Unit 5

Arithmetic in Base Ten

Unit Narrative

In this unit, students solidify their understanding of the base-ten number system, extend their use of the standard algorithms to add, subtract, and multiply decimals beyond tenths and hundredths, and learn to use algorithms to calculate quotients. The work here builds on what students learned in earlier grades about operations on whole numbers and decimals.

Students begin by exploring the use of decimals in a shopping context and by revisiting addition and subtraction of decimals, using both concrete representations and numerical calculations. The activities in the first section reinforce ideas...

to access Pre-Unit Assessments.

Section A

Section Goals

Section Narrative

This section deepens students’ understanding of the base-ten structure and extends their ability to add and subtract decimals beyond hundredths.

Students begin by revisiting decimal operations in the context of money. This exploration is followed by an optional lesson to revisit place-value concepts. It allows students to make sense of place-value relationships and use base-ten diagrams to represent decimals, their...

Let’s use what we know about decimals to make shopping decisions.

Let’s represent addition and subtraction of decimals.

Let’s add and subtract decimals.

Let’s practice adding and subtracting decimals.

to access Section Checkpoints.

Section A

Let’s use what we know about decimals to make shopping decisions.

Let’s represent addition and subtraction of decimals.

Let’s add and subtract decimals.

Let’s practice adding and subtracting decimals.

Section B

Section Goals

Section Narrative

In this section, students learn to multiply decimals by building on their understanding of whole-number multiplication. As done in earlier grades, they find products by reasoning about place value, using representations such as base-ten blocks and area diagrams, and finding partial products, before arriving at an algorithm.

Students begin finding products by using the relationship between decimals and fractions. They...

Let’s look at products that are decimals.

Let’s look at some ways we can represent multiplication of decimals.

Let’s use area diagrams to find products.

Let’s multiply decimals.

to access Section Checkpoints.

to access Mid-Unit Assessments.

Section B

Let’s look at products that are decimals.

Let’s look at some ways we can represent multiplication of decimals.

Let’s use area diagrams to find products.

Let’s multiply decimals.

Section C

Section Goals

Section Narrative

In this section, students reason about quotients of multi-digit numbers and work toward the standard algorithm for division.

The section begins with an optional lesson that revisits concepts from grade 5 and reinforces the role of place value in division. Students use base-ten diagrams to represent division and use strategies based on place value and properties of operations to find...

Let's use base-ten diagrams to find quotients.

Let’s divide whole numbers.

Let’s use long division.

Let’s find quotients that are not whole numbers.

Let’s divide a decimal by a decimal.

to access Section Checkpoints.

Section C

Let's use base-ten diagrams to find quotients.

Let’s divide whole numbers.

Let’s use long division.

Let’s find quotients that are not whole numbers.

Let’s divide a decimal by a decimal.

Section D

Section Narrative

In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions. The final lesson in this section is optional because it offers additional opportunities to practice standards that are not a focus of the grade.

Let’s solve some problems using decimals.

Let’s use what we know about decimals to make and measure boxes.

to access Section Checkpoints.

Section D

Let’s solve some problems using decimals.

Let’s use what we know about decimals to make and measure boxes.

to access End-of-Unit Assessments.

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Arithmetic in Base Ten

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