Comparing and Scaling concentrate

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					                                      Grade 7 Lesson
                                 Comparing and Scaling
                              Investigation 3.1 Mixing Juice
                Explore Learning - Part: Part and Part: Whole Ratios Gizmo

Lesson Objectives:
To recognize situations in which a part is compared to another part, or a part is compared
to the whole.
To form, label, and interpret ratios from given numbers or implied in a situation.

State Standards:
Use ratios and proportions in the solution of problems involving unit rates, scale
drawings, and reading of maps..

CMP Comparing and Scaling student edition
CMP Comparing and Scaling teacher edition
Computer with internet access
Infocus projector

Major Mathematical Ideas:
Use ratios to compare part-to-part or part-to-whole
Ratios of part-to-whole may also be written as percents
Ratios of part-to-part must be change to part-to-whole before changing to percent

Key Questions
What is a ratio?
What is a percent?
What is a decimal?
How are the three related?
Does the order in which a ratio is written matter?
How are ratios similar to fractions?
Can a ratio be scaled up/down? How?
What is the difference between a part-to-part ratio and a part-to-whole ratio?
Does a percent compare a part to a part or a part to a whole?

As directed in CMP Comparing and Scaling on page 36a.

As directed in CMP Comparing and Scaling on pages 36a-b.

Call on students to share their ideas about part A and B. Ask how they determined
which mix was the most orangey. Did they use ratios or percents or decimals, or a
combination? When they used the ratios, were they comparing part-to-part or part-to-
whole? How do you determine the whole? Once you determined the ratio of concentrate
to the whole mix, how did you compare them? (find common denominators, change to

Stress to students the importance of thinking about how they form ratios. Ask what is the
ratio of concentrate to water in Mix A? (2:3) What is the ratio of concentrate to the entire
Mix A? (2:5) Ask the same questions for Mix B, C, and D.

Pass out copies of 10 x 10 grids to students. Tell students to shade in first two columns
of 10 x 10 grid. Ask them to write a ratio representing what part of the entire grid is
shaded. Write this ratio as a percent, and as a decimal. They should also write a ratio
comparing unshaded to the entire grid. Then write that ratio as a percent and decimal.

Teacher: Go to
      -Select Browse Gizmos
      -Select Number and Operations 6-8
      -Select Part:Part and Part:Whole Ratios
Next: Click and drag on grid to shade in two columns. Make sure you have checked off
the box that says Show part: whole ratios.
Ask the students if their grid looks like this. Do they have the correct fraction and

Now ask students to use the same shaded grid, but write a ratio that compares shaded part
to unshaded part. Write that as a ratio, decimal, and percent. Write ratio, decimal, and
percent comparing unshaded to shaded.

Teacher: On same screen, check off Show part: part ratios.

Ask the students if their work matches that shown on the screen.

Now have the students shade in 75 squares on another grid. Have them write ratios,
percents and decimals comparing shaded part to entire grid and unshaded part to whole

Teacher: Shade in 75 squares on grid, again making sure Show part : whole ratios is
checked off.
Ask students if their grid, ratio, decimal, matches the one on the screen,

Now have students use the same grid to compare shaded to unshaded, and unshaded to
shaded. Write these ratios as decimals and percents.

Teacher: On same screen, check off Show part: part ratios.
Ask students if their work matches the data on the screen.

Review with students the importance of reading carefully the order of the words when
asked to write a ratio. Ask someone to explain the difference between part-to-part and
part-to-whole ratios.

Distribute worksheets.
Name_______________________________________________ Date_______________

For each grid or pitcher fill in required ratio or percent or decimal.



                             5 cups concentrate              What percent of this mix is
                             7 cups water                          concentrate?


                           3 cups water                        What part of the mix is
                           5 cups concentrate                       concentrate?


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