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

9.4 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

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.
  1. 1 MULTIPLE CHOICE

    At $12 per car, how much does the student council raise by washing 20 cars?

    1. A$240
    2. B$32
    3. C$120
    4. D$200
    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. 2 MULTIPLE CHOICE

    The price is set at $12 per car. Which is the DEPENDENT variable at the car wash?

    1. AThe total amount of money raised
    2. BThe number of cars washed
    3. CThe price of $12 per car
    4. DThe number of students on the council
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    The order requires 1,000 cars. Using 2.5h = 1,000, how many hours will the plant need?

    1. A400 hours
    2. B2,500 hours
    3. C997.5 hours
    4. D40 hours
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  4. 4 MULTIPLE CHOICE

    The plant needs 400 hours to fill the order. Running 24 hours a day, about how many days is that?

    1. AAbout 17 days
    2. B400 days
    3. C50 days
    4. D4 days
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    The goal is $500 at $12 per car. Using 12n = 500, at least how many cars must be washed?

    1. A42 cars
    2. B41 cars
    3. C40 cars
    4. D50 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?
  6. 6 MULTIPLE CHOICE

    Can the student council wash 41 cars at $12 each and meet the $500 goal?

    1. ANo — 41 cars raise $492, which is less than $500
    2. BYes — 41 cars raise $502
    3. CYes — 41 rounds up to 42, so it counts
    4. DNo — 41 cars raise $412
    ✏️ 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