Unit 5: Arithmetic in Base Ten

Students solidify their understanding of the base-ten number system, extend the standard algorithms to add, subtract, and multiply decimals beyond tenths and hundredths, and learn to use algorithms to calculate quotients including long division.

Worksheets

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Unit

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Concept

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Practice

Set 1

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Set 2

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Advanced

Set 1

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Set 2

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What this unit covers

A Exploring, Adding, and Subtracting Decimals · 4 lessons

Goals

• Explain the sum or difference of two decimals in terms of combining like base-ten units and composing (or decomposing) a larger unit from (or into 10) units of a lower value.
• Use the standard algorithm to add or subtract decimals with multiple non-zero digits.

Lessons

1. Using Decimals in a Shopping Context
2. Using Diagrams to Represent Addition and Subtraction (Optional)
3. Adding and Subtracting Decimals with Few Non-Zero Digits
4. Adding and Subtracting Decimals with Many Non-Zero Digits

B Multiplying Decimals · 4 lessons

Goals

• Calculate the product of two decimals and explain the solution method.
• Use an algorithm to calculate the product of whole numbers, and justify how to use that value to find the product of two decimals with the same significant digits.

Lessons

1. Using Fractions to Multiply Decimals
2. Methods for Multiplying Decimals
3. Using Diagrams to Represent Multiplication
4. Calculating Products of Decimals

C Dividing Decimals · 5 lessons

Goals

• Calculate the quotient of a whole-number or a decimal dividend and a decimal divisor, and explain the solution method.
• Use long division to divide a multi-digit whole number or a decimal by a whole number.

Lessons

1. Using Base-Ten Diagrams to Divide (Optional)
2. Using Partial Quotients
3. Using Long Division
4. Dividing Numbers that Result in a Decimal
5. Dividing a Decimal by a Decimal

D Let’s Put It to Work · 2 lessons

Lessons

1. Solving Problems Involving Decimals
2. Making and Measuring Boxes (Optional)

Helpful to know first

The curriculum says this unit builds on these.

Grade 6 Math · Unit 4 Dividing Fractions

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