Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.49.4–9.4 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 9.4–9.4 by using each lesson's big idea in mixed practice.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
solutionSpanish: solución A value of the variable that makes an equation true. the number you solve for
substituteSpanish: sustituir To replace a variable with a number so you can compute. put 8 in for x
at leastSpanish: al menos That amount or more — the smallest amount that still works. “At least $500” means $500 counts, and so does anything more.
predictSpanish: predecir To make a reasonable guess about a future amount using information you already have. We measured up to 5 minutes → 6,000 feet. Reach PAST what was measured: 6 minutes should be about 7,200.
justifySpanish: justificar To explain WHY an answer or recommendation makes sense, using the mathematics. “35 cars at $14.30 raises $500.50, which clears the $500 goal.”
equationSpanish: ecuación A math sentence with an equals sign. c = 4n

How it worksWorked examplesubstituting to find the output

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A press makes 22 posters each hour. Write an equation, then find the posters made in 15 hours.

  1. Define: h = hours running, p = posters made. Posters depend on hours.
  2. The rate is 22 posters for each hour, so the rule is p = 22h.
  3. Substitute 15 for h: 22 × 15 → 330 posters.
  4. Check the context: many more hours gave a much larger count, so this fits.

Answer: p = 22h, so a 15-hour run makes 330 posters.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A juicer fills 13 bottles each minute. Write an equation, then find the bottles filled in 40 minutes.

  1. Define: m = , b = .
  2. The rate is bottles for each minute, so the rule is b = m.
  3. Substitute 40 for m: × 40 → bottles.
  4. Check the context: does your answer fit that many minutes?
Answer:equation; bottles in 40 minutes

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • I let stand for and stand for .
  • My equation is , so I substitute for .
  • The solution is , which means in this situation.
  • This answer is reasonable because .

Word bank equationsubstitutesolutionratevariablemultiplypertotalreasonablecheckinputoutput

Watch outA common mistake

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.

Grade 6 Mathematics · Unit 9: Relationships Between Two VariablesStandard 6.AT.11

Lesson 9.49.4–9.4 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can show I am caught up on Lessons 9.4–9.4 by using each lesson's big idea in mixed practice.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 9.4) The assembly line produces 2.5 cars per hour. How many cars does it produce in one 8-hour shift?

    1. A10.5 cars
    2. B16 cars
    3. C20 cars
    4. D25 cars

    Hint How many cars come off the line in ONE hour?
    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. 2Circle the letter of the best answer. Show how you know.

    (Lesson 9.4) 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

    Hint Say it in words: the cars produced equal 2.5 ___ the hours.

    Show your work
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help