6.AT.3a Lesson 3-3-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.3 · Part II

Supported Application · Guided Entry to Today's Problem

Ratio Tables · Ratio table

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 3.3 · Part II
1Equivalent Ratios & Ratio Tables
2Strategy Model — step by step
  1. Multiply or divide both terms in a ratio by the same non-zero scale factor
  2. In a ratio table, rows and columns maintain the same proportional unit rate
  3. Use additive or multiplicative patterns to find missing values in the table
3Mathematical 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.
4Watch 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.
  1. 1 MULTIPLE CHOICE

    A ratio table for 2:5 starts with 2:5, 4:10. What is the third row?

    1. A6:15
    2. B6:12
    3. C8:15
    4. D5:10
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 3.1) A recipe uses 4 cups of milk and 1 cup of cream. What is the ratio of milk to cream?

    1. A4:1
    2. B1:4
    3. C4:5
    4. D5:1
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    (Lesson 3.1) Chef Reyes uses 6 strawberries and 2 bananas in a smoothie. What is the part-to-whole ratio of bananas to total fruit?

    1. A2:8
    2. B6:2
    3. C2:6
    4. D8:2
    ✏️ Workspace & Solution Steps
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It
6.AT.3a Lesson 3-3-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.3 · Part II

On-Level Application · Standard Rigor

Ratio Tables · Ratio table

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.3 · Part II
1Equivalent Ratios & Ratio Tables
2The Structural Procedure
  1. Multiply or divide both terms in a ratio by the same non-zero scale factor
  2. In a ratio table, rows and columns maintain the same proportional unit rate
  3. Use additive or multiplicative patterns to find missing values in the table
3Mathematical 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.
4Watch 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.
  1. 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?

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

    1. A3
    2. B2
    3. C5
    4. D8
    per 1
  3. 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?

    1. A$15
    2. B$11
    3. C$12
    4. D$30
    ✏️ Workspace & Solution Steps
📐 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
6.AT.3a Lesson 3-3-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.3 · Part II

Extension & Non-Routine Application

Ratio Tables · Ratio table

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.3 · Part II
1Equivalent Ratios & Ratio Tables
2The Structural Procedure
  1. Multiply or divide both terms in a ratio by the same non-zero scale factor
  2. In a ratio table, rows and columns maintain the same proportional unit rate
  3. Use additive or multiplicative patterns to find missing values in the table
3Mathematical 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.
4Watch 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 ratio table pairs 3 cups of flour with 2 cups of water. If the recipe is scaled to use 12 cups of flour, how much water is needed?

    1. A8 cups
    2. B6 cups
    3. C11 cups
    4. D24 cups
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 2 OPEN RESPONSE

    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.

    ✏️ Mathematical Justification & Response
📐 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