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Hands-On Equations

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Hands-On Algebra with Fractions and Mixed Numbers

Hands-On Equations

- When you hear the word “algebra”, what do you think of?
- What are some things you know about algebra?
- How might you use algebra in real-life?
- Think of a time when you have used algebra. Why was this important? (Money, “how much more do I need to have a certain amount?”, etc.)

What is an equation?

An equation is a number sentence that contains an equal sign.

Example of an equation: x+ ½ = 1

What is a variable?

A variable is a letter or other symbol that represents an unknown number in an equation.

Example of a variable: x + ½ = 1

We do not yet know what the value of “x” is, so “x” is the variable.

In Hands-On Equations, the blue pawns represent the variable in your equation.

- Yellow “Balance” board
- Each side of your balance is equal to the other!
- Your goal is to have only pawns on one side, and only numbers/fractions on the other.
- Let’s make a balance. How can I keep it in balance? What can I do to make it balanced?

- Blue Pawns “x”
- The blue pawns represent your variables.
- All your blue pawns have the same value in each equation, it’s your job to find the value!

- Red Number Cubes
- The red cubes represent your whole numbers.

- Fraction Squares
- The fraction squares represent your fractions.

Solve for x without using a calculator.

x + ½ = 7/8

x = _____

Chk: _____ = _____

Think- What does “x” have to be equal to in order for the sum of the addition problem to be 7/8?

- We will now work through problems 1-10 on your Hands-On Guided Practice page.

- X + 2/5 = 1
x = _____

Chk: _____ = _____

- 4x + 1/6 = 4 1/6
x = ______

Chk: _____ = _____

- With your partner, make up some hands-on equations yourself.
- You will have to test out some different ways!
- Be sure to check your equations for correctness and create a separate answer key for your equations.