3.3 Small Group · Group 1
Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems
Ratio Tables · Ratio table · Procedural Fluency · Reasoning & Critique
- A ratio table lists equal ratios in rows. To make a new row, you multiply BOTH numbers by the same amount, called the scale factor. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
- The pancake recipe is 2 cups of mix for every 3 cups of milk, so the ratio is 2:3.
- To make 2 batches, my scale factor is 2.
- I multiply both numbers by 2: 2 x 2 = 4 cups of mix, and 3 x 2 = 6 cups of milk.
- Now my row is 4:6, which is the same ratio as 2:3.
- I do NOT add 2 to each number; I multiply both by the same factor.
- Ratio Tables (Tablas de razones) — Tables that organize pairs of equivalent ratios.
- Ratio table (Tabla de razones) — A table of equal ratios that shows a pattern.
- Equivalent ratio (Razón equivalente) — Two ratios that mean the same thing, like 1:2 and 2:4.
- Scale factor (Factor de escala) — The number you multiply both parts of a ratio by to get an equal ratio.
- Pattern (Patrón) — A rule that numbers follow again and again.
- Additive pattern (Patrón aditivo) — Building new rows of a ratio table by adding each column's own constant amount, so the two columns grow together.
- A common mistake in Ratio Tables is scaling only ONE part of the ratio, or adding the scale factor to a part instead of multiplying by it — for example, turning 2:3 into 6:3 (multiplying only the first number by 3 and forgetting the second) or into 4:5 (adding the scale factor 2 to the second number instead of multiplying, since 3+2=5 but 3×2=6). Before you submit, multiply BOTH numbers by the same scale factor and check that your new ratio simplifies back to the original.
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1 MULTIPLE CHOICE
In a ratio table, the ratio of sugar to butter is 3:2. If you use 12 cups of sugar, how many cups of butter do you need?
- A8
- B6
- C10
- D9
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
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2 MULTIPLE CHOICE
A ratio table shows 5:8, 10:16, 15:24. What scale factor was used from the first row to the third row?
- A3
- B2
- C5
- D8
per 1 - 1LabelWrite what each column is.
- 2Find per 1Divide to get one.
- 3ScaleMultiply up to what is asked.
- 4CheckDoes the size make sense?
-
3 MULTIPLE CHOICE
The food truck sells tacos at a steady rate: 2 tacos cost $5. At that rate, how much do 6 tacos cost?
- A$15
- B$11
- C$12
- D$30
✏️ Workspace & Solution Steps -
4 MULTIPLE CHOICE
A smoothie recipe at the truck uses 4 cups of mango for every 3 cups of pineapple. How many cups of mango are needed for 9 cups of pineapple?
- A12
- B10
- C13
- D9
✏️ Workspace & Solution Steps
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5 ERROR ANALYSIS
Catch Priya's Mistake
- 1Read the order:A trail mix recipe uses 2 cups of nuts for every 5 cups of raisins (2:5). Priya wants to make a bigger batch using a scale factor of 4.
- 2Pick a scale factor:Priya's scale factor is 4. A scale factor should multiply BOTH parts of the ratio.
- 3Scale the nuts:2 × 4 = 8 cups of nuts
- 4Scale the raisins:5 + 4 = 9 cups of raisins
Which step contains the error? Explain the mathematical misconception and write the correct calculation below.
✏️ Corrected Mathematical Work & Explanation -
6 ERROR ANALYSIS
Catch Marcus's Mistake
- 1Read the table:A ratio table starts with 3:8. Marcus needs to find the row where the first value is 12.
- 2Find the change:Marcus sees the first value went from 3 to 12, a difference of 9.
- 3Apply the change:Marcus adds 9 to the second value: 8 + 9 = 17
- 4Write the new row:Marcus's answer: 12:17
Which step contains the error? Explain the mathematical misconception and write the correct calculation below.
✏️ Corrected Mathematical Work & Explanation
Writing Task: Justify why your mathematical solution is accurate and complete.