6.AT.3a Lesson 3-3-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.3 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

Ratio Tables · Ratio table · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — How do ratio tables work?
1To keep a ratio the same, multiply both numbers by the same scale factor — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
2Worked Example — Watch me
  1. The pancake recipe is 2 cups of mix for every 3 cups of milk, so the ratio is 2:3.
  2. To make 2 batches, my scale factor is 2.
  3. I multiply both numbers by 2: 2 x 2 = 4 cups of mix, and 3 x 2 = 6 cups of milk.
  4. Now my row is 4:6, which is the same ratio as 2:3.
  5. I do NOT add 2 to each number; I multiply both by the same factor.
3Second Model — Try it together — then prove it
  1. A drink uses 1 cup of juice for every 4 cups of water, so the ratio is 1:4.
  2. To double it, what scale factor do we use? We use 2.
  3. Multiply both by 2: 1 x 2 = 2 cups of juice and 4 x 2 = 8 cups of water, giving 2:8.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical Word Bank
  • 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.
5Watch out
  • 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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A recipe uses 3 eggs for every 5 cups of flour. How many eggs are needed for 15 cups of flour?

    1. A9
    2. B6
    3. C10
    4. D12
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Which row does NOT belong in a ratio table for 4:5?

    1. A6:10
    2. B8:10
    3. C12:15
    4. D16:20
    ✏️ Workspace & Solution Steps
  3. 3 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?

    1. A8
    2. B6
    3. C10
    4. D9
    per 1
  4. 4 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?

    1. A3
    2. B2
    3. C5
    4. D8
    per 1
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:A ratio table shows 5:8, 10:16, 15:24. What scale factor was used from the first row to the third row?
    2. 2A classmate at our table answered:8

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Catch Marcus's Mistake

    1. 1Read the table:A ratio table starts with 3:8. Marcus needs to find the row where the first value is 12.
    2. 2Find the change:Marcus sees the first value went from 3 to 12, a difference of 9.
    3. 3Apply the change:Marcus adds 9 to the second value: 8 + 9 = 17
    4. 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
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It