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What you will learn from this videoWhat you will learn
- That an algebraic equation is an equation with an unknown number.
- How to solve algebraic equations using inverse operations.
- That this knowledge can help us count our savings, sell cupcakes, and even take care of pets!
- Discussion Questions
Before Video
What is [ggfrac]3/3[/ggfrac] equal to? What about [ggfrac]5/5[/ggfrac]? [ggfrac]12/12[/ggfrac]?ANSWERAny fraction that has the same numerator and denominator is equal to 1.
I can write any whole number as a fraction with a 1 in the denominator. When I multiply fractions, I multiply the numerators together and the denominators together. So I multiply 3 by 4 to get 12, and 1 by 7 to get 7. The answer is [ggfrac]1/2[/ggfrac]7, or 1[ggfrac]5/7[/ggfrac].
4, 7, and 8. In each case, I multiply by a number and divide by the same number. It’s like I do an operation, and then undo it. This is why my answer is the same as the number that the inverse operations are done to: it is like nothing happened to it!
? = 2. Since 5 is multiplied by 2, I can do the inverse operation, division, to undo the multiplication.
? = 6. Since 7 is divided by 6, I can multiply it by 6 to get back to 7.
After Video
What is a variable? What does it look like in an equation?ANSWERA variable represents an unknown quantity. In an equation, I can use an x to represent it, or any other letter of symbol I choose.
ANSWER8 is subtracted from x, and since I want x to be alone on the left side, I should add 8 to it. I also have to add 8 on the right side to keep the equation balanced.
ANSWERx is multiplied by 7, so I should divide it by 7 to get 1x, which is the same as x. Then I also have to divide the other side by 7.
On the left side of the equation, Joe multiplied both the numerator and denominator by 4. That does not help him solve for x, since [ggfrac]4/4[/ggfrac] is equal to 1. To multiply x by 4, he should multiply only the numerator on both sides.
If I substitute 6 for x in the equation, I get 4∙6 on the left side, which is equal to 24. I have 20 on the right side. 24 is not equal to 20, therefore 6 is not the value of x.
- Vocabulary
- Equation DEFINE
Two expressions that have equal value separated by an = sign.
- Algebraic equation DEFINE
An equation that has a symbol representing an unknown number.
- Variable DEFINE
A symbol, like x, used to represent an unknown number.
- Inverse Operations DEFINE
Opposite operations, like addition to subtraction and multiplication to division.
- Addition DEFINE
Adding to a group.
- Subtraction DEFINE
Taking away from a group.
- Multiplication DEFINE
Combining equal groups.
- Division DEFINE
Splitting into equal groups.
- Equation DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide