Problem Solving
How can you use what you’ve learned to solve a real-world problem?
Goal:
Goal:
Practice!
Goal: Apply what you've learned in this lesson to solve a real-world problem.
Logan is helping his friend Zoe set up chairs in the school gym for an awards ceremony. Zoe is trying to figure out how to set up the chairs so that people can move around easily to get their awards. Click through the slides to see how Logan helps her set up the chairs.
Shape of the Space
Logan and Zoe figure out the best shape to set the chairs up.
Zoe is trying to figure out how to set up the chairs in the gym. She wants everyone to be able to see, but they also need to be able to easily get up and get their awards. Zoe and Logan draw pictures of their ideas. Zoe thinks about 2 long rows. But the kids toward the ends won’t be able to see, and the kids in the middle will have to walk around a lot of people. Logan likes the idea, but he thinks they should add more rows so that each row isn’t too long. They decide to make a rectangle using 4 rows, with 10 chairs in each row.
Zoe chair arrangement idea 2 rows and 2 columns of chairs. Logans chair arrangement idea 4 rows and 10 columns of chairs.
The Middle Aisle
Zoe wonders how to make it easier for everyone to get their awards.
Logan suggests that they make a middle aisle for everyone to walk through.
“Will everyone still be able to see?” Zoe asks.
“Of course! We’ll make sure both sides are symmetrical.” Logan says. “How?” Zoe wonders.
Logan explains to her that a rectangle has a line of symmetry right down the middle of it. That means that both sides of the shape are exactly the same. He draws a line in the middle of the chairs to show her.
A symmetrical chair arrangement with an aisle through the center vertically. One side 4 rows and 5 columns. The second side 4 rows and 5 columns.
Another Aisle
Zoe is still worried there might not be enough room to get around.
Logan has another solution. He says that they can use symmetry again to help them. He explains that a rectangle also has a line of symmetry across the middle of it. Logan draws another line across the middle of the rectangle.
“Now the top of the rectangle and the bottom of the rectangle are the same.” Logan explains.
“Oh, I see it now!” exclaims Zoe. “We will have a middle aisle and one that goes across the rows.”
A symmetrical chair arrangement with an aisle through the center vertically and horizontally. 4 groups of 2 rows and 5 columns.
The Set Up
Zoe thinks this is perfect!
“I think this is perfect!” Zoe exclaims.
“Everyone can see the stage, and they can get around easily to accept their awards. Thank you so much, Logan!”
“You’re welcome!” Logan says.
“I’m always amazed at how many things in the real world have symmetry. I never thought of a group of chairs as being symmetrical, but there they are!”
4 groups of chairs, 2 rows 5 columns of chairs.
If Zoe and Logan add another row of chairs to the back row, would everything still be symmetrical?
2 groups of 2 rows and 5 columns of chairs. 2 groups of 3 rows and 5 columns of chairs.
- Yes. The rectangle is still symmetrical because the sides are still identical. There are 5 rows of chairs on each side of the rectangle.
- No. The rectangle is NOT symmetrical because the top and bottom of the rectangle have different numbers of chairs. There are 2 rows of chairs on the top of the rectangle and 3 rows of chairs on the bottom of the rectangle.
Think about what makes a shape symmetrical. Does the image still look symmetrical?
Correct! The rectangle is not symmetrical.
Summary
Questions answered correctly:
Questions answered incorrectly: