Summer Math Practice 2020: 7 Pre-Algebra Entering 8 Algebra 1 · 2020-06-01 · Summer Math Practice 2020: 7th Pre-Algebra Entering 8th Algebra 1 Dear Students and Parents, This math

Summer Math Practice 2020: 7th Pre-Algebra Entering 8th Algebra 1 Dear Students and Parents, This math requirement is due to Mr. Cyrus when we return to school. The objective is to make sure you have a solid foundation to help you make a successful transition to the pace and depth of Algebra 1 coursework. Specific algebra-readiness skills include flexibility with rational number operations, fluency with algebraic language, and understanding of properties used when solving equations. Successful Algebra 1 students are curious problem-solvers, willing to think, to reason, and to apply different strategies. Because of the unusual situation in the last quarter of this year, we did not have a final exam or any time to review. That means an important second objective of this work is to help you review and practice skills and concepts. As such, this required assignment contains content we have explored in class this year. And of course, any skills we didn’t get a chance to explore in enough depth will be reviewed and extended in your 8th grade classes. There are 10 two-sided pages. The required work consists of eight two-sided problem sets. The last two pages are optional challenges, explorations, extensions, and problem solving. Spread this work throughout the summer and fit it sensibly into your summer schedule. Please do not complete it all at once either at the beginning or the end of summer. Read questions and directions carefully. Legibility and proper steps (you know what they are!) are expected. Dazzle Mr. Cyrus with the awesome work I know you can do! Calculators are not permitted. Please be thorough, legible, and show your thinking. Think about what the best strategy for the problem would be, and if it doesn’t work, try again. Check to see if you have really answered the question and if your answers are reasonable. You have sharp number sense; don’t forget to use it! Work smarter, not harder! The back of this page has some reminders and ideas about resources to help review skills as you complete your work. I am sad that our time together this year being “mathy” together was cut short, but I am so very proud of your efforts and attitude during remote learning. I know it wasn’t easy, but you approached challenges with grit and a growth mindset. You were all willing to show up and play along in a game with brand-new rules; I am so grateful! Have a wonderful summer and I can’t wait to SEE you when we return to school! Mrs. Matthews NOTE: If your work was done with help from a tutor, we would like to know.

Please write the name of the tutor or program here _________________________________

Some ideas and reminders about skills and resources…. If you don't remember a skill, please get help to fill in the gap. DO NOT just guess or fill something in randomly. Take advantage of your digital notes and your math notebook. You will find some problems are straightforward, while others may require more thinking. Examples of skills and ideas easily forgotten or mixed up:

• distributing negative 1 when simplifying an expression like (𝟎. 𝟐𝒙 − 𝟎. 𝟑) − (𝒙 − 𝟎. 𝟏) • knowing who’s your base in an expression like −𝟓𝟐 versus (−𝟓)𝟐 • substituting negatives when evaluating an expression like |−𝒙 + 𝒚| − 𝒙 given 𝒙 = −𝟖.

• solving more complex equations such as 𝟑𝒙𝟓+ 𝒙$𝟏

𝟑= 𝟐

𝟏𝟓.

The Solve Me Mobiles app is a great way to build visual thinking and reasoning for equations and systems. Check out some higher levels and explore different features. Take some time to explore the Desmos graphing calculator app. (not student.desmos.com site). We didn’t get a chance to play with this, but as you move up in math, a graphing calculator will become an essential tool. Curious? Check out to see what it can do…

Input a set of ordered pairs to see the graph. Input a line in slope-intercept form; change the slope and y-intercept. Input lines with the same slope to see that they are parallel. Input a line not in slope-intercept form, see how it rewrites it for you. Input a system of equations to see the graph and solution.

