NF Cluster 1: Extend understanding of fraction equivalence and ordering. / 7 days
Florida Standard(s) / Domain/Big Idea / Essential Question(s) / Vocabulary / Instructional Resources
MAFS.4.NF.1.1Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. / Domain: Number and Operations - Fraction
Cluster 1: Extend understanding of fraction equivalence and ordering. /
- How can you use models to show equivalent fractions?
- Equivalent fractions
Investigate: Equivalent Fractions
Students must use visual fraction models (limit to number lines, rectangles, circles, and squares) for all problems in this lesson.
Fractions can be fractions greater than one and students should not be guided to put fractions in lowest terms or to simplify.
Denominators limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.
MAFS.4.NF.1.1Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. / Domain: Number and Operations - Fraction
Cluster 1: Extend understanding of fraction equivalence and ordering. /
- How can you use multiplication to find equivalent fractions?
- Equivalent fractions
Generate Equivalent Fractions
Fractions can be fractions greater than one and students should not be guided to put fractions in lowest terms or to simplify.
Denominators limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.
MAFS.4.NF.1.1Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. / Domain: Number and Operations - Fraction
Cluster 1: Extend understanding of fraction equivalence and ordering. /
- How can you write a fraction as an equivalent fraction in simplest form?
- Simplest form
Simplest Form
MAFS.4.NF.1.1Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. / Domain: Number and Operations - Fraction
Cluster 1: Extend understanding of fraction equivalence and ordering. /
- How can you write a pair of fractions as fraction with a common denominator?
- Common denominator
Common Denominators
Students do not have to find the LEAST common denominator.
Fractions can be fractions greater than one and students should not be guided to put fractions in lowest terms or to simplify.
Denominators limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.
MAFS.4.NF.1.1Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. / Domain: Number and Operations - Fraction
Cluster 1: Extend understanding of fraction equivalence and ordering. /
- How can you use the strategy make a table to solve problems using equivalent fractions?
- Equivalent fractions
Problem Solving: Find Equivalent Fractions
MAFS.4.NF.1.2
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. / Domain: Number and Operations - Fraction
Cluster 1: Extend understanding of fraction equivalence and ordering. /
- How can you use benchmarks to compare fractions?
- Benchmark
Compare Fractions Using benchmarks
Only have students compare two fractions and they must use >, <, or = to show the results of the comparisons.
Students must be able to justify the conclusion by using a visual fraction model or explaining in words.
Students must understand that these comparisons are valid only when the two fractions refer to the same whole.
Fractions can be fractions greater than one and students should not be guided to put fractions in lowest terms or to simplify.
Denominators limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.
Benchmarks limited to: 0, ¼, ½, ¾, 1.
MAFS.4.NF.1.2
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. / Domain: Number and Operations - Fraction
Cluster 1: Extend understanding of fraction equivalence and ordering. /
- How can you compare fractions?
Compare Fractions
Students should learn to compare fractions both by using a common denominator (doesn’t have to be the least common denominator) or by using a common numerator.
Only have students compare two fractions and they must use >, <, or = to show the results of the comparisons.
Students must be able to justify the conclusion by using a visual fraction model or explaining in words.
Students must understand that these comparisons are valid only when the two fractions refer to the same whole.
Fractions can be fractions greater than one and students should not be guided to put fractions in lowest terms or to simplify.
Denominators limited to: 2, 3, 4, 5, 6, 8, 10, 12, 100.
Formative Assessment Options / Summative Assessment Options
- Math Formative Assessment System
- School/Grade/Teacher Created
- PLC Created Assessment
Bay District Schools
Unit/Big Idea for Learning Goal 10 / Pacing / Date(s)NF Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. / 12 days / Nov. 17- Dec. 9
Florida Standard(s) / Domain/Big Idea / Essential Question(s) / Vocabulary / Instructional Resources
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- When can you add or subtract parts of a whole?
- Fraction
- Numerator
- Denominator
Add and Subtract Parts of a Whole
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you write a fraction as a sum of fractions with the same denominators?
- Unit fraction
Write Fractions as Sums
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you add fractions with like denominators using models?
- How can you subtract fractions with like denominators using models?
Ch. 7 Lesson 4
Subtract Fractions Using Models
Add Fractions Using Models
Students should not be guided to put fractions in lowest terms or to simplify.
Limit denominators to 2,3,4,5,6,8, 10,12,100
Students should not be guided to put fractions in lowest terms or to simplify.
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you add and subtract fractions with like denominators?
Add and Subtract Fractions
Students should not be guided to put fractions in lowest terms or to simplify.
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you rename mixed numbers as fractions greater than one, and rename fractions greater than one as mixed numbers?
- Mixed number
Rename Fractions and Mixed Numbers
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you add and subtract mixed numbers with like denominators?
Add and Subtract Mixed Numbers
Students should not be guided to put fractions in lowest terms or to simplify.
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.3
Understand a fraction a/b
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you rename a mixed number to help you subtract?
Subtraction With Renaming
Students should not be guided to put fractions in lowest terms or to simplify.
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and
subtraction. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you add fractions with like denominators using the properties of addition?
- Associative Property of Addition
- Commutative Property of Addition
Algebra: Fractions and Properties of Addition
MAFS.4.NF.2.3
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you use the strategy Act It Out to solve multistep problems with fractions?
Problem Solving: Multistep Fraction Problems
Formative Assessment Options / Summative Assessment Options
- Math Formative Assessment System
- School/Grade/Teacher Created
- Go Math! Mid-Chapter and Chapter Assessments
- School/Grade/Teacher Created
Unit/Big Idea for Learning Goal 11 / Pacing / Date(s)
NF Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. / 6 days / Dec. 10-Dec. 17
Florida Standard(s) / Domain/Big Idea / Essential Question(s) / Vocabulary / Instructional Resources
MAFS.4.NF.2.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you write a fraction as a product of a whole number and a unit fraction?
- Multiple
- Factor
- Fraction
- Unit Fraction
- Identity Property of Multiplication
- Product
Multiples of Unit Fractions
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you write a product of a whole number and a fraction as a product of a whole number and a unit fraction?
Multiples of Fractions
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you use a model to multiply a fraction by a whole number?
Multiplying a Fraction by a Whole Number Using Models
Limit denominators to 2,3,4,5,6,8, 10,12,100
MAFS.4.NF.2.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? / Domain: Number and Operations - Fraction
Cluster 2: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. /
- How can you use the strategy Draw A Diagram to solve comparison problems with fractions?
Problem Solving: Comparison Problems With Fractions
(Do NOT use the mixed numbers in the problems, you have to change them to fractions such as ¾.)
You may also supplement this lesson by using another resource such as CPALMS.
Limit denominators to 2,3,4,5,6,8, 10,12,100
Formative Assessment Options / Summative Assessment Options
- Math Formative Assessment System
- School/Grade/Teacher Created
- Go Math! Mid-Chapter and Chapter Assessments
- School/Grade/Teacher Created
Unit/Big Idea for Learning Goal 12 / Pacing / Date(s)
NF Cluster 3: Understand decimal notation for fractions, and compare decimal fractions. / 8 days / Jan. 5–Jan. 14
Florida Standard(s) / Domain/Big Idea / Essential Question(s) / Vocabulary / Instructional Resources
MAFS.4.NF.3.6
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. / Domain: Number and Operations - Fraction
Cluster 3: Understand decimal notation for fractions, and compare decimal fractions. /
- How can you record tenths as fractions and decimals?
- How can you record hundredths as fractions and decimals?
- Equivalent fractions
- Fraction
- Compare
- Decimal
- Decimal point
- TenthHundredth
Relate Hundredths and Decimals
Relate Tenths and Decimals
MAFS.4.NF.3.6
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. / Domain: Number and Operations - Fraction
Cluster 3: Understand decimal notation for fractions, and compare decimal fractions.
MAFS.4.NF.3.5
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
MAFS.4.NF.3.6
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. / Domain: Number and Operations - Fraction
Cluster 3: Understand decimal notation for fractions, and compare decimal fractions. /
- How can you record tenths and hundredths as fractions and decimals?
- Equivalent decimals
Equivalent Fractions and Decimals
MAFS.4.NF.3.6
Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. / Domain: Number and Operations - Fraction
Cluster 3: Understand decimal notation for fractions, and compare decimal fractions. /
- How can you relate fractions, decimals and money?
Relate Fractions, Decimals, and Money
Ch. 9 Lesson 5 is being skipped right now, and is placed to be taught in in Chapter 12.
MAFS.4.NF.3.5
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. / Domain: Number and Operations - Fraction
Cluster 3: Understand decimal notation for fractions, and compare decimal fractions. /
- How can you add fractions when the denominators are 10 or 100?
Add Fractional Parts of 10 and 100
MAFS.4.NF.3.7
Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. / Domain: Number and Operations - Fraction
Cluster 3: Understand decimal notation for fractions, and compare decimal fractions. /
- How can you compare decimals?
Compare Decimals
Formative Assessment Options / Summative Assessment Options
- Math Formative Assessment System
- School/Grade/Teacher Created
- Go Math! Mid-Chapter and Chapter Assessments
- School/Grade/Teacher Created
3rd Nine Weeks: