Created for Morehouse Parish School System

by Dr. Stacey Pullen

6thGrade

Math Aligned

Sample Items

Created for Morehouse Parish School System by Dr. Stacey Pullen

6th Grade

Sample Math Items Aligned to CCSS

Table of Contents

CCSS Code / Page # / CCSS Code / Page #
6.RP.A.1 / 3 / 6.EE.B.7 / 42
6.RP.A.2 / 5 / 6.EE.B.8 / 44
6.RP.A.3 / 7 / 6.EE.C.9 / 45
6.RP.A.3a / 9 / 6.G.A.1 / 47
6.RP.A.3b / 10 / 6.G.A.2 / 48
6.RP.A.3c / 11 / 6.G.A.3 / 49
6.RP.A.3d / 12 / 6.G.A.4 / 50
6.NS.A.1 / 13 / 6.SP.A.1 / 52
6.NS.B.2 / 15 / 6.SP.A.2 / 53
6.NS.B.3 / 16 / 6.SP.A.3 / 55
6.NS.B.4 / 17 / 6.SP.B.4 / 56
6.NS.C.5 / 18 / 6.SP.B.5 / 58
6.NS.C.6 / 20 / 6.SP.B.5a / 60
6.NS.C.6a / 21 / 6.SP.B.5b / 61
6.NS.C.6b / 23 / 6.SP.B.5c / 62
6.NS.C.6c / 24 / 6.SP.B.5d / 64
6.NS.C.7 / 25 / Answer Key / 65
6.NS.C.7a / 26 / Rubrics / 67
6.NS.C.7b / 27 / Origination of Items / 74
6.NS.C.7c / 28
6.NS.C.7d / 30
6.NS.C.8 / 31
6.EE.A.1 / 32
6.EE.A.2 / 33
6.EE.A.2a / 34
6.EE.A.2b / 35
6.EE.A.2c / 36
6.EE.A.3 / 38
6.EE.A.4 / 39
6.EE.B.5 / 40
6.EE.B.6 / 41

6th Grade

Sample Math Items Aligned to CCSS

6. RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."(Conceptual Understanding)

What test questions look like:

Sample 1:

The table below shows the number of pets, by type, the sixth grade students have at Middleton Elementary School.

Pets

Pet Type / Number of Pets
dog / 54
cat / 42
fish / 14
hamster / 8

What is the ratio of cats as pets to fish as pets?

A1 to 3

B3 to 1

C9 to 7

D7 to 9

Sample 2:

Desean counted the e-mails he sent and received last week. The ratio of e-mails he sent to e-mails he received is 2:3. Which statement about the e-mails Desean sent and received last week must be true?

  1. Desean sent and received a total of 5 e-mails last week.
  1. Desean sent more e-mails than he received last week.
  2. A total of of the e-mails Desean counted from last week were e-mails he sent.
  3. For every 3 e-mails Desean received last week, he sent 2 e-mails.

6. RP.A.2

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."(Conceptual Understanding)

What test questions look like:

Sample 1:

Mr. Zenon makes baby food. The baby food is a mixture of apples and pears. The ratio of cups of apples to cups of pears in the baby food is 5:2.

Which statements about the baby food that Mr. Zenon makes are true?

Select all the correct statements.

  1. The total volume of the baby food is always 7 cups.
  1. The total volume of the baby food, in cups, is always a multiple of 7.
  1. The baby food always has exactly 3 more cups of apples than cups of pears.
  1. For every cup of pears in the baby food, Mr. Zenon includes 2 cups of apples.
  1. For every cup of apples in the baby food, Mr. Zenon includes cup of pears.

Sample 2:

There are 18 gallons of juice and 30 gallons of milk at a restaurant. Which statement correctly describes the unit rate of juice to milk at the restaurant?

  1. There are 0.6 gallon of juice for every 1 gallon of milk.
  1. There are 1.8 gallons of juice for every 1 gallon of milk.
  1. There is 1 gallon of juice for every 12 gallons of milk.
  1. There is 1 gallon of juice for every 3 gallons of milk.

6. RP.A.3

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.(Conceptual Understanding & Application)

What test questions look like:

Sample 1:

Mr. Patterson wants to buy the brand of socks that gives him the best deal. This table shows the prices for different packages of socks.

Brand / Number of
Pairs of Socks / Price
A-One Socks / 1 / $1.69
Hop-Around Socks / 2 / $3.99
Super Socks / 4 / $6.49
Lots of Socks / 5 / $8.99

Which brand should Mr. Patterson buy?

  1. A-One Socks
  2. Hop-Around Socks
  3. Super Socks
  4. Lots of Socks

Sample 2:

Chloe places one red ball on one side of this scale. She places two yellow triangles on the other side. The scale is balanced.

Which picture shows another way that the scale willbalance?

6. RP.A.3a

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.(Conceptual Understanding & Procedural Skill and Fluency & Application)

What test questions look like:

Sample 1:

The ratio of the sales tax to the amount of purchase is a fixed number in Town Q. The table shows the sales tax for a purchase of $1,200. Town Q Tax

Purchase / Sales Tax
$1,200 / $72
$2,500 / ?
? / $108

Part A

What is the sales tax for a purchase of $2,500?

