BANANA MATH SCRABBLE

Grade Level: Middle School to early High School

Learning Goals: Developing a deeper understanding and increased fluency of numbers and operations, Improving mental math speed and accuracy

Materials:
50 Number Cards
50 Symbol Cards
8 Goal Cards
1 Timer/Stopwatch

NCTM Standards:
Reasoning with Algebra
Representation of Number and Operations
Problem Solving and Sense Making
Communication

The purpose of this math game is to help students gain a stronger understanding of numbers and order of operations and its applications in computational procedures. This activity represents operations to encourage students to visually represent equations as well as apply reasoning and problem-solving abilities to find the optimal solution to the problem given his or her constraints (or in this case, numbers and symbol cards). Students are required to use sense making to represent quantitative relationships and to look for patterns that will help improve his or her accuracy and mental math speed. Lastly, after students have played a few rounds, students are prompted to discuss with each other their thinking processes to illustrate understanding of the subject and to articulate what patterns and skills they have developed through this activity.

Preparation:

Prepare a set of goal cards, number cards, and symbol cards. The exact number of these cards is arbitrary, and can be changed depending on the number of people playing and the objective of the game. For example, for a 2~6 person game, about 8 goal cards, about 50 number cards and 50 symbol cards is recommended. (Index cards cut in half could be used, a recommendation would be to have the different types of cards be different colors.)

For a 50 number card, 50 symbol card deck:

Number Cards:           Have 5 cards each of: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Symbol Cards:            Have 7 cards each of:

+          -          x         ¸         (           )          ^(exponent)    and one wild card

Goal Cards:    The goals can be changed depending on the math level of the students.

Examples of Goals can be Largest number, Smallest number, Most Negative Number, Largst Prime, etc.

Before playing the game, it is best review with the student the order of operations.  Also, when explaining the game to the students, make sure to give an example or two using the cards. It is a good idea to go through an example step by step with the class so that every student understands the rules of the game.

Objective:

The objective of the game is to use the cards in your hand to construct an equation. In each round, students will have to reach a different goal, whether it is finding the solution that is the largest number, smallest number, prime, negative, etc.  Each solution will be decided by drawing the “goal” card at the start of each round. The players will have a certain amount of time (ex: 2 minutes) to construct an equation. At the end of the time, the players will present their equation, and winner will be decided. The winner of that round is allowed to have one extra each of number cards and symbol cards on the next round.

This game is aimed to strengthen students’ understanding of mathematical operations and improve their speed and accuracy on mental math.

Teaching Points:

• Have students develop their skills and become comfortable with mental calculation, not on paper. The objective is for students to be able to do simple calculations quickly and accurately without the aid of paper and writing utensils.
• Have students focus on learning patterns and techniques to improve their calculations.
• Have students become comfortable with order of operations.

Debrief Questions:

1) Which rounds were harder to play? Which rounds were easier to play? Why?

2) How did you approach the problem? What cards did you look for first when you were creating the equations?

3) Do you think the rounds would be easier if you had a writing utensil? How about a calculator?

4) Did you notice patterns in approaching each round?

5) Do you think your speed of forming equations changed as you played more rounds? If yes, why do you think so?

6) What are some examples in which we can apply this knowledge?

BANANA MATH SCRABBLE

# of players: 2~6 people

Materials:

50 Number Cards, 50 Symbol Cards, 8 goal cards, Timer

Rules:

The goal of this game is to create a math equation using numbers and operations to best match the “goal” of each round. Use your mental math and your understanding of order of operations to win the round!!

Before the start of each round, the number cards and the symbol cards will be shuffled well and placed upside down in two separate piles in the center. A goal card will be drawn, and that will be the “goal” of the round.

Each player will take 5 number cards and 6 symbol cards and keep it face down in front of them.

Everyone will flip over their cards at the same time and will have two minutes to construct an equation. Each person must use at least five number cards and four symbol cards for their equation. The answer to your equation should try to best match the “goal” of the round.

Once the time is up, each player will present their equation to the group, and the player with who has the solution closest to the “goal” will win the round.

The winner of the round is also allowed to have one extra number card and one extra symbol card on the next round. They still however, only have to use five number cards and four symbol cards, just like anyone else.

At the end of the round, all players will return their cards to the respective piles in the center. At the beginning of the next round, each player will take the 5 number cards and 6 symbol cards (winner of the previous round gets one extra card each).

Side note: Feel free to experiment with new round “goals” and change the time limit.

Example:

Let’s say you have the following numbers and symbols:

5, 3, 9, 1, 1                 +  -  x  (  )  +

Here are some equations you can make.

This equation will give you the largest number: 9 x (5 + 3) – 1 + 1 = 72

This equation will give you the smallest number: 9 – (5 + 3) x 1 + 1 = 2

This equation will give you the largest number divisible by 4:  9 x (5 + 1) + 1 – 3 = 52

Solutions/Guidance to Debrief Questions:

Debrief Questions:

• Which rounds were easier? Which rounds were harder? Why?

This question is intended to check whether students recognize and can articulate the differences between the rounds. Different rounds require different modes of approach and techniques to effectively solve the problem. If students can use various techniques depending on each round and not just stick to one method, it shows that the students have a deeper understanding of the subject matter rather and can improvise/adapt rather than simply repeating a process.

• Here are some techniques that people use for the game: Estimation, Order of Operations, Guessing. Which ones did you use? If you used any other methods to approach this game, explain that too.

This question is intended to obtain a sense of how the students’ approach the problem and their methods to solve the game. The teacher can take this information to modify their future lesson plans so that it is more reflective of how students learn and solve problems. In addition, the teacher can choose to develop certain skills that students are not using through additional lessons and problems.

• How did you speed and accuracy change as you played the game?

This question’s purpose is to obtain a sense of the students’ understanding of the subject matter and how their progress as they played the game.

Most students’ speed and accuracy should improve as they play the game. If they do, then it is a good indication that the student has a good grasp of the game and understands order of operations well. If a student has indicated that their speed and accuracy did not change or found the game to be consistently difficult, it may be a good idea to follow-up on the student with additional instruction or follow-up questions.

Let’s do the same Banana math Scrabble but on paper

1) You have: 5                       4          4          9          0 and + ( ) x - +

1) Make the smallest positive number

(5 + 4 + 4 – 9) x 0 = 0

There are several more answers, and this is allowing 0.

2) Make the largest prime number

(5 + 4 x (4 + 9) – 0 = 57         There may be other solutions.

Now that you have a better understanding of Order of Operations, try these:

• 2 – (3+9) ^ 2

= 2 – (12) ^ 2

= 2 – (144)

= -142

• (2 x 3 + 4) – 7 x 9

= (6 + 4) – 7 x 9

= 10 – 7 x 9

= 10 – 63

= -53

• (9+5) ¸ 5 + 3^0

= 14 ¸ 5 + 3 ^0

= 14 ¸ 5 + 3

= 14/5 + 3

= 29/5

This lessons is written by students at Massachusetts Institute of Technology (M.I.T.), as part of their coursework for 11.124, Introduction to Teaching and Learning Science and Math.