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Math 6 Spring Break Review Packet Name ______________________ Due ____________________ Integers Integers- all whole numbers and their opposites […-3, -2, -1, 0, 1, 2, 3…] NOT a fraction, decimal, or percent -4.5, ¾, 85% 1. Compare the integers below using <,>, = -19 ____ 5 -6 ____ -7 20 ____ -11 Graphing Inequalities < Less than > Greater than ≤ Less than or equal to ≥ Greater than or equal to Open dot means < or > “less than” or “greater than” Closed dot means ≤ or ≥ “less than or equal to” or “greater than or equal to” Always read the answer starting with the variable to find out which direction the arrow points. 2. Graph each inequality. 1. r > -1 2. p≤3 Measures of Central Tendency Mean- the average (add up all of the numbers and divide by the number of items) * Mean works well for sets of data with no very high or low numbers Example: Test scores from the last unit test 82 95 73 100 85 79 64 88 91 76 Median- the middle number in a set of data 833 10 = 83.3 % * Median is a good choice when data sets have a couple of values much higher or lower than most of the others Example: The number of fish in a pond: Put the numbers in order: 3, 6, 1, 0, 5, 3, 4 0, 1, 3, 3, 4, 5, 6 3 is the median Example: The number of cookies each student ate at lunch Put numbers in order 4 1 5 2 0 8 4 3 0 6 0 0 1 2 3 4 4 5 6 8 3.5 is the median Mode- the number that occurs most often * There can be more than one mode or no mode at all * If there are exactly two modes, it is called bimodal * Mode is a good descriptor to use when the set of data has some identical values Example: The number of points Victoria scores in each basketball game 12 5 18 10 12 9 18 12 7 15 Put numbers in order: 5 7 9 10 12 12 12 15 18 18 12 is the mode 3.Find the mean, median, and mode of the following sets of data. Example: The number of hours kids watch TV per week 11 5 22 14 8 13 Mean = 6 16 Median- Mode- Mean as a balance point- the point on a number line where the data distribution is balanced 4. Find the mean as a balance point for the following set of data. “Number of Siblings” Multistep Word Problems Six Step method to solving a word problem 1) The Question 3) The Plan 5) The Action 2) 4) 6) The Facts The Picture The Check Practice- Show all of your work and circle the best answer. 5.Martha is covering picture frames with ribbon. Each frame takes ¾ of a yard of ribbon. How many frames can she cover with 6 yards of ribbon? A. 7 yds. B. 4 ½ yds. C. 3/24 yds. D. 8 yds. 6. Mr. Rico’s class decided to invite their parents to their National Hugging Day party. Amber, Jordan, and Brian made the invitations. Item Cost Package of Paper $3.92 Package of Stickers $3.42 Box of Envelopes $5.13 Stamps $0.32 each It took one package of paper and one package of stickers to make the invitations. They used one box of envelopes and twenty five stamps. About how much did it cost in all to make the invitations? Fractions Numerator- the top number in a fraction 3 numerator Denominator- the bottom number in a fraction 8 denominator Improper Fraction- the numerator is greater than the denominator Mixed Number- the combination of a whole number and a fraction Adding Fractions- find a common denominator, make equivalent fractions, add the numerators 2/4 + 3/8 4/8 + 3/8 = 7/8 Subtracting Fractions- find a common denominator, make equivalent fractions, subtract the numerators 2/4 – 1/3 6/12 – 4/12 = 2/12 = 1/6 Multiplying Fractions- multiply straight across, simplify your answer 4/5 2/3 = 8/15 Dividing Fractions- change the problem into multiplication, flip the second fraction (reciprocal), multiply straight across (KFC) 1/5 ÷ 2/7 1/5 7/2 = 7/10 Always change mixed numbers into improper fractions when multiplying or dividing Practice: 7. Change 18/5 into a mixed number _____ 8. Change 3⅘ into an improper fraction _____ 9. 