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Worksheet Grade 7 Art & Music

Sedge Creek Turbidity Color Card: A Ratio Worksheet

A grade 7 art-and-math worksheet where students work with a constant paint-mixing ratio for a turbidity color card at a fictional water lab.

Objectives

  1. Students will find the constant of proportionality in a paint-mixing recipe.
  2. Students will write an equation for a proportional relationship.
  3. Students will decide whether a mixed batch keeps the correct ratio.

Vocabulary

Turbidity
Turbidity is a measure of how cloudy or murky water looks because of tiny particles floating in it. Clear water has low turbidity, and muddy water has high turbidity.

Also: ratio, constant of proportionality, proportional, tint

Teacher overview

Water labs measure how cloudy water is in units called NTU, and plants that filter river or lake water must keep treated water at or below 0.3 NTU in at least 95 percent of monthly samples. To help visitors picture cloudiness, a lab can paint a color card with swatches that go from clear to muddy. This worksheet uses the fictional Sedge Creek water lab, which mixes each shade on its card from a fixed recipe so that every batch of that shade matches. Students find the recipe's constant ratio, write it as an equation, and check whether sample batches match. The math is the same proportional reasoning that keeps any color set consistent.

Sedge Creek Turbidity Color Card: A Ratio Worksheet — Grade 7 Art & Music
Name: ____________________________ Date: ______________

Student Worksheet

Suppose the fictional Sedge Creek water lab paints a turbidity color card. The card's cloudy swatch uses one recipe: 3 drops of brown tint for each cup of white base, and every batch of it must match.

  1. The recipe is 3 drops of tint for each cup of base. How many drops go in 2 cups?
  2. How many drops go in 4 cups?
  3. A large batch uses 5 cups of base. How many drops of tint does it need?
  4. What is the constant of proportionality? Give it as drops per cup.
  5. Write an equation for the number of drops (d) from the number of cups (c).
  6. A worker mixes 18 drops into 6 cups. Does that batch match the recipe? Show why.
  7. Another worker uses 10 drops in 4 cups. Is that batch too light or too dark? Show why.
  8. A big batch of the cloudy swatch uses 24 drops. How many cups of base keep the recipe?
  9. Explain why every batch of the cloudy swatch must use the same ratio.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 6 drops.
    3 drops per cup times 2 cups equals 6 drops.
  2. Answer: 12 drops.
    3 drops per cup times 4 cups equals 12 drops.
  3. Answer: 15 drops.
    3 drops per cup times 5 cups equals 15 drops.
  4. Answer: 3 drops per cup.
    The recipe adds 3 drops for every 1 cup, so the constant of proportionality is 3.
  5. Answer: d = 3c.
    The drops equal 3 times the cups, since each cup adds 3 drops.
  6. Answer: Yes, it matches.
    18 drops divided by 6 cups equals 3 drops per cup, the same ratio as the recipe.
  7. Answer: Too light.
    10 drops divided by 4 cups equals 2.5 drops per cup, which is less than 3, so the batch is lighter than the recipe.
  8. Answer: 8 cups.
    24 drops divided by 3 drops per cup equals 8 cups of base.
  9. Answer: The ratio sets the shade, so batches at the same ratio match; a batch at a different ratio would come out lighter or darker and show the wrong cloudiness.

Differentiation

Support

Give students a ratio table with the first row filled in (1 cup, 3 drops) so they extend the pattern by adding 3 each row. Allow a calculator for items 6 through 8.

Extension

Ask students to design a lighter swatch that uses 2 drops per cup, write its equation, and compare its batches to the 3-drops-per-cup recipe at the same cup counts.

ELL supports

Pre-teach "tint," "ratio," and "proportional" with a simple picture of drops added to a cup. Provide the sentence frame "The batch is ___ because ___ drops per cup" for the explain items.