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.

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 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.

Define: h = hours running, p = posters made. Posters depend on hours.
The rate is 22 posters for each hour, so the rule is p = 22h.
Substitute 15 for h: 22 × 15 → 330 posters.
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.

Define: m = , b = .
The rate is bottles for each minute, so the rule is b = m.
Substitute 40 for m: × 40 → bottles.
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 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 ___.

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