Algebra Spoons lesson plan

Teacher Instructions

Grades: 5-8 (Once algebraic equations have been introduced)

Materials:

• Uno Deck (use only 0-9)
• Use wild cards to make operations (10 each of +, -, *, /), variables (10 each of X, Y), and 10 equals signs (cover original wild cards with paper)
• One spoon for each player
• Score Card
• Scratch paper
• Large sheets of paper to hide equations

Learning Goals: Practice and become comfortable constructing and solving algebraic equations with one and two variables.

Game Type: Develop Skills and Use Mathematical Notation

Preparation: Students should already be comfortable with the concept of algebraic equations and basic strategies for solving such equations.

NCTM Standards:

This game satisfies the following National Standards:

MATHEMATICS: Algebra

GRADES 3 - 5

NM-ALG.3-5.1 Understand Patterns, Relations, and Functions

NM-ALG.3-5.2 Represent and analyze mathematical situations and structures    using algebraic symbols

NM-ALG.3-5.3 Use mathematical models to represent and understand quantitative relationships

GRADES 6 - 8

NM-ALG.6-8.1 Understand Patterns, Relations, and Functions

NM-ALG.6-8.2 Represent and analyze mathematical situations and structures    using algebraic symbols

NM-ALG.6-8.3 Use mathematical models to represent and understand quantitative relationships

Directions:

Groups should be 3-5 students of similar skill level to begin with. The teacher may introduce the game by playing an example round with two volunteers in front of the class, and/or by having the class work on a few word problems that involve creating algebraic equations to solve for the answer. After introductory activity, distribute a game deck and spoons to each group.

Deal 5 number cards, two operation cards, one variable, one equals sign and one spoon to each player. Remaining number and operation cards are placed in 2 separate draw piles; remaining variable cards and equals signs are left out of play until Round 3 (rounds described at end of instructions).

Each player secretly constructs an algebraic equation (fitting the rules for the first round; see below) out of the cards they have been dealt and covers the equation with a large sheet of paper. The youngest player should reveal their equation once everyone is ready, placing the spoon next to it; other players attempt to solve the equation. Make sure that the equation faces the other players. Once a player has the answer written on their scratch paper (in the form ‘X = number’ or ‘Y = number’), they grab the spoon. A player with the correct answer (written on their paper) and spoon receives one point. If the player grabbing the spoon reveals either an incorrect answer or no answer, they must return the spoon and get no points, and may not grab the spoon for this equation again. Other players may now grab the spoon. After the equation has been solved successfully by one player, the player who constructed the equation discards their used number and operation card(s), keeping their variable card(s) and equals sign and drawing new operation and number cards to replace their used ones. For example, if they constructed the equation 3 + X = 5, they will discard 3, 5, and + and draw 2 number cards and 1 operation card. Two discard piles are created (1 operations and 1 number), then shuffled and used as draw piles if original draw piles run out.

Play continues to the left with the player to the left of the youngest player revealing the next equation and so on. After every equation has been solved, players should take approximately 1 minute to construct their next equations, then repeat play as described above. Once every player has gained at least one point from a round, proceed to the next round until all players have completed Round 3.

At end of game, points from Round 1 are counted in the total at face value. Points from Round 2 are multiplied by 2, and points from Round 3 are multiplied by 3, giving a greater weight to more difficult questions.

In order to use double digit numbers in equations, students must use 2 number cards next to one another (i.e. a 1 card and a 0 card represent 10).

Rounds: players may create equations that fit the following guidelines:

• Single variable single operation (ex: 3+X=5)
• Single variable two operations (ex: 3+X-4=2)
• Two variables two equations (deal one more variable, one more equals sign to each player)

(ex: X+Y=10, X-Y=2)

Facilitation Questions:

If students solving equations are having trouble solving an equation, the instructor may ask the equation creator to create a simple word problem that can be modeled by their equation, or they can create such a word problem themselves. This may help students understand how to approach the variables as symbols for something else, adding a concrete aspect to the abstract equations.

