Download Unit.1-3: Solving Equations with Models

Unit.1-3: Solving Equations with Models-1
Explaining solving equations
A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers
asserted at the previous step, starting from the assumption that the original equation has a solution.
Construct a viable argument to justify the solution method.
A-REI.3. Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
Let’s play “What’s My Number?”
1. Determine my number, and explain how you came up with the solution.
2. Determine my number, and explain how you came up with the solution.
3. Determine my number, and explain how you came up with the solution.
4. How did finding the number in Item 3 compare to finding the numbers in Items 1 and 2?
Unit.1-3: Solving Equations with Models-2
5. Determine my number and explain how you came up with the solution.
If you multiply 4 times the sum of 3 and me, and subtract 8 from that value, I am 12. What’s
My Number?
6. How did finding the number in Item 5 compare to finding the numbers you found in Item
1 through 3?
7. Write each of the “What’s My Number?” problems as an equation.
You have probably used or seen different methods to solve equations. Different methods
are useful in different situations.
The working backwards (“the undoing method”) Method
The undoing method “undoes” or reverses the order of operations in an equation. To solve
an equation using the undoing method:
 Create a flowchart to show what happens to the variable. Follow the order of
operations/
 One the line below, work backward by doing the inverse operations.
8. Example 1: Solve 5(x+30) – 18 = 17 using the undoing method. Check your solution.
x
17
Unit.1-3: Solving Equations with Models-3
9. Try to solve this “What’s My Number?” problem using the undoing method. What
problems do you run into?
If you multiply me by 7, subtract 9, and add twice me to that value, I am 90! What’s My
Number?
Algebra Tiles Method
The undoing method can be effective to solve equations that have only one variable term,
When equations become more complex, you may want to use another method, such as
using algebra tiles, to solve.
The pairs (1 and -1 and x and –x) are the additive inverses of each other. They are called
zero pairs since adding them together yields 0.
10. Example 2:
2x + 3 = 5 using algebra tiles.
Remove 3 from both sides
So x has an equivalent value of 1
Try B:
Solve this problem using algebra tiles
Because you can’t remove
2x - 3 = 5
-3 from both sides we need to add zero pairs to the right side.
Unit.1-3: Solving Equations with Models-4
Now we can remove
-3 from both sides.
What will the value of
x be in this problem?
Solve the following problem using algebra tiles: If you multiply two times the sum of 2 and
me, I am 10. What’s my number?
11. Use “undoing” or algebra tiles to solve these two “What’s My Number?” problems.
Which of the methods did you use? Why? What are some of the drawbacks of the two
methods?
(a) If you multiply me by 25 and subtract 37 from that value, I am 113!
1
(b) If you multiply me by ½ and subtract ¾ from that value, I am 3 .
4
Balancing Method
The balancing method is useful when the undoing method or algebra tiles are too
cumbersome. This method is also called the symbolic method or solving equations using
symbols. Keep the ideas from the other two methods in mind as you use this new method.
Example : Solve the equation
4x + 5 = 13using the balancing method.
Example : Solve the equation
x+3
= 2using the balancing method. Check your solution.
5
Example : Solve the equation
x
- 5 = -2 using the balancing method. Check your solution.
3
Check your solution.
Skills Work: Textbook: Page 144 #3-14 all, 15-23 odd, 27-35 odd, Worksheet: How does the
solution change.