Complete Chapter 7 answer key

Lesson 1: Picture Graphs and Bar Graphs

Entry

1. 6 — 2 equal groups with 3 in each group make 2 × 3 = 6. This is prerequisite equal-group reasoning.
2. 18 — 3 equal groups with 6 in each group make 3 × 6 = 18. This is prerequisite equal-group reasoning.

Worked checks

1. 14 — The Trains row has 7 symbols and each means 2 vehicles, giving 7×2=14.

2. 15 — The Science row has 3 symbols and each means 5 books, giving 3×5=15.

3. 5 — The Science row has 5 symbols and each means 1 books, giving 5×1=5.

Guided

1. 7 — The two rows contain 3+4 symbols. Multiply by the key 1: 7 items.

2. 22 — The two rows contain 4+7 symbols. Multiply by the key 2: 22 items.

3. 75 — The two rows contain 5+10 symbols. Multiply by the key 5: 75 items.

4. 12 — The two rows contain 6+6 symbols. Multiply by the key 1: 12 votes.

Independent

1. 25 — Drama has 10 symbols, or 50 votes; Art has 5 symbols, or 25 votes. Difference 25.

2. 4 — Art has 6 symbols, or 6 votes; Music has 2 symbols, or 2 votes. Difference 4.

3. 10 — Drama has 9 symbols, or 18 votes; Music has 4 symbols, or 8 votes. Difference 10.

4. 15 — Art has 8 symbols, or 40 votes; Drama has 5 symbols, or 25 votes. Difference 15.

5. 5 — Music has 8 symbols, or 8 votes; Art has 3 symbols, or 3 votes. Difference 5.

6. 0 — Apples has 4 symbols, or 8 fruits; Pears has 4 symbols, or 8 fruits. Difference 0.

7. 15 — Peaches has 8 symbols, or 40 fruits; Apples has 5 symbols, or 25 fruits. Difference 15.

8. 4 — Pears has 8 symbols, or 8 fruits; Peaches has 4 symbols, or 4 fruits. Difference 4.

Challenge

1. 35 books — Each star represents 5 books; multiply 7×5=35. Read the key before counting.
2. 30 votes — Six symbols represent six equal groups of five; 6×5=30, not six.

Exit

1. 14 — There are 14 symbols across all categories. The key makes each symbol worth 1, so 14×1=14 fruits.

2. 2 — Pears has 5 symbols, or 10 fruits; Apples has 4 symbols, or 8 fruits. Difference 2.

3. 15 — Trains has 8 symbols, or 40 vehicles; Buses has 5 symbols, or 25 vehicles. Difference 15.

Lesson 2: Bar Graphs and Tables

Entry

1. 85 — There are 17 symbols across all categories. The key makes each symbol worth 5, so 17×5=85 fruits.

2. 16 — There are 16 symbols across all categories. The key makes each symbol worth 1, so 16×1=16 fruits.

Worked checks

1. 10 — Greatest value 14; least value 4; their difference is 10 fruits.

2. 30 — Greatest value 50; least value 20; their difference is 30 fruits.

3. 1 — Greatest value 7; least value 6; their difference is 1 vehicles.

Guided

1. 25 — The bars represent 50 and 25 vehicles. Their difference is 25.

2. 0 — The bars represent 6 and 6 vehicles. Their difference is 0.

3. 18 — Its current count is 14; adding 4 makes 18 vehicles. The axis scale represents quantities, not number of bars.

4. 50 — Its current count is 40; adding 10 makes 50 vehicles. The axis scale represents quantities, not number of bars.

Independent

1. 16 — The Science bar reaches 16 on the numeric scale, meaning 16 books.

2. 15 — The Science bar reaches 15 on the numeric scale, meaning 15 books.

3. 5 — The Science bar reaches 5 on the numeric scale, meaning 5 books.

4. 14 — The Science bar reaches 14 on the numeric scale, meaning 14 books.

5. 15 — The bars represent 40 and 25 books. Their difference is 15.

6. 2 — The bars represent 6 and 4 books. Their difference is 2.

7. 0 — The bars represent 14 and 14 items. Their difference is 0.

8. 10 — The bars represent 50 and 40 items. Their difference is 10.

Challenge

1. 15 books — The height difference is 3 grid spaces, and 3×5=15 books.
2. 5 — 28−23=5. A truncated axis makes the bars’ visible heights 3 and 8, exaggerating their relative-looking difference.

Exit

1. 15 — Greatest value 35; least value 20; their difference is 15 items.

2. 4 — Greatest value 10; least value 6; their difference is 4 items.

3. 2 — Greatest value 16; least value 14; their difference is 2 items.

Practice

Solutions

1. 10 — Music has 7 symbols, or 35 votes; Art has 5 symbols, or 25 votes. Difference 10.

2. 6 — Drama has 8 symbols, or 8 votes; Music has 2 symbols, or 2 votes. Difference 6.

3. 6 — Art has 7 symbols, or 14 votes; Music has 4 symbols, or 8 votes. Difference 6.

4. 10 — Art has 8 symbols, or 40 votes; Music has 6 symbols, or 30 votes. Difference 10.

