Day 033Tape Diagrams and Totals

Standards 6.RP.A.3a

LEARNING TARGET

I can use equal-size tape sections to solve a ratio problem.

01 · LEARN

Build the idea

For a ratio a:b, draw a sections for one quantity and b sections for the other. A total covers a+b sections. Divide the total by a+b to find one section, then multiply by each part count.

WORKED EXAMPLE 1

The ratio of oak trees to pine trees is 4:3. There are 35 trees altogether. Draw a tape diagram and find each count.

20 oaks and 15 pines

7 equal sections total; each section is 35 ÷ 7 = 5.

WORKED EXAMPLE 2

The ratio of oak trees to pine trees is 3:2. There are 15 trees altogether. Draw a tape diagram and find each count and the difference between the counts.

9 oaks and 6 pines; difference 3

5 equal sections total; each section is 15 ÷ 5 = 3.

02 · PRACTICE

Your turn

Work in order. Start with the foundations, then build toward explanation and application.

The ratio of oak trees to pine trees is 8:7. There are 60 trees altogether. Draw a tape diagram and find each count.
The ratio of oak trees to pine trees is 2:2. There are 8 trees altogether. Draw a tape diagram and find each count.
The ratio of oak trees to pine trees is 2:3. There are 15 trees altogether. Draw a tape diagram and find each count.
The ratio of oak trees to pine trees is 6:2. There are 32 trees altogether. Draw a tape diagram and find each count.
The ratio of oak trees to pine trees is 7:7. There are 28 trees altogether. Draw a tape diagram and find each count.
The ratio of oak trees to pine trees is 6:5. There are 66 trees altogether. Draw a tape diagram and find each count.
The ratio of oak trees to pine trees is 3:3. There are 12 trees altogether. Draw a tape diagram and find each count and the difference between the counts.
The ratio of oak trees to pine trees is 4:4. There are 32 trees altogether. Draw a tape diagram and find each count and the difference between the counts.
The ratio of oak trees to pine trees is 4:2. There are 18 trees altogether. Draw a tape diagram and find each count and the difference between the counts.
The ratio of oak trees to pine trees is 4:5. There are 27 trees altogether. Draw a tape diagram and find each count and the difference between the counts.

03 · CHECK

Answers and reasoning

Reveal the teacher answer key

32 oaks and 28 pines
15 equal sections total; each section is 60 ÷ 15 = 4.
4 oaks and 4 pines
4 equal sections total; each section is 8 ÷ 4 = 2.
6 oaks and 9 pines
5 equal sections total; each section is 15 ÷ 5 = 3.
24 oaks and 8 pines
8 equal sections total; each section is 32 ÷ 8 = 4.
14 oaks and 14 pines
14 equal sections total; each section is 28 ÷ 14 = 2.
36 oaks and 30 pines
11 equal sections total; each section is 66 ÷ 11 = 6.
6 oaks and 6 pines; difference 0
6 equal sections total; each section is 12 ÷ 6 = 2.
16 oaks and 16 pines; difference 0
8 equal sections total; each section is 32 ÷ 8 = 4.
12 oaks and 6 pines; difference 6
6 equal sections total; each section is 18 ÷ 6 = 3.
12 oaks and 15 pines; difference 3
9 equal sections total; each section is 27 ÷ 9 = 3.

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