6.AT.1 Lesson 3-1-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

3.1 Small Group · Group 2

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

Understand Ratios · Ratio · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is a ratio?
1A ratio compares two quantities, and the order you write them in matters. You can write a ratio in words or with a colon, and you can draw it with a tape diagram or a double number line — 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. Chef Reyes uses 3 cups of apple juice for every 2 cups of sparkling water.
  2. I am comparing two amounts: apple juice and sparkling water.
  3. I write apple juice to sparkling water, in that order, as 3 to 2, or 3:2.
  4. I can also draw the ratio. On a tape diagram I give apple juice 3 equal parts and sparkling water 2 equal parts, so one batch is 5 parts in all.
  5. Those same 5 parts show a second ratio: apple juice to the whole fruit drink is 3 to 5.
  6. On a double number line I line the two amounts up: 5 cups of fruit drink pairs with 3 cups of apple juice, and 10 cups of fruit drink pairs with 6 cups of apple juice.
3Second Model — Try it together — then prove it
  1. A bowl has 4 apples and 1 orange. What two amounts are we comparing?
  2. We write apples to oranges in order: 4 to 1, or 4:1.
  3. Now draw it: 4 equal parts for apples beside 1 part for oranges, 5 parts of fruit in all.
  4. So apples to total fruit is 4 to 5.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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 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
  2. 2 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
  3. 3 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Level 2 Extension — Chef Mateo's Pizza Topping Ratio

    1. 1Read the problem:A pizza has 6 olives, 2 peppers, and 4 tomato slices. Write the part-to-whole ratio of peppers to the total toppings.
    2. 2Count the whole:6 + 2 + 4 = 12 total toppings.
    3. 3Write the ratio:Chef Mateo writes peppers to total as 2:6.
    4. 4Answer:The ratio of peppers to total toppings is 2:6.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:“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:
    2. 2A classmate at our table answered:13:4

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Spot the Mistake — Part-to-Whole Ratio

    1. 1Read the problem:A class has 9 boys and 6 girls. Write the part-to-whole ratio of girls to the whole class.
    2. 2Count the whole:9 + 6 = 15 students in all.
    3. 3Write the ratio:A student writes girls to the whole class as 6:9.
    4. 4Answer:The part-to-whole ratio of girls to the whole class is 6:9.

    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