Expressions & Equations
5-‐‑D process (or any other method that works for you)
In the first three football games of the season, Carlos gained three times as many yards as
Alston. Travis gained ten yards more than Carlos. Altogether, the three players gained a total of 430
yards. How many yards did Carlos gain?
Solving an equation mat
What does x need to equal to make the statement true?
Be principled --Do your own work (and show your thinking). --Check your work in another color. --Post to Seesaw (folder: Assessments). --Complete the Reflection (and post as well)
Name __________________________________
Chapter 6 – Practice Exam
Graphing & Solving Inequalities
Write an inequality to represent each of the graphs below.
Zerivon has two new cell phone plans. The first, called The Texter, has a base charge of $4.00 per month plus 10¢ per character texted. The second plan, called The Talker, has a base charge of only $2.00 per month plus 15¢ per character texted. Under what conditions would you choose TheTexter plan? When would you choose TheTalker plan? What is the significance of the boundary point? Explain completely and make recommendations.
Writing expressions
Kindra would like to have at least $1500 in her savings account.
• If she starts with $61 in her savings account, write an inequality to show how much she wants to have.
• How much does Kindra need to save? Show your solution as an inequality with symbols, in words, and on a number line.
Evaluating expressions
Check (How do you know this is the correct answer?)
8m −17 = −41
Statistics & Probability/ Number System
Probability/fractions
Hawkeye and BJ love to buy chocolate.
On a recent trip to Tokyo, Hawkeye bought of a pound at the first candy store they visited, and of a pound at the second store.
BJ bought only of a pound at the first store, and of a pound of chocolate at the second candy store. How many pounds of chocolate did they buy altogether? Write your answer as a fraction larger than one, and as a mixed number.
Diamond problems with +/-‐‑ (multiply to get the top number -‐‑-‐‑-‐‑ add to get the bottom)
Ratios & Proportions
Scale factor (figures)
Triangles XYZ and LMN are similar.
• By what ratio was triangle XYZ enlarged by to create triangle LMN? Explain how you know.
• What is the ratio of side lengths of triangle XYZ to triangle LMN?
• Calculate the length of the missing side of triangle LMN. Show your work.
CPM- Chapter 6- Practice Exam Reflection and “Moving Forward” plan
___________ (Student initials when complete): Go to Google Classroom (filter: Solutions) and check your work (different color). Big Idea Skill Level & Plan for Practice/Challenge
RED (don’t get it) YELLOW (sort of get it and made mistakes) GREEN (get it, but made small mistakes) PURPLE (totally get it and no mistakes-- ready to take it to the next level)
Expressions & Equations Word Problems (5-‐‑D) Solving an equation mat Graphing & Solving Inequalities Writing expressions Evaluating expressions
Study Guide & Course 2 Simplifying Expressions 5-‐‑D Process (on an expression mat) p. 73 #1-‐‑12 p. 58 #1-‐‑15 Comparing Quantities Solving Equations in Context (on an expression mat) p. 89 #1-‐‑20 p. 83 #1-‐‑12 Graphing & Solving Inequalities Writing Equations For Word Problems (also equations) p. 79 #1-12 p. 86 #1-9 p. 87 #1-9
Proportions (Ratios & Proportions) Scale Factor
Study Guide & Course 2 Scaling Figures & Scale Factor p. 44 #1-‐‑6
Statistics & Probability Number System Probability/fractions
Diamond Problems (+/-‐‑)
Integers
Study Guide & Course 2 Fraction Decimal Percent Operations with Fractions p. 23 #1-‐‑24 p. 32 #1-‐‑4, p. 33 #1-‐‑6 Operations with Integers Diamond Problems (subtraction) (+ and – integers) p. 36 #1-‐‑15 p. 18 #1-‐‑16 Operations with Integers (Multiplication & Division) p. 29 #1-‐‑40
______________Student Initials: Photo this entire document into Seesaw (folder Assessments) so that you can use it remember what you were thinking—and study again if you want. ______________Parent Initials: Bring this document home and show your parents. Once you have a parent signature, photo it into Google Classroom. (Google Classroom: Where you turn things in that require a signature.
