Unit 4

Wrapping Up Multiplication and Division with Multi-digit Numbers

Unit Goals

Unit Narrative

In this unit, students multiply multi-digit whole numbers, using the standard algorithm, and begin working toward end-of-grade expectations for fluency. They also find whole-number quotients, with up to four-digit dividends and two-digit divisors.

In IM Grade 4, students used 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 to multiply a pair of two-digit numbers. They decomposed the factors by place value, and used diagrams and algorithms using partial products to record their...

Section A

Section Goals

Section Narrative

This section introduces the standard algorithm for multiplication, extending students’ earlier work on multiplication. In grade 4, students used diagrams and partial-products algorithms to find the product of a number up to four digits and a one-digit number, and the product of 2 two-digit numbers. They attended to the role of place value along the way.

Students revisit these strategies...

Let's estimate and calculate products.

Let's interpret diagrams that can help us find products.

Let’s find partial products.

Let’s use the standard algorithm to multiply multi-digit numbers by one-digit numbers.

Let’s use the standard algorithm to multiply three-digit numbers by two-digit numbers.

Let’s multiply with the standard algorithm and compose new units.

Let’s multiply multi-digit whole numbers, using the standard algorithm.

Let’s solve multiplication problems.

Section A Practice Problems

to access Section Checkpoints.

Section A

Let's estimate and calculate products.

Let's interpret diagrams that can help us find products.

Let’s find partial products.

Let’s use the standard algorithm to multiply multi-digit numbers by one-digit numbers.

Let’s use the standard algorithm to multiply three-digit numbers by two-digit numbers.

Let’s multiply with the standard algorithm and compose new units.

Let’s multiply multi-digit whole numbers, using the standard algorithm.

Let’s solve multiplication problems.

Section B

Section Goals

Section Narrative

In grade 4, students found whole-number quotients and remainders, with up to four-digit dividends and one-digit divisors, using strategies based on place value and partial quotients. In grade 5, they extend this work to include quotients involving two-digit divisors.

Students begin with an exploration that relates division of large numbers to a real-world context, a world-record event for making the...

Let’s explore division with multi-digit numbers.

Let’s use what we know about multiplication and place value to find quotients.

Let’s make sense of a partial-quotients algorithm.

Let's use a partial-quotients algorithm to divide three-digit and four-digit dividends by two-digit divisors.

Let's practice using a partial-quotients algorithm.

Let’s use the relationship between multiplication and division to solve problems.

Let’s solve a problem with large numbers, using division.

Let’s use fractions to help us divide whole numbers.

Section B Practice Problems

to access Section Checkpoints.

Section B

Let’s explore division with multi-digit numbers.

Let’s use what we know about multiplication and place value to find quotients.

Let’s make sense of a partial-quotients algorithm.

Let's use a partial-quotients algorithm to divide three-digit and four-digit dividends by two-digit divisors.

Let's practice using a partial-quotients algorithm.

Let’s use the relationship between multiplication and division to solve problems.

Let’s solve a problem with large numbers, using division.

Let’s use fractions to help us divide whole numbers.

Section C

Section Goals

Section Narrative

The final section invites students to use multiplication and division of whole numbers to estimate large quantities and solve real-world and mathematical problems.

Students encounter area and volume problems in the context of geography—the area of U.S. states—and everyday consumption—the volume of milk consumed, the area of plastic waste in the Pacific Ocean, and the volume of recyclable plastic shipped...

Let's make estimates with big numbers.

Let’s multiply to solve problems about the area of the Great Pacific Garbage Patch.

Let’s estimate volumes.

Let's use multiplication and division to think about food waste.

Section C Practice Problems

to access Section Checkpoints.

Section C

Let's make estimates with big numbers.

Let’s multiply to solve problems about the area of the Great Pacific Garbage Patch.

Let’s estimate volumes.

Let's use multiplication and division to think about food waste.

to access End-of-Unit Assessments.

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Wrapping Up Multiplication and Division with Multi-digit Numbers

Unit Goals

Unit Narrative

Section Goals

Section Narrative

Section A Practice Problems

Section Goals

Section Narrative

Section B Practice Problems

Section Goals

Section Narrative

Section C Practice Problems

Unit 4 Resources

About Unit 4

Other Resources

Section Goals

Section Narrative

Section B Practice Problems

Section Goals

Section Narrative

Section A Practice Problems

Section Goals

Section Narrative

Section C Practice Problems