Download Math (On-level 6th to On-level 7th)

SummerWork
6thGradeMathto7thGradeMath
AttachedisapacketforSummer2017.Takeyourtime.Donotwaituntiltheweeksrightbeforeschooltobegin.The
benefitofsummerworkisthatyouworkonitthroughoutthesummer.
Showyourwork.
Whenasked,givethoroughexplanations.
Havefun!Remember,youcanfindmatheverywhere.
Afewotherresources:
FactorGame:
https://illuminations.nctm.org/Activity.aspx?id=4134
ProductGame:
https://illuminations.nctm.org/Activity.aspx?id=4213
PickaPath:
https://illuminations.nctm.org/pickapath/
alsoavailableasaniPadapp
MathPlaygroundRatio,Proportion,Percentgames:
http://www.mathplayground.com/index_ratio_proportion_percent.html
MathPlayEquationsGames:
http://www.math-play.com/equation-games.html
Summer 2017 #1 Number Expressions & Factors
Name:_______________________
If the first prime number 2 = a, the second prime number 3 = b, the third prime number 5 = c and so
on, create a chart for the alphabet and it's corresponding prime number (attach your chart). Using
your chart, take your name and convert it into prime factors, then multiple the factors. What number
do you get?
For example, the word ACE = 2 ! 5 ! 7 = 70
Your first name:
Now take the number 3,446,695. Find the prime factorization of your number, use your chart, and
convert your prime numbers back to the alphabet. You may use a calculator to help you find the
prime factorization. Unscramble your letters to create a word. Show your prime factorization below:
BOWLINGWITHMATH
Directions:Roll4dice(orrandomlyselectfournumbers),andwritedowneachnumberintheframebox.Usingallfour
numbers,trytofindanequationwithananswerthatisoneofthenumbersonthebowlingpins.(Example:ifyourolla
3,4,2,2,youcouldthenmaketheequation(4+3)+2–2=7.Youwouldthencolorinpin#7)Dothisasmanytimesas
youcanandtrytoknockoverallthepins.Onceyourunoutofpossibilitiesorthetimehasrunout(spendatmost5
minutesoneachframe),moveontothenextframe.
Frame1:
Frame2:
Frame3:
Frame4:
Frame5:
Frame6:
Frame7:
Frame8:
Frame9:
Lastframe:
Use the following numbers and order of operations for your last frame:
Number of letters in your first name: _________
(for example, Melissa = 7)
The number of letters in the month you were born: ______________ (for example, May = 3)
The last digit of the day you were born: ____________ (for example mine is 4, however, if it was 28, I would use 8 & if it zero,
use the tens digit, for 20, I would use 2)
Finally, pick a prime number of your choice: __________ (You can pick any prime number, I'll pick 5).
Frame10:
Summer 2017 #2 Integers & the Coordinate Plane
Name:_______________________
On the following co-ordinate plane, draw the following items and record the coordinates:
1.) a square that is in only two quadrants, label the vertices A, B, C & D
A ( _____, ______) B ( _____, ______) C ( _____, ______) D ( _____, ______)
2. ) a triangle that is in an unoccupied quadrant, label the vertices E, F, G
E ( _____, ______) F ( _____, ______) G ( _____, ______)
3.) a parallelogram that is in all four quadrants, label the vertices H, I, J, K
H ( _____, ______) I ( _____, ______) J ( _____, ______) K( _____, ______)
4.) a rectangle that shares a vertex with point K from the previous parallelogram, label the
vertices K, L, M, N. K ( ____, _____) L ( ____, _____) M ( ____, _____) N ( ____, _____)
Summer 2017 #3 Ratio, Rate & Percent
Name:_______________________
Show your work. Explain your answers.
Measure your arm span from fingertip to fingertip (you can use string, and then measure the string, if
you do not have a measuring tape). Measure your height. Find the ratio of your arm span to your
height.
Measure the length of your foot and the length of your arm (shoulder to fingertip). Find the ratio of
the length of your foot to the length of your arm.
The majority of people have about a 1:3 head-to-height ratio, meaning your height is three times the
circumference of your head.
Find the head-to-height ratio for 4 people of varying ages.
Age
Head
circumference
Height
Ratio (in fraction
form)
What was the average, ratio (in decimal form) of your four people?
Why might age be a factor in determining body ratios?
Ratio as a
decimal
Find the ratio of the vertical height to foot length for 4 different people.
Foot Length
Height
Ratio (in fraction Ratio as a
form)
decimal
Using your four people, find the average ratio (in decimal form) for vertical height to foot length.
Find the length of arm (shoulder to finger tip) to foot length for 4 different people.