The list below gives a reference to IXL if you need reminders. NOTE: The IXL system remembers if you have done a skill previously. That’s okay – keep working from where you start, and the system will reset any skill completed to 100%. You’re using IXL to review, not to get a grade. IXL Level I and J References for Pre-Algebra Skills Fraction Applications and Computation IXL Level I, skills G1 - G18 Percent IXL Level I, skills L1 - L10 Algebraic Expressions IXL Level I, skills R1 - R7; R10; R13 - R16

Solving One-Variable Equations IXL Level J, skills W1 - W15 Inequalities IXL Level J, skills X1 - X9 Proportional Relationships IXL Level I, skills K1 - K8 Lines and Angles IXL Level I, skills W16 – W20 Linear Equations in Two Variables IXL Level I, skills U7, U8 Slope IXL Level J, skills Y1 - Y8 Linear Systems IXL Level J, skills AA1-AA4; AA8, AA9

SET 1a SUMMER SKILLS 2020 7TH Pre-Algebra Entering 8th Algebra NO Calculators. Support answers by showing thinking and justifying reasoning. Circle answers.

Heights of students at a school vary from 2 !!!"

feet to 5 "# feet. Find the range of the heights,

expressed in feet. (no decimals).

Find the perimeter and area of this right triangle. Measurements are in inches. 2 "# 5 $

%&

4 '

(

Simplify. a.) −5 %

#− 9 "

&

b.) −3 &

$ 1 %(

%"

Simplify the numerical expressions. Order of operations! a.) 90 − (12 ÷ 0.3) ÷ 2(

b. ) &−12)

"− &−

34) ∙ &

29)

Solve the equation.

%'𝑥 −%

'+%

)= 6

Ralphie spent 35% of his total savings on a laptop that cost $700. How much money did he have in his savings before he bought the laptop?

•

SET 1b SUMMER SKILLS 2020 7TH Pre-Algebra Entering 8th Algebra NO Calculators. Support answers by showing thinking and justifying reasoning. Circle answers.

I am making costumes for a play. Each needs 2 ¼ yards of fabric. How many complete costumes can I make from 7 ½ yards of fabric? How much FABRIC will be leftover?

The sum of two rational numbers is −8 "#. One of

the numbers is 5 #$. What is the other?


)+ 2 $

#

b.) ""

$#× %(

%%" simplify before you multiply

Simplify the numerical expression. 102.64 ÷ (0.4 − 1.2) + (

$(−0.42)

Solve the equation. 5.4𝑥 + 1 = 5𝑥 − 15

25% of the people attending the basketball game are women. 25% are girls, 20% are boys, and the remaining 180 people are men. Find the total number of people attending the game.


The division expression !%÷ "

#

(Think; answer questions; DO NOT calculate)

• shows how many groups of __________ go into __________

• has a divisor of ________ and a dividend

of ________

• has a quotient less than or greater than 1. (circle)

I used #& of a 5 "

# pound bag of apples for a pie.

a.) How many pounds did I use? b.) How many pounds are left?


#− 9 "

&

b.) 6 %

*÷ 3 '

(

Simplify. Careful. −5" is not the same as (−5)" (Who's your base?) Follow order of operations. −5' + 21 ÷ (

) ∙ ('

Solve the equation. '"𝑥 − %

)(𝑥 − 8) = %(

'

Of the four sets of numbers, circle the letter of the set that best describes the points shown.


A bucket can hold 6 ½ liters of water when it is full. A 500-milliliter jug is used to fill the bucket. How many full jugs of water are needed to fill the bucket?

Ralphie has a large tropical fish collection. He gives 2/3 of his fish to a local high school. Then he gives 2/5 of the remaining fish to a middle school. In the end he has 30 fish left. How many did he have at first? A diagram may help.

Find the product or quotient. a.) − #

%"÷ 32

b.) 1 (

) ∙ 3 (

%)

Evaluate the expressions given 𝒙 = −𝟔𝑎𝑛𝑑𝒚 = −𝟕

𝑎. )6 − ?−18𝑥@ + 7𝑦

𝑏. )|−𝑥 + 𝑦| ∙ 𝑥'

Write and solve an equation to find the value of x. Then find the side length and perimeter of this regular hexagon.

This year there are 36 students playing baseball. This is a 20% increase from the number of students playing last year. How many students played last year?


a.) What is one-third of three-fourths? Draw a diagram to support your answer. b.) How many fourths are in two and a half? Draw a diagram to support your answer.

Ralphie earns $2400 each month. He spends 25% of his salary on food, 40% of his salary on rent, and 10% on student loans. He puts 20% of what's left in his savings account. How much does he put into his savings account?

