Unit 3 · Standard 6.RP.3a
Ratio Tables
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
Cups of juice: 2, 4, 6 | Cups of water: 3, 6, 9
Ratio table
A table of equal ratios that shows a pattern.
2:3 = 4:6 = 6:9
Equivalent ratio
Two ratios that mean the same thing, like 1:2 and 2:4.
2:3 × 2 → 4:6 (scale factor is 2)
Scale factor
The number you multiply both parts of a ratio by to get an equal ratio.
Each row adds 2 cups juice and 3 cups water
Pattern
A rule that numbers follow again and again.
2:3 → 4:6 → 6:9 (add 2 and 3 each time)
Additive pattern
Adding the same amount to both parts of a ratio table to make new rows.
Key Ideas & Notes
- Chef Academy is hosting a pancake breakfast for the whole school!
- Chef Reyes's famous pancake batter uses 2 cups of mix for every 3 cups of milk.
- The team needs to scale the recipe to feed 4 times as many people.
- Can you help them build a ratio table to figure out how much of each ingredient they need?
- Chef Reyes's pancake recipe uses 2 cups of mix for every 3 cups of milk. Complete the ratio table to scale the recipe for more students.
Think About It
- What two quantities are being compared in the recipe?
- What happens to both quantities when you double the recipe?
- How could a table help you organize the scaling?
My Notes
Guided Examples
Example 1
A recipe uses 3 eggs for every 5 cups of flour. How many eggs are needed for 15 cups of flour?
Solution: The scale factor is 15 ÷ 5 = 3. Multiply the eggs by 3: 3 × 3 = 9 eggs.
Answer: A. 9
Example 2
Which row does NOT belong in a ratio table for 4:5?
Solution: 6:10 simplifies to 3:5, not 4:5. The other ratios (8:10, 12:15, 16:20) all simplify to 4:5.
Answer: A. 6:10
Example 3
A ratio table shows 3:7, 6:14, and 9:21. What is the next row?
Solution: The pattern adds 3 to the first value and 7 to the second each time. After 9:21: 9+3=12 and 21+7=28. The next row is 12:28.
Answer: A. 12:28
Write About the Math The Writing Revolution
I can explain my table using the words ratio table, equivalent ratio, scale factor, and pattern.
1. Kernel Sentence subject + verb
Model: Ratio table is a table of equal ratios that shows a pattern.Tabla de razones es una tabla de razones iguales que muestra un patrón.
Write a kernel sentence about ratio table. Use a subject and a verb.Escribe una oración base sobre tabla de razones. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Ratio table matters in mathTabla de razones importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Ratio table matters in math because ___.Tabla de razones importa en matemáticas porque ___.
Ratio table matters in math, but ___.Tabla de razones importa en matemáticas, pero ___.
Ratio table matters in math, so ___.Tabla de razones importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about ratio table.Di un hecho verdadero sobre ratio table.
Ratio table ___.
Ask a question about ratio table.Haz una pregunta sobre ratio table.
How does ___ ?¿Cómo ___ ?
Show excitement about ratio table.Muestra entusiasmo sobre ratio table.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with ratio table.Dile a un compañero qué hacer con ratio table.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I multiplied both numbers by ___.Multipliqué ambos números por ___.
The ratios are equal because ___.Las razones son iguales porque ___.
A table helps when ___.Una tabla ayuda cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. A ratio table shows 5:8, 10:16, 15:24. What scale factor was used from the first row to the third row?
- 3
- 2
- 5
- 8
2. A recipe uses 4 cups of flour for every 3 cups of sugar. A student filled in a ratio table: 4:3, 8:6, 12:9, 14:12. Find and fix the error in the last row. Explain what went wrong.
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Find Devon's Mistake — find the error, then write the correct reasoning.
Reflect — Exit Ticket
A salad dressing recipe uses 2 tablespoons of oil for every 5 tablespoons of vinegar. How many tablespoons of oil are needed for 20 tablespoons of vinegar?
- 8
- 10
- 7
- 12
Answer Key & Teacher Guide
- Try It 1: A. 3 — From 5 to 15: 15 ÷ 5 = 3. From 8 to 24: 24 ÷ 8 = 3. The scale factor is 3.
- Try It 2: The last row is wrong. The pattern multiplies by the same scale factor. 4×1=4, 4×2=8, 4×3=12, so the 4th row should be 4×4=16 cups of flour and 3×4=12 cups of sugar → 16:12. The student added 2 to 12 instead of adding 4. Or: 12+4=16, not 12+2=14.
- Exit Ticket: A. 8 — Scale factor: 20 ÷ 5 = 4. Multiply oil by 4: 2 × 4 = 8 tablespoons of oil.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Ratio table is a table of equal ratios that shows a pattern.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).