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

Lesson 9.49.4 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can write an equation to represent the relationship between two variable quantities and use it to solve a real problem — one step at a time, with support.

Why This Matters This is your support small group for Lesson 9.4. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.

Start hereWords for this lesson

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

Word	What it means	Example
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 example

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

A bakery makes 24 rolls each hour: r = 24h. Is 5 hours enough for 150 rolls?

Substitute h = 5: r = 24 × 5 = 120 rolls.
Compare: 120 < 150.

Answer: No, 5 hours makes only 120 rolls

Now you trySame steps, your turn

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

Last year the student council washed 34 cars and raised $408. This year the goal is $500. At the same price, how many cars must they wash?

Answer:

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 out!A common mistake

Adding the rate instead of multiplying

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

Lesson 9.49.4 Small Group · Group 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target With my small group, I can write an equation to represent the relationship between two variable quantities and use it to solve a real problem — one step at a time, with support.

1Complete each step, then write the final answer.
The bakery makes 1.5 cakes each hour.
A bakery makes 1.5 cakes every hour. It gets an order for 60 cakes. Let h = hours and c = cakes. How many hours does the bakery need? It works 8 hours a day. How many days is that?
1. 1Write an equation for the cakes made in h hours.
2. 2Substitute 60 for c. What equation do you get?
3. 3Divide both sides by 1.5. How many hours?
4. 4The bakery works 8 hours a day. How many days is that?
Final answer:
2Complete each step, then write the final answer.
Each bracelet raises $3.
A club sells bracelets for $3 each. Their goal is $100. Let b = bracelets sold and t = total raised. How many bracelets must they sell?
1. 1Write 1 bracelet → $3. What scale factor takes $3 to $100?
2. 2How much money do 33 bracelets raise?
3. 3What is the least number of bracelets that reaches $100?
Final answer:
3Complete each step, then write the final answer.

The machine fills 5 boxes each minute.
A machine fills 5 boxes every minute. Let m = minutes and b = boxes. How many minutes does it take to fill 45 boxes?
Show your work
Hint The equation is b = 5m. Put in 45 for b. Then divide both sides by 5.
Final answer:
4Complete each step, then write the final answer.

The factory makes 3.5 bikes each hour.
A factory makes 3.5 bikes every hour. Let h = hours and b = bikes. How many hours does the factory need to make 280 bikes?
Show your work
Hint Write b = 3.5h. Put in 280 for b. Which operation undoes multiplying by 3.5?
Final answer:
5Complete each step, then write the final answer.

Each plant earns $8.
A school earns $8 for each plant it sells. The goal is $150. Let p = plants sold. What is the least number of plants they must sell to reach the goal?
Show your work
Hint Solve 8p = 150. The answer is not whole. Check the whole numbers on each side of it.
Final answer:
6Circle the letter of the best answer. Show how you know.
Each notebook costs $3. Kim has $20.
Kim has $20. Notebooks cost $3 each. She solves 3n = 20 and gets n ≈ 6.7. She says she can buy 7 notebooks. Is she right?
1. ANo. 7 notebooks cost $21, so she can buy 6.
2. BYes. 6.7 rounds up to 7.
3. CNo. She can buy 6.7 notebooks.
Hint Find the cost of 7 notebooks. Can Kim pay for them with $20?
Show your work

Explain your thinkingThe bracelets needed 34, not 33.3. Kim could buy 6, not 6.7. When do you round up, and when do you round down?

Sentence starter I round up when ___. · I round down when ___.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked

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