MCAS and Common Core Mathematics Student Set

Transcription

1 Grade SAMPLER MCAS and Common Core Mathematics Student Set Click on the book titles below to navigate. MCAS Finish Line MCAS Performance Indicator Finish Line for the Common Core State Standards

2 Contents Introduction to MCAS Finish Line Mathematics Understanding Mathematical Processes Unit : Number Sense Lesson Whole Number and Decimal Place Value Lesson Fractions and Mixed Numbers Lesson Percents and Equivalent Forms Lesson Integers Lesson Comparing and Ordering Numbers Lesson Primes, Composites, and Divisibility Lesson 7 Factors and Multiples Number Sense Review Unit : Operations Lesson Operations with Decimals Lesson Operations with Fractions Lesson Operations with Percents Lesson Adding and Subtracting Integers Lesson Order of Operations Lesson Estimation Operations Review Unit : Geometry, Part Lesson Points, Lines, and Planes Lesson Angles Lesson Plane Figures Lesson Angles of Polygons Lesson Solid Figures Geometry, Part Review

3 Unit : Geometry, Part Lesson Coordinate Geometry Lesson Transformations Lesson Congruence Lesson Symmetry Geometry, Part Review Unit : Patterns, Relations, and Algebra Lesson Algebraic Expressions Lesson Patterns Lesson Equations Lesson Functions Lesson Graphing Relationships Patterns, Relations, and Algebra Review Unit : Measurement Lesson Customary Units of Measurement Lesson Metric Units of Measurement Lesson Rates and Scale Drawings Lesson Perimeter and Circumference Lesson Area Lesson Surface Area and Volume Measurement Review Unit 7: Data Analysis, Statistics, and Probability Lesson Minimum, Maximum, and Range Lesson Mean, Median, and Mode Lesson Line Plots Lesson Stem-and-Leaf Plots Lesson Circle Graphs Lesson Probability Lesson 7 Compound Events Data Analysis, Statistics, and Probability Review

4 LESSON Operations with Fractions Indicators.N.,,,, To add or subtract fractions with unlike denominators, first rewrite them as equivalent fractions with like denominators. Start by finding the least common denominator (LCD) of the fractions. The LCD is the same as the least common multiple (LCM) of the denominators. The LCM of and 8 is. So rewrite the fractions with a denominator of Then subtract: To multiply fractions, multiply the numerators and multiply the denominators As a shortcut, you can cancel common factors. 7 To divide fractions, multiply by the reciprocal of the divisor. Again, you can cancel common factors Remember Finding the least common multiple (LCM): Multiples of :,, 8,, 0 Multiples of 8: 8,,,, 0 The LCM of and 8 is. To find the reciprocal of a fraction, simply switch the numerator and denominator. The reciprocal of a whole number is divided by the number. Dividing is the same as multiplying by the reciprocal. Multiplying is the same as dividing by the reciprocal. 0 0 efore multiplying or dividing mixed numbers, change them to improper fractions. 7 If an answer is a fraction, reduce it to lowest terms. If an answer is an improper fraction, you can change it to a mixed number. 8 Unit Operations The Continental Press, Inc. Do not duplicate.

5 Read each problem. Circle the letter of the best answer. On Friday, inches of snow fell. y Saturday, there was a total of inches. How much snow fell Saturday? A inches C inches inches D inches The correct answer is. First change into the improper fraction. Change 7 to. Find equivalent fractions with like denominators. The LCM of and is, so multiply: and. 8 8 Subtract:. Finally, write the answer as a mixed number:. To divide by, what would you do? A add and multiply by C multiply by D subtract from Jarrod waited hour for a bus. Spencer waited hour. How much longer did Jarrod wait than Spencer? A hour C hour 0 0 hour D hour 0 Eleanor is making a costume for a play. She used yards of black fabric and yards of green fabric. How many yards of fabric did she use? A 7 C 8 7 D 8 8 Charles spent 7 hours working on his homework this week. He spent of the time working on a science report. How many hours did Charles spend on his science report? A C D 0 A building lot for a warehouse measured of an acre. When the warehouse was built, it covered of the lot. What fraction of an acre did the warehouse cover? A 7 A shopkeeper had pound of an expensive spice. She repackaged the spice in small jars containing only pound. How many jars did she fill? C D 8 A C D 0 Unit Operations The Continental Press, Inc. Do not duplicate.

