# PARCC Math Practice – Calculator (Grade 6)

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## PARCC Math Practice – Calculator

1.

Which expression represents "[math]y[/math] less than one-half"?

- [math]y + 1/2[/math]
- [math]y - 1/2[/math]
- [math]1/2 + y[/math]
- [math]1/2 - y[/math]

2.

Evaluate [math]3x^2 + 5[/math] when [math]x = 4[/math]

Enter your answer below.

Enter your answer below.

3.

Let [math]x[/math] represent any number in the set [math]{3, 6, 7, 9}[/math].

Which inequality is true for all values of [math]x[/math]?

Which inequality is true for all values of [math]x[/math]?

- [math]x > 5[/math]
- [math]x < 5[/math]
- [math]x > 10[/math]
- [math]x < 10[/math]

4.

Harper is training for a triathlon. The ratio of the distance Harper bikes, in miles, to distance she runs, in miles, is a fixed number each day. The table shows the number of miles she runs on a day she bikes 48 miles.

Triathlon Training | |
---|---|

Bike | Run |

48 | 12 |

? | 18 |

32 | ? |

A.

How many miles does Harper bike on a day she runs 18 miles?

- 4.5 miles
- 32.0 miles
- 54.0 miles
- 72.0 miles

B.

How many miles does Harper run on a day she bikes 32 miles?

- 8 miles
- 24 miles
- 40 miles
- 128 miles

5.

The graph shows the location of point [math]P[/math]. Tom needs to plot point [math]R[/math] on the graph at [math](7, 5)[/math] and point [math]Q[/math] at the same x-coordinate as [math]R[/math] and 5 units below [math]R[/math].

What is the distance from point [math]P[/math] to point [math]R[/math]? What is the coordinate pair for point [math]Q[/math]? Explain how you determined the distance from point [math]P[/math] to point [math]R[/math] and the coordinate pair for point [math]Q[/math].

Enter your answers and explanations in the space provided.

What is the distance from point [math]P[/math] to point [math]R[/math]? What is the coordinate pair for point [math]Q[/math]? Explain how you determined the distance from point [math]P[/math] to point [math]R[/math] and the coordinate pair for point [math]Q[/math].

Enter your answers and explanations in the space provided.

6.

The table shows the distance a radio controlled toy car has traveled, in meters (m), after each second (s) of use.

A.

Which equation represents the relationship between position, [math]m[/math], and time, [math]s[/math] shown in the table?

- [math]m = 6s[/math]
- [math]s = 6m[/math]
- [math]m = 6 + s[/math]
- [math]s = 6 + m[/math]

B.

Based on the relationship shown in the table, how far will the car have traveled at the end of 7 seconds?

Enter your answer in the space provided. Enter ONLY your answer.

Enter your answer in the space provided. Enter ONLY your answer.

7.

Riley babysits for Marcus and she also babysits for Kelly. The table shows the number of hours Riley babysat for Marcus over a period of three months.

[math]*[/math]Riley expects the number of hours she will babysit Marcus to continue to increase in July.

[math]*[/math]Riley also expects that the ratio of the hours she babysits for Marcus to the hours she babysits for Kelly to be about [math]2:1[/math].

[math]*[/math]Riley earns an average babysitting fee of $6.00 per hour when babysitting for Marcus or Kelly.

Estimate Riley's total earnings, in dollars, for babysitting in July. Show all your work. Explain how you determined your estimate.

Enter your estimate, your work, and your explanation in the space provided.

Babysitting Marcus | |
---|---|

Month | Hours |

April | 4 |

May | 6 |

June | 9 |

[math]*[/math]Riley expects the number of hours she will babysit Marcus to continue to increase in July.

[math]*[/math]Riley also expects that the ratio of the hours she babysits for Marcus to the hours she babysits for Kelly to be about [math]2:1[/math].

[math]*[/math]Riley earns an average babysitting fee of $6.00 per hour when babysitting for Marcus or Kelly.

Estimate Riley's total earnings, in dollars, for babysitting in July. Show all your work. Explain how you determined your estimate.

Enter your estimate, your work, and your explanation in the space provided.

8.

Olivia must determine which of these four expressions are equivalent to each other.

Expression A: [math]5x + 6[/math]

Expression B: [math]3(x + 2)[/math]

Expression C: [math]3x + 3x + 6[/math]

Expression D: [math]2x + x +6[/math]

Olivia says that all four expressions are equivalent because the value of each one is 6 when [math]x = 0[/math].

