Key Concept: A digit in one place represents ten times more than it represents in the place to its right.

Topic Overview | Standards Alignment | #### Common Core

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 powers of 10.

5.NBT.B.7 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.#### Georgia

MGSE.5.NBT.1 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

MGSE.5.NBT.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 powers of 10.

MGSE.5.NBT.7 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. IEP Goals

In this topic, students apply their knowledge of place value and multiplication to multiply one and two digit decimals by 10, 100, or 1000. In the first two lessons, students are presented with frame and dot models that represent an initial decimal quantity and then multiply the quantity by a power of 10. In the third lesson, students round decimals on a number line and multiply by a power of 10 to estimate products.

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 powers of 10.

5.NBT.B.7 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.

MGSE.5.NBT.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 powers of 10.

MGSE.5.NBT.7 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.

1. Given a single-unit or 2-unit decimal to the hundredths and guided practice with models, the student will be able to multiply that decimal by 10, 100, and a 1000 with 90% accuracy over 5 consecutive sessions.

2. Given a decimal number and a model, the student will be able to verbally and visually describe how a digit in one place represents ten times more than it represents in the place to its right by end of the unit.

3. Given a decimal multiplied by 10, 100, or 1000, the student will be able to determine the product with 85% accuracy over 5 consecutive sessions.

2. Given a decimal number and a model, the student will be able to verbally and visually describe how a digit in one place represents ten times more than it represents in the place to its right by end of the unit.

3. Given a decimal multiplied by 10, 100, or 1000, the student will be able to determine the product with 85% accuracy over 5 consecutive sessions.

Unit Launcher

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5.2-1-1 Multiply Single Unit Decimals by 10, 100, or 1000 |

View Guided Lesson Students will use models to multiply single unit decimals written to the hundredths by 10, 100, or 1000. (12 - 20 min)

5.2-1-2 Multiply 2 Unit Decimals by 10, 100, or 1000 |

View Guided Lesson Students will use models to multiply two-unit decimals by 10, 100, and 1000. (12 - 20 min)

5.2-1-3 Estimate Decimal Products |

View Guided Lesson Students will round decimals on a number line and then multiply one and two-unit decimals by 10, 100, and 1000. (12 - 20 min)

Real World Investigation Part 1

View Sarah's Smoothies: Sarah's Data

Key Concept: Multiplication with a decimal is a way to find the value of groups of decimals.

Topic Overview | Standards Alignment | #### Common Core

5.NBT.B.7 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.

CCSS.MATH.CONTENT.5.NF.B.4.A

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.#### Georgia

MGSE.5.NBT.7 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.

MGSE.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction. Examples: a/b x q as a/b x q/1 and a/b x c/d = ac/bd

MGSE.5.NBT.5 Fluently multiply multidigit whole numbers using the standard algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor. IEP Goals

In this topic, students use skip-counting and an open array to develop their conceptual understanding of multiplying a decimal number by a whole number. In the first three lessons, students skip-count using a number line model to first multiply decimal fractions and then to multiply simple decimals. In the last lesson, students apply their previous knowledge of the partial product approach, the open array model, and the multiplication of simple decimals to build their understanding of how the standard multiplication algorithm works and can be used in whole number by decimal multiplication.

CCSS.MATH.CONTENT.5.NF.B.4.A

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

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.

MGSE.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction. Examples: a/b x q as a/b x q/1 and a/b x c/d = ac/bd

MGSE.5.NBT.5 Fluently multiply multidigit whole numbers using the standard algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.

1. Given a single-digit whole number multiplied by a decimal fraction (denominator of 10 or 100), the student can use repeated addition to build a model and solve the equation with 85% accuracy over 3 consecutive sessions.

2. Given a single-digit whole number multiplied by a tenth or hundredth, the student can use repeated addition to build a number line model and correctly solve the equation with 85% accuracy over 3 consecutive sessions.

3. Given a whole number multiplied by a tenth or hundredth, students can apply their knowledge of place value and multiplication to model and solve the problem. Students will use partial products and the standard multiplication algorithm with 80% accuracy over 5 consecutive sessions.

2. Given a single-digit whole number multiplied by a tenth or hundredth, the student can use repeated addition to build a number line model and correctly solve the equation with 85% accuracy over 3 consecutive sessions.

3. Given a whole number multiplied by a tenth or hundredth, students can apply their knowledge of place value and multiplication to model and solve the problem. Students will use partial products and the standard multiplication algorithm with 80% accuracy over 5 consecutive sessions.

