Section A Practice Problems

Problem 1

The table shows how a group of students chose between 4 ways they would most like to travel. Use the table to complete the picture graph.

way to travel number of
students
airplane 4
hot air balloon 7
sail boat 6
scooter 3

<p>Blank picture graph. Favorite Way to Travel. Horizontal axis: airplane, hot air balloon, sail boat, scooter.</p>

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Solution

Sample response:

Picture graph.

Problem 2

The bar graph shows students’ choices for favorite animals.

  1. How many students recorded their favorite animal?

  2. How many fewer students chose hamsters than dogs?

<p>Bar graph. Favorite animal. Vertical axis from 0 to 10 by 1's. Horizontal axis labeled hamster, horse, dog, cat. Height of bar: hamster, 2. horse, 5. dog, 9. cat, 6.</p>

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Solution
  1. 22 students
  2. 7 fewer students

Problem 3

The table shows the favorite summer vacation activity for a group of students.

vacation activities number of students
family time 6
playing sports 8
sleeping in 5
reading 3


Use the table to complete the bar graph.

Bar graph. Favorite vacation activities. Horizontal axis labeled family time, playing sports, sleeping in, reading. Vertical axis from 0 to 10 by 1s.

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Solution

Sample response:

Bar graph.

Problem 4

Find each sum or difference. Show your reasoning.

  1. 25+6225 + 62

  2. 37−937-9

  3. 24+4724 + 47

  4. 84−5984-59
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Solution
  1. 87. Sample response: I combined the tens and the ones.
  2. 28. Sample response: 37−7=3037 - 7 = 30, 30−2=2830 - 2 = 28
  3. 71. Sample response: 20+40=6020 + 40 = 60, 60+7+3+1=7160 + 7 + 3 + 1 = 71
  4. 25. Sample response: 84 is 7 tens and 14 ones. 70−50=2070 - 50 = 20, 14−9=514 - 9 = 5, 20+5=2520 + 5 = 25

Problem 5

How many objects are in each array? Explain or show your reasoning.

a.
Array. 3 rows of 5 dots.

b.
Array. 2 rows of 8 dots.

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Solution
  1. 15 objects. Sample response: There are 5, 10, 15.
  2. 16 objects. Sample response: There are 8 and 8 more, so that’s 16.

Problem 6

The graph shows some information about flowers in the garden.

<p>Bar graph. Flowers in the Garden. Vertical axis labeled number of flowers from 0 to 10 by ones. Horizontal axis labeled roses, tulips, sunflowers, daffodils. Height of bar: roses, 7. tulips, 5. sunflowers, 9. daffodils, 2.</p>

Flowers.

  1. Write 1 fact you know based on the data shown in the graph.
  2. Write 2 questions that can be answered by reading the graph.
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Solution

Sample responses:

  1. The graph shows the number of different flowers. There are more sunflowers than roses. There are fewer daffodils than any of the other flowers.
  2. How many more sunflowers are there than daffodils? How many roses and tulips are there together?

Problem 7

The bar graph shows the numbers of different types of flowers in the garden. Use the graph to answer the questions.

<p><span>Bar graph. Flowers in the Garden. Vertical axis labeled Number of Flowers from 0 to 10 by 1s. Horizontal axis labeled roses, tulips, sunflowers, daffodils. Height of bar: Roses, 7. Tulips, 5. Sunflowers, 9. Daffodils, 2.</span></p>

  1. How many flowers are represented on the graph?
  2. How many tulips, sunflowers, and daffodils are in the garden altogether?

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Solution
  1. 23 flowers
  2. 16 flowers

Problem 8

This picture graph shows the numbers of different types of balls in the gym. Use the graph to answer the questions.

Picture Graph. Balls in the Gym. Key: each circle represents 2 balls. baseball, 2 circles. basketball, 6 circles. football, 3 circles. volleyball, 4 circles.<br>

  1. How many basketballs are in the gym?
  2. How many more basketballs are there than footballs?
  3. Write 1 other question that can be answered by reading the graph.

