## Envision Math 5th Grade Textbook Answer Key Topic 20.4 Problem Solving

Problem Solving

Use Objects
A pentomino is an arrangement of 5 identical squares in a plane. The squares must be attached to one another edge to edge. Question.
Using 5 identical square tiles, how can you build 3 more pentominoes that have 3 squares in a row?

Guided Practice

Do you know HOW?
Question 1.
Is the following a pentomino? Explain. Question 2.
Are these two pentominoes the same or different? Explain. Do you UNDERSTAND?
Question 3.
In the example above, how many more pentominoes can you find with 3 in a row?

Question 4.
Write a Problem Write a real-world problem that can be solved by using objects.

Independent Practice
In 5 and 6, tell whether the pentominoes in each pair are related by a reflection or a rotation.
Question 5. Question 6. In 7 and 8, use objects to help you solve the problem.
Question 7.
How many pentominoes can you build with 5 in a row?

Question 8.
How many pentominoes can you build with 4 in a row?

What am I asked to find?
Three more unique pentominoes that have 3 squares in a row
Two pentominoes are the same if they can be matched together by rotating or reflecting. Plan and Solve
I can use objects to build 3 more pentominoes with 3 in a row. Here are 3 possible solutions.

Look Back and Check
All are attached edge to edge.
All can be rotated and reflected. None are repeated.
The 3 pentominoes I’ve made are all unique.

Question 9.
Suppose each square in a pentomino is a table that seats one person on a side. Find a table arrangement (a pentomino) that can seat 12 people. Question 10.
The figure below can be folded to form a box. After it is folded, which face will be parallel to Face ABDC? Question 11.
Maureen is buying a game that is priced at $15. She has a coupon worth$2.50 off the regular price. After Maureen gives the clerk a $20 bill, how much change does she receive? Answer: Question 12. James and Kurt were paid$176 for landscaping a yard. James worked 9 hours and Kurt worked 13 hours. How much is Kurt’s fair share of the earnings? James’s share?

Question 13.
Use objects to build pentominoes with 2 squares in a row. How many of these kinds of pentominoes can be built?