Before I introduce students to algebraic equations, they will review the previous topics of evaluating algebraic expressions, translating algebraic expressions, and simplifying algebraic expressions.
Evaluate each algebraic expression.
1) 4x3 + 6 for x = 2.1
2) 26.5 + k for k = 2.7
3) 45 - n for n = 0.86
Write as an algebraic expression.
4) 15 decreased by a number
5) 8 less than a number
Simplify the algebraic expression.
6) 3(4a + 2) + 5(8 + a) + 9
At this point, students should be able to work on these problems independently. As students work, I will circulate throughout the class monitoring their work.
Problem 1 - Students may not perform the order of operations correctly and multiply 4 times 2.1 first, instead of applying the exponent to 2.1.
Problem 2 and 3 - Students may not line up the decimal points.
Problem 5 - Students may not invert the order due to the expression "less than".
Problem 6 - Students may not clear the parentheses before combining like terms.
Before beginning the lesson on solving algebraic equations, I will discuss with students important vocabulary that will be used in the lesson. I will ask the following questions before giving students formal definitions.
What's the difference between an algebraic expression and algebraic equation?
Can you solve an algebraic expression?
What sign should be used if you're writing or solving an algebraic equation?
What is the operation that will undo addition? Is the reverse true?
What is the operation that will undo multiplication? Is the reverse true?
Equation - a mathematical statement with an equal sign
Inverse operations - operations that undo each other
For this lesson, I will use manipulatives (algebra tiles) to help students understand the work we will show for solving algebraic equations. Students will be given page 1 of the Solving Algebraic Equations with Algebra Tiles.
Example 1 - Solve the equation j + 7 = 13
Can we find out what j is using mental math? What value of j makes the equation true?
Students should know that j = 6.
I will explain that mental math is one strategy for solving algebraic equations, but when we move on to more difficult algebraic equations using mental math will not be the best strategy.
Before we solve equations algebraically, I will explain to students that the there are always two important steps to solving equations.
First, always keep the equation balanced. Whatever operation you perform on the left side of the equal sign should be performed on the right side.
Second, to undo an operation, we must perform the inverse operation.
Example 2 - Solve the equation algebraically. x + 3 = 5
For this example, each student should take 1 green rectangle tile and 8 yellow circle tiles. I will explain that we will use the tiles to represent and solve the equation. Students should begin by placing the tiles to represent the original equation (See Solving Algebraic Equations with Algebra Tiles, page 2).
If we want to solve for the variable, we have to isolate the variable. How can we get rid of the 3?
It is important for students to understand that we need to perform an inverse operation to isolate x, so we need to subtract 3 from both sides of the equal sign.
Example 3 - Solve the equation algebraically. z - 2 = 4
What tiles do we need to represent this equation?
Students should use 1 green rectangle tile, 2 red circle tiles, and 4 yellow circle tiles. (See Solving Algebraic Equations with Algebra Tiles, page 3).
What inverse operation do we need to perform to isolate z?
Students should understand that we need to add 2 to both sides of the equation.
For the remaining examples, students will have the option of using the worksheet to help them solve it algebraically. I will model solving the problem algebraically while students solve the problem in their notebooks.
Example 4 - Solve the equation algebraically.t - 21 = 9
Example 5 - Solve the equation algebraically.4z = 24
Example 6 - Solve the equation algebraically.n/4 = 7
The Independent Practice will give students an opportunity to practice solving algebraic equations. Students may continue to use the algebra tiles, although it may be more difficult for the equations that have fractions and decimals.
Solve each equation algebraically.
1) c + 3 = 12
2) y - 607 = 134
3) 6z = 1236
4) r/8 = 72
5) 13 = x + 4
6) r - 2/3 = 3/4
7) x - 4.2 = 3.7
8) 9.1 + a = 12
After 10 minutes students will compare and discuss their work with their group. They should verify that they used the same inverse operation and compare their answers.
Although I haven't introduced a formal check of their solution, I want students to begin to think about it.
How could you check to see if your solution is correct?
I will discuss with students how substituting their answer for the variable will verify if the value makes the equation true. I will choose one of the Independent Practice problems to show how to perform a check.