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.