In this unit, students will learn that the properties and meaning of operations with decimals are no different from the properties and meaning of operations with whole numbers. In the second half of the unit, they apply operations with decimals to solving realworld problems with length that involve the conversion of metric units by using powers of ten.
Key Concepts:
 The meanings of addition and subtraction are the same when used with decimals as when used with whole numbers. (Lesson 1)
 The meaning of multiplication is the same when used with decimals as when used with whole numbers. (Lesson 3)
 The meaning of division is the same when used with decimals as when used with whole numbers. (Lesson 7)
 Since the attribute length is invariant, we can measure it in different units, and we can convert between those units using multiplication and division (by powers of ten, in the case of the metric system).
Prior Knowledge Needed:
 Fluently add and subtract multidigit whole numbers using the standard algorithm (Grade 4, Unit 4; 4.NBT.B.4)
 Multiply whole numbers using various strategies (Grade 4, Unit 14; 4.NBT.B.4, 4.NBT.B.5)
 Find wholenumber quotients of whole numbers with up to fourdigit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division (Grade 5, Unit 2; 5.NBT.B.5, 5.NBT.B.6)
 Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left (Grade 5, Unit 4; 5.NBT.A.1)
 Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 (Grade 5, Unit 4; 5.NBT.A.2)
 Read, write, and compare decimals to thousandths (Grade 5, Unit 4; 5.NBT.A.3)
Units on the Horizon:
 Rates, including percents (Grade 6, Unit 2)
 Multidigit computation and finding common factors and multiples (Grade 6, Unit 3)
 Representing relationships (Grade 6, Unit 5)
Lessons

Lesson objective: Understand that adding and subtracting decimals uses the same methods as adding and subtracting whole numbers. Students bring prior knowledge of adding and subtracting whole numbers from 4.NBT.4B.4. This prior knowledge is extended to ...

Lesson objective: Apply knowledge of adding and subtracting decimal numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of adding and subtracting decimal numbers to a reallife situation. Students are ask...

Lesson objective: Understand that the meaning of multiplication is the same, whether we are working with whole numbers or decimals. Students bring prior knowledge of multidigit whole number multiplication from 4.NBT.5 and 5.NBT.5. This prior knowledge ...

Lesson objective: Multiply decimal numbers with factors greater than one. This lesson helps to build procedural skill with multiplying decimal numbers. Rectangular arrays are used here because they support the importance of place value when multiplying ...

Lesson objective: Multiply decimal numbers less than one using concrete models or drawings and strategies based on place value; relate the strategy to a written method and explain the reasoning used. This lesson helps to build procedural skill with deci...

Lesson objective: Apply the compensation method to decimal number multiplication. This lesson provides an opportunity for students to apply their knowledge and understanding of using the compensation method to multiply decimals to a reallife situation....

Lesson objective: Understand that the meaning of division is the same when used with decimals as whole numbers. Students bring prior knowledge of division of whole digit numbers from 4.NBT.5. and 5.NBT.5. This prior knowledge is extended to decimal numb...

Lesson objective: Divide decimal numbers greater than one using different representations. This lesson helps to build the procedural skill with dividing decimals. The use of 100 flats supports the connection between decimal division and whole number div...

Lesson objective: Divide decimal numbers less than one using a variety of representations and strategies. This lesson helps to build procedural skill with decimal division. The use of base 10 blocks and number lines supports the understanding of divisio...

Lesson objective: Apply what students know about dividing decimal numbers. This lesson provides an opportunity for students to apply their knowledge and understanding of dividing decimals to a reallife situation. Students are asked to convert between a...

Lesson objective: Understand that measurement of length can be expressed with different unit sizes because we can convert from larger to smaller units by using multiplication. Students bring prior knowledge of the multiplication of decimals from 4.NBT.A...

Lesson objective: Convert from larger to smaller metric measurement units by using multiplication. This lesson helps to build fluency with measurement conversion. A Metric Measurement Chart is used here because it is related to the Base10 Place Value s...

Lesson objective: Understand that metric units can be converted from smaller to greater units by using division with powers of 10. Students bring prior knowledge of the use of multiplicative comparison to convert between units of length from 4.OA.3. Thi...

Lesson objective: Convert metric units from smaller to greater units by using division with powers of 10, and greater to smaller units by using multiplication with powers of 10. This lesson helps to build fluency with metric measurement conversions. The...

Lesson objective: Solve problems that apply skills in converting metric measurement units from greater to smaller units by multiplying, or smaller to greater units by dividing. This lesson provides an opportunity for students to apply their knowledge an...