Get Twenty

1. Form small groups of 4 to 6 people.
2. Distribute one random playing card to each person.
3. If possible, avoid distributing cards with duplicate values in each group.
4. Instruct each small group to use all of their cards together with any mathematical function (add, subtract, multiply and divide) to produce an equation of exactly 20.
5. For example, King + Ace + 8 + 6 – 5 = 20.
6. Allow at least 5 to 10 minutes for each small group to problem-solve.
7. Challenge each group to produce as many different equations as possible.

First, divide your large group into smaller groups of 4 to 6 people.

Distribute one random playing card to each person, so each group has 4 to 6 cards in their possession.

Ideally, if possible, try to avoid distributing cards with a similar value within each small group. For example, a 10 and a King have the same face value (10 points) so prevent this duplication where you can.

Ask the groups to lay their cards face-up on the ground or table. This is the easy part – the next step is the most difficult.

Instruct each group to use all of their (4 or 6) cards so that when accompanied with any mathematical function – addition, subtraction, multiplication and division – the equation will total 20 exactly (no fractions or decimals.)

For example, if a group held the following cards: King (10,) Ace (1 or 11,) 5, 6 and 8, one possible solution would be to align the cards as such: King + Ace (= 11) + 8 (= 19) + 6 (= 25) – 5 (= 0.)

Answer any questions, and then allow ample time for each small group to come up with a solution that uses all of their cards.

Naturally, one group will often discover a solution quicker than others. When this occurs, and it will be when, challenge that group to look for more solutions, ie a different sequence or use of mathematical functions to produce the same (20) result.

Indeed, all groups aim to produce as many different sequences or solutions as they can in, say, 10 minutes.

If necessary, and appropriate, invite other (successful) groups to lend their expertise to assist those groups which are struggling to produce a solution.

Hint: If your group is having a hard time working out a solution, remind them that they can go below zero for their equation, ie negative numbers. For example, if your group has the following cards 2, 3, 4, 5, and 10, one possible solution could be: 2 – 5 = negative 3, plus 10 = 8, times 3 = 24, less 4 and you get twenty.

The option to challenge those groups which discover a solution earlier than others to keep looking for new sequences is useful for two reasons. One, it allows those groups with easier cards to be challenged to find more solutions, and two, it gives more time for those groups with (perhaps) more difficult cards to find a solution.

Note the audible groan that will emanate from your group when you first mention that ‘mathematics” will feature in this exercise. Rarely in my experience do people’s concerns reflect their actual mathematical prowess, yet I wonder why people feel justified to initially react this way?

Big thanks to Michelle Cummings, founder of Training Wheels, for sharing this fun group initiative.

In Michelle’s estimation, she has rarely lead this activity without all groups finding a solution. However, if this does occur, simply swap out one random card from the pack.

You could integrate Get Twenty as part of a well-designed SEL program to develop your group’s ability to manage their emotions, thoughts and behaviours effectively in different situations and to achieve goals.

Specifically, this activity offers ample opportunities to explore and practice the following social & interpersonal skills:

Self-Awareness

• Identifying Emotions
• Linking Feelings, Values & Thoughts
• Recognising Strengths, Prejudices & Biases
• Demonstrating Self-Confidence, Honesty & Integrity

Self-Management

• Demonstrating Self-Discipline & Self-Motivation
• Setting Personal & Group Goals
• Use Planning & Organisational Skills

Social Awareness

• Taking Other’s Perspectives
• Demonstrating Empathy & Compassion
• Recognising Strengths In Others
• Respecting Others

Relationship Skills

• Communicate & Listen Effectively
• Seeking and/or Offering Support
• Work Collaboratively

Responsible Decision-Making

• Demonstrating Curiosity & Open-Mindedness
• Identifying Solutions

You can learn more about SEL and how it can support character education here.

Behavioural Norms

While clearly focused on applying mathematical formulas, the focus on small group work may provide you with an opportunity to explore a range of social interactions. This is especially true because many people are influenced by a strong narrative that they tell themselves about their mathematical skills. So, in the context of the group’s development, you could choose to focus on the following:

• Goal-Setting: What was your group’s goal? Was it explicit or implicit? Did this change when you solved the equation once? Did you choose to keep seeking solutions? Why or why not?
• Resilience – If you struggled to contribute any solutions, what did you (personally) say to yourself? Were you able to engage with the exercise for a long time or not? If not, what stopped you?
• Decision-Making Skills – Were there interactions or decisions made that concerned you? If you or your group could have their time over again, would you change anything?

• Plus And Minus: Allow only the use of addition and subtraction to produce the magical 20.
• Body Math: Each person must hold their card at all times. Each small group aims to stand in one straight line to produce their equation. Useful for keeping bodies active.
• Get Ten: As above, but the equation equals ten. Or any number you choose to nominate.
• Negative Negative: The equation is not permitted to drop below zero (ie into negative numbers) at any time in order to achieve the total.
• One Of Each: To produce the desired equation, each of the four primary mathematical functions can only be used once. This is a far more challenging task, so allow each group to use only as many numbers and functions that they need to get the total.
• Take a look at Climer Cards (the numbers side) for an alternative prop to play the same exercise.
• Take a look at Your Add to enjoy another fun maths-based game.
• Open the Virtual Adaptation tab to learn how to present this activity online.

• With your group glued to their video monitors, produce a deck of cards and reveal the face-value of the first 4 to 6 cards from a shuffled deck. Ask your participants to record these cards on a sheet of paper, and describe the challenge. To manage responses, especially for the easier equations, require all entries to be typed into the chat room facility, eg A + K + 9 – (2 x 5) = 20. Challenge your group to record as many different equations as possible. And repeat.
• For large groups, divide into a number of smaller breakout rooms (involving 2 to 4 people) after you have described the instructions. Give each group the exact same series of cards, or ask them to select their own.
• If you do not have an actual deck of cards, you can access a number of free online software programs that simulate a shuffled deck of cards, eg click this link for one option. To this end, share your screen as you click through the first five randomised cards, or direct each breakout room to do the same.

There is a saying that suggests that if you ask an accountant to calculate how much profit did you make, they will answer ‘What do you want it to add up to?’ In some ways, this is true of this next exercise…

As soon as I mention the word mathematics, many of your inner voices will start whispering “I’m not good at maths.” This may or may not be true, but what if I gave you the answer, do you think you could work out the equation…

Most of you will have played Black Jack, right? In that game, the prize is to get twenty-one. In this next problem-solving exercise, you will be challenged to get twenty…

Coupled with one or more reflection strategies, here are some sample questions you could use to process your group’s experience after playing this fun, mathematical group initiative:

• How did your group work together to come up with 20?
• ?Were you able to come up with more than one solution?
• How did you involve everyone in your group?
• What leadership attributes were exhibited during the exercise?