Mathematics | Grade 5 · 2017-06-19 · 1 . Mathematics | Grade 5 . In Grade 5, instructional time...

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Mathematics | Grade 5 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.

(1) Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

(2) Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.

(3) Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.

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Contents Mathematics | Grade 5 ................................................................................................................................. 1

Grade 5 Overview ......................................................................................................................................... 3

Operations and Algebraic Thinking 5.OA ............................................................... 4

Write and interpret numerical expressions. (5.OA.A) .......................................................................... 4 Analyze patterns and relationships. (5.OA.B) ....................................................................................... 7

Number and Operations in Base Ten 5.NBT ............................................................... 9

Understand the place value system. (5.NBT.A) .................................................................................. 10 Perform operations with multi-digit whole numbers and with decimals to hundredths. (5.NBT.B) . 16

Number and Operations—Fractions 5.NF ............................................................ 24

Use equivalent fractions as a strategy to add and subtract fractions. (5.NF.A) ................................. 24 Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (5.NF.B) ............................................................................................................................... 29

Measurement and Data 5.MD ........................................................... 50

Convert like measurement units within a given measurement system. (5.MD.A) ............................. 50 Represent and interpret data. (5.MD.B) ............................................................................................. 52 Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. (5.MD.C) .......................................................................................................................... 53

Geometry 5.G .................................................................. 61

Graph points on the coordinate plane to solve real-world and mathematical problems. (5.G.A) ..... 61 Classify two-dimensional figures into categories based on their properties. (5.G.B) ........................ 66

Performance Task Example: 72

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Grade 5 Overview Operations and Algebraic Thinking

• Write and interpret numerical expressions. • Analyze patterns and relationships.

Number and Operations in Base Ten

• Understand the place value system. • Perform operations with multi-digit whole

numbers and with decimals to hundredths. Number and Operations—Fractions

• Use equivalent fractions as a strategy to add and subtract fractions.

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Measurement and Data

• Convert like measurement units within a given measurement system.

• Represent and interpret data. • Geometric measurement: understand concepts

of volume and relate volume to multiplication and to addition.

Geometry

• Graph points on the coordinate plane to solve real-world and mathematical problems.

• Classify two-dimensional figures into categories based on their properties.

Mathematical Practices 1. Make sense of problems and

persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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Operations and Algebraic Thinking 5.OA

Write and interpret numerical expressions. (5.OA.A) 1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

(5.OA.A.1) (DOK 1) a. Example: Solution (DOK 1)

b. Example: Solution (DOK 2)

https://www.illustrativemathematics.org/content-standards/5/OA/A/1/tasks/555


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c. Example: Solution (DOK 1)

2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without

evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize


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that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. (5.OA.A.2) (DOK 1,2)

a. Example: Solution (DOK 2)



d. Example: Solution (DOK 3)

e. Example: Tyler is 8 years old. His sister Olivia is 4 years less than twice his age.

Write a numerical expression for Olivia’s age.





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Item Claim Domain Target DOK CONTENT MP Key

#12 1 OA A 2 5.OA.A.2 N/A (2x8) – 4 or equivalent

Analyze patterns and relationships. (5.OA.B) 1. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.

Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. (5.OA.B.3) (DOK 1,2)


Example: (Former NAEP question) (DOK 1)

https://www.illustrativemathematics.org/content-standards/5/OA/B/3/tasks/1895

https://www.educateiowa.gov/sites/files/ed/documents/NAEP%20-%20Grade%205%20Tasks%20-%20Operations%20%26%20Algebraic%20Thinking.pdf

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Answer: C, the 7th term

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Number and Operations in Base Ten 5.NBT Example: Five swimmers compete in the 50-meter race. The finish time for each swimmer is shown.

Explain how the results of the race would change if the race used a clock that rounded to the nearest tenth. (DOK 3)


#28 3 NS 3D, 3F 1 5.NBT.3 N/A Sample top-score response: There would be three swimmers with the same time, and the other two swimmers would also have the same time. Instead of having one clear winner, there would be a tie for first place.

