## Envision Math 5th Grade Textbook Answer Key Topic 18.4 Problem Solving

Problem Solving

Work Backward
Symbols can show movement of points on a coordinate plane.

Symbols
move right →
move left ←
move up ↑
move down ↓

Starting Position (2, 3)
5 units → (7, 3)
3 units ↑ (7, 6)
4 units → (3, 6) Ending Position

Guided Practice

Do you know HOW?
Question 1.
Work backward to find the starting position.
Starting (x, y)
3 units → (6, 14)
5 units ↓ (6, 9)
2 units → (8, 9) Ending

Do you UNDERSTAND?
Question 2.
How can you check the starting position in the answer from the example at the top?

Question 3.
Write a Problem Write a problem involving movement of points on a coordinate plane that can be solved by working backward.

Independent Practice

In 4 and 5, work backward to find each starting position.
Question 4.
Starting (x, y)
4 units ←
6 units ↑
2 units ↓
3 units → (3, 9) Ending

Question 5.
Starting (x, y)
2 units ↓
7 units →
2 units ↑
14 units → (21, 2) Ending

What is the starting position?
If you know the ending position and the motions used, you can work backward to find the starting position.
Starting (x, y)
5 units → (7, 3)
3 units ↑   (7, 6)
4 units → (3, 6) Ending

Plan and Solve
Begin at the ending position. Do the opposite motions and work backward.
Ending (3, 6)
4 units → (7, 6)
3 units ↓ (7, 3)
5 units ← (2, 3) Starting
The starting position is (2, 3).

Solve.
Question 6.
Pat decided to bake one evening. First, she used a certain amount of flour to make biscuits. Then, Pat used 3$$\frac{3}{4}$$ cups of flour to make bread and 1$$\frac{1}{4}$$ cups of flour to make pretzels. If Pat used a total of 7$$\frac{1}{4}$$ cups of flour for all of her baking, how much flour did she use to make biscuits?

Question 7.
The Tigers scored 20 points during a basketball game. The team scored 6 points during the fourth quarter, 4 points during the third quarter, and the same number of points in both the second and first quarters. How many points did the Tigers score in the first quarter of the game? The second quarter?

Question 8.
Heather is thinking of a solid that is made up of a couple of shapes. The solid has 5 faces. One of the faces is a shape that has sides of equal length. The other 4 faces are shapes that have three sides. What is the name of the solid Heather is thinking of?