HONORS ALGEBRA 1 Summer Math Packet · HONORS ALGEBRA 1 Summer Math Packet For all incoming Honors Algebra 1 students, the summer math packet will be on the school website. Students

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HONORS ALGEBRA 1

Summer Math Packet

For all incoming Honors Algebra 1 students, the summer math packet will be on the school website. Students

will need to print a copy of the packet and complete problems on the packet.

In this packet, you will be learning the material covered in the first chapter of your book (YOU DO NOT NEED

YOUR BOOK FOR THIS PACKET). In each section, you will have notes to fill out from a video, practice

problems (answers provided ON THE WEBSITE beneath each video), and an application page. Make sure to

do the practice problems and use the answers to assess yourself on the material. The application pages do not

have the answers and you will have to apply what you learned in the section.

HOW DO I FILL OUT THE NOTES?

You will go to http://www.flippedmath.com/ and go to “Courses” and click on “Algebra 1 Traditional” (as

pictured above). Use the Semester 1 tab at the top of the page to find the correct sections from this packet. You

will be covering sections in Chapter 1 and Chapter 2 (1.1, 1.2, 2.1, 2.2, 2.3, and 2.4). When you click on the

tab, it will bring you to a video which will step you through the notes. Fill out the notes as the video goes along

and pause when needed. After the video try the practice problems as well as the application page for each

section.

SUMMER MATH PACKETS

The purpose of the summer math packets is to review topics needed in the course you are taking in the fall. The

math department expects you to review and know these topics as we start the new school year.

― Every summer math packet will be due on MONDAY, AUGUST 19TH and worth 25 POINTS.

― A Summer Math Packet Summative Assessment will be due within the first two weeks of school

worth 50 POINTS, and calculators WILL NOT be allowed when taking the summative

assessment.

If you have any questions regarding this summer packet, do not hesitate to email me, [email protected]

Michelle Treese

http://algebra.flippedmath.com/

Write your

questions here!

1.1EvaluatingExpressionsandOrderofOperations

Variable:

AlgebraicExpression():

Evaluate:

Evaluateeachexpressionwhenn=3

Power:

Writethepowerinwordsandasaproduct:

ORDERofOPERATIONS:

G‐

E‐

M‐ D‐

A‐ S‐

NOTES

Simplify each expression:

Evaluate each expression:

You try!

SUMMARY:

NOTES

Now,

summarize

your notes

here!


Evaluate the expression:

1) .4r when r=6 2) .8 + h when h = 3.7 3)

1 2k when k =

2 3

Write the power in words and as a product.

4) 125

5)

81

2

Describe AND correct the error in evaluating the power.

6) 2(0.4) 2(0.4) 0.8

Evaluate the power.

7) 15

8) 26

9)

31

6

Evaluate the expression.

10) x + y when x = 11 and y = 6.4


11) 13 – 8 + 3

12) 5 ∙ 2 7 13) 2 ∙ 4 2/8

PRACTICE

14) 24+4(3+1)

15) 21(21 2 )

2

16) 8[20 ‐ (9 ‐ 5)2]

Describe and correct the error in evaluating the expression.

17)

2 2120 - 6 =20 - 3

2 =20 - 9

=11


18) 6t2 – 13 when t = 2 19) 3(m2‐2) when m=1.5 20)

3 21 when b = 3

5 9

b

b

Skillz Review

Plot the points: Simplify: Simplify:

1) (4, ‐2) 2) (0, 3)

3) 4) 2 1 4

5) 6) 4 5 1

h

b2

b1


Directions:EVALUATE:

1) 3 2 when n =

3n 2)

2 1 when h = 5

3

h

h

3)Foryourbirthdayyougetani‐Tunesgiftcard.Thetotalcostforyoutobuy3albumsat$9.99eachandthen5individualsongseachworth$1.29isgivenbytheexpression3(9.99)+5(1.29).

a)Findthetotalcostofyouri‐Tunespurchases.

b)Supposeyourgiftcardisworth$50.Howmuchmoney(ifany)doyouhaveleft?

