6 th Grade Math STAAR Review Booklet

Transcription

1 6 th Grade Math STAAR Review Booklet Reporting Category 1 Numerical Representations and Relationships Student Name: Teacher Name: 1

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3 Table of Contents Reporting Category 1 Classify Rational Numbers.4-5 Numbers, Opposites, & Absolute Value..6-7 Locating, Comparing, and Ordering on a number line..8-9 Order a Set of Rational Numbers Interpret Fractions as Division Multiplicative Comparisons of Two Quantities Examples of Rates Representing Ratios, Rates, Percents Equivalency (fractions, decimals, and percents) Equal Parts of the Same Whole Order of Operations and Prime Factorization Distinguish between Expressions and Equations Equivalent Expressions Properties of Operations

4 6.2A: classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers Complete the diagram below to show the relationship between sets of numbers.. Classify each given number in the table. You may check more than one classification. Number 0 5 Natural Number Whole Number Classification Integers Rational Numbers

5 Practice Questions Which best describes the classification for the following number set? { 4, 3, 8, 6, 2} 4 I. Rational numbers II. Integers III. Whole Numbers A. I only B. I and II only C. I and III only D. II and III only Two sets of numbers are shown in the Venn diagram? Which of these numbers can be placed in the shaded area of the diagram? A. 4.2 B. 5 C. 1.5 D. 7 5

6 6.2B: identify a number, its opposite, and its absolute value is the distance of a number from on a number line. How far is 3 from 0? How far is 3 from 0? Use the number line to answer the following questions. Write the following values. B Opposite of B Absolute Value of B E Opposite of E Absolute Value of E 6

7 Practice Questions What integer is the opposite of point u on the number line? Record your answer and fill in the bubbles on the grid below. Be sure to use the correct place value. Which of the following equations is not true? I. 20 = 20 III. 5 = 5 II. 4 = 4 IV. 9 = 9 A. I only C. II and IV only B. I and III only D. II, III and IV only 7

8 6.2C: locate, compare and order integers and rational numbers using a number line Using the number line, place the following points in the appropriate position on the number line. Label each point above the line. A. 1 2 B C. 3 2 D Use the number line to arrange the following numbers in order from least to greatest. 1.5, 3 4, 2 1 4, 2 Compare using >, < or =

9 Practice Questions Use the number line below to answer the question. Which of the following points best corresponds to 4 4 5? Based on the model below, which of the following is a true statement? 1 A. 1 > C B. < D = > 3 4 Order the following numbers from least to greatest. 3, 0.5 3, 1 3, 4 A. A. 3, 1 3 4, 0.5, 3 C. 3, 0.5, 1 3 4, 3 B. 0.5, 3, 1 3, 3 D. 1 3, 3, 0.5,

10 6.2D: order a set of rational numbers arising from mathematical and real-world contexts When ordering a set of rational numbers convert the numbers to the same form before ordering. Convert the following to a decimal. 29 = 35 = 3 8 = 1 5 = % = 89% = Be sure to read the question carefully. It may ask you to order from least to greatest or greatest to least What does ascending order mean? What does descending order mean? 10

11 Practice Questions A store manager analyzed the change in sales of various products from last month to this month. The percent increases and decreases in sales are shown in the table. These values will be ordered from greatest to least. Which list of the products matches this order? A Pants, shirts, watches, shoes, ties B Ties, shoes, watches, shirts, pants C Watches, shirts, pants, shoes, ties D Ties, shoes, pants, shirts, watches The table shows the heights in feet of several students in Mrs. Brown s class. Which list shows the heights in order from tallest to shortest? A. Carmela, Feng, Olivia, James B. Olivia, James, Feng, Carmela C. James, Olivia, Feng, Carmela D. Carmela, James, Feng, Olivia 11

12 6.2E: extend representations for division to include fraction notation such as a/b represents the same number as a b where b 0 Fractions may be thought of as division Write two expressions to represent each fraction Find the quotient for each expression above. 12

13 Practice Questions Which two expressions each represent A and ? B and 12 3 C and 3 12 D and 12 3 Rebecca had 10 pieces of candy to share equally among her 4 children. Which equation shows how Rebecca can determine the number of candies each child will receive? A = 4 B = 0.4 C = 2.2 D =

14 6.4C: give examples of ratios as multiplicative comparisons of two quantities describing the same attribute What is the ratio of pencils to paperclips? The number of paperclips is times the number of pencils. The number of pencils is times the number of paperclips. 14

15 Practice Questions Use the drawings below to complete the following statement. The number of apples is times the number of pears. 3 A. 2 2 B. 3 C. 2 D. 3 15

16 6.4D: give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients. Rate: A ratio that compares different kinds of units. Use the goldfish label to answer questions 1 and 2. Express answers as fractions in simplest form. 16

17 1. According to the information provided in the label, what is the rate of calories per goldfish? 2. What is the rate of goldfish per calorie? 3. Calculate each of the following a. Number of calories per fat gram b. Number of calories per gram of carbohydrates c. Number of grams of saturated fat per gram of fat 17