Compare with >, <, or =. Use number sense and reasoning. NO actual computation. a.) %

#÷ 2 ______ %

#÷ %

'

b.) %

'× %

' ______ − %

'+ D− %

'E

c.) − %

(+ (

) _______ − (

)+%

(

d.) "

&× '

( _______ '

(

Simplify the expressions.

−3?12𝑥 − 4@ − 2𝑥

4(0.2𝑥 − 0.3) − (𝑥 − 0.1) (distribute the -1)

Ralpie is saving for 12 weeks to buy a laptop that costs $1345. He has already saved $145. How much should he save each week so he can buy the laptop? Write and solve an equation.

Compare these real numbers with >, <, or = (careful with negatives). √190______16 −√18_______ − 4

15______

>100225

(√𝑥)"______𝑥


“If 𝑎 and 𝑏 are positive integers, then 𝑎 − 𝑏 MUST be a positive integer.” Is this correct? Support your answer with a number example. If 𝑎 is a negative integer and 𝑏 is a positive integer, tell whether the expression 𝑎 − 𝑏 represents a positive or a negative integer. Support your thinking with a number example.

Mom collected toys for charity. She donated 3⁄4 of the toys to Charity A. Then she donated 1/3 of the remaining toys to Charity B. If she has 10 toys left, how many toys did she collect?

Find the sum. a.) 3 #

$+ B−5 !

&C

b.) −4 (%&+ D−2 %

&E

Simplify the expressions. −3(𝑥 − 6) + 8𝑥 − 2 + 5.25

−3.6 ?𝑥 −12@ − 7 + 5𝑥

Write the sentence as an inequality; solve and graph the solution. "Five more than the quotient of a number and negative 6 is at least 9."

In the diagram, the ratio a:b is 2:3. Find the values of a and b.

6

10

? 2x


Circle the equation NOT equivalent to

𝟏𝟖(𝟒𝒙 − 𝟓) = −𝟑

4𝑥 − 5 = −24 𝑥 = − %*

)

%'𝑥 − "

#=−3 4𝑥 − 5 = − (

#

𝐵𝐸G⃖GGG⃗ 𝑎𝑛𝑑𝐶𝐴G⃖GGG⃗ are straight lines. Find the values of the variables and the missing angle measures.

First, write an expression for the missing measurement. Then write and simplify an expression for the area of this polygon.

Factor these expressions completely. a.) 3𝑥 + 57𝑦 + 15 b.) −12𝑥 − 16𝑦 c.) 55𝑥 + 11𝑦 + 132𝑧

Solve the inequality. Graph the solution. 38(6𝑥 − 4) > −

12

Make a table of values following our guidelines. (three x values: pos, zero, neg)

Then graph the equation. 𝒚 = − 𝟏𝟑𝒙 + 𝟒


The cost of seeing a weekday show is 75% of the cost of a weekend show. Last month on vacation, Maddie saw 4 weekday shows and 3 weekend shows. She spent $90 in all. Write and solve an equation to find the price of a weekend show. Let the variable x stand for weekend show price.

Solve the inequality. Graph the solution. Remember when to reverse the inequality sign. −𝟖𝒙 + 𝟎. 𝟒 ≤ 𝟕. 𝟐

Ralphie paid x dollars for a camera and $120 for an extra lens. The sales tax rate is 6%. Write an algebraic expression to show how much he paid for the camera and the lens including sales tax.

At the library, it costs $0.12 to print a page. Mom wants to buy a printer for $125; this printer will cost $0.02 to print a page. She is trying to decide if it is cost effective to buy the printer. Write and solve an equation to find how many pages will make the cost of buying her own printer the same as using the printer at the library.

Make a table of values following our guidelines. (three x values: pos, zero, neg) Then graph the equation. 𝒚 = 𝟐𝒙 − 𝟑

𝟒


Solve the equation. 13𝑥 − (𝑥 + 7) = 29

This month a club has 72 members. This is a 50% increase from the number of members in the club last month. How many members were in the club last month?

Identify the parts of this expression. −𝒂 − 𝟑𝒃 + 𝟐𝒄 + 𝟒 coefficients: constants: how many terms? how many variables?

First, write an expression for the perimeter of this rectangle; then simplify your expression.

Solve the equation. 23(3𝑥 − 9) = −36

Find the measure of the numbered angle.


