ISTEP Grade 6 Sample Open Response Test Answers

1. 

ISTEP Grade 6 Sample Open Response Test Answers 

The highest mountain in the world is Mount Everest, which has a peak of 29,028 

ft above sea level. The deepest point in the Atlantic Ocean is 30,246 ft below sea 

level. What is the difference in elevation between the peak of Mount Everest and 

the deepest point in the Atlantic Ocean? 

Show your work. 

Mount Everest = 29,028 ft 

deepest point in the Atlantic Ocean = –30,246 ft 

29,028 – (–30,246) = 29,028 + 30,246 = 59,274 ft 

Answer 59,274 ft 

Course 1, Lesson 9-1 

Copyright © by Holt, Rinehart and Winston. All rights reserved.

2. 


Write each number in the list below in decimal form and then order the decimals 

from least to greatest. Explain how you write fractions as decimals 

Decimal Form 

1 

2 

= 0.5 

–2 = –2.0 

1 

7 4 = 7.25 

0.6 = 0.6 

1 

− 2 = −2.2 

5 

7.4 = 7.4 

1 

, −2, 

2 1 

7 4 , 0.6, 

1 

− 2 , 7.4 

5 

To write a fraction as a decimal, divide the numerator by the denominator. 

Course 1, Lessons 3-1, 4-4, and 9-2 

Ordered from least to greatest 

– ____ 2.2 , – ____ 2.0 , ____ 0.5 , ____ 0.6 , ____ 7.25 , ____ 

7.4 


3. 


A country-music band takes about 5 hours to rehearse 2 new songs. If they are 

going to play 9 new songs in their show, how many hours should they plan to 

rehearse? Write a proportion to solve the problem. 


5 hours h hours 

= 

2 songs 9 songs 

5• 9 = h •2 

45 = 2h 

45 2h 

= 

2 2 

22.5 = h 

Answer h = 22.5 hours 



4. 


Paul wants to buy a book about the history of the Super Bowl. The regular price 

of the book is $27.90, but it is on sale for 30% off the regular price. What is the 

sale price of the book? 


To write a percent as a decimal, move the decimal point 2 places to the left 

OR divide the percent by 100. 

Possible methods for solving: 

$27.90 × 30 % = $27.90 × 0.30 = $8.37 

$27.90 – $8.37 = $19.53 

OR 

$27.90 × 70 % = $27.90 × 0.70 = $19.53 

Answer $19.53 

Use the lines below to explain how to convert from a percent to a decimal. 



5. 


A toy manufacturer is building a child’s playhouse based on the model shown 

below. The size of the playhouse is going to be 4 times the size of the model. 

Use the dimensions of the model to determine the dimensions (in feet and in 

inches) of the playhouse. 


Length 

length = 4 × 12.25 = 49 

in. 

length = 49 in. 

Width 

width = 4 × 14 = 56 in. 

width = 56 in. 

Now write the dimensions of the playhouse in feet and inches. 

Copyright © by Holt, Rinehart and Winston. All rights reserved. 

Height 

height = 4 × 18.5 = 74 in. 

height = 74 in. 

length = 4 ft 1 in. width = 4 ft 8 in. height = 6 ft 2 in. 


Height = 

1 

18 2 in. 

Length = 

1 

12 in. 

4 

Width = 14 in.

6. 


Sara spent $28 at the county fair. If the cost of admission was $6 and each ride 

cost $2, how many rides did Sara ride? Define a variable. Then write an equation 

and solve it. 


Variable: Let r = the number of rides Sara rode. 

Equation: 6 + 2r = 28 

Answer 11 rides 


6 + 2r = 28 

– 6 – 6 

2r = 22 

2 2 

r = 11 


7. 


Use the order of operations to evaluate the expression 

3 · 4 + (5 2 + 4 · 2) – 9. Explain your method. 


3 · 4 + (5 2 + 4 · 2) – 9 

= 3• 4 + (25+ 8) −9 

= 3• 4 + (33) −9 

= 12 + 33 −9 

= 36 

Perform the operations inside the parentheses first; square 5 and multiply 4 and 2, 

and then add 25 and 8. Perform all multiplication from left to right, and then add and 

subtract from left to right. 

Answer 36 



8. 


Complete the table of values for the equation below. Then, using the ordered 

pairs, graph the line on the grid provided. 

SOLUTION 

x y 

–1 

0 

1 

2 

x y 

–1 −4 

0 −2 

1 0 

2 2 

2x – y = 2 

Course 1, Lessons 12-1 and 12-2 

−5 −4 −3 −2 −1 1 2 3 4 5 

−1 

−2 

−3 

−4 

−5 


y 

5 

4 

3 

2 

1 

y 

5 

4 

3 

2 

1 

−5 −4 −3 −2 −1 1 2 3 4 5 

−1 

−2 

−3 

−4 

−5 

x 

x

9. 


