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OAT Lesson 21: Using Equations to Solve Problems

Last updated over 2 years ago
18 questions
Develop Understanding
Today's Learning Goal: (G7, U6, L11)
  • Interpret and coordinate tape diagrams, equations, and verbal descriptions for situations involving signed numbers.
  • Solve an equation of the form px+q=r or p(x+q)=r to determine an unknown quantity in a situation, and present the solution method (orally, in writing, and through other representations).
  • Write an equation of the form px+q=r or p(x+q)=r to represent a situation involving signed numbers.
Today's Materials:
  • Laptop
  • Laptop charger
  • Pen/Pencil/Paper/Expo Marker (optional)
Please complete the Jump Start (activator). You have 5 minutes before we review. This is independent it should be silent.
Reminders:
1. Ready for class
2. No cellphones
3. Volume must be low.
4. Read and follow all directions
5.) Take your bag off and immediately begin the Activator.

JUMP START: Remeber Tape Diagrams - ( 5min)

Required
1

Write a story that could be represented by this tape diagram.

Write an equation that could be represented by this tape diagram.

Launch: - (10 min)

I do (question
We do (question
You do (question)
Required
0

The baby giraffe weighed 132 pounds at birth. He gained weight at a steady rate for the first 7 months until his weight reached 538 pounds. How much did he gain each month?

Required
0

Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. Now there are 78 players on the field. Write and solve an equation whose solution is the number of players on each team.

Required
1

Match each equation to the story it describes

Draggable itemCorresponding Item
A club puts its members into 5 groups for an activity. After 7 students have to leave early, there are only 3 students left to finish the activity. How many students were in each group?
A musical instrument company reduced the time it takes for a worker to build a guitar. Before the reduction it took 5 hours. Now in 7 hours they can build 3 guitars. By how much did they reduce the time it takes to build each guitar?
The temperature is -7. Since midnight the temperature tripled and then rose 5 degrees. What was temperature at midnight?
Jada has 7 pink roses and some white roses. She gives all of them away: 5 roses to each of her 3 favorite teachers. How many white roses did she give away?

Activity 1: At the Fair

(15 min)

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.

Required
0

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.

Required
0

How many invitations should Tyler make each day to finish his goal within a week? Explain or show your reasoning.

Required
0

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.

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.
Required
0

Explain how the diagram represents the situation.

Required
0

Noah writes the equation 3(x + 7) = 57. Do you agree?

Required
0

How many stickers is Noah's sister putting in each prize bag? Explain or show your reasoning.

Required
0

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.

Activity 2: Running Around

(15 min)

Required
0

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

Required
0

Elena wrote the equation:
  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?

Required
0

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?

Required
0

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?

Required
0

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?

Lesson Synthesis: - (5 min)

Required
0

  • What strategies have you learned so far?
  • What kinds of problems can you solve that they weren’t able to, previously?
  • Is there something you still confused about?

Cool Down: The Basketball Game - (5 min)

Required
4

Diego scored 9 points less than Andre in the basketball game. Noah scored twice as many points as Diego. If Noah scored 10 points, how many points did Andre score?

Closure Questions:

How was material so far?
What is the inverse of addition? Subtraction? Multiplication? Division?
Why do we use variables?