Learn on PengiIllustrative Mathematics, Grade 5Chapter 4: Wrapping Up Multiplication and Division with Multi-Digit Numbers

Lesson 1: Estimate and Find Products

In this Grade 5 Illustrative Mathematics lesson from Chapter 4, students estimate and calculate products of multi-digit numbers using place value understanding and properties of operations. Building on their Grade 4 work with partial products, students apply strategies for multiplying numbers such as 15 × 121 and multiples of 10 and 100, then evaluate whether their estimates are too large or too small. The lesson prepares students for the standard algorithm for multi-digit multiplication addressed in 5.NBT.B.5.

Section 1

Multiplying Multiples of 10

Property

To multiply multiples of 10, multiply the non-zero digits and then adjust the place value based on the units being multiplied.

Tens $\times$ Tens = Hundreds: $(a \times 10) \times (b \times 10) = (a \times b) \times 100$
Tens $\times$ Ones = Tens: $(a \times 10) \times c = (a \times c) \times 10$

Examples

Section 2

Estimating Products by Rounding

Property

To estimate the product of two numbers, round one or both factors to a nearby place value (like the nearest ten or hundred) to make the multiplication easier to perform mentally.
The symbol $\approx$ means "approximately equal to".

Examples

To estimate $48 \times 7$ , round $48$ to the nearest ten, which is $50$ . Then, calculate $50 \times 7 = 350$ . So, $48 \times 7 \approx 350$ .

To estimate $615 \times 4$ , round $615$ to the nearest hundred, which is $600$ . Then, calculate $600 \times 4 = 2400$ . So, $615 \times 4 \approx 2400$ .

Section 3

Using the Distributive Property for Partial Products

Property

The distributive property allows us to multiply a sum by multiplying each addend separately and then adding the products.
When we decompose factors by place value, the results of these smaller multiplications are called partial products.

a \times (b + c) = (a \times b) + (a \times c)

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Multiplying Multiples of 10

Property

To multiply multiples of 10, multiply the non-zero digits and then adjust the place value based on the units being multiplied.

Tens $\times$ Tens = Hundreds: $(a \times 10) \times (b \times 10) = (a \times b) \times 100$
Tens $\times$ Ones = Tens: $(a \times 10) \times c = (a \times c) \times 10$

Examples

Section 2

Estimating Products by Rounding

Property

Examples

To estimate $48 \times 7$ , round $48$ to the nearest ten, which is $50$ . Then, calculate $50 \times 7 = 350$ . So, $48 \times 7 \approx 350$ .

To estimate $615 \times 4$ , round $615$ to the nearest hundred, which is $600$ . Then, calculate $600 \times 4 = 2400$ . So, $615 \times 4 \approx 2400$ .

Section 3

Using the Distributive Property for Partial Products

Property

a \times (b + c) = (a \times b) + (a \times c)

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Multiplying Multiples of 10

Property

To multiply multiples of 10, multiply the non-zero digits and then adjust the place value based on the units being multiplied.

Tens $\times$ Tens = Hundreds: $(a \times 10) \times (b \times 10) = (a \times b) \times 100$
Tens $\times$ Ones = Tens: $(a \times 10) \times c = (a \times c) \times 10$

Examples

Section 2

Estimating Products by Rounding

Property

Examples

To estimate $48 \times 7$ , round $48$ to the nearest ten, which is $50$ . Then, calculate $50 \times 7 = 350$ . So, $48 \times 7 \approx 350$ .

To estimate $615 \times 4$ , round $615$ to the nearest hundred, which is $600$ . Then, calculate $600 \times 4 = 2400$ . So, $615 \times 4 \approx 2400$ .

Section 3

Using the Distributive Property for Partial Products

Property

a \times (b + c) = (a \times b) + (a \times c)