Get signed in and take a seat. We will start at 1:10pm

Read through all of this before taking any further action. Adults are welcome to participate too.

Calvin is thinking of 2 consecutive integers from 1 to 5 (inclusive). � He will provide you with some information:� To some of you, he will tell you the EVEN integer.� To some of you, he will tell you the ODD integer.� To some of you, he will tell you NOTHING.� Do not share your information with anyone. Not your mum, not your friend, not your dog. �� When we start the session, Calvin will sequentially ask:� 1. To those who got the EVEN integer: Do you know the ODD integer?� 2. To those who got the ODD integer: Do you know the EVEN integer?� 3. To those who got NOTHING: Do you know EITHER of the integers?

If you’re confused about the above instructions, ask a helpful adult. �Once you understand the instructions, you may come to the front and pick up a single folded piece of paper from the bag, along with a green and a red piece of paper. �You may open the folder paper when you’re back at your seat to view the information you received.

Game 1: 2 consecutive integers

1. To those who got the EVEN integer: Do you know the ODD integer? NO�2. To those who got the ODD integer: Do you know the EVEN integer? NO

�3. To those who got NOTHING: Do you know EITHER of the integers? YES / NO

​

Games of logic

Norman Math Circle 10/1/23

Welcome!

Interactive

(and a lil chaotic)

Welcome!

Be helpful

(not disruptive)

Welcome!

Takeaway

(jot them down)

Game 1 - What just happened?

What are some observations? What were your thoughts?

Not everyone was good at keeping their numbers secret.

Knowing the even integer doesn’t determine the odd integer.

If she thought the even integer was 2 or 4, her number must have been 3.

The people with no information were the only ones who knew enough to know what was going on.

Framework: 5 steps in problem solving

1. Define / Understand the problem�
2. Analyze the problem�
3. Choose an approach�
4. Implement the approach�
5. Review and reflect�

Framework: 5 steps in problem solving

• Define / Understand the problem�Do you know all of the terms? Do you understand the instructions?
• Analyze the problem�What information do you know? What are the constraints/resources?
• Choose an approach�What tools do we have? What has worked for a similar problem?
• Implement the approach�Does the tool work? What modifications should we make?
• Review and reflect�Are the steps actually correct? Is there a better approach? What if we change some condition? What was the crux? How can we generalize this?

Game 1 - Problem solving steps

Calvin is thinking of 2 consecutive integers from 1 to 5 (inclusive). � He will provide you with some information.� To some of you, he will tell you the even integer.� To some of you, he will tell you the odd integer.� To some of you, he will tell you nothing.� Do not share this information with anyone.�� When we start the session, Calvin will sequentially ask:� 1. To those who got the EVEN integer: Do you know the ODD integer?� 2. To those who got the ODD integer: Do you know the EVEN integer?� 3. To those who got NOTHING: Do you know EITHER of the integers?

Game 1 - Game board

When learning a new skill

See one…

Game 2 - Red or Black

Split up into groups of 3 students, with 1 adult.

Game 2 - Red or Black

Split up into groups of 3 students, with 1 adult.

At the end of the instructions, I’m going to be distributing hats

Game 2 - Red or Black

Split up into groups of 3 students, with 1 adult.

At the end of the instructions, I’m going to be distributing hats.

The adult will get an envelope containing 3 cards, and place one card on your hat. �You do not know the color of your card. �You can see the color of other people’s cards. �At least one of the cards in your group is red.

Game 2 - Red or Black

Split up into groups of 3 students, with 1 adult.

At the end of the instructions, I’m going to be distributing hats.

The adult will get an envelope containing 3 cards, and place one card on your hat. �You do not know the color of your card. �You can see the color of other people’s cards. �At least one of the cards in your group is red. ��When we start the game, Calvin will sequentially ask everyone:� 1. Do you know the color of your card?� 2. Do you know the color of your card?� 3. Do you know the color of your card?

Game 2 - Red or black?

When we start the game, Calvin will sequentially ask:� 1. Do you know the color of your card? YES/NO� 2. Do you know the color of your card? YES/NO� 3. Do you know the color of your card? YES/NO

Game 2 - What just happened?

What are some observations? What were your thoughts?

​

Game 2B - Red or Black

The adult will get an envelope containing 3 cards, and place one card on your hat. �You do not know the color of your card. �You can see the color of other people’s cards. �At least one of the cards in your group is red. ��When we start the game, Calvin will sequentially ask everyone:� 1. Do you know the color of your card?� 2. Do you know the color of your card?� 3. Do you know the color of your card?

Game 2B - Red or black?

When we start the game, Calvin will sequentially ask everyone:� 1. Do you know the color of your card? YES/NO� 2. Do you know the color of your card? YES/NO� 3. Do you know the color of your card? YES/NO

Game 2B - What just happened?

What are some observations? What were your thoughts?

​

Game 2C - Red or Black

The adult will choose what card to place on your hat. �You do not know the color of your card. �You can see the color of other people’s cards. �At least one of the cards in your group is red. ��When we start the game, Calvin will sequentially ask everyone:� 1. Do you know the color of your card?� 2. Do you know the color of your card?� 3. Do you know the color of your card?

Game 2C - Red or black?

When we start the game, Calvin will sequentially ask everyone:� 1. Do you know the color of your card? YES/NO� 2. Do you know the color of your card? YES/NO� 3. Do you know the color of your card? YES/NO

Game 2C - What just happened?

What are some observations? What were your thoughts?

