Download 1-3 Solving Equations with Models 2015 V2

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 in pairs, show on your white board, you came up with the
solution.
2. Determine my number, and in pairs, show on your white board, you came up with the
solution.
3. Determine my number, and in pairs, show on your white board, you came up with the
solution.
4. How did finding the number in Question 3 compare to finding the numbers in Questions
1 and 2?
Unit.1-3: Solving Equations with Models-2
5. Determine my number and, in pairs, show on your whiteboard 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 Question 5 compare to finding the numbers you found in
Question 1 through 3?
7. Can each of the “What’s My Number?” problems be expressed as an algebraic 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 and solve using the undoing method.
If you multiply me by 7, subtract 9, and add twice me to that value, I am 90! What’s My
Number?
What problems do you run into?
Write an equation in which the undo method way is a suitable way to solve the equation.
Write an equation in which the undo method way is an unsuitable way to solve the
equation.
Algebra Tiles 1 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.
Use algebra tiles to make a model that represents this expression and draw
it in your workbook.
use a rectangle for x
use a rectangle for -x
and a for
and a
1.
for -1.
Unit.1-3: Solving Equations with Models-4
The pairs (1 and -1 and x and –x) are additive inverses. 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
Unit.1-3: Solving Equations with Models-5
Try B:
Solve this problem using algebra tiles
Because you can’t remove
Now we can remove
2x - 3 = 5
-3 from both sides we need to add zero pairs to the right side.
-3 from both sides.
What will the value of
x be in this problem?
Solve the following problems using algebra tiles:
a) 3x +1 = 7
b) 2x - 5 = 1
c) 2x +1 = x + 3
d)
1
(3x -1) = 4
2
What is the problem using algebra tiles for part d? Give an example of a problem that you
cannot use algebra tiles to solve the problem.
Unit.1-3: Solving Equations with Models-6
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
Skills Work:
Solve:
1. 3x+7=19
2. 5h+4=19
3. 7d-1=13
4. 2g-13=3
5. 10=7-m
6. 11 = 12-q
𝑎
7. 3 + 4 = 6
Check your solution.
Unit.1-3: Solving Equations with Models-7
𝑤
8. 17= 5 + 13
𝑏
9. 2 − 9=11
𝑧
10. −6 = 4 − 3
5
11. 7 = 6 𝑐 − 8
2
12. 10 = 7 𝑛+4
13. 8y + 3y =44
14. 11x – 9x =18
15. -32 = -5k + 13k
16. 5.6=1.1p + 1.2
17. 1.2j – 4.3 = 1.7
18. 14.4m – 5.1 = 2.1
19.
𝑐
5.3
+ 8.3 = 11. 3
20. −1.2 =
𝑧
4.6
− 2.7
Worksheet: How does the solution change from the blog.