STUDY GUIDE
Expressions & Equations
5-‐‑D process
A rectangle has a perimeter of 30 inches. Its length is one less than three times its width. What are the length and width of the rectangle?
Solving an equation mat
1.) Alex was freaking out when he saw this equation mat. He instantly started whining to his team. "I can’t do that! I’ve never seen one with an xy tile on it . I’m doomed!"
"Relax," Tisha said calmly. "Look, it might have something different added, but I think you can still do this problem like all the others ones we have done. Try it!"
What do you think: can this be done like all the other ones as Tisha suggested?
Or, is Alex doomed?
Justify your answer.
2.) Represent using an expression mat and algebra tiles. Sketch each representation.
3.) Simplify the mat and, if possible, decide which expression is greater.
Are there any values of x that would make both sides equal? Explain.
Simplify each of the expression mats as much as possible. Which is greatest? Which has the smallest value? Record all your work carefully.
Graphing & Solving Inequalities
Complete the Inequalities Web/Table below. Graph
Words
Symbols
Writing expressions
How can you represent the description below with an expression?
Julian is three inches less than twice Maureen’s height.
Now, if Maureen is 32 inches tall, how tall is Julian? Why?
x ≥ −5
638 Core Connections, Course 2
6.1.4 How can I find all solutions? • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Solving One Variable Inequalities In this lesson, you will work with your team to develop and describe a process for solving linear inequalities. As you work, use the following questions to focus your discussion.
What is a solution?
What do all of the solutions have in common?
What is the greatest solution? What is the smallest solution? 6-35. Jerry and Ken were working on
solving the inequality 3x �1� 2x . They found the boundary point and Ken made the number line graph shown at right.
Jerry noticed a problem. “Doesn’t the line at the bottom of the � symbol mean that it
includes the equal part? That means that x = 1 is also a solution. How could we show that?”
“Hmmm,” Jerry said. “Well, the solution x = 1
would look like this on a number line. Is there a way that we can combine the two number lines?”
Discuss this idea with your team and be prepared to share your ideas with the class. 6-36. The diagram at right shows three possible ways to
represent inequality statements. Review the meanings of the inequality symbols >, <, � , and � with your team. Then, generate the two missing representations from each inequality described in parts (a) through (c) below.
a. x < �1 12 b. x is greater than or equal to two.
[ x is less than negative one and one-half ] [ x � 2 ]
c. [ x is less than or equal to two, x � 2 ]
graph
words
symbols
1 2 3 40–1 –2–3 –4 x
1 2 3 40–1 –2 –3 –4 x 1 2 3 4 0 –1–2–3–4 x
x
x
Word
SymbolGraph
�<�
Andy has started reading a 250-page book. He can read 20 pages each day.
Which expression represents how many pages he will have left after x days?
A. –20x – 250
B. 250 + 20x
C. 250 – 20x
D. 250 – 20
D. 20x – 250
Evaluating expressions
Check!
Check!
Statistics & Probability/ Number System
Probability/fractions
Calculate the value of each variable
14x −12 = 7x + 2
9w + 2 + 3w = 2 4w − 3( )
Calculate
Diamond problems with +/-‐‑
Ratios & Proportions
Scale factor (figures)
The actual height of the car is shown in the scale drawing. Use the scale ratio indicated to determine the appropriate height for the scaled drawing.
The actual width of the car is shown in the scale drawing below. Use the scale ratio indicated to determine the appropriate width for the scaled drawing.
Triangle ABC is similar to triangle DEF. Solve for both of the unknown sides.
Each pair of figures below is similar. Calculate the length of the unknown side.
a.
b.
c.
d.