DIRECTIONS:Evaluatethegivenformulaforeachgeometricshape.

1 2( )Area of Trapezoid =

2

b b h

4)L=15,w=7 5)L=8.25,w=4.5

6) 1 22, 4, 4b b h 7)

1 220, 24, 14b b h

APPLICATION

Perimeter = 2(l + w )

w

l

Write your

questions here!

1.2WritingExpressions,EquationsandInequalities

Translating verbal phrases to mathematical operations

Addition Subtraction Multiplication Division

Translate the following phrases

Rate:

Unit rate:

EX:

Write Equations and Inequalities

Equation:

Inequality:

NOTES

Useful Conversions

Symbol Meaning Other Words

Solution of an Equation or Inequality:

Ex:

Use mental math to solve:

You try!

SUMMARY:

Now,

summarize

your notes

here!


Translatetheverbalphraseintoanexpression.1)8morethananumberx

2)50dividedbyanumbery

3)Thequotientoftwiceanumbertand12 4)5morethan3timesanumberw

Writeanexpressionforthesituation.5)Numberoftokensneededforvvideogamesifeachgametakes4tokens.

6)Amountyouspendifyoubuyashirtfor$20andjeansforjdollars

7)Numberofmonthsinyyears

Findtheunitrateinfeetpersecond.

8)180 miles

2 hours

Describeandcorrecttheerrorintheunits.

9)9 ∙

∙

$

$

Writeanequationoraninequality10)Thesumof42andanumbernisequalto51.

11)Thesumof12andthequantity8timesanumberkisequalto48

12)Thesumofanumberb and3isgreaterthan8andlessthan12.

13)Writeaninequalityforthepricep(indollars)described.

PRACTICE

Describeandcorrecttheerrorinwritingtheverbalsentenceasanequationoraninequality.14)Thequotientofanumbertand4.2isatmost15.

154.2

t

Checkwhetherthegivennumberisasolutionoftheequationorinequality.15)9+4y=17;1 16) 4 4;12

3

r

17)y–3.5<6;9 18)4z– 5<3;2

Solvetheequationusingmentalmath.19)y+16=25 20)8b=72

Skillz Review

Plot the points: Simplify: Simplify:

1) (‐3, 4) 2) (5,0)

3) 4) 2 2 4

5) 6) 5 2 4 8/2


1)Findtheunitrateinfeetpersecond: 2)Checktoseewhether5isasolution:

240 yards

1 hour 10+7g<44

3)ThefootballteamneedstobuyGatoradeforSaturday’sbiggame.Theyhavetwooptions.Thefirstoptionistheycanbuyitpre‐madein48ouncebottlesfor$3.84foreachbottle.Ortheycanbuypacketsandmixwithwater.Eachpacketmakes64ouncesandwillcost$4.80.

a)Findthecostperounceofeach.

b)Whichsizecostsless?

c)Theteamwillneedtobuy192ouncesofGatorade.Howmuchdoyousaveusingthechoicefromanswerb?

4)YourfamilytakesaroadtriptoBerlinfortheweekend.You’vedriven120milessofar,butneedtotravel400milestotal.Howmanymoremilesmustyoutravel?

5)Youandafriendarediscussinghowmanysectionsyou’vecompletedsofarinAlgebraI.Youtellyourfriend“I’vefinished3timesasmanysectionsasyou.”Yourfriendreplies“You’veonlyfinished4moresectionsthanIhave”.Howmanysectionshaveyouandyourfriendcompleted?

APPLICATION

NOTES

Write your questions here!

2.1 Real Numbers

Set Notation:

REAL NUMBERS

Natural Numbers = Whole Numbers = Integers = Rational Numbers = Irrational Numbers =

Rational Numbers Irrational Numbers

−18 16

11

√2 𝜋

Label the following

5 Whole Integer Rational Irrational

0.6 Whole Integer Rational Irrational

−24 Whole Integer Rational Irrational


√11 Whole Integer Rational Irrational

2.823�� Whole Integer Rational Irrational


Convert mixed numbers into fractions.

