7thGradeHonorsAlgebra1SummerAssignment2017 DUE:SEPTEMBER13TH,2017

Name:_______________________________________________________

Asanincoming7thgradeHonorsAlgebra1student,itisimportantthatyouareproficientinseveralskillsfrompreviousmathcourses.Thisassignmentcontainsexamplesoftheskillsyouareexpectedtoknow,suchasplacevalue,wholenumber,decimalandfractionoperations,asyouenteryourAdvancedMath6

classthisSeptember. **Completionofthispacketwillcounttowardsyourfirstassessment

grade**

**AllstudentsenteringMath7HonorsAlgebra1willbeassessedontheskillsreviewedinthisassignment**

Ifyouneedassistancewithanyoftheseskills,westronglyrecommendthatyouutilizethevideosthatareprovidedforeachsection.

IntegerOperations7.NS.1-Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. Online Lesson and Practice: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-add-and-subtract/cc-7th-add-and-sub-integers/v/adding-and-subtracting-negative-number-examplesOnlinePractice:https://www.ixl.com/math/grade-7/add-and-subtract-integersPRACTICEPROBLEMSShow the addition on the number line. Then write the sum. 1. 2 + (−3) 2. −3 + (−4)

_______________________________________ ________________________________________

Show the subtraction on the number line. Then write the difference. 3. 3 − 8 4. −5 − (−1)

_______________________________________ ________________________________________

Find the value of each expression. 5. 7 12 15− + + 6. 5 9 13− − −

_______________________________________ ________________________________________ 7.NS.2-Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. Online Lesson and Practice: khanacademy.org – Multiply and Divide Integers

• https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-negative-numbers-multiply-and-divide/cc-7th-mult-div-negatives/v/multiplying-positive-and-negative-numbers

OnlinePractice:• https://www.ixl.com/math/grade-7/multiply-and-divide-integers

PRACTICE PROBLEMS

Simplify.

1. (−4)(7) 2. (−3)(−4) 3. 27 ( 3)÷ − 4. 287−

5. ( 6 4) 2− − ÷ 6. 5( 8) 4− ÷ 7. 6( 2) 4( 3)− − ÷ −

7.NS.3-Solve real-world and mathematical problems involving the four operations with rational numbers. PRACTICE PROBLEMS

1. At 3 P.M., the temperature was 9°F. By 11 P.M., it had dropped 31°F. What was the temperature at 11 P.M.?

________________________________________________________________________________________

2. A submarine submerged at a depth of −40 feet dives 57 feet more. What is the new depth of the submarine?

________________________________________________________________________________________

3. The high temperature on Saturday day was 6°F. The low temperature was −3°F. What was the difference between the high and low temperatures for the day?

________________________________________________________________________________________

4. The outdoor temperature gets 1 degree colder each hour for 3 hours. What is the change in temperature at the end of those 3 hours?

________________________________________________________________________________________ SimplifyAlgebraicExpressions(combineliketermsanddistribute)

6.EE.3-Apply the properties of operations to generate equivalent expressions. CombiningLikeTerms-OnlineLesson:

• https://learnzillion.com/lessons/3275-simplify-algebraic-expressions-by-combining-like-terms

OnlinePractice:• https://www.ixl.com/math/grade-7/multiply-and-divide-integers• http://www.buzzmath.com/Docs#CC06E114

DistributiveProperty-OnlineLessons:

• https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-distributive-property

OnlinePractice:• https://www.ixl.com/math/grade-6/distributive-property• http://www.buzzmath.com/Docs#CC06E116

PRACTICEPROBLEMS

Simplify each expression. 1) −6k+7k 2) 12r−8−12

3) n−10+9n−3 4) −4x−10x

5) −r−10r 6) −2x+11+6x

Use the distributive property to rewrite the expression without parentheses 1. 3(x + 4)

2. - (y – 9)

3. 2(3x – 1)

4. (2x – 4)(-3)

6.EE.4-Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them) Online Lessons and Practice:

• https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-equivalent-expressions

