Name____________________________________Date_______________Section___________
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
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!
1.1EvaluatingExpressionsandOrderofOperations
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
Evaluate the expression:
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
Evaluate the expression:
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
1.1EvaluatingExpressionsandOrderofOperations
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!
1.2WritingExpressions,EquationsandInequalities
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
1.2WritingExpressions,EquationsandInequalities
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
97 Whole Integer Rational Irrational
√11 Whole Integer Rational Irrational
2.823���� Whole Integer Rational Irrational
223 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
Whole Integer Rational Irrational
3. 157
Whole Integer Rational Irrational
4. |−18|
Whole Integer Rational Irrational
5. 8.3145454545 …
Whole Integer Rational Irrational
6. √7
Whole Integer Rational Irrational
7. 3.6712�
Whole Integer Rational Irrational
8. 7.5182386 …
Whole Integer Rational Irrational
9. (−5)2
Whole Integer Rational Irrational
10. −|4|
Whole Integer Rational Irrational
11. 𝜋
Whole Integer Rational Irrational
12. 5 34
Whole Integer Rational Irrational
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?
Whole Integers Rational Irrational
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?
Whole Integers Rational Irrational
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.
Write your questions here!
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,
summarize your notes
here!
2.2 Add and Subtract Real Numbers
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
Associative Property of Addition
Neither Commutative Property of Addition
Associative 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
Associative Property of Addition
Neither Commutative Property of Addition
Associative Property of Addition
Neither Commutative Property of Addition
Associative 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)
2.2 Add and Subtract Real Numbers
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
Write your questions here!
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,
summarize your notes
here!
2.3 Multiply and Divide Real Numbers
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
Associative Property of
Multiplication
Neither Commutative Property of
Multiplication
Associative Property of
Multiplication
Neither
24. 𝑎(9 ∙ 𝑏) = (𝑎 ∙ 9)𝑏 25. 𝑥𝑥 = 𝑥𝑥 26. 4(2 ∙ 5) = 8 ∙ 20
Commutative Property of
Multiplication
Associative Property of
Multiplication
Neither Commutative Property of
Multiplication
Associative Property of
Multiplication
Neither Commutative Property of
Multiplication
Associative Property of
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
2.3 Multiply and Divide Real Numbers
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.
Write your questions here!
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,
summarize your notes
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