223 −3

45

Absolute Value = Simplify the absolute value expressions.

|−8| |9| �−234� |12 − 7| − �

53�

Put in order from least to greatest. Graph on the number line.

3.6 , |−3.2| ,134

, 338

−1 ,−43

,−1.2 ,−√7

SUMMARY:

Now,

summarize your notes

here!

2.1 Real Numbers

Circle the number set or number sets in which the number lies.

1. 4.5

Whole Integer Rational Irrational

2. √64


3. 157


4. |−18|


5. 8.3145454545 …


6. √7


7. 3.6712�


8. 7.5182386 …


9. (−5)2


10. −|4|


11. 𝜋


12. 5 34


Convert the mixed number into an improper fraction.

13. 6 15

14. 1 27 15. −4 3

4 16. −5 1

2

Express the following as decimals rounded to the nearest thousandth.

17. 134

18. 5 56 19. √67 20. √12

Plot each number on the number line then fill in the circle with > , < , or = .

21. 94

2.5

22. −3 23 −�17

21. 75

|−2|

Simplify each absolute value expression.

24. |−7|

25. |24| 26. − �23� 27. −|−4.5|

Order the numbers from least to greatest.

28. 1.6, |−1|, 53

,√4

29. −25

,−0.6,−1,−1 13

30. √2, 1.66, 43

, |−1.6|

31. −5.15,−5.2,−163

,−√26

PRACTICE

TRUE or FALSE.

35. |8(−2)| = |8| ∙ |−2|

36. |8 + (−2)| = |8| + |−2|

37. � 8−2� = |8|

|−2|

38. |8 − (−2)| = |8| − |−2|

SKILLZ REVIEW

GRAPH Plot the points: 1. A (−3, 4) 2. B (0, 1)

SIMPLIFY

3. 5−3

−10−6

4. 5−(−3)3−2

ORDER OF OPERATIONS 5. 2(−3)2 − 4

6. −2 + 4(3) + 42

2.1 Real Numbers

1. Put in order from least to greatest.

−2.47 ,−38

,−2 ,−134

, |−4|

2. Circle the number set or number sets in which the number lies.

−√9

Whole Integers Rational Irrational

3. Tiger Woods shot four rounds of golf. To win golf you must have the lowest score possible. Your score is determined by how far from par you are.

a. Which round did Tiger score the lowest?

b. Which round did Tiger do the worst in?

c. Tiger’s scores fall in which number set?


APPLICATION

Tiger Woods Golf Score

4. Here is probably the coolest math puzzle that you will do today. Rules: Plot on the number line. Don’t forget to label your points to unlock the hidden phrase.

U M H I A V L T

−𝟐 3.75 √𝟓𝟓 −𝟔.𝟓 |−𝟒| 0 −𝟏𝟏𝟒

𝟏𝟏𝟑

5. Given the set of numbers in the domain below, use the function to find the range. Remember Domain is the input

and Range is the output!

Domain �−2.5 ,−34

, 0 , 4 �

Function 𝑦 = |𝑥|

Range

For 6 and 7, circle the correct number set, then EXPLAIN why you chose it!

6. Mr. Brust is going to write a function to represent how much money is made from selling t-shirts. The domain of this function is the number of shirts sold. What is the most appropriate set to use for the domain?


Why? 7. Mr. Kelly is going to write a function to represent how much money he would spend on filling up his car with gas.

What is the most appropriate set to use for the domain?

Whole Integers Rational Irrational Why? 8. Create a situation like the ones above where the domain is the set of whole numbers.


2.2 Add and Subtract Real Numbers

ADD! INTEGERS

3 + 5

−3 + −5 3 + −5

−3 + 5

RATIONAL NUMBERS 7.4 + (−9.5) −

25

+45

−38

+ �−23�

|3 + (−11)| √−5 + 30

TRY IT! −2.3 + (−14.8)

�−47

+13�

COMMUTATIVE PROPERTY

OF ADDITION

ASSOCIATIVE PROPERTY OF ADDITION

NOTES

SUBTRACT! INTEGERS

3 − 5 3 −−5 −3− 5 −3— 5

RATIONAL NUMBERS 12.4 − (−3.5)

−29−

49

234− 4

|3 − (−14)| √39 − 30

COMMUTATIVE PROPERTY AND ASSOCIATIVE PROPERTY OF SUBTRACTION ???

