6 th Grade Enriched Math to 7 th Grade Pre-Algebra

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Ethel May
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1 Summer Work th Grade Enriched Math to 7 th Grade Pre-Algebra 6 th Grade Skills that are necessary for success in 7 th grade and beyond: - ability to add subtract, multiply and divide decimals, fractions & integers - solve one-step algebraic equations - graph points in the coordinate plane - understanding ratio and calculating percentages - fluency with numbers Attached is a packet for Summer 2018 reviewing these many of these skills. 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. If you would like extra practice, below are IXL skills and links to other on-line resources: IXL Resources, Level H: Number Theory E.1 to E.9 Decimals F.1 to F.9, Decimal +-: G.1 to G.4 & x :H.1 to H.8 Fractions & Mixed Numbers I.1 to I.11, Fraction +-: J.1 to J.9 & x:k.1 to K.13 & : L.1 to L.8 Integers: M.1 to M.6 Operations with Integers: N.1 to N.11 Ratios & Rate: R.1 to R.9 Percentages: S.1 to S.9 Coordinate Plane: X.1 to X.6 One-Step Equations: Z.1 to Z.8 A few other resources: Solve Me: Who Am I? *Solve Me Mobiles: Factor Game: Product Game: *Pick a Path: Math Playground 6 th grade: * also available as an ipad app

2 Number Toolbox Mathematician: Write in exponential form. 1.) 5 x 5 x 5 x 5 x 5 x 5 x 5 2.) 3 x 3 x 3 x 3 x 3 Write as repeated multiplication. 3.) ) 3 5 Find each value. 5.) 3 3 6) ) 5 4 Compare using <, >, or =. 8.) ). 10, ) Simplify each expression. 11.) (32 11) 7 12.) x ) ) (17 + 8) 15.) ( ) (23 18) 3 16.)

3 Number Theory Mathematician: Tell whether each number is divisible by 2, 3, 4, 5, 6, 9 and 10 1.) ) Tell whether each number is prime or composite. 3.) 47 4.) 112 List all of the factors of each number. 5.) 49 6.) 100 Write the prime factorization of each number. 7.) 45 8.) 132 Find the Greatest Common Factor (GCF) of each set of numbers. 9.) 54 and ) 52 and 26 Find the Least Common Factor (LCM) of each set of numbers. 11.) 36 and ) 20 and 45

4 Fractions/Mixed Numbers - All Operations Mathematician: Add, subtract, multiply or divide. Watch the signs. Write your answer in simplest form Find the Least Common Multiple for the following sets of numbers , 8, and and 12 Find the reciprocal for each number

5 Decimals Operations Mathematician: Order the decimals from least to greatest. 1.) 5.3, 5.2, ). 6.18, 6.3, 6.37 Add, subtract, multiply or divide. Watch the signs. 3.) ) ) ) ) ) ) ) ) = 12.) ) ) Evaluate each of the following. 3 points 15.) x, for x = ) 5.12 x, for x = ) 19x, for x = ) 8.4 x, for x = 0.03 Convert each measure. 19.) 83.2 cm = mm 20.) 71 kl = L

6 Ratio, Rate & Percent Mathematician: Use the shapes pictured to write the following ratios.!!!!""""""### 1.) squares to circles 2. stars to squares 3.) Write 3 equivalent ratios to compare the number of circles to stars. 4.) If there are 11 boys on a soccer team and 4 of them scored goals at the last game, what is the ratio of boys that scored to boys that did not score? Write each percent as a fraction in simplest form and as a decimal. 5.) 25% 6.) 35% 7.) 44% 8.). 60% Write each decimal or fraction as a percent. Round to the nearest tenth of a percent ) ) ) ) 9 Find each percent. 13.) 60% of ) 50% of ) 9% of ) 30% of ) 15% of ) 125% of 32

7 Algebraic Equations Mathematician: 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

Integers Mathematician: Name a positive or negative number to represent each situation. 1.) 40 below zero 2.) a bank withdraw of $45 3.) a gain of 15 yards 4.

8 Integers Mathematician: Name a positive or negative number to represent each situation. 1.) 40 below zero 2.) a bank withdraw of $45 3.) a gain of 15 yards 4.) an increase of 12 C Write the opposite of each integer. 5.) -5 6.) 12 7.) ) 0 Find the absolute value. 9.) 8 10.) ) ) 48 Compare. Write < or >. 13.) ) ) ) Order each set of integers from least to greatest. 17.) 20, -18, ) -12, 0, 5, - 4, 11 Order each set of integers from greatest to least. 19.) -12, 6, -8, 3 20.) -13,-1, -22, -7, 0 Graph each point on a coordinate plane. Give the quadrant in which each point lies. 21.) A(3,2) 22.) B(3, -1) 23.) C(1,0) 24.) D(-2,3) 25.) E(2,0) 26.) F(-2, -1)

9 Add, subtract, multiply or divide. Watch your signs. 27.) 5 + ( 5) 28.) ) ) 15 (- 5) 31.) 42 (-7) 32.) 7 (-12) 33.) ) 15 + (-7) 35.) ) 5 (-6) 37.) ) 7 9 Evaluate each expression for the given value of the variable. 39.) x + 3; x = ) 10 y; y = ) b 5; b = ) ; a = 4 a 43.) r + (-14); r= ) w (-8); w= 15 Solve, using order of operations. 45.) ) 32 4(-2) 47.) 16 4(8) + 18 (-9) 48.) 20 3(-2) + (-20) (-5) 49.) (-56) (-7) + 30 (-15) 50.)

10 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. Frame 1: Frame 2: Frame 3:

11 Frame 4: Frame 5: Frame 6: Frame 7:

12 Frame 8: 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 I was born on the 4 th, so 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:

13 Integers & the Coordinate Plane Mathematician: 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 (, )

14 Ratio, Rate & Percent Mathematician: 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?

15 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

16 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?

17 Integers & Algebra Mathematician: 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 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

18 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

NFC ACADEMY MATH 600 COURSE OVERVIEW

NFC ACADEMY MATH 600 COURSE OVERVIEW Math 600 is a full-year elementary math course focusing on number skills and numerical literacy, with an introduction to rational numbers and the skills needed for