𝑨𝑩G⃖GGG⃗ is parallel to 𝑪𝑫G⃖GGG⃗ . Use the diagram to answer these questions. 1. Name one pair of corresponding angles. 2. Name one pair of alternate interior angles. 3. Name one pair of alternate exterior angles. Solve the equation. 2(2 − 1.5𝑥) = −8

Solve the equation.

()*+ )$+

(= ,

+*

Write and solve an equation to find the value of x; then find the side length of this regular hexagon.

Ralphie says the line in Graph B has a greater slope than the line in Graph A because it is "steeper". Is he correct? Use slope to justify your answer.


Find the slope of each line from the graph. a. b.

Write the slope and the y-intercept. Then graph the equation. 𝒚 = −𝟐𝒙 + 𝟑 slope: ______ y-intercept: _____

Graph the line passing through (-3, 5) with a slope of -3/4. (Graph the point, then use the slope to get the next point.)

Find the slope of the line passing through the pair of points. No graph; support your answer with slope formula. (ratio of change in y over change in x) (-2, 3) (-4, -1)

Solve for y to express in slope-intercept form. Then graph the equation. No table of values. 4𝑥 + 2𝑦 = 6

Circle the statement that is true. a.) Line b has a slope of zero.

b. ) The equation of line b is x=3.

c.) The equation of line a is y=3.

d.) Line a has a slope of zero.


Find the measures of the numbered angles.

Solve the equation.

6 +13(𝑥 − 9) =

12(2 − 𝑥)

Look at this list of six different inequalities. Think and circle the ones that have a solution with values greater than 5. 5 < 𝑥 −2𝑥 < 10 𝑥 − 3 > 2 −𝑥 − 7 < 2 −𝑥 > 5 3𝑥 − 4 < 2𝑥 + 1

Which is steeper, the boat ramp or a road with a 20% grade? Clearly support your answer.

An equation of a line is 2𝑦 = 6 − 3𝑥. Solve for y to answer these questions. a.) What is the slope? b.) What is the y-intercept?

Sketch (just sketch, no equation or points) a line with a positive slope and a negative y-intercept. Through which three quadrants does it pass?


a.) If -. = 22 and the value of r is 242, what is the

value of s? b.) If 𝑥 is a rational number such that 𝑥 divided by

$# is (

", what is the value of 𝑥?

Graph a line with a slope of -3/4 and a y-intercept of 3.

Apply your number sense and reasoning. Circle the larger amount in each row. Think. No need for calculations. Really. Row 1 60%𝑜𝑓9950%𝑜𝑓199 Row 2 75%𝑜𝑓8080%𝑜𝑓90 Row 3 25%𝑜𝑓95090%𝑜𝑓200 Row 4 30%𝑜𝑓15150%𝑜𝑓12

Evaluate this expression given 𝑥 = −7; 𝑦 = 7 .

−0.6(5𝑥 − 8𝑦) + √225

Factor these expressions completely. a.) −5𝑥 + 120𝑦 b.) −8𝑥 − 16𝑦 + 24 c.) 51𝑥 − 39𝑦 − 66𝑧

A laptop's original price is $800. It is on sale for 25% off. The sales tax rate is 8.5%. How much did I pay for the laptop?


When 12 is subtracted from a number n, the result is one-third of n. What is the value of n?

If 2𝑥 − 1 = 6 , what is the value of 4𝑥' − 1?

Careful. 4𝑥" and (4𝑥)"are not the same.

Simplify. a.) !'

"'× #($(× !("(

simplify before you multiply! b.) − "

)− B− !

#C − B− #

'C

Graph the line passing through (-3, 5) with a slope of -3/4.

Solve the system graphically. Make sure to write the solution as an ordered pair (x,y). 𝑦 = 3𝑥 − 4

𝑦 = −12𝑥 + 3

Solve the system with substitution. Make sure to write the solution as an ordered pair (x,y). 2𝑥 + 𝑦 = 5 𝑦 = 4𝑥 − 7


Solve the inequality. Graph the solution. Remember when to switch the inequality sign. −3𝑥 − 2 ≥ 5𝑥 + 1

Evaluate given 𝑥 = −3 and 𝑦 = 2 Think. Careful. Who's your base?

a.) 2𝑥" − *!

