~ 6.11 ~

Learning Targets

• I can solve story problems by drawing and reasoning about a tape diagram or by writing and solving an equation.

Many problems can be solved by writing and solving an equation. Here is an example:

Clare ran 4 miles on Monday. Then for the next six days, she ran the same distance each day. She ran a total of 22 miles during the week. How many miles did she run on each of the 6 days?

One way to solve the problem is to represent the situation with an equation, 4 + 6x = 22, where x represents the distance, in miles, she ran on each of the 6 days. Solving the equation gives the solution to this problem.

4 + 6x = 22

6x = 18

x = 3

1. Tyler is making invitations to the fair. He has already made some of the invitations, and he wants to finish the rest of them within a week. He is trying to spread out the remaining work, to make the same number of invitations each day. Tyler draws a diagram to represent the situation.
   • Explain how each part of the situation is represented in Tyler’s diagram:

How many total invitations Tyler is trying to make.

How many invitations he has made already.

How many days he has to finish the invitations.

• How many invitations should Tyler make each day to finish his goal within a week? Explain or show your reasoning.
• Use Tyler’s diagram to write an equation that represents the situation. Explain how each part of the situation is represented in your equation.
• Show how to solve your equation.

2. Noah and his sister are making prize bags for a game at the fair. Noah is putting 7 pencil erasers in each bag. His sister is putting in some number of stickers. After filling 3 of the bags, they have used a total of 57 items.

• Explain how the diagram represents the situation.
• Noah writes the equation 3(x + 7) = 57 to represent the situation. Do you agree with him? Explain your reasoning.
• How many stickers is Noah's sister putting in each prize bag? Explain or show your reasoning.

3. A family of 6 is going to the fair. They have a coupon for $1.50 off each ticket. If they pay $46.50 for all their tickets, how much does a ticket cost without the coupon? Explain or show your reasoning. If you get stuck, consider drawing a diagram or writing an equation.

Priya, Han, and Elena, are members of the running club at school.

1. Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.
   • How many miles did Priya run last week?
   • Elena wrote the equation (1/9) (x - 7) = 4 to describe the situation. She solved the equation by multiplying each side by 9 and then adding 7 to each side. How does her solution compare to the way you found Priya's miles?
2. One day last week, 6 teachers joined 5/7 of the members of the running club in an after-school run. Priya counted a total of 31 people running that day. How many members does the running club have?
3. Priya and Han plan a fundraiser for the running club. They begin with a balance of -80 because of expenses. In the first hour of the fundraiser they collect equal donations from 9 parents, which brings their balance to -44. How much did each parent give?
4. The running club uses the money they raised to pay for a trip to a canyon. At one point during a run in the canyon, the students are at an elevation of 128 feet. After descending at a rate of 50 feet per minute, they reach an elevation of -472 feet. How long did the descent take?

This summary video is joined with 6.12 Solving Problems about Percent Increase or Decrease.