6.AT.11 Lesson 9-4-group1 🟡 Group 1 · Support & Scaffolding
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

9.4 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

solution · substitute · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Use the equation to answer a real question
1Write the relationship as an equation, substitute the known value, solve for the unknown, then interpret the solution in context.
  • Writing the equation is only half the job. Applying it means substituting what you know, solving for what you don't, and checking whether the answer makes sense in the situation. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me test the car order
  1. The number of cars produced depends on the number of hours of operation. Every hour, the plant produces 2.5 cars.
  2. Let h = hours and c = cars. The equation is c = 2.5h. Check with the table: 8 hours gives 2.5 × 8 = 20 cars per shift.
  3. The order needs 1,000 cars, so substitute: 2.5h = 1,000.
  4. Divide both sides by 2.5: h = 1,000 ÷ 2.5 = 400 hours.
  5. Interpret it: 400 hours running 24 hours a day is about 17 days — about 2.5 weeks. That fits inside 3 weeks only if the plant runs 24 hours a day, 7 days a week.
3Mathematical Word Bank
  • solution (solución) — A value of the variable that makes an equation true.
  • substitute (sustituir) — To replace a variable with a number so you can compute.
  • at least (al menos) — That amount or more — the smallest amount that still works.
  • predict (predecir) — To make a reasonable guess about a future amount using information you already have.
  • justify (justificar) — To explain WHY an answer or recommendation makes sense, using the mathematics.
4Watch out
  • Adding the rate instead of multiplying — writing 2.5 + 8 = 10.5 cars for an 8-hour shift instead of 2.5 × 8 = 20. The rate applies to EVERY hour, so the total is always rate × amount.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each statement about c = 2.5h.

    Target Categories: True False
    • In 4 hours the line produces 10 cars
    • h is the independent variable
    • The unit rate is 2.5 cars per hour
    • In 2 hours the line produces 4 cars
    • c is the input of the equation
    • In 5 hours the line produces 25 cars
  2. 2 FILL TABLE

    The assembly line produces 2.5 cars per hour. Complete the production table.

    Hours (h)Substitute c = 2.5hCars produced (c)
    4
    8 (one shift)
    100
    ✏️ Scratchpad / Reasoning
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 3 MULTIPLE CHOICE

    The assembly line produces 2.5 cars per hour. How many cars does it produce in one 8-hour shift?

    1. A20 cars
    2. B10.5 cars
    3. C16 cars
    4. D25 cars
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  2. 4 MULTIPLE CHOICE

    Let h = hours of operation and c = cars produced. Which equation represents the assembly line?

    1. Ac = 2.5h
    2. Bc = 2.5 + h
    3. Ch = 2.5c
    4. Dc = h ÷ 2.5
    ✏️ Workspace & Solution Steps
  3. 5 MULTIPLE CHOICE

    Using the table (1 hour, 2.5 cars; 8 hours, 20 cars; 16 hours, 40 cars), how many cars are produced in 24 hours?

    1. A60 cars
    2. B26.5 cars
    3. C40 cars
    4. D50 cars
    ✏️ Workspace & Solution Steps
  4. 6 MULTIPLE CHOICE

    Last year the student council washed 34 cars and raised $408. How much did they charge per car?

    1. A$12
    2. B$374
    3. C$34
    4. D$10
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The ratio remains equivalent because both quantities are scaled by the exact same multiplicative factor.
BUT Two ratios may look similar, but inverting the order of terms fundamentally changes the comparison.
SO The recipe requires 3 parts flour to 2 parts water, so the unit rate is 1.5 cups of flour per cup of water.
📐 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