## Challenge 2: What's so Sneaky About Exponential Growth?

## (45 minutes)

During “What’s so sneaky about exponential growth?” your students will race against the clock to create two piles of something in order to experience first-hand the true meaning of exponential growth. They make their first pile linearly by adding 10 items to each subsequent round for 10 rounds. Then they make their second pile exponentially by doubling the amount of items for each subsequent round for 10 rounds. Their analysis of their experience reveals why exponential growth is so sneaky. If available your students can conclude this challenge by listening to Alan Atkisson’s humorous and disturbing song, “Exponential Growth.”

If your class has convenient access to a forest with lots of leaves on the ground, do this challenge there. If not, complete the challenge with paper squares instead of leaves.

If your class has convenient access to a forest with lots of leaves on the ground, do this challenge there. If not, complete the challenge with paper squares instead of leaves.

## Materials: Inside or Outside

Each of the 4 stations will need:

1. Challenge Card, “What’s so sneaky about exponential growth?”

2. Exponential Growth Chart – Empty

3a. Inside version: 1200 1” square pieces of paper in a large plastic or cardboard container (large enough for 6 kids to reach in and count the number of squares they will need for each round).

3b. Outside version: 30’ x 30’ area with lots of fallen leaves. Mark off the perimeter of each area with colored ribbons.

4a. Inside version: Two tall thin clear cylinders, big enough to fill with 1024 1” squares. Label “Pile 1” and “Pile 2” respectively.

4b. Outside version: Two tall thin containers (clear if possible), big enough to fill with 1024 leaves. Label “Pile 1” and “Pile 2” respectively.

5. Exponential Growth Chart – Completed

3b. Outside version: 30’ x 30’ area with lots of fallen leaves. Mark off the perimeter of each area with colored ribbons.

4a. Inside version: Two tall thin clear cylinders, big enough to fill with 1024 1” squares. Label “Pile 1” and “Pile 2” respectively.

4b. Outside version: Two tall thin containers (clear if possible), big enough to fill with 1024 leaves. Label “Pile 1” and “Pile 2” respectively.

5. Exponential Growth Chart – Completed

6. Exponential Growth Graph

7. Optional: Alan Atkisson’s song, “Exponential Growth.”

## Procedure

If a procedure doesn’t indicate “inside” or “outside” then it can be applied to either setting.

1. Read aloud:

a. You have 7 minutes to create Pile #1. You will then have 7 minutes to create Pile #2.

b. Outside: You can only collect leaves in the area within the indicated blazing. Leaves should be ON THE GROUND and close to their full size.

c. You must complete the chart, “Exponential Growth Chart - Empty” before you begin collecting.

d. Collect the exact number of items you think you need for each round and put them into their bin. You must complete each round before you can begin the next round.

e. Any questions? (Pause) You have 7 minutes to complete the chart and create pile 1. Begin. (Begin timing)

2. Let students know when 1 and 2 minutes remain during each pile race. Stop after 7 minutes. Start pile #2 as soon as pile #1 is over. If necessary say,

a. You can still earn an Earthstone if you didn’t complete pile 1.

b. Do not press down on your piles.

3. Regroup the teams after 7 minutes have passed for creating pile #2 and say,

“If you didn’t complete all 10 rounds for pile 2, you can still earn an Earthstone if your chart matches the chart, “Exponential Growth Chart – Completed.” Have each group compare its chart with the completed one.

4. Distribute and/or hold up the “Exponential Growth Graph” and ask, “Which graph, “A” or “B,” represents how you made pile 2?”

5. After they state their answer say, “Look at the chart or graph. Notice which pile was gathering more items each round for the first 5 rounds? (Pause. They should notice that they collected fewer items in pile 2 during rounds 2-5.) What happened after the 5th round? (Pause. They should notice that they collected a lot more items for pile 2 during rounds 6-10.) Why do you think exponential growth is considered to be so sneaky? (Pause. They should explain that something can grow exponentially for a long time before one notices that it’s going to grow at an extraordinary pace.)

6. Play Alan Atkisson’s song, “Exponential Growth.”

7. Tell students they can pick an Earthstone if their group’s chart matched your chart AND / OR if their group said Graph B represents how they went about creating pile #2.

1. Read aloud:

a. You have 7 minutes to create Pile #1. You will then have 7 minutes to create Pile #2.

b. Outside: You can only collect leaves in the area within the indicated blazing. Leaves should be ON THE GROUND and close to their full size.

c. You must complete the chart, “Exponential Growth Chart - Empty” before you begin collecting.

d. Collect the exact number of items you think you need for each round and put them into their bin. You must complete each round before you can begin the next round.

e. Any questions? (Pause) You have 7 minutes to complete the chart and create pile 1. Begin. (Begin timing)

2. Let students know when 1 and 2 minutes remain during each pile race. Stop after 7 minutes. Start pile #2 as soon as pile #1 is over. If necessary say,

a. You can still earn an Earthstone if you didn’t complete pile 1.

b. Do not press down on your piles.

3. Regroup the teams after 7 minutes have passed for creating pile #2 and say,

“If you didn’t complete all 10 rounds for pile 2, you can still earn an Earthstone if your chart matches the chart, “Exponential Growth Chart – Completed.” Have each group compare its chart with the completed one.

4. Distribute and/or hold up the “Exponential Growth Graph” and ask, “Which graph, “A” or “B,” represents how you made pile 2?”

5. After they state their answer say, “Look at the chart or graph. Notice which pile was gathering more items each round for the first 5 rounds? (Pause. They should notice that they collected fewer items in pile 2 during rounds 2-5.) What happened after the 5th round? (Pause. They should notice that they collected a lot more items for pile 2 during rounds 6-10.) Why do you think exponential growth is considered to be so sneaky? (Pause. They should explain that something can grow exponentially for a long time before one notices that it’s going to grow at an extraordinary pace.)

6. Play Alan Atkisson’s song, “Exponential Growth.”

7. Tell students they can pick an Earthstone if their group’s chart matched your chart AND / OR if their group said Graph B represents how they went about creating pile #2.