5.2-2-1 Multiply Decimal Fractions by Whole Numbers |

Lesson Plan

View Guided Lesson Students will use a paraphrase tool and a number line model to multiply a fraction by a whole number. (12 - 20 min)

5.2-2-2 Multiply Tenths by a Single Digit Whole Number |

Lesson Plan

View Guided Lesson Students will use a number line model to multiply a tenth by a single digit whole number. (12 - 20 min)

5.2-2-3 Multiply Hundredths by a Single Digit Whole Number |

Lesson Plan

View Guided Lesson Students will use the number line and open array models to multiply hundredths by a single digit whole number. (12 - 20 min)

5.2-2-4 Multiply Tenths and Hundredths by Whole Numbers |

Lesson Plan

View Guided Lesson Students will use partial products, the open array, and the standard equation to multiply tenths and hundredths by whole numbers. (12 - 20 min)

Real World Investigation Part 2

View Sarah's Smoothies: Create Some Data

Key Concept: When multiplying two numbers, the digits in the product are the same no matter where the decimal point is placed.

Topic Overview | Standards Alignment | #### Common Core

5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.7 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.

5.NF.B.4.A Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)#### Georgia

MGSE.5.NBT.5 Fluently multiply multidigit whole numbers using the standard algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.

MGSE.5.NBT.7 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.

MGSE.5.NF.4 Apply and extend previous

understandings of multiplication to multiply a fraction

or whole number by a fraction. a. Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction. Examples: a/b x q as a/b x q/1 and a/b x c/d = ac/bd IEP Goals

In this topic students build their understanding of multiplying with quantities that are less than 1. In the first lesson students relate fractions and decimals through multiplying a decimal fraction by a decimal fraction. In lessons 2-4 students work through a progression in which they multiply tenths by tenths, ones and tenths by tenths, and finally ones and tenths by ones and tenths. In each case, students use the open array model, partial products, and the standard algorithm to develop a deep understanding of decimal multiplication and place value. At the end of each lesson students solve the problems using only the algorithm.

5.NBT.B.7 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.

5.NF.B.4.A Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

MGSE.5.NBT.7 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.

MGSE.5.NF.4 Apply and extend previous

understandings of multiplication to multiply a fraction

or whole number by a fraction. a. Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction. Examples: a/b x q as a/b x q/1 and a/b x c/d = ac/bd

1. Given two decimal fractions (denominator of 10 or 100), students can multiply the two fractions using a model and ultimately the equation only with 85% accuracy over 3 consecutive sessions.

2. Given two decimals (tenths) to multiply, students can apply their previous knowledge of multiplication facts to model and solve the problem using the standard multiplication algorithm with 85% accuracy over 5 consecutive sessions.

3. Given a tenth and a one and a tenth to multiply, students can apply their previous knowledge of place value and partial products to model and solve the problem using the standard multiplication algorithm with 80% accuracy over 5 consecutive sessions.

4. Given one and a tenth multiplied by one and a tenth, students can apply their previous knowledge of place value and partial products to model and solve the problem using the standard multiplication algorithm with 75% accuracy by the end of the term.

2. Given two decimals (tenths) to multiply, students can apply their previous knowledge of multiplication facts to model and solve the problem using the standard multiplication algorithm with 85% accuracy over 5 consecutive sessions.

3. Given a tenth and a one and a tenth to multiply, students can apply their previous knowledge of place value and partial products to model and solve the problem using the standard multiplication algorithm with 80% accuracy over 5 consecutive sessions.

4. Given one and a tenth multiplied by one and a tenth, students can apply their previous knowledge of place value and partial products to model and solve the problem using the standard multiplication algorithm with 75% accuracy by the end of the term.

5.2-3-1 Multiply Decimal Fractions |

Lesson Plan

View Guided Lesson Students will use a paraphrase tool and an area model to multiply a fraction by a fraction. (12 - 20 min)

5.2-3-2 Multiply Tenths by Tenths |

Lesson Plan

5.2-3-3 Multiply Ones and Tenths by Tenths |

Lesson Plan

View Guided Lesson Students will use partial products in order to multiply ones and tenths by tenths. (12-20 min)

5.2-3-4 Multiply Ones and Tenths by Ones and Tenths |

Lesson Plan

View Guided Lesson Students will use the partial products model to multiply ones and tenths by ones and tenths. (12-20 min)

Real World Investigation Part 3

View Your Smoothies: Your Data

This Big Idea builds upon students’ understanding of place value and of fraction and whole number multiplication. The unit opens by having students multiply decimals by multiples of 10, 100, and 1000 which further develops students’ understanding of place value. The Big Idea then has students use skip counting and an open array model when multiplying decimals to build a conceptual connection to the more abstract partial products and the standard algorithm procedures. This unit follows this progression first for multiplying decimals by whole numbers and then decimals by decimals, particularly decimals that include ones and tenths.

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 powers of 10.

5.NF.B.4.A

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.7 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.

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

MGSE.5.NBT.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 powers of 10.

MGSE.5.NBT.5 Fluently multiply multidigit whole numbers using the standard algorithm (or other strategies demonstrating understanding of multiplication) up to a 3 digit by 2 digit factor.

MGSE.5.NBT.7 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.

MGSE.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Apply and use understanding of multiplication to multiply a fraction or whole number by a fraction. Examples: a/b x q as a/b x q/1 and a/b x c/d = ac/bd