What about irrational numbers?

Rational + Rational

𝟐 +𝟒𝟓

Rational + Irrational

𝟐 + √𝟑

Irrational + Irrational

√𝟕 + √𝟐

SUMMARY:

Now,


here!


Evaluate each expression. Reduce fractions when possible. Leave as improper fractions.

1. 14 + 9

2. −12 − 7 3. 4 + (−6) 4. −10 − (−5)

5. |−4 + (−7)| 6. |−18 − 5| 7. 34.125 + (−21.4) 8. −21 − 3.5

9. − 73

+ 23

10. 89− �−5

9� 11. −4

5+ �−2

5� 12. 1

2− 3

2

13. 25

+ 34

14. −27− 5

2 15. −7

8+ �− 2

5� 16. 2 − �− 5

4�

17. −3 27− 1 1

2 18. 4

23

+ �−3 16� 19. |8 + (−5)| + 7 20. 4 + √16 + 9

Circle the correct property.

21. 7 + 9 = 9 + 7 22. 7 + 9 + 6 = 7 + 15 23. (8 + 3) + 1 = 8 + (3 + 1)

Commutative Property of Addition

Associative Property of Addition

Neither Commutative Property of Addition




Neither

24. 𝑎 + (9 + 𝑏) = (𝑎 + 9) + 𝑏 25. 𝑥 + 𝑦 = 𝑦 + 𝑥 26. 4(2 + 5) = 8 + 20

Commutative Property of Addition






Neither

Find the error. 27. Mr. Kelly refuses to believe that the associative property doesn’t work for subtraction. He works the following problem to “prove” that it does work. He is wrong. Circle the mistake in his “proof”. Correct his “proof” by showing that both sides are NOT equal to each other.

9 − (8 − 4) = (9 − 8) − 4 9 − 12 = 1 − 4

−3 = −3

PRACTICE

Evaluate each expression to determine if the answer is a rational number or irrational number.

28. 7 − √49

29. |9 − 12| + 2 34 30. 12 − √7 − 4

Rational Irrational Rational Irrational Rational Irrational

SKILLZ REVIEW

GRAPH Plot the points: 1. A (−3,−4) 2. B (2, 0)

SIMPLIFY

3. −2−30−6

4. −5−(−3)3−8

ORDER OF OPERATIONS 5. 4 − 2(3)2 6. 2 + 4(−3)


Find the sum or difference.

1. −5 − (−3) = 2. −12

+ 116

=

Find the perimeter of the following:

3. Rectangle

4. Isosceles Triangle

5. Isosceles Trapezoid

APPLICATION

16 m

7 m 34 cm

2.5 in

4.3 in

10.2 in 34 cm

158

cm

4.3 in

6. Mr. Brust, Mr. Kelly, and Mr. Sullivan decide to call in sick and play Call of Duty all day instead. Below is a bar graph showing the results of their epic day long battles. Use the graph to answer the questions.

a. Who is the best the player? By how much.

b. How many total games did the math teachers play?

c. Explain what the expression calculates in this situation.

21 − 6

7. Given the set of numbers in the domain below, use the function to find the range.

Domain �−2.5 ,−34

, 0 , 4�

Function 𝑦 = 4 + 𝑥

Range

8. Which is an example of the sum of a rational number and irrational number being irrational?

A) 𝜋 + 𝜋 B) √3 + √9 C) 5 + √64 D) 𝜋 + √2 E) √7 + √5

Wins

Player


2.3 Multiply and Divide Real Numbers

MULTIPLY! INTEGERS

3 ∙ 5

−3(−5) 3(−5)

−3(5)

RATIONAL NUMBERS 7.4(−2.5) −

25∙

34

�−45� 4

�−134� �−

43�

�3(12)