6 Read each problem. Write your answers. 8 The Monster Cookie Factory makes cookies that weigh of a 0 pound each. Mr. Harvey bought pounds of these cookies. How many cookies did he buy? Answer: To find the number of cookies in pounds, divide by the weight of cookie, pound: 0. To divide by a fraction, multiply by the reciprocal of the divisor. The reciprocal of is. Change to an improper fraction,, and multiply by to get. Reduce to 0 0 lowest terms:. So Mr. Harvey bought cookies. In a certain neighborhood, of the families have children. Of the families with children, also have pets. What fraction of the neighborhood families have both children and pets? Answer: 7 0 Jimmy picked of a quart of blueberries. Ramona picked of a 8 quart of blueberries. How many quarts did they pick all together? Answer: Trees cover 7 acres of a -acre park. A lake covers the remaining acres. How many acres does the lake cover? Answer: Find this product. Express your answer in lowest terms. Answer: Unit Operations The Continental Press, Inc. Do not duplicate.

7 Read the problem. Write your answer for each part. The map shows the lengths of three bicycle paths near Antwon s apartment. mile School miles Antwon s Apartment Library mile Polar Ice Cream Stand a. Antwon bicycled from his apartment to the Polar Ice Cream Stand along these three paths. What is the total distance he bicycled? Give your answer as a mixed number in lowest terms. Show or explain how you found your answer. Ask Yourself What is the least common multiple of,, and? b. What is the total distance from Antwon s apartment to the ice cream stand and back? Show or explain how you found your answer. Unit Operations The Continental Press, Inc. Do not duplicate.

8 Which two streets on the map below appear to be parallel? rd St. th St. 7 A radio station broadcasts a 00,000- watt signal. Which of the following equals 00,000? Robin St. A 0 0 Jay St. C 0 D 0 A rd St. and th St. rd St. and Robin St. 8 What temperature is shown on the thermometer below? C Jay St. and th St. ºF D Jay St. and Robin St. Marcus has a number cube with faces numbered through A 8. F 8.7 F C. F D. F If he rolls the cube one time, what is the probability the result will be a number less than? A C D What is the value of the expression below when y? A 0 C D 80 0 y Session One The Continental Press, Inc. Do not duplicate. Go On

9 Questions 8 0 are short-answer questions. Write your answers below. You may do your figuring in the test booklet. 8 The overnight low temperatures (in C) on five consecutive nights in Greenfield, Massachusetts, are shown below. 0 List these five temperatures in order from greatest to least. Answer: The table shows how the cost of a bicycle rental depends on the number of hours the bicycle is rented. Number of Hours ICYCLE RENTAL COSTS Cost of Rental $ $8 $ $ $7 Nicole rented a bicycle for a certain amount of time, and the total cost was $. For how many hours did she rent the bicycle? Answer: 0 What is the area of the parallelogram shown below? 7 cm cm 8 cm Answer: Session Two The Continental Press, Inc. Do not duplicate. Go On

10 Table of Contents Introduction... Unit Ratios and Percents...7.RP. Lesson Ratios...8.RP..a Lesson Equivalent Ratios....RP.,.RP..b Lesson Rates....RP..d Lesson Measurement Conversions...0.RP..c Lesson Percents... Review Ratios and Percents...8 Unit Operations....NS. Lesson Dividing Whole Numbers....NS. Lesson Dividing Fractions....NS. Lesson Adding and Subtracting Decimals...0.NS. Lesson Multiplying and Dividing Decimals... Review Operations...8 Unit Factors and Multiples....NS. Lesson Greatest Common Factors....NS. Lesson Least Common Multiples... Review Factors and Multiples...0 Unit Positive and Negative Numbers....NS. Lesson Integers....NS..a, c Lesson Rational Numbers on Number Lines...8.NS..b, c;.ns.8 Lesson Coordinate Graphing...7.NS.7.a, b Lesson Comparing Integers...7.NS.7.c, d Lesson Absolute Value...80 Review Positive and Negative Numbers...8 Unit Expressions...87.EE.;.EE..a, b Lesson Writing Expressions...88.EE.,.EE..c Lesson Evaluating Expressions....EE.,.EE. Lesson Operation Properties... Review Expressions... 00

