SREB Readiness Indicators Addressed: Write, Simplify, and Solve Algebraic Equations Using

SREB Readiness Indicators Addressed: Write, simplify, and solve algebraic equations using substitution, the order of operations, the properties of operations, and the properties of equality (SREB Indicator # 10).

Activity Rationale: This activity is designed to give students experience with properties of operations, order of operations, and balanced equations in a problem-solving context. It provides an opportunity for students to understand the meaning of an equality. In order for students to understand an equality, they must understand is that equality is a relationship, not an operation. According to NCTM’s Principles and Standards for School Mathematics, they should have experiences that help them “view the equals sign as a symbol of equivalence and balance” (p.39).

Experience It!

1. Go to the NCTM Number Pan Balance tool.
http://illuminations.nctm.org/Activity.aspx?id=3530

2. Click in the red box.

3. Type 40.

4. Click in the blue box.

5. Type 60 and notice what happens.

6. Change the value in the blue box to 40 and notice what happens.

Part A: Balancing Equations

Answer the following questions supplied by the NCTM site.

1. Put 4 onto the left pan by typing in the red space above the pan. What happens? Why?

2. Now put 9 onto the blue right pan by typing in the space above the pan. What happens? Why?

3. Reset the balance (by clicking Reset Balance). Put 12 into the right pan.
Now put a sum (two numbers added together) onto the left pan that will balance with 12.

4. Write another sum that balances with 12. How many sums can you find?
List them on your paper.
Can you add up three numbers? Four numbers?
What is the largest number of numbers that you can use to balance with 12? What is the smallest number of numbers?

5. Reset the balance. Now put 12 into the left pan. Put a sum onto the right pan that will balance with 12.

6. Now put 3 + 9 on the left pan. Put something onto the right pan that will make it balance. Then find something else that will balance with 3 + 9. How many answers can you find?

Part B: Checking for Equality

In the following examples, the Number Pan Balance is used to check to see if the given equations are balanced (both sides are equal). In the tool, the following notation represents the given functions:

Operation / Symbol / To calculate this: / Enter this in the tool:
Addition / + / 3 + 5 / 3 + 5
Subtraction / - / 3 - 5 / 3 - 5
Multiplication / * / 3(4) or 3 x 4 / 3 * 4
Division / / / or / 3 / 4
Exponent / ^ / / 3 ^ 2
Parentheses / ( ) / 3(5-1) / 3*(5-1)

Example 1

Check 3(5 - 2) = 15 – 6

Solution:

This equation is balanced because 3(5-2) is equal to 3(3), which is 9 and 15-6 is 9. So, 9 is equal to 9 and the equation balances.

Example 2

Check 4-3(2) = 1+1(1)

Solution:

This equation is not balanced because 3 times 2 is 6 and 4-6 is -2. On the other side, 1 times 1 equals 1 plus 1 equals 2. -2 is not equal to 2.

If you change the equation to 4-3(2) = 1+1(-1), it balances.

Check to see if the equations below are balanced (both sides are equal). Use the Number Pan Balance tool to help explain why or why not. If the equation does not balance, modify the equation so it will balance.

1. 3(12)+15 = 25(2)+1

2. 25+8(2) = 20+2+1

3. –1(11)+(2-1) = -3(7)+10

4. 5(42) = 5(4)(2)

5. –48 = -3(42)