Aim
I can review for my Unit 5 review test by using the slides to review the past modules.
MODULE 11
11.1 WRITING EQUATIONS TO REPRESENT SITUATIONS
Vocabulary:
- Equation: An equation is a mathematical statement that two expressions are equal. An equation may or may not contain variables, for an equation that has a variable.
- Solution: A solution of the equation is a value of the variable that makes the equation true.
Types:
- Numerical
- Words
- Algebraic
Equation Chart:
Expression
5+4
A number plus 4
n+4
Equation
5+4=9
A number plus 4 is 9
n+4=9
An expression represents a single value. An equation represents a relationship between two values. An equation relates two expressions using symbols or is or equals.
EXAMPLES
Example 1
x+9=15; X=6
- 6+9=15 (Substitute)
- 15=15 (Check the Equation)
Example 2
y/4 = 32;y=8
- 8/4 = 32 (Substitute)
- 8/4 = 8 × 4 = 32 (Check the equation)
Example 3
8x = 72; x=9
- 8 (9) = 72
- 72 = 72
Example 4
11 = n+6;n=5
- 6+5 = 11 (Substitute)
- 11 = 11 (Check the Equation)
MINI - LESSON: WRITING EQUATIONS TO REPRESENT SITUATIONS
Example 1
Mark scored 17 points for the home team in a basketball game. His teammates as a group scored p points. Write a equation to represent this situation.
Mark's Points = 17
Teammates Points = р
Total Points = 46
MINI- LESSON: WRITING AN EQUATION AND CHECKING SOLUTIONS
Example 1
Sarah used a gift card to buy $24 worth of groceries. Now, she has $18 left on her gift card. Write an equation to represent this situation.
x-24=18
42=24 = 18
18=18
(Substitute)
(Checking the Equation)
11.2: ADDITION & SUBTRACTION EQUATIONS MODELING EQUATIONS
Modeling Equations:
A puppy weighted 6 ounces at birth. After two weeks, the puppy weighed 14 ounces. How much weight did the puppy gain?
Let x represent the number of ounces gained.
Weight at birth + Weight Gained = 6x + x Weight after 2 weeks = 14
To answer this question, you can solve the equation 6 + x = 14
MINI-LESSON USING SUBTRACTION TO SOLVE EQUATIONS
Example 1
a+15=26
- a+15=26
- 15-15 = x 26-15 = 11
- a= 11
- 11 + 15 = 26
MINI-LESSON USING ADDITION TO SOLVE EQUATION
Example 1
y-21 18
- y-21 18
- =
- 21- 21 =
- 18+ 21 = 39
- 39 21 = 18
MINI-LESSON: SOLVING EQUATIONS THAT REPRESENT GEOMETRIC CONCEPTS
You can write equations to represent geometric relationships.
Recall that a straight line has an angle measure of 180°. Two angles whose measures have a sum of 180°, these are called supplementary angles. Two angles whose measures have a sum of 90° are called complementary angles.
Example 1
Unknown Angle + 60° = 180°
x+60=180
60=60 = x = 180
- 60 = 120
X = 120
The unknown angle measures 120°.
MINI-LESSON: WRITING REAL-WORLD PROBLEMS FOR A EQUATION
You can write a real-world problem for a given equation. Examine each number and mathematical operation in the equation.
Example 1
- 21.79
- X= 25
- 21.79 21.79 = x = 25
- 21.79 3.21
- x= 3.21
11.3 MULTIPLICATION & DIVISION EQUATIONS MODELING EQUATIONS
Deanna has a cookie recipe that requires 12 eggs to make 3 batches of cookies. How many eggs are needed per batch of cookies?
Let x represent the number of eggs needed per batch. Number of batches X Number of eggs per batch = Total eggs
3
X
X
||
12
Using multiplication and common knowledge you can figure the solution to the equation by modeling the equation differently stating the information.
STEPS TO SOLVE A WORD PROBLEM:
Junita is scrapbooking. She usually completes about 9 pages per hour. One night last night she completed pages 23 through 47 in 2.5 hours. Did she work at her average rate?
Steps:
- Analyze Information
- Formulate a Plan
- Solve
- Justify and Evaluate
HOW TO SOLVE WORD PROBLEMS
- Analyze Information:
Identify the important information:
- Worked for 2.5 hours
- Starts on pg 23 and ends on page 47
- Scrapbooking rate: 9 pages per hour
Formulate a Plan:
Solve an equation to find the number of pages Junita can expect to complete ?
Compare the number of pages Junita can expect to complete with the number of pages she actually completedSolve:
Let n represent the number of pages Junita can expect to complete in 2.5 hours if she works at her average rate of 9 pages per hour.
n/2.5
Juanita can expect to complete 22.5 pages in 2.5 hours. Juanita completed pages 23 through 47, a total of 25 pages. Because 25 > 22.5, she worked faster than her expected rate.
Justify & Evaluate:
= 9 2.5 x 9 = 22.5 n = 22.5
You used an equation to find the number of pages. Juanita could expect to complete in 2.5 hours if she worked her average rate. Y
