7th Grade Form B Summer Math Review Packet

2012

(For students entering 7th grade)

Name _________________________ 6th Grade Math Teacher ________________

Objectives for the Math Summer Packet Grade 7

2011-2012

I. Exponents (Problems 1 to 5)

• Apply the definition of exponents. • Use expanded form to express exponents. • Evaluate exponential expressions.

II. Order of Operations (Problems 6 to 10)

• Review the correct order of operations. • Evaluate and simplify algebraic expressions using the correct order of

operations. III. Rounding and Estimating (Problems 11 to 15)

• Round whole numbers to specific place values. • Real world applications of estimating monetary values. • Estimating quotients.

IV. Decimals (Problems 16 to 20)

• Add, subtract, multiply, and divide decimals. V. Fractions and Decimals (Problems 21 to 25)

• Understanding that a fraction and decimal represent the same value. • Convert a fraction to a decimal. • Convert a decimal to a fraction. • Real life application of converting a decimal to a fraction.

VI. Triangles (Problem 26 to 30)

• Identify the different types of triangles. • Sketch triangles. • Find the missing angle measures of triangles.

VII. Perimeter (Problems 31 to 35)

• Find the perimeter of various polygons. • Apply algebraic applications to perimeter. • Find the dimensions of a polygon, given the perimeter.

VIII. Area (Problems 36 to 40)

• Find the area of various polygons using their formulas • Sketch a square and find its area

IX. Mean, Mode, and Median (Problems 41 to 45)

• Analyze and interpret data • Find the mean, mode, and median of a given set of data.

X. Sequences (Problems 46 to 50)

• Discover the difference between an arithmetic and geometric sequence.

• Find the missing terms of a given sequence. • Create a sequence.

Directions: Complete each problem showing all work. You must show work in order to receive credit for the answer.

EXPONENTS

Question Hint 1. Write 4●4●4●4●4 using exponents 34 = 3●3●3●3 2. Write 63 in expanded form. 82 = 8 ●8 3. Evaluate 2 12 6+ Evaluate means to simplify the exponents 4. Evaluate (32 ) 2 Add up the exponents then take 3 to that power 5. Evaluate 7● 58 1− Follow PEMDAS

ORDER OF OPERATIONS

Question Hint 6. 4 + 8●2 Follow PEMDAS. Parenthesis, exponents, multiplication, division, addition, and subtraction 7. 12 3 9÷ + Follow PEMDAS 8. (3 + 1) + (2 + 10) Follow PEMDAS 9. 2 ● 10 ÷ 5 Multiply and divide from left to right 10. 18 + 2 – 8 + 1 – 7 Add and subtract from left to right

ROUNDING AND ESTIMATING

Question Hint

11. Round 213,789 to the nearest hundred. Underline the place value and then look at the digit to the right to decide if you round up or down.

12. Round $45.275 to the nearest cent. Cent is the same as the hundredths place. 13. Tom went shopping at the food store. First, round each item In his cart were the following items, a to the nearest dollar. 2-liter bottle of soda for $2.97, one bag Then add. of chips for $1.29, and a hoagie for $4.89. Estimate the total amount of money that Tom will spend. 14. Diego wanted to find the 7% sales tax Round to the nearest cent on purchases that total $15.99. On his calculator the display showed $1.1193 as the tax. How much sales tax will Diego pay? 15. Estimate 41.79 divided by 7.23 Round first, then divide.

DECIMALS

Question Hint

16. 15.62 + 35.7 = Line up the decimal point. 17. 7.3 + 18 + 0.49 = The decimal is behind a whole

number. 18. 18 – 6.89 = Add in a decimal point and zeroes. 19. 0.45 X 0.003 = Multiply the numbers and then count

decimal spaces. 20. 0.462 ÷ 0.3 = The number after the ÷ is the divisor.

The divisor must be a whole number.

FRACTION AND DECIMALS

Question Hint

Change the following fraction to a decimal.

21. 38

Numerator ÷ denominator

22. 23

If it is a repeating decimal,

use the bar notation 0.4444… = 0.4

Change the following decimals to fractions: 23. 0.3 The way you read it is the way

you write it. 24. 0.64 Simplify your fraction Divide out any common factors 25. The tooth fairy left Emily $0.95 under her pillow. Write Emily’s money as a fraction, in simplest form.

TRIANGLES

Question Hint

26. Find a ruler and accurately An equilateral triangle draw an equilateral triangle. has 3 congruent sides. Label the lengths of each side. 27. Name an object in your house A right Triangle has only that contains the shape of a one right angle Right triangle. 28. Name and sketch a pattern in your house that contains triangles. 29. The measure of the angles of a The sum of three angles triangle are 52°, 37°, and x °. of a triangle equals 180°. Find the measure of “x”. 30. Each angle in an equilateral All three angles in an

equilateral triangle are triangle = ___________° congruent.

PERIMETER

Question Hint

31. Find the perimeter of a triangle Perimeter is the with sides of 4.8 cm, 9.6 cm and distance around an 5.3 cm. object. 32. Find the perimeter of a regular Regular means all hexagon with sides of 0.75 m. sides congruent. 33. Farmer Fred’s field is a rectangle Find the length first. 32 yd wide. The length of the Opposite sides of a field is twice the width. How rectangle are congruent. much fencing does he need Sketch the rectangle. to go around it? 34. The perimeter of a “STOP” sign A stop sign is an is 112 inches. What is the length octagon. of each side? 35. The frame around a square poster A square has 4 congruent is 96 inches long. How long is sides. each side of the poster?

AREA Question Hint

Find the area of the shapes below. 36. Rectangle A = lw 4cm 12cm 37. Triangle A = ½ bh 10ft. 15ft. 38. 12 miles Square A = s2 s - side 39. Circle A = 2rπ Diameter = 10m radius = half of a diameter 3.14π ≈ 40. Find something that is a Square square in your house. Measure A = s2 it and find its area. Item_________________ Length of side____________ Area___________

MEAN, MODE, AND MEDIAN

Question Hint

Use the data below to answer questions 41 to 43.

17, 14, 17, 11, 21, 20, 19 41. Find the mean To find the mean, add up the numbers and divide by the number of items in your data set 42. Find the mode Mode occurs most often 43. Find the median Median is the middle number when the data is in numerical order 44. If your grades for the quarter Mean = average are 85, 93, 90, and 88, what is your mean for the quarter? 45. What is the median of the If there are 2 numbers in following data: 0, 3, 3, 5, 7, 9, 10, 11 the middle, then you have to find the average of those 2 numbers

SEQUENCES

Question Hint

46. Name the next 3 numbers in Arithmetic sequences- the arithmetic sequence below same number is added to and describe the pattern. find the pattern 25, 29, 33, 37, … 47. Name the next 3 numbers in Geometric sequence - the geometric sequence below multiply by a common and describe the pattern. ratio to get the next term 2, 10, 50, … 48. Create a sequence using the rule Multiply by .5 is the below. Provide 4 terms same as dividing by 2 start with 84; multiply by .5 49. Find the missing terms in the Find the pattern of sequence the numbers to find the missing terms 12, 15, _____, 21, 24, ______ 50. Name the next 3 numbers in the Find the pattern of sequence below and describe the the numbers given pattern. 4, 14, 12, 22, 20, 30,…