For full credit: The response demonstrates a full and complete understanding of communicating reasoning. The response contains the following evidence:

-The student explains how the race results would change (e.g. three swimmers would tie for first place)

Example: Choose True or False for each equation. (DOK 2)

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#29 1 NS 1D 1 5.NBT.5, 5.NBT.6 N/A T, F, F, T

Understand the place value system. (5.NBT.A) 1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the

place to its right and 1/10 of what it represents in the place to its left. (5.NBT.A.1) (DOK 1) a. Example: Solution (DOK 3)



https://www.illustrativemathematics.org/content-standards/5/NBT/A/1/tasks/1562



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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. (5.NBT.A.2) (DOK 1,2)






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c. Example: Which number is equal to 10⁴? (DOK 1)

1. 100 2. 1,000 3. 10,000 4. 100,000


#1 1 NBT C 1 5.NBT.A.2 N/A 3

d. Example: (Former NAEP question) (DOK 1)

Answer: B, 150

1. Read, write, and compare decimals to thousandths. a. 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). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <

symbols to record the results of comparisons. (5.NBT.A.3) (DOK 1) 1. Example: Solution (DOK 2)

2. Example: Solution (DOK 1)

https://www.educateiowa.gov/sites/files/ed/documents/NAEP%20-%20Grade%205%20Tasks%20-%20Number%20%26%20Operations%20in%20Base%2010.pdf



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5. Example: Which number makes this inequality true?

a. 4253.664 b. 4253.655 c. 4253.649 d. 4253.638


#11 1 NBT C 2 5.NBT.A.3b N/A d

6. Example: (Former NAEP question) (DOK 1)

Answer: H, 1 dollar and 10 cents


Answer: B





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Answer: E


Answer: B


Answer: A


Answer: A


Answer: C

2. Use place value understanding to round decimals to any place. (5.NBT.A.4) (DOK 1) a. Example: Solution (DOK 1)






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b. Example: (Former NAEP question) (DOK 1)

Answer: D

Perform operations with multi-digit whole numbers and with decimals to hundredths. (5.NBT.B) 3. Fluently multiply multi-digit whole numbers using the standard algorithm. (5.NBT.B.5) (DOK 1)


b. Example: Write the product. (DOK 1)

4238 X 32 =


https://www.illustrativemathematics.org/content-standards/5/NBT/B/5/tasks/1812

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Answer: 135,616


#5 1 NBT D 1 5.NBT.B.5 N/A 135616

c. Example: (Former NAEP question) (DOK 2)

Answer: A


Answer: C

4. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using

strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (5.NBT.B.6) (DOK 1,2)


b. Example: Jasmine solves the equation ÷ 4 = 363 using this area model.




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Which statement explains how Jasmine should solve for the missing number in the model?

1. Jasmine should divide 60 by 4. 2. Jasmine should divide 1200 by 12. 3. Jasmine should multiply 3 times 60. 4. Jasmine should multiply 4 times 60.


#9 3 NBT A 3 5.NBT.B.6 1, 3 4

c. Example: Write the quotient. (DOK 1)

3125 ÷ 25 = Item Claim Domain Target DOK CONTENT MP Key

#2 1 NBT D 1 5.NBT.B.6 N/A 125


Answer: Edward, because he is dividing by a small number, the pieces will always be bigger.

e. Example: (Former NAEP question) (DOK 1)

Answer: B, 10



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5. 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. (5.NBT.B.7) (DOK 1,2,3)



c. Example: The bed of a truck is stacked with boxes of paper. The boxes are stacked 5 boxes deep by 4

boxes high by 4 boxes across, as shown in the picture. (DOK 2)



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#18 4 MD, NBT D 2 5.MD.C, 5.NBT.B.7 1, 2, 5, 6 3

d. Example: Connor is buying tickets to a concert. The concert he and his friends want to see costs $4.75

per ticket. Connor has $26.00 total. (DOK 1) What is the greatest number of tickets Connor can buy?

1. 4 2. 5 3. 6 4. 7


#6 2 NBT C 2 5.NBT.B.7 2 2

e. Example: Use this pentagon to solve the

problem. Write the perimeter, in centimeters, of the pentagon. (DOK 1)


#4 2 MD, NBT A 2 5.MD.A.1, 5.NBT.B.7 2 1435

f. Example: (Former NAEP question) (DOK 1)


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Answer: 41.65

g. Example: (Former NAEP question) (DOK 1)

h. Example: (Former NAEP question) (DOK 2)

Answer: $10.66 (rounded). First add the prices of cereal and milk, then multiply the amount by the tax to find the taxed number. Then, add the tax to the milk+cereal total.

i. Example: (Former NAEP question) (DOK 1)




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Answer: A

j. Example: (Former NAEP question) (DOK 2)

Answer: D

k. Example: (Former NAEP question) (DOK 2)

Answer: Robert can buy 11 bags of peanuts. He can then buy a fruit drink with the remaining $1.95 he has.

l. Example: (Former NAEP question) (DOK 2)

Answer: B

m. Example: (Former NAEP question) (DOK 2)





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Answer: E n. Example: (Former NAEP question) (DOK 1)

Answer: C

o. Example: (Former NAEP question) (DOK 1)

Answer: E

p. Example: (Former NAEP question) (DOK 1)

Answer: B




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Number and Operations—Fractions 5.NF

Use equivalent fractions as a strategy to add and subtract fractions. (5.NF.A) 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.) (5.NF.A.1) (DOK 1)




https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/839



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e. Example: Solution (DOK 2)

f. Example: Solution (DOK 2)




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g. Example: Solution (DOK 2)

h. Example: Select two fractions that can be rewritten with a denominator of 24.

1. 16

2. 15

3. 57

4. 910

5. 19

6. 78


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#20 1 NF E 1 5.NF.A.1 N/A

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. (5.NF.A.2) (DOK 1,2,3)



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c. Example: Jason begins at the start of a path and rides his bike 11 ½ miles on the path. The path

is 12 ¼ miles long. Write the distance, in miles, Jason must ride to reach the end of the path.


#19 1 NF E 2 5.NF.A.2 N/A 34

d. Example: Jan measured the growth of a sunflower. (DOK 2)

• In week one, it grew 2 12

inches.

• In week two, it grew 2 34

inches.

• In week three, it grew 3 14

inches. How much did the sunflower grow over all three weeks?

1. 5 34

in

2. 7 12

in


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3. 8 in

4. 8 12

in


#7 1 NF E 2 5.NF.A.2 N/A 4


Apply and extend previous understandings of multiplication and division to multiply and divide fractions. (5.NF.B)

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? (5.NF.B.3) (DOK 1,2)


https://www.educateiowa.gov/sites/files/ed/documents/NAEP%20-%20Grade%205%20Tasks%20-%20Number%20%26%20Operations%20-%20Fractions.pdf

https://www.illustrativemathematics.org/content-standards/5/NF/B/3/tasks/292

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e. Example: Darcy likes to eat peanut butter and raisins on apple slices. On each apple slice she

puts 116

cup of peanut butter and 8 raisins.

Darcy has 25

cup of peanut butter and 80 raisins. She eats a whole number of apple slices until

the peanut butter is all gone. What fraction of 80 raisins did she eat? Write the fraction.


#14 4 NS, NF A 3 6.NS.A, 5.NF.B.3 1, 6

4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a

fraction. 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.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the


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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. (5.NF.B.4) (DOK 1,2) 1. Example: Solution (DOK 3)






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10. Example: Look at the equation. (DOK 1)

23

× ?? = n

Sarah claims that for any fraction multiplied by 23, n will be less than 23

.

To convince Sarah that this statement is only sometimes true:

Part A: Write one number in each box so the product, n , is less than 23

.

23

× = 𝑛𝑛

Part B: Write one number in each box so the product, n , is not less than 23.


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23

× = 𝑛𝑛

Item Claim Do

main

Target

DOK

CONTENT

MP Key

#11 3 NF A 3 5.NF.B.4 2, 3, 7

11. Example: Select all expressions that are equal to 3 14

. (DOK 1)

a. 26 × 18

b. 2 18

× 2

c. 4 × 13

d. 14

× 3

e. 13 14


#26 1 NF F 1 5.NF.B.4a N/A

12. Example: Lola has 4 orange juice containers. Each container is 5/8 full. (DOK 1)

Lola claims to have a total of 2 ½ gallons of orange juice in the 4 containers. Which of these statements must be true in order for Lola’s claim to be correct?

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#23 3 NF C 2 5.NF.B.4 3 B

13. Example: Write one number in each box to create a fraction that correctly completes each

statement.


#17 3 NF D 3 5.NF.B.4 2, 6 or any fraction less than 1

or any fraction equal to 1

or any fraction greater than 1

14. Example: Use this rectangle to solve the problem.

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What is the area, in square centimeters, of the rectangle?

i. 32 14

ii. 32 12

iii. 32 12

iv. 38 12


#15 1 NF F 2 5.NF.B.4b N/A C

14. Example: Look at the fraction model shown.

The shaded area represents

32

. Draw rectangles the size of A, B, C, and D in the answer

space to construct a model that represents 3 X 32

. Label your rectangles you draw.

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#13 3 NF B 3 5.NF.B.4a 3 Student draws any combination of shapes equivalent to:

15. Example: Which fraction model best represents 4 × 23

? (DOK 1)


#3 1 NF F 1 5.NF.B.4 N/A C

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. 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. (5.NF.B.5) (DOK 1,2,3) 1. Example: Solution (DOK 1)




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10. Example: Write a value for b that makes this statement true: 5 × b is less than 5, but greater

than 0.


#25 1 NF F 2 5.NF.B.5a N/A 0<b<1

11. Solve real world problems involving multiplication of fractions and mixed numbers, e.g.,

by using visual fraction models or equations to represent the problem. (5.NF.B.6) (DOK 1,2)









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e. Example: Solution (DOK 2)


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f. Example: Solution (DOK 2)

g. Example: Solution (DOK 2)

h. Example: Solution (DOK 2)




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12. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

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.

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.

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? (5.NF.B.7) (DOK 1,2)


1 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.


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9. Example: Ryan has 12

pound of chocolate. He divides it into 4 equal portions.

Write the amount of chocolate, in pounds, in each portion.


#24 1 NF F 1 5.NF.B.7c N/A


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Measurement and Data 5.MD

Convert like measurement units within a given measurement system. (5.MD.A) 1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05

m), and use these conversions in solving multi-step, real world problems. (5.MD.A.1) (DOK 1,2) a. Example: Solution (DOK 2)


c. Example: Susan has 4 gallons of juice. How many cups of juice does she have?

Cups=______


#14 1 MD G 1 5.MD.A.1 N/A 64

d. Example: Use this pentagon to solve the problem.

Write the perimeter, in centimeters, of the pentagon.

https://www.illustrativemathematics.org/content-standards/5/MD/A/1/tasks/293

https://www.illustrativemathematics.org/content-standards/5/MD/A/1/tasks/878

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#4 2 MD, NBT A 2 5.MD.A.1, 5.NBT.B.7 2 1435

e. Example: (Former NAEP Question) (DOK 2)

Answer: E. 25,000,000 yen

https://www.educateiowa.gov/sites/files/ed/documents/NAEP%20-%20Grade%205%20Tasks%20-%20Measurement%20%26%20Data.pdf

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f. Example: (Former NAEP question) (DOK 1)

Answer: E. 39 AU

g. Example: (Former NAEP question) (DOK 1)

Answer: C. 10

h. Example: (Former NAEP question) (DOK 1)

Answer: B. A 16 pint water jug

Represent and interpret data. (5.MD.B) 2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this

grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. (5.MD.B.2) (DOK 1,2)





https://www.illustrativemathematics.org/content-standards/5/MD/B/2/tasks/1563

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Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. (5.MD.C)

Example: The bed of a truck is stacked with boxes of paper. The boxes are stacked 5 boxes deep by 4 boxes high by 4 boxes across, as shown in the picture.

Write the minimum number of boxes of paper the driver must deliver at the first stop to be allowed to drive over the bridge.


#18 4 MD, NBT D 2 5.MD.C, 5.NBT.B.7 1, 2, 5, 6 3

3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

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a. A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. (5.MD.C.3) (DOK 1) 1. Example: The rectangular prism shown has 4 layers with 6 cubes in each layer.

Write the volume, in cubic centimeters, of the rectangular prism.


#8 1 MD I 2 5.MD.C.4, 5.MD.C.3 N/A 24

4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. (5.MD.C.4) (DOK 1,2)

a. Example: The rectangular prism shown has 4 layers with 6 cubes in each layer.

Write the volume, in cubic centimeters, of the rectangular prism.


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#8 1 MD I 2 5.MD.C.4, 5.MD.C.3 N/A

b. Example: (Former NAEP question) (DOK 2)

Answer: B. 4

5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.


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(5.MD.C.5) (DOK 1,2) 1. Example: Solution (DOK 2)



https://www.illustrativemathematics.org/content-standards/5/MD/C/5/tasks/1308



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5. Example: Brady started to fill the box shown with some unit cubes.

