Equation Creation

Students are introduced to an activity called Equation Creation. In the first several rounds, the student randomly chooses seven numbers from a deck of cards with the numbers 0 through 9 (three of each). They write as many equations as they can with those seven numbers.

For example, if the numbers selected are 0, 2, 3, 5, 5, 8, and 9, some possible equations are:

2 + 3 = 5 85 + 5 = 90 80/2 = 35 + 5

3 + 5 = 8 90 - 5 = 85

In a second version of Equation Creation the student writes equations that include one variable. Then they must be able to say what value the variable represents.

For example:

80/ x = 35 + 5, x = 2

Preparation and Materials

Before the session, gather the following materials:

► A set of thirty number cards (three each of the whole numbers 0 through 9)

► A set of operation cards (three each of +, -, x, and /; two each of ( and ); and one = card)

► A watch, clock or other timer

Process:

1. Review the meaning of the term equation. An equation is a number sentence that includes an equal sign. For example:

3 + 4 = 7

3+ 4 = 5 + 2

7 x 3 = 23 - 2

2(10-7)=18/3

4n = 322

These are equations because the expressions on either side of the equal sign are equal.

2. Play a demonstration round of Equation Creation Have students randomly choose seven of the thirty number cards. The goal for the student is to write as many equations as possible with those seven numbers.

Give the student their operation cards. There should be a total of 17 cards (three each of +, -, x, /; two each of the parentheses, and 1 equal sign). Explain that they may use any of these cards in each of their equations.

Using the 7 number cards and the set of operation cards ask the student to make an equation. Once the student is sure they have an equation, have them record it on a piece of paper.Using the same 7 number cards, ask the student to make a new equation. Any of the operation cards may be used in each new

equation. The student should use the actual cards to make the equation, and then record their equations so they can reuse the cards.

Examples:

Suppose the following number cards are drawn:

0, 0, 1, 2, 4, 5, 8

The following number sentences, as well as others, could be made:

2 x 4 = 8 5 x 4 = 20 8/2 = 4

8/2 = 4 80/40 = 2 2 + 4 = 5 + 1

100/4 = 25

Rules for Equation Creation:

-Draw 7 number cards from the deck. (Some numbers may be repeated.)

-Make as many equations as you can using those 7 numbers.

-You can use each of the 7 numbers only once in each equation, but you do not need to use all 7.

-You can use any operations you want.

-You may combine digits to form larger numbers. For example: 5 and 7 to make 75 or 57.

A Process for Moving from Words to Equations:

1. Discuss the statement: “A child’s movie ticket costs half the price of an adult ticket.” Ask the student: which movie ticket costs more, an adult ticket or a child ticket? Once the student can successfully describe the situation (e.g., the adult ticket costs more; the adult ticket costs two times more than the child’s ticket), move to the next step.

2. Answer questions about the situation.

If an adult ticket costs $8, how much does a child’s ticket cost? [$4]

If an adult ticket costs $14.50, how much is a child’s ticket? [$7.25]

If a child’s ticket costs $5.50, how much is an adult ticket? [$11]

If a child’s ticket costs $4.25, how much is an adult ticket? [$8.50]

If two child’s tickets cost $12, how much is one adult ticket? [$12]

If two adult tickets cost $18, how much is one child’s ticket? [$4.50]

3. Choose the equation that represents the situation.

Explain that you will use the letter C to represent the cost of a child’s ticket and the letter A to represent the cost of an adult ticket. Present these four equations. Ask the student to choose one equation from the list below that represents the situation.

C = 2A, C = 1/2A ,2A = C ,1/2C = A

4. Check the equation by substituting values for the letters. Have the student check the equation they chose by replacing C with $5. What value do you get for A? Does that value make sense? Does the equation make sense? One correct equation is C = 1/2A. Another correct equation is 2C = A. If your student chooses an equation that does not make sense, help her determine why the equation does not work for the situation. Invite the student to choose a different equation and check it. Second, check for numerical understanding. For example: if a child’s ticket costs $5, how much is an adult ticket? Third, check for conceptual understanding. For example: write an equation to represent this situation (or choose one from a list of equations).

Review the process introduced earlier for moving from words to equations. Steps for moving from words to equations:

1. Discuss the problem and describe the situation, in other words, tell what the problem is about.

2. Ask and answer questions about the situation using real numbers, for example, if an adult ticket costs $8, how much does a child’s ticket cost?

3. Choose or write an equation to represent the situation.

4. Check the equation by substituting values for the letters in the equation. Use this same process to discuss and evaluate the problem situations on Student : Situations and Equations. The student page provides additional practice analyzing situations and choosing appropriate equations to represent those situations. In the second part of the student page, students are given an equation and asked to write a corresponding situation. Equations for each of the situations as reference.