11 Unit Equations and Inequalities... 0.EE. Lesson Equations and Inequalities... 0.EE. Lesson Writing Equations EE.7 Lesson Solving Equations....EE.8 Lesson Representing Inequalities... Review Equations and Inequalities...0 Unit 7 Relationships etween Two Variables....EE. Lesson Functions....EE. Lesson Graphing Relationships...8 Review Relationships etween Two Variables... Unit 8 Geometry....G. Lesson Area....G. Lesson Volume... 0.G. Lesson Nets and Surface Area....G.,.NS.8 Lesson Coordinate Geometry...8 Review Geometry... Unit Data and Statistics....SP. Lesson Collecting Data....SP.,.SP. Lesson Data Distributions...0.SP..a d Lesson Measures of Central Tendency....SP..a d Lesson Measures of Spread...8.SP. Lesson Representing Data...7 Review Data and Statistics...7 Practice Test...7 Glossary...

12 LESSON Dividing Fractions.NS. The product of a number and its reciprocal is always. To multiply fractions, multiply the numerators. Then multiply the denominators. 8 To change a mixed number to a fraction greater than, multiply the whole number part by the denominator. Then add the numerator. This becomes the new numerator of the fraction. The denominator stays the same. To change a fraction greater than to a mixed number, divide the numerator by the denominator. Write the remainder as a fraction. To divide fractions, multiply by the reciprocal of the second fraction. The numerator and denominator of a reciprocal switch places. What is the reciprocal of each number? 8 Switch the numerator and the denominator. The reciprocal of is. The reciprocal of 8 is 8 8. As a fraction,. The reciprocal of is. What is the quotient of 8? First rewrite as multiplication using the reciprocal of 8. The reciprocal of 8 is 8, so the equivalent multiplication expression is 8. Multiply and reduce to lowest terms if necessary. The quotient of 8. 8 UNIT Operations The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL.

13 Read each problem. Circle the letter of the best answer. SAMPLE Travis has a -foot long rope. He ties a knot in the rope every foot. How many knots are tied in the rope? A 8 C D The correct answer is C. To find the number of knots, divide by. First write as the fraction. Use it to write the division problem:. Multiply by the reciprocal of and reduce: 8 knots. Choice A is not correct because the numbers are multiplied, not divided. Choices and D are not correct because a mathematical error was made. What is the reciprocal of? What is the quotient of 0? A C A 8 C D D 8 Which number sentence shows the product of a number and its reciprocal? A C D A hiking trail is -mile long. A total of 8 markers are placed equal distances apart to help guide hikers. How far is one marker from the next? A 0 mi C mi A piece of land is acre. It is divided evenly into pieces. What is the size of each piece of land? A acre C acres acre D acres A bottle contains 8 cups of juice. The juice is poured into glasses that hold cup each. How many glasses can be filled with the juice? A C 0 mi D mi 8 D The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT Operations 7

14 Read each problem. Write your answer. SAMPLE Carmen walked miles in hour. What was her average walking speed, in miles per hour? Answer To find the average walking speed, divide by. Change the mixed number to a fraction:. Now divide: 0 0. The fraction 0 0. The average walking speed was miles per hour. 7 It rained a total of inch in hours. What was the average amount of rainfall each hour? Show your work. Answer 8 A recipe makes a total of cups of pudding. A serving of pudding is cup. How many servings of pudding does the recipe make? Show your work. Answer Horses are measured in units called hands. One hand equals foot. A horse is feet tall. How tall is this horse in hands? Show your work. Answer 8 UNIT Operations The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL.

15 Read the problem. Write your answer to each part. 0 Jada surveyed some students to see which tool they most favored for communicating with friends. The results of her survey are shown in this circle graph. Text Messages FAVORITE COMMUNICATION TOOL Phone 0 Letters Part A What is the reciprocal of each fraction in the circle graph? Answer Part A total of 0 students said they favored text messages to communicate with friends. How many total students did Jada survey? Show your work or explain how you know. What division expression can be used to answer this question? The Continental Press, Inc. DUPLICATING THIS MATERIAL IS ILLEGAL. UNIT Operations