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Name Date 5.NF.A.2 Class

Benchmark FractionsKey Takeaways

Standard: 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.

Previously, we learned how to plot proper and improper fractions on a number line. Now, we can think of which benchmark/landmark fractions the values are closest to, by visualizing a number line. By adding or subtracting the benchmark/landmark fractions, we can get an estimate for the solution to determine if an answer is reasonable.

Vocabulary: Numerator: The numerator contains the number of those parts being described by the fractionDenominator: The denominator of a fraction shows how many equal parts or pieces the whole has been split intoEquivalent fractions: Fractions that represent the same number are called equivalent fractions.Improper fraction: When a fraction’s numerator is greater than the fraction’s denominatorMixed number: A whole number and fractionConvert: To changeBenchmark/Landmark: Common fractions or numbers that are end points or easy to recognize are benchmark numbers. For example, 0, ½, and 1 are all benchmarks.

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Activating Prior Knowledge

For each fraction below decide if it is closest to 0, 12 , or 1.

1) 89

A. 0

B. 12

C. 1

2) 25

A. 0

B. 12

C. 1

3) 210

A. 0

B. 12

C. 1

4) 49

A. 0

B. 12

C. 1

5) 45

A. 0

B. 12

C. 1

6) 1615

A. 0

B. 12

C. 1

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Let’s Explore!

Eli spent 25 of an hour on his math homework. Then he spent 12 of an hour on his English

homework. He wants to add 25 + 12 to find the total amount of time he spent

on homework so far. The sum he got was 37 . He plotted his answer on the number line below.

Part AUse the number line above to explain why 37 is an unreasonable answer to the problem25+ 12 .

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Part BShould Eli’s answer be closer to 12, 1, or 1 12 ? Explain how you know.

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Independent Practice (Mild) 1) For each fraction, identify whether it is less than or greater than 12.

a. 27 greater than 12 less than 12

b. 920 greater than 12 less than 12

c. 59 greater than 12 less than 12

d. 511 greater than 12 less than 12

e. 1022 greater than 12 less than 12

f. 610 greater than 12 less than 12

2) Are the following expressions greater than or less than 1? Circle the correct answer for each.

a. 12+27 greater than 1 less than 1

b. 58+35 greater than 1 less than 1

c. 1 14−23 greater than 1 less than 1

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d. 3 18−289 greater than 1 less than 1

3) Are the following expressions greater than or less than 12 ? Circle the correct answer.

a. 14 + 23 greater than 12 less than12

b. 37−18 greater than 12 less than12

c. 1 17−78 greater than 12 less than12

d. 37+26 greater than 12 less than12

4) Samuel was asked to choose the problem with the sum closest to 12. Which answer did he choose?

A. 13+45

B. 29+14

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C. 25+38

D. 37+49

5) Zatchi was asked to choose the problem with the sum closest to 1. Which answer did she choose?

A. 3/8 + 5/9

B. 2/9 + 4/16

C. 7/8 + 4/6

D. 1/8 + 2/5

Explain your reasoning: ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5) Is the sum of 12+38greater than or less than 1? Circle the correct answer.

Greater than 1 Less than 1

Show how you know.

6) Is the difference greater than or less than ½?

37−18

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Greater than 12 Less than 12

Show and explain how you know.

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Independent Practice (Medium)

7) Arabia is making a cake. The cake requires 35 cups of flour and 78 cup of sugar. Arabia thinks she needs less than 1 total cup of ingredients. Is her estimate reasonable? Use benchmark fractions to explain how you know.

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8) Several expressions are shown. Decide if the value of each expression is closest to ½, 1 or 1 ½. Write each expression in the correct category in the chart. There is space to show your work below.

7/12 + 3/8 2/9 + 3/11 3/6 + 7/8 10/18 + 3/7

Closest to ½ Closest to 1 Closest to 1 ½

Work space:

Independent Practice (Spicy)9) Which is a reasonable estimate for the difference, 5 ½ −¿ 3 5/9? Circle the letter of the

correct answer. You can use the number line to help you.

A. Between ½ and 1B. Between 1 and 1 ½C. Between 1 ½ and 2D. Between 2 and 2 ½

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10) Several expressions are shown. Decide if the value of each expression is less than 1 ½, between 1 ½ and 2, or greater than 2. You can use the number line to help you.

2 ½ −¿ 1 1/8 1 5/11 + ¾ 3 4/5 – 1 1/3 3/8 + 9/10

Write each expression in the correct category in the chart.Less than 1 ½ Between 1 ½ and 2 Greater than 2

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Name Date 5.NF.A.2 Class

Benchmark FractionsExit Ticket

1) For each sum or difference below, determine whether the result is greater or less than 1.

a. 12+512 greater than 1 less than 1

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b. 2 78−1 79 greater than 2 less than 2

c. 1 112−110 greater than 12 less than 12

d. 37+18 greater than 1 less than1

2) The sum of 1 56 and 1 58 would be closest to:

A 2 12B 3C 312 D 4

Explain how you know:

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Name Date 5.NF.A.2 Class

Benchmark Fractions11

Homework1) Are the following expressions greater than or less than 1? Circle the correct answer.

a. 12+49 greater than 1 less than 1

b. 58+35 greater than 1 less than 1

c. 1 15−13 greater than 1 less than 1

2) Are the following expressions greater than or less than 12? Circle the correct answer.

a. 15+14 greater than 12 less than12

b. 67−16 greater than 12 less than12

c. 1 17−56 greater than 12 less than12

3) Jose’s football weighs 78

pound. His football helmet weights 5 16

pounds.

Estimate how much more the helmet weighs. Explain your estimate.

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4) William compares monthly rainfall amounts for the summer months using the table below.

Month Monthly Rainfall

June 3 310 inches

July 3 34 inches

August 3 12 inches

About how much more rain fell in July than in June?

A 14 inch

B 12 inch

C 1 inch

D 1 12inches

Mixed Review

5) Mr. Desrivieres purchased 3 cases of pencils. Each case of pencils contains 144 pencils. Mr. Desrivieres then purchased 4 cases of pens. Each case of pens contains 95 pens. How many pens and pencils did Mr. Desrivieres purchase in total?

A 52 B 380 C 812 D 432

6) Megan had 71 pieces of candy. She gave 4 pieces each to 9 friends. How many pieces of candy does Megan have left?

A 35 13

B 36 C 107 D 71

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