Unit 2

Multi-Digit Whole Number and Decimal Fraction Operations

 

Grade 5

Math

Unit Length and Description:

 

40 days

 

Students use place value understanding and properties of operations to perform multi-digit operations with whole numbers and decimals.  Students extend division to 2-digit divisors, develop understanding of operations with decimals to hundredths, and develop fluency with whole number and decimal operations.

Students use learned strategies, and standard algorithm to perform operations.  In applying the standard algorithm, students recognize the importance of place value.  Students fully understand the distributive property.  Students extend their experiences with division to dividing by two-digit divisors.  Students use strategies, illustrations, and explanations including base ten models and area models.

As students develop fluency with whole number operations, they will also develop efficient strategies with decimal operations.  Students estimate decimal computations before they compute with pencil and paper. 

Students apply their knowledge of place value, decimals, multiplication and division to conversions within the metric system and to solve multi-step problems through modeling and writing simple equations. 

Standards:

 

NBT - Number and Operation in Base Ten

Understand the place value system.

5.NBT.A.1

Recognize that in a multi-digit 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.

5.NBT.A.2

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.  Use whole-number exponents to denote power of 10.

5.NBT.A.4

Use place value understanding to round decimals to any place.

5.NBT.B.5

Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.6

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.  Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.B7

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

MD – Measurement and Data

Convert like measurement units within a given measurement system.

5.MD.A.1

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

(Note:  Unit 2 addresses the metric system component of this standard.)

OA – Operations and Algebraic Thinking

Write and interpret numerical expressions

5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.A.2

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Standards for Mathematical Practices

1.   Make sense of problems and persevere in solving them.

2.   Reason abstractly and quantitatively.

3.   Construct viable arguments and critique the reasoning of others.

4.   Model with mathematics.

5.   Use appropriate tools strategically.

6.   Attend to precision.

7.   Look for and make use of structure.

8.   Look for and express regularity in repeated reasoning.

 

Instructional Outcomes:

 

5.NBT.A.1:

I can understand and explain the value of digits.

I can recognize that in a multi-digit number, a digit in one place represents 1/10 of the place value to its left.

5.NBT.A.2:

I can represent powers of 10 using whole number exponents (103 = 10 x 10 x 10 = 1000)

I can explain patterns when multiplying a number by powers of 10.

I can explain the relationship in the placement of the decimal point when a decimal is multiplied or divided by powers of 10.

5.NBT.B.4

I can round decimals to any place.

5.NBT.B.5

I can fluently multiply multi-digit whole numbers using the standard algorithm.

I can illustrate and explain place value when multiplying multi-digit whole numbers using the standard algorithm.

5.NBT.B.6

I can divide a 4-digit dividend by a two digit divisor to find a quotient with no remainder.

I can use strategies to solve division problems.

I can illustrate and explain division problems.

5.NBT.B.7

I can add, subtract, multiply and divide decimals to hundredths.

I can explain the reasoning used to solve decimal problems in written form.

5.MD.A.1

I can divide and multiply to convert metric measurements.

I can convert units of measurement within the metric system.

I can solve multi-step, real world problems that involve converting metric measurement units.

5.OA.A.1

I can use order of operations including parenthesis, brackets, or braces.

I can evaluate expressions using the order of operations (including parenthesis (), brackets [], or braces {}.

5.OA.A.2

I can describe the relationship between expressions without calculating them.

I can write numerical expressions for numbers with operation words.

I can interpret numerical expressions without evaluating them.

 

Enduring Understandings:

 

·         The properties of multiplication and division help us solve computation problems easily and provide reasoning for choices we make in problem solving.

·         Patterns and relationships among operations are essential to making estimates and computing fluently.

·         An algebraic expression or equation can be represented in a variety of ways that have the same value.

·         There is an order of operations that must be followed in all mathematical expressions.

·         Selection of measurement tools and units depends on real-world situation.

·         Decimals allow us to express quantities with greater precision.

 

Essential Questions:

 

·         How can I write an expression that demonstrates a situation or context?

·         Why express measurements in different ways?

·         How does the position of a digit affect its value?

·         Why is it important to follow an order of operations?

·         How does multiplying or dividing a number by a power of ten affect the product or quotient?

·         How can we use models to help us multiply or divide decimals?