Summer Work. 6 th Grade Enriched Math to 7 th Grade Pre-Algebra

Transcription

1 Summer Work 6 th Grade Enriched Math to 7 th Grade Pre-Algebra Attached is a packet for Summer Take your time. Do not wait until the weeks right before school to begin. The benefit of summer work is that you work on it throughout the summer. Show your work. When asked, give thorough explanations. Have fun! Remember, you can find math everywhere. A few other resources: Factor Game: Product Game: Pick a Path: also available as an ipad app Math Playground Ratio, Proportion, Percent games: Math Play Equations Games:

2 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: BOWLING WITH MATH Directions: Roll 4 dice (or randomly select four numbers), and write down each number in the frame box. Using all four numbers, try to find an equation with an answer that is one of the numbers on the bowling pins. (Example: if you roll a 3, 4, 2, 2, you could then make the equation (4+3) = 7. You would then color in pin #7) Do this as many times as you can and try to knock over all the pins. Once you run out of possibilities or the time has run out (spend at most 5 minutes on each frame), move on to the next frame.

3 Frame 1: Frame 2: Frame 3: Frame 4:

4 Frame 5: Frame 6: Frame 7: Frame 8:

5 Frame 9: Last frame: 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). Frame 10:

6 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 (, )

7 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?

8 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.

9 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?

10 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!!! farm? of a mile wide. What is the area of the 3. There is! of a pizza left. If Jamie eats another!!! original pizza is left over? of the original whole pizza, what fraction of the 4. In Sam s fifth grade class,! of the students are boys. Of those boys,!!! the class is red-haired boys? have red hair. What fraction of 5. Only! of the guests at the party wore both red and green. If!!"! of the guests who wore red also wore green? of the guests wore red, what fraction 6. Alex was planting a garden. He planted! of the garden with potatoes and!!! lettuce. What fraction of the garden is planted with potatoes or lettuce? of the garden with

11 7. At the start of the trip, the gas tank on the car was!! fraction of a tank of gas is left at the end of the trip? full. If the trip used!! of the remaining gas, what 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!!! boys at the daycare are under one year old? of the boys are under 1 year old. How many 10. The track at school is!! a mile has he run? 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 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

12 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 If x = -2 and y = -2, then the product is less than -1 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 between -3 and 3 The product is x 2 y 2 or has an exponent of 4 The sum is always divisible by 2 Total

13 Tiles, cut out for golf game: x x x x y y y y x 2 x 2 x 2 x 2 y 2 y 2 y 2 y 2

14 Summer 2017 #6 Algebraic Equations Name: Solve. Use properties of equality and show your work. 1.) = w )!! = q +!! 3.) p - 5!! = 2!! 4.) = d ) y = ) 1!! = r -!! 7.) -5 = z ) c = -4 9.) 6 =!! c 10.)!! g = ) -8t = )!! = ) = -0.9p 14. )!!.! = 7