Arm length
Foot Length
Ratio (in fraction Ratio as a
form)
decimal
Using your four people, find the average ratio (in decimal form) for length of arm to foot length.
The length of the Statue of Liberty's sandal is 25 feet, using your ratios find both the total height of
the Statue of Liberty and the length of her arm.
Using the picture of the Statue of Liberty and the fact that her nose measure 4 feet 6 inches from the
bridge to the tip, determine the length of the Statue of Liberty's right arm, the one holding the
torch. Show your thinking, how did you solve this problem.
What is the ratio of the measurement of the length of the your nose to the length of your arm?
Is it the same as the ratio of the Statue of Liberty's? Why or why not?
Summer 2017 #4 Fraction & Mixed Number
Name:_______________________
Some of the problems below can be solved by multiplying
!
!
×
!
!
while others need a different operation.
Select the ones that can be solved by multiplying these two numbers. For the remaining, tell what operation
is appropriate. In all cases, solve the problem (if possible) and include appropriate units in the answer.
1. Two-fifths of the students in Anya’s class are girls. One-eighth of the girls wear glasses. What fraction
of Anya’s class consists of girls who wear glasses?
2. A farm is in the shape of a rectangle
farm?
3. There is
!
!
!
!
of a mile long and
of a pizza left. If Jamie eats another
original pizza is left over?
4. In Sam’s fifth grade class,
!
!
!
!
!
!
of a mile wide. What is the area of the
of the original whole pizza, what fraction of the
of the students are boys. Of those boys,
the class is red-haired boys?
5. Only
!
!"
of the guests at the party wore both red and green. If
of the guests who wore red also wore green?
6. Alex was planting a garden. He planted
!
!
!
!
!
!
have red hair. What fraction of
of the guests wore red, what fraction
of the garden with potatoes and
lettuce. What fraction of the garden is planted with potatoes or lettuce?
!
!
of the garden with
7. At the start of the trip, the gas tank on the car was
!
!
full. If the trip used
fraction of a tank of gas is left at the end of the trip?
8. On Monday,
that
flu?
!
!
!
!
!
!
of the remaining gas, what
of the students in Mr. Brown’s class were absent from school. The nurse told Mr. Brown
of those students who were absent had the flu. What fraction of the absent students had the
9. Of the children at Molly’s daycare,
!
!
are boys and
boys at the daycare are under one year old?
10. The track at school is
a mile has he run?
!
!
!
!
of the boys are under 1 year old. How many
of a mile long. If Jason has run
!
!
of the way around the track, what fraction of
Fraction operations.
11. Use the fraction ¾ and find another fraction or mixed number that combines to meet the criteria:
a.) Multiply and give an answer larger than 2
c.) Divide and give an answer less than 1
e.) Divide and give an answer greater than 1
b.) Add and gives an answer of 1
!
!
d.) Subtract and given an answer greater than 1
Summer 2017 #5 Integers & Algebra
Name:_______________________
Hole in One
The object of the games is the get the lowest score, as in golf.
Each hole has a different rule to follow. Each hole, draw two tiles from the pile (cut out the 20 tiles and use
for this game) and follow the rule for the hole. If the rule is satisfied, your score is 1. If not, continue drawing
two tiles until the rule is satisfied or until all tiles are drawn. The score of the number of draws required.
Record your score and the tiles that satisfy the rule in the table below.
If the rule has not been satisfied after all tiles have been drawn, score 9 for the hole. The tiles are returned to
the pile for the next hole. Play 4 rounds.
Hole
Round 1
1
2
3
4
5
6
7
8
9
Total
Round 2
Round 3
Round 4
Rule
If x = 2 and y = 3, then the
product is even
If x = 2 and y = 3, the
difference is greater than 5
If x = 1 and y = 2, the sum
is greater than 4
The product is cubic
(meaning an exponent of 3)
The quotient is 1
The sum is x + y
If x=2 and y = 3, the
difference is 1
The product is x2y2 or has
an exponent of 4
The sum is always divisible
by 2
Tiles, cut out for golf game:
x x x x y
2
2
y y y x x
2
2
2
2
2
x x y y y
2
y
Summer 2017 #6 Algebraic Equations
Name:_______________________
Solve. Use properties of equality and show your work.
1.) 14 = w + 3.7
!
!
!
!
3.) p - 4 = 2
2.)
!
!
=q+
!
!
4.) 11.3 = d- 6.8
!
!
!
!
5.) 9.2 + y = 11.1
6.) 2 = r -
7.) 15 = z - 22
8.) c - 6.8 = 8
10.)
!
11.) 12t = 24
12.)
!
13.) 9.84 = 0.9p
14. )
9.) 12 =
!
!
c
!
g = 25
= 36
!
!
!.!
= 12