• http://www.buzzmath.com/Docs#CC06E117 PRACTICE PROBLEMS Drawlinestomatchtheequivalentexpressions 2(𝑏 − 6) 12𝑏 𝑏(3+ 9) 𝑏 − 𝑏 3𝑏 + 2𝑏 − 5𝑏 24𝑏 6𝑏(8÷ 2) 2𝑏 − 12

7.EE.1-Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. Online Lessons and Practice:

• http://www.buzzmath.com/Docs#CC07E10514• https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-

expressions/cc-7th-factoring/v/factoring-algebraic-expressionsPRACTICEPROBLEMS

Factor. The first one is done for you. 1. 5x + 10y + 30z = 2. 7a + 21b + 42c =

5 • x + 5 • 2y + 2 • 3 • 5z = ___ • a + ___ • 3b + ___ • ___ • ___c =

5 • (x + 2y + 6z) ______ • (a + 3b + ______c)

3. 4x + 12 4. 6s + 18t + 3w

_______________________________________ ________________________________________

Solve1&2stepequationswithFractionsandDecimals6.EE.5-Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Online Lesson:

• https://learnzillion.com/lessons/2514-understand-that-equations-have-one-solution-using-a-pan-balance

Practice Game:

• http://www.mathnook.com/math/bike-racing-math-algebra.html PRACTICE PROBLEMS

Write each sentence as an equation.

9. Eight less than 13

a number n is 13. 10. A number f multiplied by 12.3 is 73.8.

_______________________________________ ________________________________________ 7.EE.4-Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Online Lessons and Practice Problems:

• http://www.buzzmath.com/Docs#CC06E125&page=1 (Solving Equations Practice) • http://www.buzzmath.com/Docs#CC06E129 (Writing Algebraic Expressions) • http://www.buzzmath.com/Docs#CC07E268 (Writing Algebraic Expressions) • http://www.buzzmath.com/Docs#CC07E10537 (Solving 1 and 2 step Equations) • https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-

variables/cc-6th-alg-expression-word-problems (Writing Algebraic Expressions) PRACTICE PROBLEMS

Here is a key to solving an equation.

Example: Solve 3x − 7 = 8.

Step 1: • Describe how to form the expression 3x − 7 from the variable x: • Multiply by 3. Then subtract 7.

Step 2: • Write the parts of Step 1 in the reverse order and use inverse operations: • Add 7. Then divide by 3.

Step 3: • Apply Step 2 to both sides of the original equation. • Start with the original equation. 3x − 7 = 8 • Add 7 to both sides. 3x = 15 • Divide both sides by 3. x = 5

Describe the steps to solve each equation. Then solve the equation. 1. 4x + 11 = 19

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2. −3y + 10 = −14

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3. 113

r − = −7

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Write 2 variable equations for situations 6.EE.9-Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. 7.EE.4a-Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. Online Lesson-

• https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/8th-linear-functions-modeling/v/exploring-linear-relationships

Online Practice Problems: • https://www.ixl.com/math/algebra-1/write-a-function-rule-word-problems

PRACTICE PROBLEMS Write an equation with two variables to represent each situation. 1. The freshman class is planning a car wash to raise money for your class. The cost per car is $5 and your class already raised $75 from previous fundraisers. How much money can the freshman class make? 2. An electrician charges $80 for a house call plus $50 per hour. How much will the electrician charge? Givenanequation,createinput/outputtablestographaline6.EE.9- Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. OnlineLessonandPractice:http://www.buzzmath.com/Docs#CC06E137PRACTICEPROBLEMSCompleteeachinput/outputtableandthenplotthexandycoordinatesonthegraph.1.2.

12 𝑥 − 3 = 𝑦x y-2 0 2 3

y=-3x+1.5x y-3 0 2 3

MapYourMathematicalRoadTrip!

Directions:Solveeachofthefollowingproblems.Remembertoshowallofyourwork.The

solutionswillgiveyouthexandy-coordinatesofthepointsyouwillplotonyourmap,inorder,

asyoutravelaroundthecountryandback.NOTE:Youdonotretraceyourpathtoreturn

home.

BonVoyage:StartyourtripfromNewJersey!

