In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.
Use equivalent fractions as a strategy to add and subtract fractions.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Add (fractions with unlike denominators by replacing given fractions with equivalent fractions)
2 - Subtract (fractions with unlike denominators by replacing given fractions with equivalent fractions)
3 - Produce (an equivalent sum or difference of fractions with like denominators)
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2 - I can add fractions with unlike denominators by replacing given fractions with equivalent fractions.
2 - I can subtract fractions with unlike denominators by replacing given fractions with equivalent fractions.
3 - I can produce an equivalent sum or difference of fractions with like denominators.
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A. Equivalent fractions are used when finding common denominators for fraction addition and subtraction.
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A.1 How do I use equivalent fractions when adding and subtracting fractions?
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Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Solve (word problems involving addition of fractions referring to the same whole)
2 - Solve (word problems involving subtraction of fractions referring to the same whole)
2 - Solve (word problems involving unlike denominators referring to the same whole)
3 - Use (visual fractions models to represent the problem)
3 - Use (equations to represent the problem)
3 - Use (benchmark fractions to estimate mentally)
3 - Use (number sense of fractions to estimate mentally)
5 - Assess (reasonableness of answers)
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2 - I can solve word problems involving addition of fractions referring to the same whole.
2 - I can solve word problems involving subtraction of fractions referring to the same whole.
2 - I can solve word problems involving unlike denominators referring to the same whole.
3 - I can use visual fractions models to represent the problem.
3 - I can use equations to represent the problem.
3 - I can use benchmark fractions to estimate mentally.
3 - I can use number sense of fractions to estimate mentally.
5 - I can assess reasonableness of answers.
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A. Word problems can involve fraction addition or subtraction.
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A.1 Can I do word problems with fractions in them?
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Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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2 - Interpret (a fraction as division of the numerator by the denominator)
2 - Solve (word problems involving division of whole numbers with answers in fraction form or mixed numbers)
3 - Use (visual fraction models to represent the problem)
3 - Use (equations to represent the problem)
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2 - I can interpret a fraction as division of the numerator by the denominator.
2 - I can solve word problems involving division of whole numbers with answers in fraction form or mixed numbers.
3 - I can use visual fraction models to represent the problem.
3 - I can use equations to represent the problem.
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A. One can represent division of whole numbers by using a fraction.
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A.1 What does a fraction have to do with division?
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Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Product (a/b)x q [a]
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3 - Apply (previous understandings of multiplication to multiply a fraction by a whole number)
3 - Apply (previous understandings of multiplication to multiply a fraction by a fraction)
2 - Extend (previous understandings of multiplication to multiply a fraction by a fraction)
2 - Interpret (the product a/b x q as parts of a partition of q into b equal parts [a])
2 - Interpret (the product a/b x q as the result of a sequence of operations, a x q divided by b [a])
2 - Find (the area of a rectangle with fractional side lengths by tiling with unit squares of the appropriate unit fraction side lengths [b])
1 - Show (the area is the same as would be found by multiplying the side lengths [b])
2 - Multiply (fractional side lengths to find areas of rectangles [b])
3 - Represent (fraction products as rectangular areas [b])
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3 - I can apply previous understandings of multiplication to multiply a fraction by a whole number.
3 - I can apply previous understandings of multiplication to multiply a fraction by a fraction.
2 - I can extend previous understandings of multiplication to multiply a fraction by a fraction.
2 - I can interpret the product a/b x q as parts of a partition of q into b equal parts [a].
2 - I can interpret the product a/b x q as the result of a sequence of operations, a x q divided by b [a].
2 - I can find the area of a rectangle with fractional side lengths by tiling with unit squares of the appropriate unit fraction side lengths [b].
1 - I can show the area is the same as would be found by multiplying the side lengths [b].
2 - I can multiply fractional side lengths to find areas of rectangles [b].
3 - I can represent fraction products as rectangular areas [b].
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A. Fractions can be multiplied by other fractions or whole numbers.
B. There is more than one way to find the area of a rectangle.
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A.1 How do I multiply fractions?
B.1 How do I find the area of a rectangle?
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Interpret multiplication as scaling (resizing), by:
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Fraction multiplication
Multiplication [b]
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2 - Interpret (multiplication as scaling or resizing)
2 - Compare (the size of a product to the size of one factor based upon the size of the other factor without performing the indicated multiplication [a])
2 - Explain (why multiplying a given number by a fraction greater than one results in a product greater than the given number [b])
2 - Explain (why multiplying a given number by a fraction less than one results in a product smaller than the given number [b])
2 - Relate (the principle of fraction equivalence to the effect of multiplying a/b by one [b])
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2 - I can interpret multiplication as scaling or resizing.
2 - I can compare the size of a product to the size of one factor based upon the size of the other factor without performing the indicated multiplication [a].
2 - I can explain why multiplying a given number by a fraction greater than one results in a product greater than the given number [b].
2 - I can explain why multiplying a given number by a fraction less than one results in a product smaller than the given number [b].
2 - I can relate the principle of fraction equivalence to the effect of multiplying a/b by one [b].
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A. One can assess the reasonableness of a product by looking at the factors of the problem.
B. Knowing the relationship between a product and its factors makes reasoning about the answer easier.
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A.1 Is there any way to make a prediction about the answer to a fraction multiplication problem?
B.1 Why should I understand about products and factors?
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Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Problem solving
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2 - Solve (real world problems involving multiplication of fractions)
2 - Solve (real world problems involving multiplication of mixed numbers)
3 - Use (visual fraction models)
3 - Use (equations)
3 - Represent (problems)
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2 - I can solve real world problems involving multiplication of fractions.
2 - I can solve real world problems involving multiplication of mixed numbers.
3 - I can use visual fraction models.
3 - I can use equations.
3 - I can represent problems.
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A. Many real world problems involve operations with fractions and mixed numbers.
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A.1 When will I have to multiply fractions and mixed numbers?
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Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
| Content | Skills | Learning Targets | Big Ideas | Essential Questions |
|---|---|---|---|---|
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Fractions [a,b]
Real world problems [c]
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3 - Apply (previous understandings of division)
3 - Extend (previous understandings of division)
2 - Divide (unit fractions by whole numbers)
2 - Divide (whole numbers by unit fractions [b])
2 - Interpret (division of unit fraction by whole number [a])
2 - Interpret (division of whole number by unit fraction [b])
2 - Compute (quotients [b])
2 - Solve (real world problems involving division of unit fractions by non-zero whole numbers [c])
2 - Solve (real world problems involving division of whole numbers by unit fractions [c])
3 - Use (visual fraction models [c])
3 - Use (equations [c])
2 - Represent (problems [c])
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3 - I can apply previous understandings of division.
3 - I can extend previous understandings of division.
2 - I can divide unit fractions by whole numbers [a].
2 - I can divide whole numbers by unit fractions [b].
2 - I can interpret division of unit fraction by whole number [a].
2 - I can interpret division of whole number by unit fraction [b].
2 - I can compute quotients [b].
2 - I can solve real world problems involving division of unit fractions by non-zero whole numbers [c].
2 - I can solve real world problems involving division of whole numbers by unit fractions [c].
3 - I can use visual fraction models [c].
3 - I can use equations [c].
2 - I can represent problems [c].
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A. Division of all types of numbers, fractions as well as whole numbers occurs when solving real world problems.
B. Division of whole numbers and fractions can be represented on several ways.
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A.1 When will I need to divide fractions and whole numbers?
B.1 What models can I use for division with fractions?
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