Key Concept: Decimals use place value to represent fractions.

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

5.NBT.A.3 Read, write and compare decimals to thousandths.

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5.NBT.A.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

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

MGSE5.NBT.3 Read, write, and compare decimals to thousandths.

MGSE5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

MGSE5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE5.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 fractions to build a foundation for understanding decimals. Students connect decimal numbers to the denominators of base 10 fractions and write fractions to represent decimals to the hundredths place value. Then students work with models of familiar benchmark fractions (fourths, eighths) to develop an understanding of equivalent decimals (to the thousandths place) and to write them. Students continue to build conceptual understanding of decimals by comparing them to benchmark fractions on a number line and by comparing decimals without using a model.

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5.NBT.A.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

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.

MGSE5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

MGSE5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE5.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 decimal (to the tenths or hundredths place) and asked to model an equivalent base 10 fraction, the student will understand the relationship between the decimal's place value and the fraction's denominator and will write the correct fraction to represent it 90% of the time in three consecutive sessions.

2. Given a benchmark fraction (in fourths or eighths), the student will learn the decimal equivalent and will write the decimal with 90% accuracy in three consecutive sessions.

3. Given two benchmark fractions, the student will use knowledge about the decimal equivalents and fraction denominators to properly place the fractions on a decimal number line 80% of the time by the end of the first marking period.

4. Given two decimals of the same value as benchmark fractions (fourths and eighths), the student will correctly compare the decimals and assign the proper comparison symbol (<, =, >) 80% of the time by the end of the first marking period.

2. Given a benchmark fraction (in fourths or eighths), the student will learn the decimal equivalent and will write the decimal with 90% accuracy in three consecutive sessions.

3. Given two benchmark fractions, the student will use knowledge about the decimal equivalents and fraction denominators to properly place the fractions on a decimal number line 80% of the time by the end of the first marking period.

4. Given two decimals of the same value as benchmark fractions (fourths and eighths), the student will correctly compare the decimals and assign the proper comparison symbol (<, =, >) 80% of the time by the end of the first marking period.

Unit Launcher

View The Olympics and BMX Cycling: Discussion Guide and KWL Chart

5.1-1-1 Connecting Decimals to Base 10 Fractions |

5.1-1-2 Writing Decimals to Represent Fractions |

5.1-1-3 Comparing Decimals |

View Guided Lesson Compare representations of fourths and eighths using hundredths and thousandths. (12-18 min)

Real World Investigation Part 1

View The Olympics and BMX Cycling: The Olympic's Data

Key Concept: Decimals can be written in standard and expanded form, and they can be rounded.

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

5.NBT.A.3 Read, write and compare decimals to thousandths.

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5.NBT.B.4 Use place value understanding to round decimals to any place.#### Georgia

MGSE5.NBT.3 Read, write, and compare decimals to thousandths.

MGSE5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

MGSE5.NBT.4 Use place value understanding to round decimals up to the hundredths place. IEP Goals

In this topic, students continue to develop their conceptual understanding of decimals to the thousandth place. In the first lessons, students build models to reinforce place value concepts and to write the decimal number in standard and expanded form. In subsequent lessons, students use a number line to apply their understanding of place value as they round decimal numbers. Each lesson progresses from the use of models and tools to just numbers.

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5.NBT.B.4 Use place value understanding to round decimals to any place.

MGSE5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

MGSE5.NBT.4 Use place value understanding to round decimals up to the hundredths place.

1. Given a decimal number (to the thousandths place) written in standard form, the student will apply knowledge of place value and the significance of the decimal point in order to correctly write the decimal in expanded form with 90% accuracy in five consecutive sessions.

2. Given a decimal number (to the thousandths place) written in expanded form, the student will apply knowledge of place value to correctly write the number in standard form, including proper placement of the decimal point, with 90% accuracy in five consecutive sessions.

3. Given a decimal number to the thousandth place, students will apply previous understanding of place value and rounding to identify the place value they are rounding to and place the rounded decimal on a number line with 80% accuracy by the end of the second marking period.

4. Given a decimal number to the thousandth place and the place value to which the decimal is to be rounded, students will complete a rounding sentence identifying the number to be rounded, the place value to which it is rounded, and the rounded value with 80% accuracy by the end of the second marking period.

2. Given a decimal number (to the thousandths place) written in expanded form, the student will apply knowledge of place value to correctly write the number in standard form, including proper placement of the decimal point, with 90% accuracy in five consecutive sessions.