COMMUTATIVE PROPERTY OF MULTIPLICATION

ASSOCIATIVE PROPERTY OF MULTIPLICATION

DIVIDE! INTEGERS

8 ÷ 2 8 ÷ (−2) −82

−8−2

NOTES

RATIONAL NUMBERS 12.4 ÷ (−3.5)

−29

÷49

−35

÷ �−23�

234

÷ 4 �−21

7 �

TRY IT! 5

4÷ �−

56� �−

47

÷ 3�

COMMUTATIVE PROPERTY AND ASSOCIATIVE PROPERTY OF DIVISION ???

BRING THE PAIN!

8𝑥 − 124

2𝑥 + 9

3

SUMMARY:

Now,


here!


Evaluate each expression. Reduce fractions when possible. Leave as improper fractions.

1. 4 ∙ 9

2. (−2)(−7) 3. 18 ÷ (−6) 4. −105

5. �204� 6. |−8(5)| 7. 4.25(−2.4) 8.

−7.2−3.5

9. − 73�2

3�

10. 89

÷ �−52� 11. −4

5�−2

3� 12. 1

8÷ �3

2�

13. �25� �3

4�

14. −3 �− 52� 15. �4 2

3� ÷ �−3 1

6� 16. 2 ÷ �− 5

4�

17. 2|8(−5)| 18. 3 �15−5� + 5 19. 4√9 20. −3�4(9)

Circle the correct property.

21. (8 ∙ 3)4 = 8(3 ∙ 4) 22. 7(2)6 = 7(12) 23. 7(9) = 9(7)

Commutative Property of

Multiplication

Associative Property of

Multiplication

Neither Commutative Property of

Multiplication


Multiplication


Multiplication


Multiplication

Neither

24. 𝑎(9 ∙ 𝑏) = (𝑎 ∙ 9)𝑏 25. 𝑥𝑥 = 𝑥𝑥 26. 4(2 ∙ 5) = 8 ∙ 20

Commutative Property of

Multiplication


Multiplication


Multiplication


Multiplication


Multiplication


Multiplication

Neither

Find the error. 27. Mr. Sullivan refuses to believe that the associative property doesn’t work for division. He works the following problem to “prove” that it does work. He is wrong. Circle the mistake in his “proof”. Correct his “proof” by showing that both sides are NOT equal to each other.

16 ÷ �8 ÷12� = (16 ÷ 8) ÷

12

16 ÷ 16 = 2 ÷12

1 = 1

PRACTICE

Simplify the expression. Reduce fractions when possible. Leave as improper fractions.

28. 6𝑥−142

29. 9𝑧−6−3

30. −6𝑝+15

6

31. −10−24𝑎

−8

32. 36−27𝑐

9

SKILLZ REVIEW

GRAPH Plot the points: 1. A (−2, 1) 2. B (−3, 0)

SIMPLIFY

3. 7−109−6

4. 12−(−2)5−2

ORDER OF OPERATIONS 5. (−3)2 − 4 + 7

6. 123

+ 2(3) − 1


Find the product or quotient.

1. 3.5(4) = 2. 54

÷ 27

=

Find the area of the following:

3. Rectangle 𝐴 = 𝑏ℎ

4. Triangle

𝐴 =12𝑏ℎ

5. Parallelogram 𝐴 = 𝑏ℎ

APPLICATION

34 feet

5 feet

6.5 cm

4 cm

2 25 in

3 in 2.5 in

6. Use the bar graph to answer the following:

a. Estimate the population of each country. Write your estimate in the box at the end of the each bar of the graph.

b. Brazil wants to divide its population into

three equal sections. Approximately how many people would be in each section? Label your answer!

c. Approximately, how many times bigger was China’s population than the United States?

d. Write a sentence describing one uninteresting thing about the population of the top 5 most populated countries.

e. Write a sentence describing one interesting thing about the population of the top 5 most populated countries. 7. Mr. Sullivan aka Sully is a well-respected culinary genius in the Cupcake Community where he is

affectionately known as Chef-Boy-R-Sully. He is making his famous cupcakes (Sully Cakes) for a birthday party. He wants to triple the recipe. Change the recipe so that it makes three times as much.


