6.AT.1 Lesson 3-1-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.1 · Part II

Supported Application · Guided Entry to Today's Problem

Understand Ratios · Ratio

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 3.1 · Part II
1Understanding Ratios
2Strategy Model — step by step
  1. A ratio compares two quantities; order of quantities matters
  2. Part-to-Part compares two distinct subgroups (e.g. boys to girls)
  3. Part-to-Whole compares one subgroup to the total (e.g. boys to class)
3Mathematical Word Bank
  • Understand Ratios (Comprender razones) — Use a ratio to compare two quantities by division.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Comparison (Comparación) — Looking at two or more amounts to see how they are related.
  • Part-to-part (Parte a parte) — A ratio comparing one part of a group to another part.
  • Part-to-whole (Parte a todo) — A ratio comparing one part to the whole group.
  • Colon notation (Notación con dos puntos) — Writing a ratio with two dots between the numbers, like 3:2.
4Watch out
  • A common mistake in Understand Ratios is writing the ratio in the wrong order: when asked for the ratio of apple juice to sparkling water in a recipe that uses 3 cups of apple juice for every 2 cups of sparkling water, some students write 2:3 (sparkling water to apple juice) because they list the ingredients in whatever order comes to mind rather than the order the question asks for. The two ratios describe different drinks — 3:2 means 3 cups of juice for every 2 cups of water, while 2:3 would mean only 2 cups of juice for every 3 cups of water. Always match the order of your ratio to the order named in the question: "apple juice to sparkling water" means the apple juice number comes first, giving 3:2.
  1. 1 MULTIPLE CHOICE

    A pet store has 5 dogs and 9 cats. What is the ratio of dogs to cats?

    1. A5:9
    2. B9:5
    3. C5:14
    4. D14:5
    ✏️ 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.1 Lesson 3-1-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.1 · Part II

On-Level Application · Standard Rigor

Understand Ratios · Ratio

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.1 · Part II
1Understanding Ratios
2The Structural Procedure
  1. A ratio compares two quantities; order of quantities matters
  2. Part-to-Part compares two distinct subgroups (e.g. boys to girls)
  3. Part-to-Whole compares one subgroup to the total (e.g. boys to class)
3Mathematical Word Bank
  • Understand Ratios (Comprender razones) — Use a ratio to compare two quantities by division.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Comparison (Comparación) — Looking at two or more amounts to see how they are related.
  • Part-to-part (Parte a parte) — A ratio comparing one part of a group to another part.
  • Part-to-whole (Parte a todo) — A ratio comparing one part to the whole group.
  • Colon notation (Notación con dos puntos) — Writing a ratio with two dots between the numbers, like 3:2.
4Watch out
  • A common mistake in Understand Ratios is writing the ratio in the wrong order: when asked for the ratio of apple juice to sparkling water in a recipe that uses 3 cups of apple juice for every 2 cups of sparkling water, some students write 2:3 (sparkling water to apple juice) because they list the ingredients in whatever order comes to mind rather than the order the question asks for. The two ratios describe different drinks — 3:2 means 3 cups of juice for every 2 cups of water, while 2:3 would mean only 2 cups of juice for every 3 cups of water. Always match the order of your ratio to the order named in the question: "apple juice to sparkling water" means the apple juice number comes first, giving 3:2.
  1. 1 MULTIPLE CHOICE

    A fruit salad has 5 pieces of melon, 3 pieces of pineapple, and 2 grapes. What is the ratio of pineapple to melon?

    1. A3:5
    2. B5:3
    3. C3:10
    4. D3:2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    A parking lot has 10 cars and 6 trucks. What is the part-to-whole ratio of trucks to total vehicles?

    1. A6:16
    2. B10:6
    3. C6:10
    4. D16:6
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Prep Bowl A: Chef Reyes stirs 7 cups of flour with 4 cups of water to make dough. What is the part-to-part ratio of flour to water?

    1. A7:4
    2. B4:7
    3. C7:11
    4. D11:4
    ✏️ 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.1 Lesson 3-1-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.1 · Part II

Extension & Non-Routine Application

Understand Ratios · Ratio

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 3.1 · Part II
1Understanding Ratios
2The Structural Procedure
  1. A ratio compares two quantities; order of quantities matters
  2. Part-to-Part compares two distinct subgroups (e.g. boys to girls)
  3. Part-to-Whole compares one subgroup to the total (e.g. boys to class)
3Mathematical Word Bank
  • Understand Ratios (Comprender razones) — Use a ratio to compare two quantities by division.
  • Ratio (Razón) — A way to compare two amounts, like 3 to 2.
  • Comparison (Comparación) — Looking at two or more amounts to see how they are related.
  • Part-to-part (Parte a parte) — A ratio comparing one part of a group to another part.
  • Part-to-whole (Parte a todo) — A ratio comparing one part to the whole group.
  • Colon notation (Notación con dos puntos) — Writing a ratio with two dots between the numbers, like 3:2.
4Watch out
  • A common mistake in Understand Ratios is writing the ratio in the wrong order: when asked for the ratio of apple juice to sparkling water in a recipe that uses 3 cups of apple juice for every 2 cups of sparkling water, some students write 2:3 (sparkling water to apple juice) because they list the ingredients in whatever order comes to mind rather than the order the question asks for. The two ratios describe different drinks — 3:2 means 3 cups of juice for every 2 cups of water, while 2:3 would mean only 2 cups of juice for every 3 cups of water. Always match the order of your ratio to the order named in the question: "apple juice to sparkling water" means the apple juice number comes first, giving 3:2.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    A class has 12 sixth graders and 18 seventh graders. What is the ratio of sixth graders to the TOTAL number of students, written in simplest form?

    1. A2 : 5
    2. B2 : 3
    3. C12 : 18
    4. D3 : 5
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    “For every” language: Chef Reyes says, “My glaze uses 9 spoons of honey for every 4 spoons of lemon.” Written in colon notation, the ratio of honey to lemon is:

    1. A9:4
    2. B4:9
    3. C9:13
    4. D13:4
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 OPEN RESPONSE

    A bag of marbles has 8 red, 6 blue, and 4 green marbles. Write three different ratios using these quantities: one part-to-part ratio, one part-to-whole ratio, and explain the difference.

    ✏️ 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