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Grade 5 Common Core State Standards
for Fractions and Decimals |
Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.1. 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.)
- Worksheet #1 (Online Sample)
- Worksheet #2
- Worksheet #3
- Worksheet #4
- Lesson: Adding Mixed Numbers with Unequal Denominators
- Worksheet #5
- Worksheet #6
- Lesson: Subtracting Fractions with Unequal Denominators
- Worksheet #7
- Worksheet #8
- Worksheet #9
- Worksheet #10
- Lesson: Subtracting Mixed Numbers with Unequal Denominators
- Worksheet #11
- Worksheet #12
Note: Addition and subtraction of fractions with different denominators are illustrated with visual fraction models in the above four lessons.
5.NF.2. 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.
- Lesson: Solving Problems - Adding Fractions and Mixed Numbers
- Worksheet #1
- Worksheet #2
Note: Addition and subtraction of fractions with like and unlike denominators are illustrated with visual fraction models to solve word problems in Addition Steps 1, 2, 3 and Subtraction Steps 1, 2, 3 TeachingFractionBarsVideos
Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.3. 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?
- Lesson: Quotients of Whole Numbers that Equal Fractions
- Worksheet #1
- Worksheet #2
Note: Paper-folding strips of paper in Division Step 3 TeachingFractionBarsVideos shows that the quotient of whole numbers m and n is the fraction m/n. The demonstrations in this video are also used to solve word problems.
5.NF.4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- Lesson: Multiplying Fractions Times Whole Numbers
- Worksheet #1
- Worksheet #2
- Worksheet #3
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.)
- Lesson: Multiplying Fractions Times Whole Numbers and Fractions
Note: There are several illustrations of (a/b) × (c/d) = ac/bd using visual fraction models to solve word problems in Multiplication Step 2 TeachingFractionBarsVideos
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.)
- Lesson: Areas of Rectangles with Fractional Side Lengths
5.NF.5. Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
- Lesson: Comparing Sizes of Products and Approximating Products
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Note: The first half of part b above requires explanations of the results when multiplying by fractions less than 1 and greater than 1, and this is done in the preceding lesson on Comparing Sizes of Products and Approximating Products. The equivalence a/b = (n x a)/(n x b) is explained with a visual model in the following lesson.
- Lesson: Obtaining and Recognizing Equal Fractions
- Worksheet #2
- Worksheet #3
Note: The above lesson, Obtaining and Recognizing Equal Fractions, uses a visual fraction model to illustrate a/b = (n × a)/(n × b).
5.NF.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
- Lesson: Solving Problems Involving Multiplication of Fractions and Mixed Numbers
- Worksheet #1
- Worksheet #2
Note: Fractions times mixed numbers and mixed number times fractions are illustrated with visual fraction models to solve word problems in Multiplication Step 3 TeachingFractionBarsVideos
5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
Note: There are visual fraction models to illustrate a fraction divided by a fraction (Measurement Concept) and a fraction divided by a whole number (Sharing Concept) in Division Step 2 TeachingFractionBarsVideos
b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
- Lesson: Division of Whole Numbers by Unit Fractions
Note: If the quotient 4 ÷ 1/5 is described in words such as, "how many times does 1/5 fit into 4", the answer 20 can also easily be seen by visual fraction models.
c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
- Lesson: Word Problems - Division of Unit Fractions and Whole Numbers
Understand the place value system.
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
- Lesson: Dividing Whole Numbers and Decimals by Powers of 10
Note: The two preceding lessons have visual decimal images to illustrate the placement of a decimal point when multiplying and dividing by powers of 10. This is done by first using products of whole numbers by powers of 10 and quotients of whole numbers divided by powers of 10 and then connecting such operations to products and quotients of decimals involving powers of 10. This approach has the advantage of reviewing products and quotients of whole numbers involving powers of 10 as well as illustrating the placement of a decimal point when a decimal is multiplied or divided by a power of 10.
5.NBT.3. Read, write, and compare decimals to thousandths.
- 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).
- Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- Lesson: Reading and Writing Decimals
- Worksheet #1
- Worksheet #2
- Worksheet #3
- Worksheet #4
- Lesson: Reading and Writing Mixed Decimals
Note: In the first of the two preceding lessons, place value is illustrated by the columns of Decimal Squares. The heavy vertical lines on the tenths squares show 10 tenths in one whole square, and these lines together with the lighter horizontal lines divide the square into hundredths. The number of full vertical columns is the number of tenths for the decimal, and a partially shaded column shows the additional number of hundredths.
Note: In the second of the two preceding lessons, mixed decimals are visually illustrated by using the backs of Decimal Squares to represent the number of units and the fronts of squares to represent decimals. This provides a meaningful model for mixed decimals.
5.NBT.4. Use place value understanding to round decimals to any place.
- Lesson: Rounding Decimals and Mixed Decimals
- Worksheet #1
- Worksheet #2
Note: Visual models and place value tables are used in the above lesson to illustrate rounding decimals and mixed decimals. The two corresponding worksheets for this lesson have examples of rounding to whole numbers and tenths, and each has word problems involving rounding.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
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.
- Lesson: Addition of Decimals with Different Numbers of Decimal Places
- Worksheet #3
- Worksheet #4
- Lesson: Addition of Mixed Decimals
- Worksheet #5
- Worksheet #6
- Worksheet #7
Note: Worksheet #3 has a sheet of Blank Decimal Squares attached for illustrating a few of the sums. Worksheet #7 has word problems involving addition of decimals and mixed decimals.
- Lesson: Subtraction of Decimals with Same Number of Decimal Places
- Worksheet #8
- Worksheet #9
- Worksheet #10
- Lesson: Subtraction of Decimals with Different Numbers of Decimal Places
- Worksheet #11
- Worksheet #12
- Lesson: Subtraction of Mixed Decimals
- Worksheet #13
- Worksheet #14
- Worksheet #15
Note: Worksheets #8 and #11 each have a sheet of Blank Decimal Squares attached for illustrating differences involving decimals and mixed decimals. On worksheets #10 and #13, each exercise for computing a difference also asks for a corresponding approximation that involves rounding to the nearest tenth or nearest whole number. Worksheet #15 has word problems involving differences of decimals and mixed decimals.
- Lesson: Multiplication by Decimals
- Worksheet #19
- Worksheet #20
- Worksheet #21
- Lesson: Multiplication with Mixed Decimals
- Worksheet #22
- Worksheet #23
- Worksheet #24
Note: Worksheet #18 has a sheet of Blank Decimal Squares attached for illustrating a few products involving decimals. On worksheet #22, there are exercises for approximating products by rounding mixed decimals to the nearest whole number. Worksheet #24 has word problems involving products of decimals and mixed decimals.
- Lesson: Division of Decimals by Whole Numbers
- Worksheet #25
- Worksheet #26
- Lesson: Division of Decimals by Decimals
- Worksheet #27
- Worksheet #28
- Worksheet #29
- Lesson: Division by Mixed Decimals
- Worksheet #30
- Worksheet #31
- Worksheet #32
Note: Worksheets #26 and#27 each have a sheet of Blank Decimal Squares attached for illustrating quotients involving decimals. Worksheet #29 has quotients that are repeating decimals. Worksheet #32 has word problems involving quotients of decimals and mixed decimals.
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© Copyright 2001-2012, Albert Bradley Bennett, Jr.
