Unit 6, Lesson 6
Percentages and Equations
Grade 6
6.1
Warm-up
Decide mentally if each statement is true or false.
- 60% of 200 is 12.
- 60% of 20 has the same value as .
- 6% of 200 has the same value as .
- If 6% of is 120, then is 20.
6.2
Activity
Write an equation to represent the relationship in each statement. Then solve the equation to answer the question. Show your reasoning.
- 40% of a number is 58. What is that number?
- 60% of is 43.2. What is the value of ?
- 38% of is 190. What is the value of ?
6.3
Activity
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
- Silently read your card and think about what information you need to answer the question.
- Ask your partner for the specific information that you need. “Can you tell me ?”
- Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”
Continue to ask questions until you have enough information to solve the problem. - Once you have enough information, share the problem card with your partner, and solve the problem independently.
- Read the data card, and discuss your reasoning.
If your teacher gives you the data card:
- Silently read your card. Wait for your partner to ask for information.
- Before telling your partner any information, ask, “Why do you need to know ?”
- Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!
These steps may be repeated. - Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
- Share the data card, and discuss your reasoning.
Student Lesson Summary
We can write equations to help us solve percentage problems.
Example: There are 455 students in school today, which is 70% school attendance. How many students go to the school?
The number of students in school today is known in two different ways: as 70% of the students in the school, and also as 455. If represents the total number of students who go to the school, then 70% of , or , represents the number of students that are in school today, which is 455.
We can write and solve the equation:
There are 650 students in the school.
The equation can also be written using the decimal equivalent of , which is 0.7:
We can check this answer by substituting 650 for in the equation and seeing if the equation is true.
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