1/3 + 4/5 = _____ 10. 7/8 – 4/16 = _____ 11. 1⅜ ● 2⅙ = _____ 12. 4½ ÷ 3/5 = _____ 13. Divide 2 3 by and write in simplest form. 4 3 Modeling Multiplication and Division of Fractions Modeling is a way of representing what happens when we multiply or dividing fractions. Modeling can help you solve problems and determine how to solve a problem. Multiplication The diagram show ¼ of the columns are blue and 2/5 of the rows are green. The blue-green squares show the region 𝟏 𝟐 × 𝟓 or 1/10 of the diagram. 𝟒 𝟑 𝟏 14. Use the diagram to model 𝟒 × 𝟒 Division 15. When we divide, we find how many ____ are in ____. 16. There are how many 2/3 in 2? 𝟐÷ 𝟐 𝟑 Converting Fractions, Decimals, and Percents Fraction Decimal if the denominator is 10 or 100, read the fraction as a decimal reduce to simplest form and divide the numerator by the denominator 3 = 0.3 10 Decimal 10 (simplify to 5/6 and do long division) = 0.833 12 Percent Dr. Pepper .DP move the decimal point two places to the right (multiply by 100) 0.82 = 82% 0.7 = 70% Percent 94% = 0.94 Decimal move the decimal point two places to the left (divide by 100) 16.2% = 0.162 17-19. Find the percent of each grid _____% _____% _____% Comparing Fractions, Decimals, and Percents Fractions find a common denominator change both fractions into decimals or percents Decimals align decimal points add zeros to even up place values compare numbers according to their place values Percents compare the whole numbers Mixed Forms change all numbers to the same form (percents are the easiest to compare) 20. Compare the following numbers using a <, >, or = sign. 0.9 ____ ½ 82% ____ 1.4 2/3 ____ 5/6 21. Put the following numbers in ascending order. 0.64, 1/5, 43%, ½ ________________________________ 22. Put the following numbers in descending order. 2/3, 0.09, 16%, 3/8 ________________________________ 23. Which statement is true? ¼ ____ 2/7 A. 𝟏 𝟓 = 𝟎. 𝟎𝟐 𝟐 𝟑 3 2 B. 𝟑 =3.4% C. 150%= D. 0.06= 0.06% Patterns & Sequences Sequence- a set of numbers that follows a numerical pattern Term- any number in a sequence Arithmetic Sequence- a sequence found by adding a fixed number to the previous term Common Difference- the fixed number being added in an arithmetic sequence 4 6 +2 8 +2 10 +2 12 2 is the common difference +2 Geometric Sequence- s sequence found by multiplying a fixed number to the previous term Common Ratio- the fixed number being multiplied in a geometric sequence 2 6 x3 18 x3 54 3 is the common ratio x3 24. Identify the common difference in the sequence and find the next three terms: 2, 5, 8, 11, 14, _____, _____, _____ common difference is _____ Perfect Squares & Square Roots Perfect Square- the product of two equal whole numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100) Square Root- a number multiplied by itself to equal a perfect square (1, 2, 3, 4, 5, 6, 7, 8, 9, 10) 25 = 5 (so 25 is a perfect square) 39 = 6.24 (so 39 is not a perfect square) 25. Circle ALL of the perfect squares in the following group of numbers: 4 6 9 10 12 16 25 30 35 42 64 100 26. What is the square root of 15? Round to the nearest hundredth. _____ Expressions, Equations, and Inequalities Expression: a math phrase containing numbers, variables, and/or operations What might you see: numbers, variables, operations 8 + 3 2a Equation: a math sentence that states two expressions are equal You must see an equal sign (=). 5x = 10 Coefficient- the number being multiplied with a variable Constant- a number by itself Inequality: a math sentence that states one expression is greater than or less than another expression You must see an inequality symbol (<,>,≤,≥,≠) 4x + 7 > 3 Variable- a letter or symbol that represents a number (x) Term- a number, a variable, or the product of a number and a variable. 