glencoe math triumphs foundations for algebra 1 (teacher handbook)

Test success indicates that a student can progress to another Math Triumphs chapter if needed or exit the intervention program.. • Diagnostic and Placement Test • Online Readiness Quiz

Contents in Brief

M a t h ematics T ea che r

Table of Contents

Vertical Alignment

Welcome to Math Connects T4

An overview of the vertical alignment of Macmillan/McGraw-Hill’s

and Glencoe’s PreK–12 mathematics programs

Implementing Intensive Intervention T6

Program Organization T7

Balanced approach of concepts, skills, and problem solving

Assessment

Comprehensive Assessment System T10

Diagnostic, Formative, and Summative assessments linked to

Data-Driven Decision Making

T4 Teacher Handbook

Concepts • Skills • Problem Solving

The only true vertically aligned PreK–12 Mathematics Curriculum

Math Connects offers three dimensions of vertical alignment.

1 Content Design

Vertical content alignment is a process

that ensures you and your students

experience an articulated, coherent

sequence of content from grade level to

grade level This provides you with the

assurance that content is introduced,

reinforced, and assessed at appropriate

times in the series, eliminating gaps and

unnecessary duplication You are able to

target your instruction to student needs

because you are not teaching content

intended to be covered later or that

students have previously mastered

2 Instructional Design

Our strong vertical alignment in instructional approach from PreKindergarten through Algebra 2 provides a smooth transition for students from elementary to middle school to high school Our common vocabulary, technology, manipulatives, lesson planning, and Data-Driven Decision Making reduce the confusion students often encounter when transitioning between grade levels without this built-in articulation

3 Visual Design

The student pages of Math Connects

have a consistent visual design from grade to grade This aids students’ transition from elementary school to middle school and from middle school

to Algebra 1 Students are more likely to succeed when they are already familiar with how to navigate student pages

6–8 Pre-Algebra and Algebra 1 Geometry and Algebra 2

According to College Board research, about 80% of students

who successfully complete Algebra 1 and Geometry by 10th

grade attend and succeed in college (Changing the Odds:

Factors Increasing Access to College, 1990) Math Connects

was conceived and developed by backmapping with the final

result in mind—student success in Algebra 1 and beyond

Math Connects was developed to specifically target the skills

and topics that give students the most difficulty, such as

Problem Solving, in each grade span

Math Connects includes diagnostic, formative, and summative

assessment; data-driven instruction; intervention options; and performance tracking, as well as remediation, acceleration, and enrichment tools throughout the program

A three-tiered Response To Intervention (RTI) is provided

1

TIERDaily Intervention Reteach masters and Alternative Strategy suggestions address concepts from

a different modality or learning style

2

TIERStrategic Intervention Teachers can use the myriad of intervention tips and ancillary materials, such

as the Strategic Intervention Guide (1–5) and Study Guide and Intervention (6–8)

3

TIERIntensive Intervention For students who are

two or more years below grade level, Math Triumphs

provides step-by-step instruction, vocabulary support, and data-driven decision making to help students succeed

Math Connects includes many opportunities for teacher

professional development Additional learning opportunities in various formats—video, online, and on-site instruction—are fully aligned and articulated from Kindergarten through Algebra 2

5 Keys to Success

T6 Teacher Handbook

Implementing Intensive Intervention 3

TIER

Data-Driven Intensive Intervention

Ongoing assessment aids the teacher in student placement, progress monitoring, and exit

Teacher prepares individual or group intervention plan(s)

Teacher modifies instruction based on results of formative assessments

Test success indicates that a student can

progress to another Math Triumphs chapter

(if needed) or exit the intervention program

• Diagnostic and Placement Test

• Online Readiness Quiz

• Chapter Preview

• Assessment Masters:

Chapter Pretest

• Student Study Guide

• Teacher Edition strategies

for

Number and Operations

Geometry and Measurement

Data Analysis

ors (LCD)

the least common multiple of the denominators of two

or more fractionsunlike denominators denominators that are not the same

To add fractions with like denominators

, add the numerators

To add fractions with unlike denomin

fractions so their denominat

ors are the same Use the least common multiple to find th

e least common denom

To add mixed numbers, convert ea

ch mixed number to an impr

oper

fraction, then add the impr

oper fractions For all addition pr

oblems,

be sure the answers ar

e written in simplest form

opyright © Glencoe/McGraw-Hill, a division o

f The McGraw-Hill Companies, Inc.