Olivia’s thinking is incorrect.

Identify the error in Olivia’s thinking. Determine which of the four expressions are equivalent. Explain or show your process in determining which expressions are equivalent.

Enter your answer and your explanation or process in the space provided.

Expression A: [math]5x + 6[/math]

Expression B: [math]3(x + 2)[/math]

Expression C: [math]3x + 3x + 6[/math]

Expression D: [math]2x + x +6[/math]

Olivia says that all four expressions are equivalent because the value of each one is 6 when [math]x = 0[/math].

Olivia’s thinking is incorrect.

Identify the error in Olivia’s thinking. Determine which of the four expressions are equivalent. Explain or show your process in determining which expressions are equivalent.

Enter your answer and your explanation or process in the space provided.

9.

The diagram shows a number line with a plotted point.

A.

Gale has a string that is [math]6/8[/math] yard long. He wants to cut the string into pieces that are each [math]1/4[/math] yard long.

How many pieces can Gale cut from the string? Explain how Gale can use the number line diagram to determine the number of pieces he can cut from the string.

Enter your answer and explanation in the space provided.

How many pieces can Gale cut from the string? Explain how Gale can use the number line diagram to determine the number of pieces he can cut from the string.

Enter your answer and explanation in the space provided.

B.

Write an equation using division that shows how Gale can find the number of pieces he can cut from the string.

Enter your equation in the space provided.

Enter your equation in the space provided.

10.

Jason calculated the volume of the rectangular prism shown, in cubic units. Jason's work is shown.

I counted that the prism is 3 cubes wide and 4 cubes long. The base layer can hold 12 cubes since 3 x 4 = 12. The prism is 3 layers high, so I added 12 + 12 + 12 to get a total of 36 cubic units for a volume.

I counted that the prism is 3 cubes wide and 4 cubes long. The base layer can hold 12 cubes since 3 x 4 = 12. The prism is 3 layers high, so I added 12 + 12 + 12 to get a total of 36 cubic units for a volume.

A.

Explain why Jason's reasoning is incorrect. Provide the correct volume, in cubic units, of the prism.

Enter your explanation and the correct volume in the space provided.

Enter your explanation and the correct volume in the space provided.

B.

A second prism has a base of 20 cubic units and has a volume of 160 cubic units.

What is the height, in unit cubes, of the second prism? Explain or show how you determined the height.

Enter the height and your explanation or work in the space provided.

What is the height, in unit cubes, of the second prism? Explain or show how you determined the height.

Enter the height and your explanation or work in the space provided.

11.

Use the information in the problems to answer Part A and Part B.

A.

Part A

Takara is working on a science experiment. She has three different liquids. The table shows the volume, in milliliters (mL), of each liquid.

Takara makes a mixture by pouring each of the three liquids into one large container. How many liters of the mixture is in the large container? Show your work or explain your answer.

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

Takara is working on a science experiment. She has three different liquids. The table shows the volume, in milliliters (mL), of each liquid.

Liquid Volume | |
---|---|

Liquid | Volume (mL) |

A | 580 |

B | 775 |

C | 845 |

Takara makes a mixture by pouring each of the three liquids into one large container. How many liters of the mixture is in the large container? Show your work or explain your answer.

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

B.

Part B

Takara must now pour equal volumes of the mixture into smaller containers. The maximum volume of each of the small containers is 250 milliliters. What is the fewest number of small containers Takara needs to hold all of the mixture? Show your work or explain your answer.

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

Takara must now pour equal volumes of the mixture into smaller containers. The maximum volume of each of the small containers is 250 milliliters. What is the fewest number of small containers Takara needs to hold all of the mixture? Show your work or explain your answer.

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

12.

A florist is creating two flower bouquets that each have exactly 24 flowers. One bouquet will include lilies and carnations. The other bouquet will include roses and carnations.

[math]*[/math]The first bouquet will have 2 lilies for every 6 flowers.

[math]*[/math]The second bouquet will have 4 roses for every 8 flowers.

What is the total number of lilies and roses the florist will need? What will be the ratio of lilies to roses? Show or explain the steps you used to solve this problem.

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

[math]*[/math]The first bouquet will have 2 lilies for every 6 flowers.

[math]*[/math]The second bouquet will have 4 roses for every 8 flowers.

What is the total number of lilies and roses the florist will need? What will be the ratio of lilies to roses? Show or explain the steps you used to solve this problem.

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

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