​

Framework: 5 steps in problem solving

• Define / Understand the problem�
• Analyze the problem�
• Choose an approach�
• Implement the approach�
• Review and reflect�

10 min Break - Grab pizza, resume at 2:10

Adults are welcome to participate� Calvin is thinking of 2 integers from 1 to 5 (inclusive). � The integers need not be consecutive or distinct. � He will provide you with some information.� To some of you, he will tell you the SUM of these integers (and that it’s the sum).� To some of you, he will tell you the PRODUCT of these integers (and that it’s the product).� To some of you, he will tell you nothing.� Do not share this information with anyone. Not your mum, not your friend, not your dog. �� When we resume the session, Calvin will sequentially ask:� 1. To those who got the SUM: Do you know the PRODUCT? No� 2. To those who got the PRODUCT: Do you know the SUM? � 3. To those who got the SUM: Do you know the PRODUCT?� 4. To those who got the PRODUCT: Do you know the SUM?� 5. To those who got NOTHING: Do you know either the SUM or the PRODUCT?

If you’re confused about the above, ask a helpful adult. �Once you understand the above, you may come to the front and pick up a folded piece of paper from the bag�You may open it when you’re back at your seat to view the information you received.

Game 3 - Sum and Product

Adults are welcome to participate.� Calvin is thinking of 2 integers from 1 to 5 (inclusive). � The integers need not be consecutive or distinct. � He will provide you with some information.� To some of you, he will tell you the SUM of these integers (and that it’s the sum).� To some of you, he will tell you the PRODUCT of these integers (and that it’s the product).� To some of you, he will tell you nothing.� Do not share this information with anyone. Not your mum, not your friend, not your dog. �� When we resume the session, Calvin will sequentially ask:� 1. To those who got the SUM: Do you know the PRODUCT? No� 2. To those who got the PRODUCT: Do you know the SUM? No� 3. To those who got the SUM: Do you know the PRODUCT? No� 4. To those who got the PRODUCT: Do you know the SUM? No� 5. To those who got NOTHING: Do you know either the SUM or the PRODUCT? Yes! PRODUCT is 4.

Game 3 - What just happened?

What are some observations? What were your thoughts?

If we knew the product was 5, we’d know the sum was 6.

If the sum is 4, the product could be 3 or 4.

If the sum is 6, the product could be 5, 8, or 9.

​

Framework: 5 steps in problem solving

• Define / Understand the problem�
• Analyze the problem�
• Choose an approach�
• Implement the approach�
• Review and reflect�

When learning a new skill

See one

Do one …

Game 3 - Game Board

Game 3B - Same instructions as before

Calvin is thinking of 2 integers from 1 to 5 (inclusive). � The integers need not be consecutive or distinct. � He will provide you with some information.� To some of you, he will tell you the SUM of these integers (and that it’s the sum).� To some of you, he will tell you the PRODUCT of these integers (and that it’s the product).� To some of you, he will tell you nothing.� Do not share this information with anyone. Not your mum, not your friend, not your dog. �� When we resume the session, Calvin will sequentially ask:� 1. To those who got the SUM: Do you know the PRODUCT?� 2. To those who got the PRODUCT: Do you know the SUM?� 3. To those who got the SUM: Do you know the PRODUCT?� 4. To those who got the PRODUCT: Do you know the SUM?� 5. To those who got NOTHING: Do you know either the SUM or the PRODUCT?

If you’re confused about the above, ask a helpful adult. �Once you understand the above, you may come to the front and pick up a single card. �You may open it when you’re back at your seat to view the information you received.

​

Game 3B - Sum and Product

Calvin is thinking of 2 integers from 1 to 5 (inclusive). � The integers need not be consecutive or distinct. � He will provide you with some information.� To some of you, he will tell you the SUM of these integers (and that it’s the sum).� To some of you, he will tell you the PRODUCT of these integers (and that it’s the sum).� To some of you, he will tell you nothing.� Do not share this information with anyone. Not your mum, not your friend, not your dog. �� When we resume the session, Calvin will sequentially ask:� 1. To those who got the SUM: Do you know the PRODUCT? No� 2. To those who got the PRODUCT: Do you know the SUM? Yes!� 3. To those who got the SUM: Do you know the PRODUCT? Yes!� 4. To those who got the PRODUCT: Do you know the SUM? Yes, still� 5. To those who got NOTHING: Do you know either the SUM or the PRODUCT? No

Game 3B - Game Board

Game 3C - Sum and Product

Calvin is thinking of 2 integers from 1 to 5 (inclusive). � The integers need not be consecutive or distinct. � He will provide you with some information.� To some of you, he will tell you the SUM of these integers (and that it’s the sum).� To some of you, he will tell you the PRODUCT of these integers (and that it’s the sum).� To some of you, he will tell you nothing.� Do not share this information with anyone. Not your mum, not your friend, not your dog. �� When we resume the session, Calvin will sequentially ask:� 1. To those who got the PRODUCT: Do you know the SUM? NO� 2. To those who got the SUM: Do you know the PRODUCT? YES/NO� 3. To those who got NOTHING: Do you know either the SUM or the PRODUCT? YES/NO

When learning a new skill

See one

Do one

Teach one

Reflect

• 5 steps in problem solving
• Define/Understand, Analyse, Choose, Implement, Review and Reflect
• Review and reflect
• What happens if we change the game slightly?
• Game 1: Choose 2 consecutive integers from 1 to 6
• Game 2: More people in the game
• Game 3: Thinking of 2 integers from 1 to 6. From 1 to 10?
• Learning a new skill: See one, Do one, Teach one.
• 5 steps of problem solving - Do one: Game 2, red or black? What is the game board?
• Sequential analysis - Teach your friend: Game 3, the sum and product game. How would you explain it to them?
• What is your main takeaway from this session?
• What caught your attention? What spoke to you?
• What would you want to remember in one month’s time? One year’s time?
• Anonymous feedback form

Q&A