In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
Explain 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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Explain (why a fraction a/b is equivalent to [nxa]/[nxb])
2 - Attend (number and size of the parts differ though the fractions are the same size)
3 - Use (differing size and parts principle to recognize equivalent fractions)
3 - Use (the differing size and parts principle to generate equivalent fractions)
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2 - I can explain why a fraction a/b is equivalent to (nxa)/(nxb).
2 - I can attend to how the number and size of the parts differ though the fractions are the same size.
3 - I can use the differing size and parts principle to recognize equivalent fractions.
3 - I can use the differing size and parts principle to generate equivalent fractions.
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A. Equivalent fractions are the same size even though the number of their parts and the size of the parts may not be the same.
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A.1 How can I recognize that two fractions are equivalent?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Compare (two fractions with different numerators and denominators by creating common numerators or denominators)
2 - Compare (two fractions by comparing to a benchmark fraction such as 1/2)
2 - Recognize (comparisons are valid if referring to the same whole)
1 - Record (results of comparisons using symbols >, =, and <)
5 - Justify (conclusions)
3 - Use (visual fraction models)
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2 - I can compare two fractions with different numerators and denominators by creating common numeraotrs or denominators.
2 - I can compare two fractions by comparing to a benchmark fraction such as 1/2.
2 - I can recognize comparisons are valid if referring to the same whole.
1 - I can record results of comparisons using symbols >, =, and <.
5 - I can justify conclusions.
3 - I can use a visual fraction model.
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A. One can compare fractions by creating common numerators or denominators.
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A.1 How can I compare fractions?
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Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Fractions
Fractions [a]
Mixed numbers [c]
Fractions [d]
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2 - Understand (fraction a/b with a>1 is the sum of fractions 1/b)
1 - 2: Understand (addition as joining parts referring to same whole [a])
2 - Understand (subtraction as separating parts referring to same whole [a])
2 - Decompose (fraction into a sum of fractions with same denominator in more than one way [b])
1 - Record (decomposition by equation [b])
5 - Justify (decompositions [b])
3 - Use (visual fraction model [b])
2 - Add (mixed numbers with like denominators [c])
2 - Subtract (mixed numbers with like denominators [c])
2 - Replace (mixed number with equivalent fraction [c])
3 - Use (properties of operations [c])
3 - Use (relationship between addition and subtraction [c])
2 - Solve (word problems involving addition of fractions having like denominators [d])
2 - Solve (word problems involving subtraction of fractions having like denominators [d])
3 - Use (visual fraction models to represent problem [d])
3 - Use (equations to represent problem [d])
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2 - I can understand that a fraction a/b with a>1 is the sum of fractions 1/b.
2 - I can understand addition as joining parts referring to same whole [a].
2 - I can understand subtraction as separating parts referring to same whole [a].
2 - I can decompose a fraction into a sum of fractions with the same denominator in more than one way [b].
1 - I can record decomposition by equation [b].
5 - I can justify decompositions [b].
3 - I can use a visual fraction model [b].
2 - Add mixed numbers with like denominators [c].
2 - I can subtract mixed numbers with like denominators [c].
2 - I can replace mixed numbers with equivalent fractions [c].
3 - I can use the properties of operations [c].
3 - I can use the relationship between addition and subtraction [c].
2 - I can solve word problems involving addition of fractions having like denominators [d].
2 - I can solve word problems involving subtraction of fractions having like denominators [d].
3 - I can use visual fraction models to represent the problem [d].
3 - I can use equations to represent the problem [d].
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A. Fractions with common denominators can easily be added together.
B. Addition and subtraction of fractions is the same concept as with whole numbers.
C. One can add different pairs of fractions with a common denominator and get the same sum.
D. Adding and subtracting fractions is a skill commonly used when solving real world problems.
E. Word problems can involve the addition and/or subtraction of fractions.
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A.1 How do I add fractions together?
B.1 How do I add and subtract fractions?
C.1 Why do I need to be able to decompose fractions?
D.1 Why should I learn how to add and subtract fractions?
E.1 How can I solve word problems with fractions?
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Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
Fractions
Fractions [a]
Fractions [b]
Fractions [c]
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3 - Apply (multiplication to multiply a fraction by a whole number)
2 - Extend (multiplication to multiply a fraction by a whole number)
2 - Understand (a/b is a multiple of 1/b [a])
2 - Understand (multiple of a/b is multiple of 1/b [b])
3 - Use (understanding to multiply fraction by whole number [b])
1 - 2: Solve (word problems involving multiplication of fraction by whole number [c])
3 - Use (visual fraction models to represent problem [c])
3 - Use (equations to represent problem [c])
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3 - I can apply understandings of multiplication to multiply a fraction by a whole number.
2 - I can extend understandings of multiplication to multiply a fraction by a whole number.
2 - I can understand that a/b is a multiple of 1/b [a].
2 - I can understand that a multiple of a/b is a multiple of 1/b [b].
3 - I can use this understanding to multiply fraction by whole number [b].
2 - I can solve word problems involving multiplication of a fraction by a whole number [c].
3 - I can use visual fraction models to represent the problem [c].
3 - I can use equations to represent the problem [c].
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A. A fraction can be multiplied by a whole number
B. Multiplication is a faster way of adding fractions with the same denominator.
C. Fractions can be multiplied by other fractions and by whole numbers.
D. Solving word problems often requires working with fractions.
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A.1 How do I multiply a fraction by a whole number?
B.1 Will I ever have to decompose a fraction into a multiplication of two factors?
C.1 Why do I need to know how to multiply fractions?
D.1 Why do I need to know how to multiply a fraction by a whole number?
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Understand decimal notation for fractions, and compare decimal fractions.
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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Express (fraction with a denominator of 10 as an equivalent fraction with a denominator of 100)
3 - Use (equivalent fractions to add 2 fractions with denominators of 10 and 100)
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2 - I can express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100.
3 - I can use equivalent fractions to add 2 fractions with denominators of 10 and 100.
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A. Fractions can be added by using common denominators.
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A.1 What do I need to do to add fractions together?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Fractions
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3 - Use (decimal notation for fractions with a denominator of 10)
3 - Use (decimal notation for fractions with a denominator of 100)
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3 - I can use decimal notation for fractions with a denominator of 10.
3 - I can use decimal notation for fractions with a denominator of 100.
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A. Fractions can be written as decimals if they have denominators of 10 or 100.
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A.1 Can any fraction be written as a decimal?
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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.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
|
2 - Compare (2 decimals to hundredths by reasoning about size)
2 - Recognize (comparisons are valid if referring to the same whole)
1 - Record (results of comparisons using symbols >, =, and <)
5 - Justify (conclusions)
3 - Use (visual models)
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2 - I can compare 2 decimals to hundredths by reasoning about their size.
2 - I can recognize that comparisons of decimals are valid if referring to the same whole.
1 - I can record results of comparisons using symbols >, =, and <.
5 - I can justify conclusions.
3 - I can use a visual model.
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A. One can use visual models to show the comparison of decimals.
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A.1 How can I justify the comparison of decimals?
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