A$18.06

B$34.72

C$144.00

D$150.00

Part B

What is the cost of an item with a sales tax of $108?

A$432

B$648

C$1,092

D$1,800

6. RP.A.3b

Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?(Application)

What test questions look like:

Sample 1:

David is conducting a survey by going door-to-door. He visited 60 homes in 2.5 hours. At that rate, how much time, in hours, will it take David to visit 90 homes?

Enter your answer in the box.

6. RP.A.3c

Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.(Conceptual Understanding & Application)

What test questions look like:

Sample 1:

Based on information from previous years, 40% of the fans at each of a baseball team’s games are female. At one of the team’s games this year, there were 480 female fans. Based on the information from previous years, what was the total number of fans at that game?


Enter your answer in the box.

6. RP.A.3d

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.(Conceptual Understanding & Procedural Skill and Fluency)

What test questions look like:

Sample 1:

Gary is installing square floor tiles on a floor with an area of 160square feet. Each tile covers 16square inches. How many tiles does he need to cover the floor?

  1. 10
  2. 120
  3. 214
  4. 1,440

Sample 2:

Marilyn sees a drawing of a footprint that was supposedly made by the creature “Bigfoot.”

The footprint covers an area of 3squarefeet. How many squareinches does the footprint cover?

  1. 9 square inches
  2. 36 square inches
  3. 108 square inches
  4. 432 square inches

6. NS.A.1

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.(Conceptual Understanding & Procedural Skill and Fluency & Application)

What test questions look like:

Sample 1:

Mr. Polandski is adding food coloring to water to create his own paint colors. He has 5 cups of water. To create a color, he needs cup of water. How many paint colors, in all, can Mr. Polandski create if he uses all the cups of water he has?

Enter your answer in the box.


Sample 2:

One size of cardboard can be purchased in sheets that are 3/16 inch thick. The sheets

of cardboard are stacked on top of each other in packages. The height of each stack is 2 ¼ inches.

•Use the model of a ruler to determine the number of sheets of cardboard in a stack.

•Explain how you used the model to find your answer.

•Write an expression that can be used to determine the number of sheets of cardboard in a stack.

•Explain how your expression relates to the model.

Enter your answer, your expression, and your explanations in the box provided.

6. NS.B.2

Fluently divide multi-digit numbers using the standard algorithm.(Procedural Skill and Fluency)

What test questions look like:

Sample 1:

What is 437 ÷ 19?

  1. 13
  2. 19
  3. 22
  4. 23

Sample 2:

What is the value of 351 ÷ 26?

  1. 12 3/20
  1. 13 5/13
  1. 13 ½
  1. 14 7/26

6. NS.B.3

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.(Procedural Skill and Fluency)

What test questions look like:

Sample 1:

Megan spent $9.85 on ingredients and made one pan of cereal bars. The pan has a length of 24 inches and a width of 16 inches.

Megan needs to cut individual cereal bars from the pan. Each cereal bar should be the same size and shape and should represent a reasonable serving.

Estimate an appropriate length and width for each cereal bar and explain your assumptions.

Based on your estimate, determine the amount each cereal bar will cost Megan to make. Show your work or explain your reasoning.

Enter your answers and your work or explanations in the box provided.

6. NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.For example, express 36 + 8 as 4 (9 + 2).(Conceptual Understanding & Procedural Skill and Fluency)

What test questions look like:

Sample 1:

What is the greatest common factor of 78 and 96?

A. 2

B. 6

C. 8

D. 12

6. NS.C.5

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.(Conceptual Understanding & Application)

What test questions look like:

Sample 1:

William and Jason are playing a game. William started at zero and moved in the negative direction 9 spaces, which he modeled with the number –9. James also started at zero and moved in the opposite direction 9 spaces.

Which number models Jason’s position in the game?

Enter your answer in the box.

Sample 2:

Holly records the temperature, in degrees Fahrenheit, for two different cities. In one of the cities, the temperature is 15 degrees above zero. Holly records this as 15. In the other city, the temperature is 15 degrees below zero. Which value represents the temperature Holly records?

  1. -30
  1. -15
  1. 15
  1. 30

6. NS.C.6

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.(Conceptual Understanding)

What test questions look like:

Sample 1:

Which number line has the values,,0.25, and0.75 placed in the correct locations?

Sample 2:

Which numbers best represent pointA on the numberline?

I.-2.2
II.-2.3
III.-2.4
IV.-215
V.-225

  1. I
  2. II
  3. I and V
  4. III and V

6. NS.C.6a

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.(Conceptual Understanding)

What test questions look like:

Sample 1:

Points P, Q, and R are shown on the number line.

PQR

−1−0.8−0.6−0.4−0.200.20.40.60.81

Part A

Find the distances between points P and Q and between points R and Q. Show your work or explain your answers. Refer to the number line in your explanation.

Enter your answers and your work or explanation in the box provided.

Part B

Point S is a different point on the number line. Point S and point R are the same distance from point Q. Explain how to determine the location of point S on the number line.

Enter your explanation in the box provided

6. NS.C.6b

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.(Conceptual Understanding)

What test questions look like:

Sample 1:

Jolie draws a map of her neighborhood on a coordinate plane. She draws her house at a point in Quadrant II of the coordinate plane.

Select all the points that could represent the location of Jolie’s house.

  1. (0, 5)
  1. (1, –4)
  1. (–2, 0)
  1. (–4, 7)
  1. (–3, –1)
  1. (–1, 9)

6. NS.C.6c

Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.(Conceptual Understanding)

What test questions look like:

Sample 1:

This number line shows four points.

ABC D

−4−3−2−101234

Which point is located at?

  1. point A
  1. point B
  1. point C
  1. point D

6. NS.C.7

Understand ordering and absolute value of rational numbers.(Conceptual Understanding)

What test questions look like:

Sample 1:

Which comparison is false?

A..4 < 5

B.. =

C..-3 < -4

D..0.32 = 0.320

Sample 2:

Select all of the inequalities that aretrue.
I. -3 > -9
II. 11 < -15
III. 25 > -40
IV. 1 > -21
V. -8 > -6

  1. II, IV
  2. I, V
  3. II, III, IV
  4. I, III, IV

6. NS.C.7a

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.(Conceptual Understanding)

What test questions look like:

Sample 1:

These five rational numbers are plotted on a horizontal number line.

,, ,

Which statement about the locations of the rational numbers on the number line is true?

A. is farthest to the left, and is farthest to the right.

B. is farthest to the left, and is farthest to the right.

C. is farthest to the left, and is farthest to the right.

D. is farthest to the left, and is farthest to the right.

6. NS.C.7b

Write, interpret, and explain statements of order for rational numbers in real-world contexts.For example, write -3oC > -7oC to express the fact that -3oC is warmer than -7oC.(Application)

What test questions look like:

Sample 1:

Kyle is thinking of a number that is greater than –6 and less than –6. Which number could be Kyle’s number?

  1. –6.7
  2. –6.6
  3. –6.5
  4. –6.4

6. NS.C.7c

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.(Conceptual Understanding)

What test questions look like:

Sample 1:

Points P, Q, and R are shown on the number line.

PQR

−1−0.8−0.6−0.4−0.200.20.40.60.81

Part A

Find the distances between points P and Q and between points R and Q. Show your work or explain your answers. Refer to the number line in your explanation.

Enter your answers and your work or explanation in the box provided.

Part B

Point S is a different point on the number line. Point S and point R are the same distance from point Q. Explain how to determine the location of point S on the number line.

Enter your explanation in the box provided

6. NS.C.7d

Distinguish comparisons of absolute value from statements about order.For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.(Conceptual Understanding)

What test questions look like:

Sample 1:

NONE Available

6. NS.C.8

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.(Procedural Skill and Fluency & Application)

What test questions look like:

Sample 1:

Ralph plotted the points (–4, 3) and (–4, –3) on a coordinate grid. What is the distance, in units, between the points Ralph plotted?

Enter your answer in the box.

6. EE.A.1

Write and evaluate numerical expressions involving whole-number exponents.(Conceptual Understanding & Procedural Skill and Fluency)

What test questions look like:

Sample 1:

Phil can pack 34 boxes into the back of a moving truck. Each box is 2 feet long, 2 feet wide, and 3 feet tall. Which expression could be used to find the total volume, in cubic feet, of all the boxes Phil can pack into the back of a moving truck?

  1. 34 + 22 + 3
  2. 34 + 22 × 3
  3. 34 × 22 + 3
  4. 34 × 22 × 3

6. EE.A.2

Write, read, and evaluate expressions in which letters stand for numbers.(Conceptual Understanding & Procedural Skill and Fluency)

What test questions look like:

Sample 1:

Angela determines that this is the formula for a number pattern.
3(n – 4)
She thinks the 10th term in the pattern is 26. Is Angela correct?

A.Yes, the 10th term is 26.

B.No, the 10th term is 6.

C.No, the 10th term is 18.

D.There is not enough information to solve this problem.

Sample 2:

Ms. Stout grows tomatoes in her garden. She uses the expression below to estimate how many tomatoes will grow after n weeks.
12+2n
Based on this expression, how many tomatoes will there be after 8weeks?
Write your answer as a whole number only. Donot add any words, symbols, or punctuation to your answer.

6. EE.A.2a

Write expressions that record operations with numbers and with letters standing for numbers.For example, express the calculation "Subtract y from 5" as 5 - y.(Conceptual Understanding)

What test questions look like:

Sample 1:

The students in a club are selling flowerpots to raise money. Each flowerpot sells for $15.

Part A

Write an expression that represents the total amount of money, in dollars, the students raise from selling x flowerpots.

Enter your expression in the box provided. Enter only your expression

Part B

The goal of the students in the club was to raise $500. They sold 43 flowerpots. By what amount did the students exceed their goal of raising $500? Show or explain all your work.

Enter your answer and your work or explanation in the box provided.

6. EE.A.2b

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.(Conceptual Understanding)