18 6.4E: represent ratios and percents with concrete models, fractions and decimals 6.4F: represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 x 10 grids, strip diagrams, number lines, and numbers Ratios: Concrete models Write as many different ratios as you can to compare the circles shown below. Write the ratio in words. 18

19 Fractions: Write each ratio that you wrote on the previous page in fraction form. Determine which ratios are actual fractions. Percents: Write each actual fraction you created above as a percent. 19

20 Decimals: Write each percent you created previously as a decimal. Add the decimal equivalent above the fractions on the double number line above. 20

21 Practice Questions 1. The shaded region of the model below represents the part of the class who completed their homework on Monday night. What percent of the students in the class did not complete their homework? A. 32% B. 34% C. 42% D. 68% 2. If the shaded region of the model below represents the part of a book that Daniela has read, what fraction of the book does Daniela have left to read? A. 2 5 C. 3 5 B. 2 3 D

22 6.4G: generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money Conversion Process fraction decimal fraction percent decimal fraction decimal percent percent fraction percent decimal 22

23 Practice Questions 1. A coat is discounted 40% off its regular price. Which value is equivalent to 40%? A B C. 40 D Alexandria answered 6 out of 15 questions correct on her math test. Expressed as a decimal, what number of questions did Alexandria answer correctly? Record your answer and fill in the bubbles on the grid below. Be sure to use correct place value. 23

24 6.5C: use equivalent fractions, decimals, and percents, to show equal parts of the same whole 1 5 of the whole 20% of a whole 0.20 of the whole These all mean the same thing 24

25 2 There are 20 cookies on a tray. of them are oatmeal 5 raisin. How many oatmeal raisin cookies are on the tray? Fractions Divide the cookies into 5 equal parts. Draw your picture below to help determine how many oatmeal raisin cookies are on the tray? Percent Use a percent bar to determine how many oatmeal raisin cookies are on the tray. Decimal Write an equation using a decimal to determine how many oatmeal raisin cookies are on the tray. 25

26 Practice Questions Bart and Nolan are trying to finish their math homework before their favorite TV show starts. Bart finishes 83% of his problems. Nolan finishes 5 out of 6 of his problems. Who finishes a greater percentage of his problems in time? Kylie s softball team is selling cookies for a fundraiser. Their coach set a goal for each girl to sell 250 boxes of cookies. The table shows the part of the goal that was met by 4 of the girls on the softball team. Cookie Sales Kylie 0.3 Rachel 46% Kennedy 2 5 Carol 1 4 What fraction of the goal did Rachel meet? 26

27 Use this page to show work for the practice problems. 27

28 6.7A: generate equivalent numerical expressions using order of operations, including whole number exponents, and prime factorization Order of Operations Mrs. Mathews has one stack of 5 books and 3 stacks of 4 books. How many books does she have in all? Write an expression to show how many books Mrs. Mathews has in all. 28

29 Factor Tree Create a factor tree to show the prime factorization for

30 Practice Questions 1. What value is equivalent to (5 2) 60? A. 3 B. 66 C. 159 D What is the value of the expression below? ( ) + (5 3) 2 Record your answer and fill in the bubbles on the grid below. Be sure to use the correct place value. 30

31 3. What is the prime factorization of 72? A. 2 2 x 3 x 6 B. 3 3 x 2 2 C. 2 3 x 3 2 D. 2 3 x 9 4. Complete the factor tree below to find the missing number. Record your answer and fill in the bubbles on the grid below. 31

32 6.7B: distinguish between expressions and equations verbally, numerically, and algebraically 32

33 Practice Questions 1. Which of these can be written as an equation? A. Two times 0.75 plus m B. Three is less than twice a C. Half the product of five and j D. Four times n is Which of the following Is NOT true about an equation? A. Must include an equal sign B. A phrase that contains a single term C. Shows two equivalent expressions D. May contain numbers and variables 33

34 6.7C: determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations Equivalent Expressions Draw a model to represent each expression above to show the expressions are equivalent, 34

35 Practice Questions 1. Look at the model below. Which of the following statements of equality are true? A. 3(x + 2) = 3x + 5 B. 3x + 26 = (3 + 2x) C. 3(2 + x) = 6 + 3x D. 6(2 + 2x) = x 2. Which of the following could NOT be used to represent the expression equivalent to the model shown below? A. 3( 4) + 3(2) C. 4(3 + 2) B D. 3( 2) 35

36 6.7D: generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties Create a model using algebra tiles to represent 3x + 9. Sketch the model you created below. Divide your algebra tile model into as many equal groups as possible. Draw your groups below. How many equal groups did you create? Write an expression to represent each group. 36

37 Practice Questions 1. Which expression is equivalent to 3(x + 6) A. 3 + x B. 3x + 6 C. 3 + x + 6 D. 3x Which number sentence correctly uses an identity property to show equivalent expressions? A. 6.25(0) = 0 B = C = 0 D. 14 ( 1 ) =