Example 2

Circle all sets

in which the number

-13 belongs.

counting numbers whole numbers integers

1 Counting n umbers are {

}

41

a counting n umber.

2 Whole num bers are {

}.

41 a whole number

3 Integers are { }

1 Use a number line Be

gin at zero and move left 7

units Plot a point at -7.

2 Count the same number o

units Plot a point

Examples

Fully worked-out Examples enable students and

parents to see how to solve problems step by step

Your Turn! gives students an opportunity to

practice skills immediately

Provide Personalized Instruction

Consumable student study guides and minimal preparation requirements allow for flexibility and

personalized instruction in any setting

• After school • Summer school

• Before school • Intersession

• Tutoring • Pull-out/Resource room

Program Organization

8 RACING Nate entered a 13 3

5 mile dirt bike race H

e

completed 7 3

8 miles when his tire blew and he had to quit the race How many miles wer

e left to race when

Step by Step Problem-Solving Practice

Skills, Concepts, and Problem Solving

3 =

13 6

7 - 9

7 =

16 6 1

2 - 2 2

_ 15 =

17 10 7 9 - 3 1 3 =

18 5 1

9 - 3 4

5 =

19 12 2

3 - 8 8

9 =

20 7 3

5 - 2 13

_ 20 =

GO ON

opyright © Glencoe/McG raw-Hill, a division of The McGraw-Hil

l Companies, Inc.

Lesson 2-2 Compare and Order Dec imals 57

In which place values are the digits the same?

After comparing th

e digits, which place value helpe

d decide which inequality symbol to use?

4 11.12 11.112After comparing th

e digits, which place va

lue helped decide which inequality symbol to use?

5 Order the numbers

-2.65, 1.56, -0.256, -2.15, and 0.615 fr

om least to greatest

Step 1 For the negative numbers,

is to the left of both and

on a number lin

left of < <

Step 2 For the pos

itive numbers, is to the right of

Guided Practice exercises provide computational practice

They can be used as formative assessment to monitor student

progress and guide your instruction

Step-by-Step Practice guides students to complete a

computational problem through a series of conceptual steps

Instructional aids are provided to students in the exercises

that follow

Step-by-Step Problem-Solving Practice walks the student through a four-step problem-solving strategy (Understand, Plan, Solve, Check) that is relevant to the word problem Aids help the student break down and visualize what the problem

is asking and how to solve it

© Glencoe/

McGraw-Hil

l, a divi sion

of The McG

raw-Hill

Companies,

Inc.

Identify all sets to which

each number belongs.

was 1.2 in Write as a fraction in simplest form.

20BASKETBALL Curtis’ scoring statistics for the first

5 games of the season are shown in the table below

.

Name the set(s) that Curtis’ scor

e from game 4 belongs

_

100

Vocabulary Check

Write the vocabulary

word that completes

each sentence

13MOVIES Len bought a lar

ge box of popcorn at the movies If the popcorn box

measured 5 inches by

3 inches by 9 inches, what was the volume of Len’s popcorn box?

14 SWIM Mr Armas filled his childr

en’s inflatable pool with 40.5 cubic feet of water The length of the pool was 6 feet and the width was 4.5 feet Use the formula

h = V _

· w to find the depth of the

water in the swimming poo

McGraw-Hill’s Math Triumphs is designed to provide students a balanced approach to

mathematics learning by offering them the opportunity to:

• investigate concepts and build their conceptual understanding;

• review, learn, and practice basic computational and procedural skills; and

• apply mathematics to problem solving in real-world situations

Independent Practice

Skill, Concepts, and Problem Solving

provide homework opportunities and

Program Organization

T10 Teacher Handbook

Comprehensive Assessment System

3

Take the Chapter 1 Pretest to find out.

them with what you will learn in this chapter.

You know how to add.

-1 -1 -1 -1

You know how to multiply.

To multiply integers, multiply their

What You Know What You Will Learn

at the beginning of the year with the

Diagnostic and Placement Tests

knowledge at the beginning of a chapter

with one of the following options

Student Study Guide

Data-Driven Decision Making

Math Triumphs offers frequent and meaningful assessment of student progress

within the curriculum structure and teacher support materials

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companie

8 triangular prism 9 rectangular prism 10 rectangular prism

b = 4 in., h = 6 in., = 0.5 yd, w = 1.2 yd, = 16 mm, w = 25 mm,

Solve.

a height of 4.5 inches If the width of the box is 3 inches, what is the volume of the box of tissue?

ground with a base length of 24 meters and a height of 45 meters

What is the area?