SolvingEquations:Solveeachequationtorevealthexandy-coordinateforeachlocation.

Showallofyourwork.

http://maps.maphill.com/united-states/simple-maps/political-map/single-color-

outside/borders-labels/political-simple-map-of-united-states-single-color-outside-borders-

labels.jpg

State1:NewJerseyx-coordinate:Solve3x=33y-coordinate:Solve!

! =1

(,)-plotthispointonyourmap!

State2:_________________

x-coordinate:Solvex+8=21y-coordinate:Solve2y–4=8

(,)-plotthispointonyourmap!

State3:_________________

x-coordinate:Solve5x–3=17y-coordinate:Solve-2y+11>3

(,)-plotthispointonyourmap!

State4:_________________

https://www.youtube.com/watch?v=xqDTNA0X-sA

x-coordinate:Solve3(2x+4)=0y-coordinate:Solve-2(4–2y)=16

(,)-plotthispointonyourmap!

State5:_________________

https://www.youtube.com/watch?v=S_OX3ByvBSc

x-coordinate:Evaluatetheexpressionb2–4acy-coordinate:Evaluatetheexpression

ifa=2,b=8,c=9ifa=4,b=5,c=-5

(,)-plotthispointonyourmap!

State6:_________________

https://www.youtube.com/watch?v=Jp25LHI9wII

x-coordinate:Solve y-coordinate:Solve

(,)-plotthispointonyourmap!

State7:_________________

x-coordinate:Solve5x–4-3x=-8y-coordinate:Solve4y+1=-3y+22

(,)-plotthispointonyourmap!

State8:_________________

https://www.youtube.com/watch?v=ClYdw4d4OmA

x-coordinate:-17+2(-3)2y-coordinate:-20+3(2)-13+3(-3)2

(,)-plotthispointonyourmap!

7thGradePARCCReferenceSheetcanbefoundonthewebsitelistedabove.

State9:_________________

https://www.youtube.com/watch?v=16ePaaLFxlg

EVALUATETHEFOLLOWINGANDTHENPLOTTHEMOSTCOMMONXANDYCOORDINATE

x-coordinate:-3+4=y-coordinate:-4+7=

-4-(-3)=4-(-7)=

6+(-5)=6+(-3)=

-23+24=23-(-2)=

1(-1)=-3(-1)=

(,)-plotthispointonyourmap!

RETURNINGHOMETONEWJERSEY

State10:_________________

https://www.youtube.com/watch?v=R3wzwGZFpxM x-coordinate:Solve-3x+2x+14=3y-coordinate:Solve4y+6–2y=10

(,)-plotthispointonyourmap!

I. TRACKYOURJOURNEY!1.ConnectalinefromthecoordinatepointsfoundinStates7,8,and9.Findtheareaofthetrianglethat

isformed.

2.WhatisthedistancefromthecoordinatepointyoufoundinState4tothepointyoufoundforState7?

II. ALONGTHEWAY

1.Youdrive120milesfromNewJerseytoPennsylvania.

a) Ifthetriptookyou2hours,whatwasyouraveragespeedinmilesperhour?

b) Writeanequationtodescribethenumberofmilesdriven,y,intermsofhoursdriven,x.

c) Useyourequationtofillinthetablebelow.

x(hours) 0 1 2 3 4 5

y(miles)

d) Doestheabovesituationrepresentaproportionalrelationship?Howdoyouknow?

e) Iffourgallonsofgascost$10,howmuchmoneywillyouspendonyourtrip?

2.YoustopatagasstationbetweenWashingtonandOregonandbuyaboxofSour

PatchKids.Theboxisarectangularprismandmeasures15x8x2centimeters.

a) Whatisthevolumeofthebox?

b) IfthevolumeofaSourPatchKidis6cubiccentimeters,approximatelyhow

manySourPatchKidswillfitintheboxifitisfull?

c) TheboxofSourPatchKidscosts$1.85.Findtheunitrate(priceperSourPatchKid)

Math7thGradeHonorsAlgebra1SummerAssignment

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DUESEPTEMBER13TH,2017

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