Other questions that may facilitate the lesson include “How can creating equations like these help us solve problems in the real world?”, and “What are some real-life variables? What changes in your day to day life?” In round 3, instructors should ask about the relationship between variable, using questions such as “Are X and Y dependent or independent?”, and “Why do you need to find one variable to be able to solve for the other?” for dependent variables.

Variation 1:

Reveal all players’ equations at once. Allow players to solve whichever equations they want and grab the spoons of the equations they have solved. Players get points for the spoons they collect, which may be more than 1.

Variation 2:

Especially for groups with students who are having particular trouble solving equations quickly, have enough spoons at each equation for each player solving the equation to take one. Instead of racing, have a set period of time (e.g. 1 minute as timed by the equation creator) for students to solve and grab one of the spoons or fail to solve, taking no spoon. Points are accrued for number of equations solved, but students do not have to race against one another.

Debriefing Questions:

Hand out the Thinking Questions worksheet after the activity and have students complete it in class or for homework. If there is enough time, have students either remain in their game groups or get into new groups and discuss what strategies worked the best for solving equations, which equations took the most time to solve, and why. Also have them discuss the difference between dependent and independent variables, and what this difference means in real-life. Have the groups make a list of possible dependent variables (i.e. speed of getting home from school and how much traffic there is on the roads) and independent variables (i.e. what the temperature is outside and how long it takes to do your homework). Then, check the lists and discuss with the class whether these variables really are independent/dependent, and discuss why. Pay close attention to the independent variable list; students may not think of all the ways things in the real world can be related.

Assessment:

Collect the students’ scorecards after the game to keep track of which students are succeeding in which rounds of the game. Also collect and grade the Thinking Questions worksheet in order to gain insight into how students are approaching algebra.

Algebra Spoons

Student Activity Sheet

Directions:

Give 5 number cards, two operation cards, one variable, one equals sign and one spoon to each player.

Each player should make an equation that fits the rules for the first round (described below) out of any number of the cards they have been dealt—you do not have to use all of your cards. Once everyone is ready, have the youngest player set their spoon in front of them and reveal their equation. Make sure the equation faces the players solving it.

Everyone else try to solve the equation fastest. Once you have the answer written on your scratch paper, grab the spoon. A player with the correct answer and spoon receives one point. A player without the correct answer returns the spoon and receives no points; other players may now grab this spoon with the correct answer. Keep track of points with tally marks on the score sheet.

The player to the left of the youngest player goes next, revealing the next equation and so on. After going around the circle one, give every player about 1 minute to make their next equation, then repeat play described above. Once every player has at least one point from a round, go to the next round.

After a turn, the player who made the equation discards the number and operation cards they used and picks up cards from the number and operation draw piles to replace used cards. For example, if you made the equation 3 + X = 5, you will discard 3, 5, and + and draw 2 number cards and 1 operation card. Used cards go into a 2 discard piles which are shuffled and used as draw piles once a draw pile runs out.

Rounds:

• Single variable single operation (ex: 3+X=5)
• Single variable two operations (ex: 3+X-4=2)
• Two variables two equations (deal one more variable, one more equals sign to each player)

(ex: X+Y=10, X-Y=2)

For Example:

If you were dealt 1, 3, 4, 6, 8, a Y variable, a minus sign, a division sign and an equals sign in round one, you might make this equation:

8-Y=6 (Answer: Y=2)

The other players race to get the answer and grab your spoon.

After tallying the points and putting the 8 and 6 in the number discard pile and the minus in the operation discard pile, take back your spoon, draw new cards to replace the discarded ones, and have the player to your left reveal the next equation.

Thinking Questions

• What strategies did you use to solve the equations?

• Did having more than one operation make the equations harder or easier to solve? Why?

• How did having two variables change the game? Was it harder with dependent variables or independent variables?

• Why can we make algebraic equations to help us figure out more complicated math questions?

• Write your own algebraic word problem as a question, and write the equation(s) that can be used to solve it as an answer. Be creative with your problem!

Score Sheet

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.