5. 7 — Drama has 10 symbols, or 10 votes; Art has 3 symbols, or 3 votes. Difference 7.

6. 4 — Peaches has 6 symbols, or 12 fruits; Apples has 4 symbols, or 8 fruits. Difference 4.

7. 6 — The bars represent 14 and 8 books. Their difference is 6.

8. 5 — The bars represent 40 and 35 books. Their difference is 5.

9. 7 — The bars represent 10 and 3 books. Their difference is 7.

10. 4 — The bars represent 12 and 8 books. Their difference is 4.

11. 25 — The bars represent 50 and 25 books. Their difference is 25.

12. 0 — The bars represent 6 and 6 books. Their difference is 0.

Chapter Review

Solutions

1. 2 — The Science bar reaches 2 on the numeric scale, meaning 2 books.

2. All three bars double in height — The represented quantities become 18,24,30; on the same scale, every bar is twice as tall.
3. 30 — The Science row has 6 symbols and each means 5 books, giving 6×5=30.

4. 30 — The Science bar reaches 30 on the numeric scale, meaning 30 books.

5. 6 points — The star difference is 2; 2×3=6 points.
6. 6 — The Science row has 3 symbols and each means 2 books, giving 3×2=6.

7. 25 — The Cans row has 5 symbols and each means 5 items, giving 5×5=25.

8. 1 symbol = 3 — All data are multiples of 3, giving 2,4,6 whole symbols; a 7-unit key requires difficult fractional marks.
9. 8 — The Trains bar reaches 8 on the numeric scale, meaning 8 vehicles.

10. 8 — The Science row has 4 symbols and each means 2 books, giving 4×2=8.

11. 36 — 8+12+16=36. Use labeled data values, not the number of categories.
12. 2 — The Trains bar reaches 2 on the numeric scale, meaning 2 vehicles.

13. 6 — The Cans row has 3 symbols and each means 2 items, giving 3×2=6.

14. 2 books per interval; 0, 2, …, 26 — A consistent two-book interval exactly represents all three counts. Other consistent readable intervals are possible.
15. 10 — The Trains bar reaches 10 on the numeric scale, meaning 10 vehicles.

16. 5 — Blue=15, green=10, difference=5.
17. It uses a consistent scale — Equal spaces must mean equal changes; otherwise the bar heights distort quantities.
18. 35 — The Trains bar reaches 35 on the numeric scale, meaning 35 vehicles.

19. 8 — The Science row has 8 symbols and each means 1 books, giving 8×1=8.

20. Inconsistent graph heights — On a shared linear scale, 40 must be twice 20, not one quarter as tall.
21. 8 — The Science bar reaches 8 on the numeric scale, meaning 8 books.

22. 7 — The Science row has 7 symbols and each means 1 books, giving 7×1=7.

23. 25 — The Science row has 5 symbols and each means 5 books, giving 5×5=25.

24. 35 — The Science bar reaches 35 on the numeric scale, meaning 35 books.

Practice Exam

Solutions

1. The scale is truncated — Cutting off the lower portion changes the visible bar-height ratio without changing the data.
2. The scale changes — Each mark represents five objects in the first graph. Count symbols and multiply by the key.
3. 8 — 32−24=8. The heights must be read using equal axis units.

4. 18 symbols — 36 cans total; at 2 cans per symbol, 36÷2=18 symbols.

   Original data table (cans)

   Category	Cans
   Paper	16
   Cans	12
   Glass	8

5. 30 — Three intervals of 10 give 30.
6. 4 — If one half stands for 2, two halves (one whole symbol) represent 4.
7. Tuesday, 18 — Draw equal-width bars starting at zero with heights 12,18,16; Tuesday is largest.

   Original data table (buses)

   Category	Buses
   Monday	12
   Tuesday	18
   Wednesday	16

8. 5 units — A vertical scale 0,5,10,15,20,25 reaches all data accurately and is easy to interpret.

9. 40 — 14+17+9=40. Use labels and units in the table.

   Original data table (votes)

   Category	Votes
   Tag	14
   Soccer	17
   Chess	9

10. 15 — Cans has 7 symbols, or 35 items; Glass has 4 symbols, or 20 items. Difference 15.

11. Tuesday, 9 mm — Tuesday has 9 mm while Wednesday has 3 mm; 9 is three times 3.

12. 15 — Greatest value 40; least value 25; their difference is 15 books.

13. 5 — Greatest value 45; least value 40; their difference is 5 items.

14. 6 — Greatest value 10; least value 4; their difference is 6 items.

15. 12 — Glass has 10 symbols, or 20 items; Cans has 4 symbols, or 8 items. Difference 12.

16. 2 — Greatest value 14; least value 12; their difference is 2 items.

17. 5 — Glass has 7 symbols, or 7 items; Cans has 2 symbols, or 2 items. Difference 5.

18. 45 — 10+15+20=45. Read the table/graph values before adding.

    Original data table (books)

    Category	Books
    Mon	10
    Tue	15
    Wed	20

19. Inconsistent scale — With the same positive equal scale, the larger quantity must have a longer bar.
20. 10 — Art has 8 symbols, or 40 votes; Drama has 6 symbols, or 30 votes. Difference 10.