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

Lesson 9.49.4 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can write an equation to represent the relationship between two variable quantities and use it to solve a real problem, explain what each part stands for, and build one for a situation I have not seen before.

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 showing two amounts are the same. 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 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can write an equation to represent the relationship between two variable quantities and use it to solve a real problem, explain what each part stands for, and build one for a situation I have not seen before.

  1. 1Complete each step, then write the final answer.
    02468101214160255075100125150175200225250275300Weeks (w)Total saved ($)start: $90
    The line starts at $90 and rises $15 each week.

    A class has already saved $90 for a trip. They save $15 more each week. Their goal is $300. Let w = weeks and t = total saved. How many more weeks do they need?

    1. 1Write an equation for the total saved.
    2. 2Substitute 300 for t. Subtract 90 from both sides. What is 15w?
    3. 3Divide both sides by 15. How many weeks?
    Final answer:
  2. 2Complete each step, then write the final answer.

    A team already has $45. They sell car magnets for $4 each. Their goal is $200. Let m = magnets sold. How many magnets must they sell?

    1. 1Write the equation with the goal.
    2. 2Subtract 45, then divide by 4. What is m?
    3. 3How much money do they have after 38 magnets?
    4. 4Why must the answer be 39, not 38.75 or 38?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A tank has 20 liters of water. A hose adds 6 liters each minute. Let m = minutes. How many minutes until the tank has 110 liters?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    An elevator holds at most 1,200 pounds. A cart on it weighs 150 pounds. Each box weighs 40 pounds. Let b = boxes. What is the greatest number of boxes it can carry?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A phone plan costs $25 each month plus $0.10 for each text. Ray's bill is $32.50. Let t = texts. How many texts did Ray send?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    Vans1?Students752× ?× ?
    Each van carries 7 students.

    A van carries 7 students. 52 students are going on a trip. Let v = vans. Solve 7v = 52. How many vans does the school need?

    Show your work
    Final answer:

Explain your thinkingThe magnets came out 38.75 and we rounded up. The boxes came out 26.25 and we rounded down. What in each situation told you which way to go?

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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