Write the total number of unit cubes needed to completely fill the box. Include the unit cubes already shown in your total.

Item Claim Domain Target DOK CONTENT MP Key #17 2 NS, MD D 2 6.NS.B.3, 5.MD.C.5 6, 7


Answer: D. 10


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Answer: A. 42 X 34 X 30

8. Example: The right rectangular prism shown has a length of 6 centimeters, width of 3 centimeters, and height of 4 centimeters.

Determine whether each equation can be used to find the volume (V) of this prism. Select Yes or No for each equation.


#27 1 MD I 2 5.MD.C.5b N/A

6. Example: Walter puts 1050 cubic inches of dirt into the tank shown. Shade in the number line to show

the height of the dirt in the tank.


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#16 1 MD I 2 5.MD.C.5 N/A

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Geometry 5.G

Graph points on the coordinate plane to solve real-world and mathematical problems. (5.G.A) 1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection

of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). (5.G.A.1) (DOK 1) a. Example: Solution (DOK 2)

b. Example: Triangle ABC is graphed in the coordinate plane.

https://www.illustrativemathematics.org/content-standards/5/G/A/1/tasks/489

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Which set of ordered pairs shows the coordinates of points A, B, C?

1. A (2,7), B (4,3), C (5,6) 2. A (2,7), B (5,6), C (4,3) 3. A (7,2), B (3,4), C (6,5) 4. A (7,2), B (4,3), C (5,6)


#10 1 G J 1 5.G.A.1 N/A A


Answer: (B, 5), (D, 1), (D, 3)

https://www.educateiowa.gov/sites/files/ed/documents/NAEP%20-%20Grade%205%20Tasks%20-%20Geometry.pdf

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2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. (5.G.A.2) (DOK 1,2) a. Example: Solution (DOK 2)

b. Example: The location of Mary’s home is plotted on the coordinate grid.

Read these clues about other places in Mary’s town.

https://www.illustrativemathematics.org/content-standards/5/G/A/2/tasks/1516

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Write in the names of each place by the correct location on the coordinate grid.

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#21 4 G F 3 5.G.A.2 1, 4


Answer: 15 minutes, 8 problems

Classify two-dimensional figures into categories based on their properties. (5.G.B)


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3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. (5.G.B.3) (DOK 1,2) a. Example: Solution (DOK 2)

b. Example: All parallelograms have opposite sides that are equal in length and parallel.

Determine whether each polygon shown is also a parallelogram. Select Yes or No for each polygon.

https://www.illustrativemathematics.org/content-standards/5/G/B/3/tasks/1941

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#22 1 G K 2 5.G.B.3 N/A


Answer: Yes, the opposites are parrellel to each other


Answer: E.

4. Classify two-dimensional figures in a hierarchy based on properties. (5.G.B.4) (DOK 1,2) a. Example: Solution (DOK 2)




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Performance Task Example:

1.

For this item, a full-credit response (1 point) includes • carrots: 10 x 30 rectangle; potatoes: 5 x 40 rectangle; broccoli: 5 x 30 rectangle; corn: 4 x 25 rectangle OR

• any four areas that are correct. For this item, a no-credit response (0 points) includes none of the features of a full-credit response.

2.

For this item, a full-credit response (1 point) includes

OR • any equivalent fraction. For this item, a no-credit response (0 points) includes none of the features of a full-credit response.

3.

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For this item, a full-credit response (2 points) includes

AND 650. For this item, a partial-credit response (1 point) includes

OR

• 650 or total square feet consistent with an error in Part A For this item, a no-credit response (0 points) includes none of the features of a full- or partial-credit response.

4.

For this item, a full-credit response (2 points) includes

• writing the correct sum: AND writing the correct sum as an equation. For example,

For this item, a partial-credit response (1 point) includes

• writing the correct sum without using an equation OR

• writing an incorrect sum, but using an equation. For example,

OR

For this item, a no-credit response (0 points) includes none of the features of a full- or partial-credit response.

Mathematics | Grade 5 · 2017-06-19 · 1 . Mathematics | Grade 5 . In Grade 5, instructional time...

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Transcript of Mathematics | Grade 5 · 2017-06-19 · 1 . Mathematics | Grade 5 . In Grade 5, instructional time...