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Solution
  1. 12 basketballs
  2. 6 more basketballs
  3. Sample response: How many volleyballs are in the gym?

Problem 9

The table shows the favorite sports of some students. Use the table to complete the scaled picture graph.

sport number
tennis 6
swimming 6
gymnastics 4
soccer 8

Picture Graph. Key: circle represents 2 people. Tennis, blank. Swimming, blank. Gymnastics, blank. Soccer, blank.

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Solution

Picture graph.

Problem 10

The table shows the numbers of different shapes in a pattern block puzzle. Use the table to complete the scaled bar graph.

shape number
triangle 13
trapezoid 10
square 9
hexagon 15

<p>Empty bar graph. Shapes in Puzzle. Vertical axis: number of shapes from 0 to 16 by twos. Horizontal axis: triangle, trapezoid, square, hexagon.</p>

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Solution
Bar graph.

Problem 11

The table shows the numbers of books some students have at home. 

Use the information from the table to create a scaled bar graph.

books number
Elena 25
Andre 9
Tyler 16
Clare 21

Blank bar graph. Books at Home.

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Solution

Sample response:

Bar graph.

Problem 12

The bar graph shows the numbers of different kinds of nuts in a bowl.

<p>Bar graph. Party Nuts. Vertical axis labeled number of nuts from 0 to 40 by fives. Horizontal axis labeled peanuts, walnuts, pecans, pistachios. Height of bar: peanuts, 27. walnuts, 11. pecans, 18. pistachios, 38.</p>

  1. How many more pistachios are there than walnuts? Explain or show your reasoning.
  2. How many fewer pecans are there than peanuts? Explain or show your reasoning.
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Solution

Student answers may differ by 1 or 2 because they may read the number of each type of nut slightly differently from the graph.

  1. 27 more pistachios. Sample response: 38−11=2738 - 11 = 27
  2. 9 fewer pecans. Sample response: 27−18=927 - 18 = 9

Problem 13

The bar graph shows how many students are in each class.

Bar graph. Students in Each Class. Vertical axis labeled number of students from 0 to 35 by fives. Horizontal axis labeled class 1, class 2, class 3, class 4. Height of bar: class 1, 24. class 2, 25. class 3, 22. class 4, 31.

  1. How many students are in the 4 classes altogether? Explain or show your reasoning.

  2. How many fewer students are in Class 1 than in Class 4? Explain or show your reasoning.

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Solution

Student answers may differ slightly because they may read the number of students in each class slightly differently from the graph.

  1. 102 students. Sample response: Class 1 has 24 students, class 2 has 25 students, class 3 has 22 students and class 4 has 31 students. The total number is 24+25+22+3124 + 25 + 22 + 31, which is 102 students.
  2. 7 fewer students. Sample response: 31−24=731 - 24 = 7

Problem 14

The bar graph shows data about 1,000 students who attend 4 schools.

What is the approximate scale for the bar graph? Explain or show your reasoning.

<p>Bar graph. Student Enrollments. Vertical axis labeled number of students. Horizontal axis labeled school A, school B, school C, school D. Height of bars: school A, second lowest. school B, second highest. school C, lowest. school D, highest.</p>

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Solution

Sample responses:

  • The bars for the students cover8 full units of the scale and some extra that cover about 2 more units in all. So, the 1,000 students cover about 10 units of the scale. 1,000 is 10 hundreds, so a scale of 100 works.
  • I tried a scale of 10, but then there were between 10 and 30 students at each school, so that is too small. Then I tried a scale of 50, but it still was not enough, as the biggest school had fewer than 200 students. A scale of 100 looked like it worked out about right.

Problem 15

Collect data of interest to you and represent the data on a bar graph. You may use the bar graph template if you wish.

Blank bar graph

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Solution
Answers vary.