3. Given a decimal number to the thousandth place, students will apply previous understanding of place value and rounding to identify the place value they are rounding to and place the rounded decimal on a number line with 80% accuracy by the end of the second marking period.

4. Given a decimal number to the thousandth place and the place value to which the decimal is to be rounded, students will complete a rounding sentence identifying the number to be rounded, the place value to which it is rounded, and the rounded value with 80% accuracy by the end of the second marking period.

5.1-2-1 Standard and Expanded Form to Hundredths |

Lesson Plan

View Guided Lesson Model decimals to the hundredths place, writing in standard and expanded form. (12-18 min)

5.1-2-2 Standard and Expanded Form to Thousandths |

Lesson Plan

View Guided Lesson Model decimals to the thousandths place, writing in standard and expanded form. (12-18 min)

5.1-2-3 Rounding Decimals to Benchmark Numbers: Tenths |

Lesson Plan

5.1-2-4 Rounding Decimals to Benchmark Numbers: Hundredths and Thousandths |

Lesson Plan

View Guided Lesson Round hundredths to the nearest tenth and thousandths to the nearest hundredth. (12-20 min)

Real World Investigation Part 2

View The Olympics and BMX Cycling: Create Some Data

Key Concept: Digits of the same place value can be added or subtracted.

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

5.NBT.B.4 Use place value understanding to round decimals to any place.

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

MGSE5.NBT.4 Use place value understanding to round decimals up to the hundredths place.

MGSE5.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 continue to develop their conceptual understanding of decimals to the hundredths place. Students build upon their understanding of adding and subtracting fractions in order to add and subtract decimals. Within each lesson students focus on adding and subtracting place values that are the same as well as regrouping a place value. In the final lesson students use estimation to add and subtract decimals in order to determine if their solution is reasonable.

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.

MGSE5.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 decimal (to the tenths or hundredths place) and asked to model an equivalent base 10 fraction, the student will understand the relationship between the decimal's place value and the fraction's denominator and will write the correct fraction to represent it 90% of the time in three consecutive sessions.

2. Given a benchmark fraction (in fourths or eighths), the student will learn the decimal equivalent and will write the decimal with 90% accuracy in three consecutive sessions.

3. Given two benchmark fractions, the student will use knowledge about the decimal equivalents and fraction denominators to properly place the fractions on a decimal number line 80% of the time by the end of the first marking period.

4. Given two decimals of the same value as benchmark fractions (fourths and eighths), the student will correctly compare the decimals and assign the proper comparison symbol (<, =, >) 80% of the time by the end of the first marking period.

5. Given two decimals, the student will accurately add the decimals, regrouping when necessary, with 90% accuracy in three consecutive sessions.

6. Given two decimals, the student will accurately subtract the decimals, regrouping when necessary, with 80% accuracy in three consecutive sessions.

2. Given a benchmark fraction (in fourths or eighths), the student will learn the decimal equivalent and will write the decimal with 90% accuracy in three consecutive sessions.

3. Given two benchmark fractions, the student will use knowledge about the decimal equivalents and fraction denominators to properly place the fractions on a decimal number line 80% of the time by the end of the first marking period.

4. Given two decimals of the same value as benchmark fractions (fourths and eighths), the student will correctly compare the decimals and assign the proper comparison symbol (<, =, >) 80% of the time by the end of the first marking period.

5. Given two decimals, the student will accurately add the decimals, regrouping when necessary, with 90% accuracy in three consecutive sessions.

6. Given two decimals, the student will accurately subtract the decimals, regrouping when necessary, with 80% accuracy in three consecutive sessions.

5.1-3-1 Adding Decimals to the Tenths Place |

Lesson Plan

5.1-3-2 Adding Decimals to the Hundredths Place |

Lesson Plan

5.1-3-3 Subtracting Decimals to the Tenths Place |

Lesson Plan

5.1-3-4 Subtracting Decimals to the Hundredths Place |

Lesson Plan

5.1-3-5 Estimating Decimal Computations |

Lesson Plan

View Guided Lesson Students will estimate the answer to a word problem in order to determine if the actual answer is reasonable. (12-20 min)

Real World Investigation Part 3

View Your Olympics: Your Data

This Big Idea introduces students to decimals by establishing the relationship between decimals and fractions. Using models and number lines, students extend their previous place value understanding to model, write, round, add, and subtract decimals to the thousandth place.

5.NBT.A.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

5.NBT.A.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.B.4 Use place value understanding to round decimals to any place.

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.

MGSE5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

MGSE5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

MGSE5.NBT.4 Use place value understanding to round decimals up to the hundredths place.

MGSE5.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.