesson 4)

Use the standard algorithm to find the value of $16, 452 \times 6$ .

Problem 10 (Lesson 5)

Find the value of $322 \times 41$ using the standard algorithm.

Problem 11 (Lesson 6)

Find the value of $562 \times 34$ using the standard algorithm.

Problem 12 (Lesson 7)

Andre is playing Greatest Product. He says the greatest product it’s possible to make in the game is $987 \times 65$ . Do you agree with Andre? Explain or show your reasoning.

Problem 13 (Lesson 8)

Using the digits 1, 2, 3, 4, and 5 make a product that is close to 8,000.

Problem 14 (Lesson 9)

The recommended side lengths for a birdhouse for a yellow-bellied sapsucker are 13 cm by 13 cm for the floor and a height of 31 to 38 cm. What are the smallest and largest volumes for these birdhouses? Explain or show your reasoning.

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 can also 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?

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 did you prefer? Why?