Use the information provided and the diagram below to find the measure of 

∠ TQS . Explain how you arrived at your answer. 

Given: PR 

is a straight line. 

SOLUTION 

Answer 38° 

Explain how you arrived at your answer. 

Since PR 

is a straight line, it measures 180°. 

∠ PQT = 90° since it is marked as a right angle. 

90° + 52° = 142° 

180° – 142° = 38° 

or 

Since ∠ PQT = 90°, ∠ TQR = 90°. 90° – 52° = 38° 


P 


Q 

T 

52º 

S 

R

10. 


Use the diagram below to find the measure of the unknown angle and then 

determine whether triangle ABC is an equilateral triangle, an isosceles triangle, 

or a scalene triangle. Explain how you arrived at your answer. 

SOLUTION 

Answer x = 52° 

A 

The triangle is a scalene triangle. 


In any triangle, the sum of the measures of the angles is 180°. The sum of the 

measures of the two given angles is 128°. 180° – 128° = 52°, so the measure of 

the third angle is 52°. Since none of the angles have equal measures, none of 

the sides have equal lengths. This means the triangle is a scalene triangle. 


48° 


C 

80° 

x° 

B

11. 


What is the degree measure of an angle that has twice the measure of its 

supplement? Write an equation and use it to find the measure of the angle. 


2x = angle, x = supplement 

2x + x = 180° 

3x = 180° 

x = 60° 

Since the angle = 2x, the answer is 2(60°) = 120°. 

Answer 120 ° 



12. 


Sarah’s mother is flying from Richmond, Virginia, to San Francisco, California. 

Her flight will stop in Houston, Texas, for 50 minutes. The flight from Richmond to 

Houston takes 1 hour 45 minutes, and the flight from Houston to San Francisco 

takes 2 hours. What is the total length of the trip, including the 50-minute stop? 


Let x = the total length of the trip. 

Add the minutes first: 

50 min + 1 h 45 min + 2 h = x 

95 min + 3 h = x 

4 h 35 min = x 

Answer 4 hours 35 minutes 



13. 


John has three 2-gallon containers of gasoline. Two of the containers are full, 

and the third is half full. How many quarts of gasoline does John have? 


2 full containers: 2 containers × 2 gallons 4 gallons 

1 half full container: 1 container × 1 gallons + 1 gallon 

5 gallons 

1 gallon = 4 quarts 

5 gallons × 

Answer 20 qt 


4 quarts 

20 quarts 

1 gallon = 


14. 


Find the area of the figure below, given that MN is the diameter of the semicircle. 

Use 3.14 as an approximation for π. Explain how you arrived at your answer. 



M N 

12 cm 

Sample explanation: Since the figure is a semicircle, you divide the equation 

for the area of a circle by 2 (or multiply it by 1 

2 ). 

A = π(r 2 ) ÷ 2 (since the figure is half a circle) 

A = π (6 2 ) ÷ 2 

A = 56.52 cm 2 

Answer 56.52 cm 2 


15. 


The Davis family’s monthly expenses are summarized in the circle graph. What 

percent of their expenses does the Davis family spend on food and housing? 



Davis Family Monthly Budget 

You are looking for the total of the two percents, so you add. 

32% + 16% = 48% 

Answer 48 % 

Course 1, Lesson 8-7 and Lab 8B 


16. 


The stem-and-leaf plot below shows a set of test scores for Ms. Garrett’s class. 

Find the mean score. Round your answer to the nearest whole number. Explain 

how you arrived at your answer. 


Answer 84 

Stem Leaves 


9 

8 

7 

6 

0 2 3 6 6 8 

1 2 4 6 6 7 9 9 

0 5 9 9 

5 8 

To find the mean, add the values and divide by the number of values. 

98 + 96 + 96 + 93 + 92 + 90 + 89 + 89 + 87 + 86 +86 +84 + 82 + 81 + 79 + 79 

1, 685 

+ 75 + 70 + 68 + 65 = = 84.25 ≈ 84 

20 


KEY 

7 9 = 79

17. 


Jerry rolls a number cube. What is the probability that he will get a 5? Use this 

probability to predict the number of times Jerry will get a 5 if he rolls the number 

cube 300 times. 


number of ways event can occur 1 

probability ≈ = 

total number of possible outcomes 6 

300 × 1 ⎛ ⎞ 

⎜ 

6 

⎟ = 50 

⎝ ⎠ 

Probability 1 

6 

Prediction 50 times

ISTEP Grade 6 Sample Open Response Test Answers

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