27. Identify what is circled in each example. Equation Expression Coefficient Term Variable – If a math sentence contains more than one operation, you must complete the operations in a certain order called the order of operations. (GEMDAS)Order of Operations evaluate exponents 20 – 8 2 + 32 multiply and divide from left to right 20 – 8 2 + 9 add and subtract from left to right 20 - 16 + 9 4+9 13* if parentheses are involved, complete all operations inside the parentheses first. 42 ÷ (8 – 6) 3 42 ÷ 2 3 16 ÷ 2 3 83 2 *if a fraction bar is involved, complete the numerator, complete the denominator, then divide. 27. Simplify the following expressions: 1 + (19 – 3) ÷ 23 28. Simplify: 20 x 5^0 x 4 – (300 – 10 x 1 92 3(25) + 5 Coordinate Plane Coordinate plane – the graph (grid) formed by the x and y axis Quadrants – the four regions on a coordinate plane Origin – the intersection of the x and y axis (the center of the coordinate plane) x-axis – the horizontal number line y-axis – the vertical number line Ordered pair – the location of a point on the coordinate plane (x,y) x-coordinate – the location of a point on the x-axis (2, -3) y-coordinate – the location of a point on the y-axis (2, -3) 28. Measurement: Measurement Facts 30. 1 inch is about ___ centimeters 31. 1 meter is a little longer than a yard, or about ___inches 32. 1 mile is slightly farther than ___ kilometers 33. 1 kilogram is a little more than ___ pounds 34. 1 quart is a little less than ___ liter 35. 1 liter is a little more than 1 ______ Temperature Facts 36. Water freezes at _ _0C and ___0F 37. Water boils at ___0C and ____0F 38. Which shows units of weight and mass listed from least to greatest? F gram, ounce, pound, kilogram, ton G ounce, gram, kilogram, pound, ton H gram, ounce, kilogram, pound, ton J ounce, gram, pound, kilogram, ton PROBABILITY 39. Jordan has 10 cards, two coins, and a spinner. Which of the following does not represent a set of independent events? A. Selecting one card and then selecting a second card without replacement B. Tossing one coin and then another coin C. Spinning the spinner and flipping one coin D. Selecting one card, replacing the card in the deck, and then selecting a second card 40. Which of the following events is not dependent? A. Selecting a marble from a bag, putting it your pocket, then selecting another marble. B. Picking a heart from a deck of cards, placing it aside, and then picking another heart. C. Choosing two different colored markers from a box, one after the other without replacement. D. Tossing a coin twice and observing a "tails" up both times. EQUATIONS Solving Equations To solve an equation: 45. A 16x = 4 B 4x = 16 C x + 4 = 16 D x – 4 = 16 46. Which is not a true statement? A 25÷5= 5÷25 B 7+0 =7 C 5•6= 6• 5 D 5(4+6)= 20+30 Ex. 𝐲 𝟓 Find what operation is taking place between the variable and the numbers. Use the inverse or opposite operation on both sides of the equation. solve for the variable. =𝟒 𝟓 𝒚 y is divided by 5 𝟓 (𝟏) 𝟓 = 𝟒 (𝟏) 𝒚=𝟓 Multiply by inverse of 5 Solve 47. Which property is shown in the following: ( 2 2 +4)• 1 = +4 5 5 F Multiplicative Inverse Property G Additive Identity Property H Multiplicative Identity Property J Additive Inverse Property Quadrilaterals 48. _________________- has only one set of parallel sides 49. _________________- has two sets of parallel sides Parallelogram Square Trapezoid Rectangle Rhombus 50. _________________- has two sets of parallel sides and four congruent sides 51. _________________- has two sets of parallel sides and four right angles 52. _________________- has two sets of parallel sides, four congruent sides, and four right angles 53. The angles of all quadrilaterals add up to 360°. What is the measure of angle A below? A C=87° B=85° D= 135°