2.4 Combine Like Terms and Distribute Property

2x - 5 + 3x

Combine Like Terms:

5c + 12f - 30 - 8c + 7 + 3f

Translate: twice the sum of a number and 2

Distributive Property:

NOTES

1. 2. 3(5x + 2) + 2x + 4 3. 8 - 3(2m - 5)

Try it!

3x + 2(4x - 8)

4 - 5(3w - 5)

SUMMARY:

SKILLZ REVIEW GRAPH

Plot the points: 1. A (4,−1) 2. B (−3, 0)

SIMPLIFY

3. 5−8−1−8

4. 4−(−1)10−0

ORDER OF OPERATIONS 5. 3(2)2 + 2 6. 12 − 4(3) + 1

Now,


here!

2.4 Combine Like Terms and Distributive Property

Simplify the expression by combining like terms. 1. 6𝑦 − 8 + 2𝑦 + 5

2. 9 − 5𝑎 + 2 + 𝑎

3. 6𝑟 + 2𝑟 + 4 − 5𝑟 + 1

4. 3𝑚 + 2𝑛 + 5𝑚 − 10 + 7𝑛

5. 7 + 5𝑤 − 4 + 3𝑤 + 2

6. 5 − 2.1𝑠 + 17𝑠

7. 12ℎ + 5 + 5

2ℎ − 3

8. 23

+ 4𝑛 − 9 − 2𝑛

Simplify the expression by using the distributive property. 9. 4(𝑥 + 3)

10. 5(𝑚 + 5)

11. −8(𝑝 − 3)

12. (2𝑟 − 3)(2)

13. 6.5(𝑣 + 1)

14. −2(3 + 𝑥)

15. 12�12𝑚 − 4�

16. 23

(6𝑛 − 9)

PRACTICE

Simplify the expression using distributive property and combine like terms. 17. 6𝑦 + 2(𝑦 + 1)

18. 2(4𝑎 − 1) + 𝑎

19. 6𝑟 − 2(𝑟 + 4)

20. 3(𝑚 + 5) − 10

21. 7.2(𝑤 − 5) + 3𝑤

22. (𝑠 − 3)(2) + 17𝑠

23. 13

(2𝑚 + 6) − 10

24. 12

+ 3 �2𝑢 + 16�

Mr. Brust tried to simplify the following but a made a really common mistake in each problem. Help a math teacher out by circling his mistake, and then show the correct solution. 25. 8 + 2(3𝑝 + 1)

26. 3𝑑 − 2(𝑑 − 4)

2.4 Combine Like Terms and Distributive Property

Simplify

1. 25

(10𝑚 − 15) 2. 3 + 2(b – 4)

Simplify the following formulas. You will have x in your answer!

3. The Perimeter of a rectangle is

2𝑏 + 2ℎ when b = 4 and h = (2x + 1)

4. The Area of a triangle is

12 𝑏ℎ

when b = 6 and h = (2x + 4)

5. Surface Area of rectangular solid is

𝑝ℎ + 2𝑙𝑤 when p = 24, h = 4x + 1, l = 4, and w = 8

6. Given the set of numbers in the domain below, use the function to find the range. (You may want to simplify the function first!)

Domain �−2.5,− 34

, 0, 4�

Function 𝑦 = 4 − 2(4𝑥 − 5)

Range

7. The expression 2𝑚 − (8 − 4𝑚) + 5 is equivalent to which of the following expressions?

A) 6𝑚 + 13 B) −2𝑚 − 3 C) 6𝑚 − 3 D) −2𝑚 + 13 E) NONE

APPLICATION

2x + 1

4 2x + 4

6

4𝑥 + 1

4 8

Documents

HONORS ALGEBRA 1 Summer Math Packet · HONORS ALGEBRA 1 Summer Math Packet For all incoming Honors Algebra 1 students, the summer math packet will be on the school website. Students