SummerWork6thGradeEnrichedMathto7thGradePre-AlgebraAttachedisapacketforSummer2017.Takeyourtime.Donotwaituntiltheweeksrightbeforeschooltobegin.Thebenefitofsummerworkisthatyouworkonitthroughoutthesummer.Showyourwork.Whenasked,givethoroughexplanations.Havefun!Remember,youcanfindmatheverywhere.Afewotherresources:FactorGame:https://illuminations.nctm.org/Activity.aspx?id=4134ProductGame:https://illuminations.nctm.org/Activity.aspx?id=4213PickaPath:https://illuminations.nctm.org/pickapath/alsoavailableasaniPadappMathPlaygroundRatio,Proportion,Percentgames:http://www.mathplayground.com/index_ratio_proportion_percent.htmlMathPlayEquationsGames: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.Usingallfournumbers,trytofindanequationwithananswerthatisoneofthenumbersonthebowlingpins.(Example:ifyourolla3,4,2,2,youcouldthenmaketheequation(4+3)+2–2=7.Youwouldthencolorinpin#7)Dothisasmanytimesasyoucanandtrytoknockoverallthepins.Onceyourunoutofpossibilitiesorthetimehasrunout(spendatmost5minutesoneachframe),moveontothenextframe.

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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).

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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)

Ratio as a decimal

What was the average, ratio (in decimal form) of your four people? Why might age be a factor in determining body ratios?

Find the ratio of the vertical height to foot length for 4 different people. Foot Length Height Ratio (in fraction

form) Ratio as a 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

form) Ratio as a 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 !! of a mile long and !

! of a mile wide. What is the area of the

farm?

3. There is !!

of a pizza left. If Jamie eats another !! of the original whole pizza, what fraction of the

original pizza is left over?

4. In Sam’s fifth grade class, !! of the students are boys. Of those boys, !

! have red hair. What fraction of

the class is red-haired boys?

5. Only !!"

of the guests at the party wore both red and green. If !! of the guests wore red, what fraction

of the guests who wore red also wore green?

6. Alex was planting a garden. He planted !!

of the garden with potatoes and !! of the garden with

lettuce. What fraction of the garden is planted with potatoes or lettuce?

7. At the start of the trip, the gas tank on the car was !!

full. If the trip used !! of the remaining gas, what

fraction of a tank of gas is left at the end of the trip?

8. On Monday, !! of the students in Mr. Brown’s class were absent from school. The nurse told Mr. Brown

that !!

of those students who were absent had the flu. What fraction of the absent students had the flu?

9. Of the children at Molly’s daycare, !! are boys and !

! of the boys are under 1 year old. How many

boys at the daycare are under one year old?

10. The track at school is !!

of a mile long. If Jason has run !! of the way around the track, what fraction of

a mile has he run?

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 b.) Add and gives an answer of 1!!

c.) Divide and give an answer less than 1 d.) Subtract and given an answer greater than 1

e.) Divide and give 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 Round 2 Round 3 Round 4 Rule

1 If x = -2 and y = -2, then

the product is less than -1

2 If x = 2 and y = 3, the

difference is greater than 5

3 If x = 1 and y = 2, the sum

is greater than 4

4 The product is cubic

(meaning an exponent of 3)

5 The quotient is 1

6 The sum is x + y

7 If x=2 and y = 3, the

difference is between -3 and 3

8 The product is x2y2 or has

an exponent of 4

9 The sum is always divisible

by 2

Total

Tiles, cut out for golf game:

x x x x y y y y x2 x2 x2 x2 y2 y2 y2 y2

Summer 2017 #6 Algebraic Equations Name:_______________________

Solve. Use properties of equality and show your work.

1.) -15.5 = w + 2.1 2.) !! = q + !

!

3.) p - 5 !! = −2 !

! 4.) -12.9 = d- 2.1

5.) 8.41 + y = 8.1 6.) −1 !!= r - !

!

7.) -5 = z - 17 8.) c - 5.1 = -4

9.) 6 = − !! c 10.) − !

! g = -14

11.) -8t = -32 12.) !

! = -3

13.) -23.4 = -0.9p 14. ) !

!.! = 7