$

b.) (𝑥 + 𝑦)" − 𝑦" c.) (2𝑥)" − 2𝑥"

Choose from the set of positive integers from 1 to 20. Create a set of five positive integers so that the values of their mean, median, and range are all the same.

Find the slope of the line passing through the pair of points. No graph; support your answer with slope formula. (ratio of change in y over change in x)

( !" , 0) and ( #

" , !$)

Translate into an algebraic expression.

• 3 less than 3% of a number n

• A number n increased by 3%

• A number n decreased by 25%

Solve the equation.

78−14𝑥 =

12𝑥 −

14


Which of these expressions is equivalent to −0.05(𝑥 − 40) ? a.) −0.05𝑥 + 20 b.) −0.05𝑥 − 20 c.) −0.05𝑥 + 2 d.) −0.05𝑥 − 2 .

Give an equation of a line parallel to the line

𝑦 = −3𝑥 − 1

Give an equation of a line with a larger slope than the slope in the equation 𝑦 = !

#𝑥 − 2.

Using only the digits 1 - 8 (without repeating any digit) fill in the boxes to create these number types:

Solve the equation. 3(𝑥 − 1) − 8 = 4(1 + 𝑥) + 5

5 '& cups of water fill 4 !

" identical water bottles.

How many cups fill each bottle?

OPTIONAL: Linear Equations Stained Glass Window Graph a set of linear equations to create a stained-glass window design Bring your colorful design to Algebra class in August! Directions: Graph the 10 lines shown on the attached coordinate grid. Use a ruler. Make sure each line extends to the edge of the 12x12 coordinate plane. Label each line with the equation and also the line number. Don't forget arrows. Color sections with colored pencils or crayons (NOT markers) to make a stained glass design. First, get your set of points. For each of these lines, fill in the table with the coordinates indicated. How? Substitute for the indicated x or y value to find the ordered pair. Having these points will make it easier for your lines to accurately extend to the edges of the grid. (I did the first equation as an example.) NOTE: You will find a few ordered pairs in your table have a y-coordinate that extends past the 12x12 grid. Just don't graph those points in your design.

Equation# Equation y-intercept where x=0

x-intercept where y=0 x = 12 x = -12

1 𝐲 = −𝟏𝟐𝐱 − 𝟒

(0, -4) (-8, 0) (12, -10) (-12, 2)

2 𝐲 =𝟑𝟐𝐱 + 𝟏𝟐

3 𝐲 = 𝟏𝟐𝐱 + 𝟒

4 𝐲 =𝟏𝟐𝐱 − 𝟒

5 𝐲 = −𝟏𝟐𝐱 + 𝟒

6 𝐲 = −𝟑𝟐𝐱 + 𝟏𝟐

7 𝐲 = −𝟑𝟐𝐱 − 𝟏𝟐

8 𝐲 =𝟑𝟐𝐱 − 𝟏𝟐

9 𝒚 = 𝟏𝟐 NA

10 𝒚 = −𝟏𝟐 NA

Blank side - back

Stained Glass Linear Equations

Blank side - back

Optional Fun Enrichment Activities Not that we need more things digital, but here are a few suggestions for great activities. Many of these activities are also available as non-digital games. 1. Mathigon Activities site. https://mathigon.org/origami One of my favorites on Mathigon is Mathematical Origami. It has instructions to create beautiful 3-D shapes. 2. Exploding Dots site. Exploding Dots Check out the introductory video Exploding dots machines contain an array of boxes containing dots plus a rule describing how to move the dots between the boxes. 3. Area Maze puzzles from this book. Areamaze.com 4. How about Set Game? Also available as a card game. Set Daily Puzzle site

5. KenKen Puzzles Lots of print book versions available too. 6. Hooda Math site Many games and puzzles – not just math. 7. Transum.org site contains a world of puzzles and games, not just math. Just a few pictured here. 8. We played the Muggins board game at Math Night. 9. Give Polyup a try! Play with numbers, functions, and coding through game challenges.

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Summer Math Practice 2020: 7 Pre-Algebra Entering 8 Algebra 1 · 2020-06-01 · Summer Math Practice 2020: 7th Pre-Algebra Entering 8th Algebra 1 Dear Students and Parents, This math