1. How can you use simple equations to solve real life problems?
Use the following quadrilaterals and their measurements provided to fill in the table. (The notation m<A denotes the measure of angle A.)
a b c. B
85° A
87° A
105° A
45° B
98° B
150°
85° C
D 72°
78° C
D 110°
80° C
D 85°
Quadrilateral
m<A
(degrees)
m<B
m<C
m<D
m<A + m<B + m<C + m<D a. b. c.
105°
98°
85°
72°
360°
45°
150°
80°
87°
78°
110°

2. Make a Conjecture.
Conjecture: an unproven statement about a general mathematics concept. Use the table in part 1 to make a conjecture about the sum of the angle measures of a quadrilateral. Discuss your conjecture with an elbow partner.

3. Apply Your Conjecture a. b. c.
Use your conjecture to write an equation for each quadrilateral. Then use your equation to find the value of x.
a b c.
85°
78°
30°
100° x°
80° x°
90°
72° x°
90°
60°
x + 80 = 360
x = 360
x = 360
x = 360
x = 150°
x = 360
x = 95°
x = 360
x = 150°

4. 1.1 Solving Simple Equations

5. Some Vocabulary for Solving Equations
Equation: a statement that two expressions are equal Solution: a value that makes the equation true Inverse Operations: two operations that undo each other (ie addition and subtraction) Equivalent Equations: equations that have the same solution

6. Core Concepts
Properties of Equality Addition Property of Equality Adding the same number to each side of an equation produces an equivalent equation. If a = b, then a + c = b + c

7. Core Concepts
Properties of Equality Subtraction Property of Equality Subtracting the same number to each side of an equation produces an equivalent equation. If a = b, then a - c = b - c

8. Example 1
x – 3 = -5
.9 = y + 2.8

9. You try!
n + 3 = -7
g – 5 = -12
6.5 = p + 3.9

10. Core Concepts
Properties of Equality Multiplication Property of Equality Multiplying each side of an equation by the same nonzero number produces an equivalent equation. If a = b, then a • c = b • c

11. Core Concepts
Properties of Equality Division Property of Equality Dividing each side of an equation by the same nonzero number produces an equivalent equation. If a = b, then a ÷ c = b ÷ c

12. Example 2
a) b.) 1 1

13. You try!
1.) )

14. Core Concepts Four-Step Approach to Problem Solving
Understand the Problem
What is the unknown? What information is given? What is being asked?
2) Make a Plan
The plan could include one or more of the problem-solving strategies.
3) Solve the Problem
Carry out your plan and check that each step is correct.
4) Look Back
Examine your solution. Check that it makes sense in the original statement of the problem.

15. Common Problem-Solving Strategies
Use a verbal model.
Draw a diagram.
Write an equation.
Look for a pattern.
Work backward.
Guess, check and revise.
Sketch a graph or number line.
Make a table.
Make a list.
Break the problem into parts.

16. Example 3
On January 22, 1943 the temperature in Spearfish, South Dakota fell from 54°F at 9:00 am to -4°F at 9:27 am. How many degrees did the temperature fall?
Understand the Problem
Make a Plan
Solve the Problem
temp at 9:00 am - # of degrees temp fell = temp at 9:27 am
t =

17. 54 – t = -4 54 – t – 54 = -4 – 54 -t = -58 -1t = -58 -1 -1 t = 58
The temperature fell 58° 4) Look Back

18. You try!
You thought the balance in your checking account was $68. When your realize that you forgot to record a check. The bank statement lists your balance as $26. Write and solve an equation to find the amount of the check you forgot to record.
previous balance – forgotten check = bank statement balance
x = 26

19. 68 – x = 26 68 – x – 68 = 26 – 68 -x = -42 x = 42 The check she wrote was for $42