Progress Check 3 (Lessons 5-5 and 5-6)

1 Between which years was the greatest decrease?

2 What was the price of a dozen eggs in 2007?

The histogram shows the number of books in 20 library branches Use this histogram to answer Questions 3 and 4.

3 How many libaries have 20,000 or more books?

4 In which interval(s) do the least number of libraries fall?

The data in the table shows the sports played by a sixth grade class Create a bar graph to display the data Use the graph to answer Questions 5–7.

Sport Number of Students

6 About how many students play football?

Annual Average Egg Prices per Dozen

Annual Average Egg Prices per Dozen

Books at Local Libraries

Number of Books (thousands)

0 2 4 6 8

5–9 10–14 15–19 20–24 25–29 30+

Books at Local Libraries

Number of Books (thousands)

0 2 4 6 8

5–9 10–14 15–19 20–24 25–29 30+

Chapter 6 Test

adequately as you teach each lesson Use the assessments to

differentiate lesson instruction and practice

Student Study Guide

• Progress Check

• Reflect

Teacher Edition

• Intervention Strategy

• Are They Getting It?

• See It, Do It, Say It, Write It

• Ticket Out the Door

• Data-Driven Decision Making

in learning the concepts in each chapter

Student Study Guide

1-1 Number Groups 4

1-2 Compare and Order Numbers 9

Progress Check 1 14

1-3 Add Integers 15

1-4 Subtract Integers 21

Progress Check 2 26

1-5 Multiply Integers 27

1-6 Divide Integers 31

Progress Check 3 35

1-7 Solve One-Step Equations 36

1-8 Graph Inequalities 41

Progress Check 4 45

Chapter Test 46

Number and Operations iv

Chapter

1

Denver, Colorado

2-1 Decimals and Place Value 50

2-2 Compare and Order Decimals 55

Progress Check 1 60

2-3 Round Decimals 61

2-4 Add and Subtract Decimals 65

Progress Check 2 69

2-5 Multiply Decimals 70

2-6 Divide Decimals 75

Progress Check 3 79

Chapter Test 80

Chapter

Albuquerque, New Mexico

3-1 Greatest Common Factors 84

3-2 Simplify Fractions 89

Progress Check 1 94

3-3 Mixed Numbers 95

3-4 Compare and Order Fractions 99

Progress Check 2 104

3-5 Multiply Fractions 105

3-6 Divide Fractions 109

Progress Check 3 113

3-7 Least Common Multiples 114

3-8 Add Fractions 119

3-9 Subtract Fractions 125

Progress Check 4 131

Chapter Test 132

Chapter 3 Fractions and Mixed Numbers vi

Niagara Falls, New York

Chapter

4-1 Rational Numbers 136

4-2 Fractions and Decimals 141

Progress Check 1 146

4-3 Decimals and Percents 147

4-4 Fractions and Percents 151

Progress Check 2 156

4-5 Squares and Square Roots 157

4-6 Compare and Order Real Numbers 161

Progress Check 3 165

Chapter Test 166

Charleston, South Carolina

viii

5-1 The Customary System 170

5-2 The Metric System 175

Progress Check 1 180

5-3 Convert Between Systems 181

5-4 Perimeter 185

Progress Check 2 190

5-5 Area 191

5-6 Volume 195

Progress Check 3 201

5-7 Surface Area 202

5-8 The Coordinate Plane 209

Progress Check 4 213

Chapter Test 214

Chapter 5 Measurement and Geometry viii

St Augustine, Florida

Chapter

6-1 Line Graphs 218

6-2 Frequency Tables and Histograms 225

Progress Check 1 230

6-3 Bar Graphs 231

6-4 Circle Graphs 237

Progress Check 2 242

6-5 Mean, Median, and Mode 243

6-6 Count Outcomes 249

6-7 Probability 255

Progress Check 3 261

Chapter Test 262

Mount Rainier National Park, Washington

Table of Contents

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Math Triumphs Assessment Masters are an important tool in the evaluation of specifi c areas

of student need, appropriate placement, and determining student success and readiness

for transitioning back to on-level curriculum The assessments in this book provide a

comprehensive system that allows for diagnostic, formative, and summative assessment

Diagnostic and Placement Test

The Diagnostic and Placement Test assesses concepts

and skills that are presented in an on-level curriculum

To determine if a student has successfully mastered

prerequisite concepts and skills for Algebra 1, use the

Algebra 1 Diagnostic and Placement Test The results

can be used to determine whether students require

intensive intervention, and, if so, what specifi c content

strands students need

The Diagnostic and Placement Test contains 30

mutiple-choice questions and addresses the content

strands: Number, Operations, and Quantitive Reasoning;

Patterns, Relationships, and Algebraic Thinking;

Geometry and Spatial Reasoning; Measurement; and

Probability and Statistics

See page Aiii for further explanation and instructions

for administering and scoring this test.

Chapter Pretest and Test

The Chapter Pretests and Tests cover concepts and skills

presented in each chapter of Math Triumphs The Chapter

Pretest is multiple-choice format and can be used to determine

specifi c student needs and assign specifi c chapters and lessons

within that chapter The Chapter Test is short-answer format

and can serve as a summative assessment of the contents of each

chapter to determine student success in learning that chapter’s

concepts and skills

Answer Key

An Answer Key at the end of this book provides reductions of

each student page with answers

Chapter Test Chapter Test

Verify the expressions are equal Name the proper

4 Multiplicative Identit y

5 Commutative Property of Addition

6 Associative Pr operty

of Multiplication

Apply the Distributive Proper

ty to simplify each expre ssion

11/22/08 9 :16:23 AM

Cop

© Glencoe/McGra w-Hill, a di vision of The McGra w-Hill Companies, Inc.

Math Triumphs

Diagnostic and Placement T

ests Av PDF Pass

Math Triump hs: Foundations for Alge bra 1

Algebra 1 S trategic Interv ention —See page Aix for materials l ist.

Glencoe Algebra 1

Placement Test

Scoring Guide Student Name

Key: Consider this student

for…

For each part, mark the box under the number of correctly answered questions.

Total 0 1 2 3 4 5 6 7 8

21 22 23 24 25 26 27 28 29 30

0 1 2 3 4 5 6 7 8

Number, Operation, an

d Quantitative Reaso ning Patterns, Relation ships, and Algebraic Thinking

Geometry and Spatial Reasonin g

12/9/08 3:46:44 PM

Using the Assessment Masters

The Diagnostic and Placement Test provides tools to assist teachers in making placement

decisions with regard to one of the following on-level, strategic intervention, or intensive intervention resources

Placement Decisions

In making placement decisions for a student, consider a variety of evidence, such as the student’s mathematics grades, classroom observations, teacher recommendations, portfolios of student work, standardized test scores, and placement test scores Use the results of these placement tests in conjunction with other assessments to determine which mathematics course best fi ts a student’s abilities and needs

These tests can help determine whether or not students need intervention as well as the level of intervention required Through strategic intervention, teachers can work with students using on-level content but strategically choose which content strand(s) need further development

Sometimes a student may struggle with a particular strand, but overall the student is able to perform on-level

Intensive intervention is used with students who are struggling with most or all strands of math content and are unable to work on grade-level These students will need alternative intervention materials to help meet their needs These materials, such as the Math Triumphs program, offer

alternatives that will accelerate achievement in mathematics

Using the Diagnostic and Placement Test

When to Use the Diagnostic and Placement Test

In most situations, these placement tests are given near the end of the current course in

order to help determine student placement for the following year You can also use these

tests in special situations, such as a student transferring into your school mid-year or

entering middle school with advanced mathematics ability

Interpreting Scores

When interpreting scores on the placement tests,

consider the student’s score on each part, as well as the

total score Scoring Guide Masters before each test can

be reproduced and used to record each student’s score

A sample of a completed Scoring Guide is shown to the

right

Sample Score and Placement Analysis

On a sample test, suppose a student scored 8 out of 8

questions correct in Number, Operations, and Quantitative

Reasoning; 5 in Patterns, Relationships, and Algebraic

Thinking; 2 in Geometry and Spatial Reasoning; 3 in

Measurement; and 2 in Probability and Statistics The total

number correct was 20 out of 30 Note: There is not a direct

correlation between the score for each strand and the total

test score Use the total score for class placement decisions

and the score by strand when working on particular

objectives

Sample Analysis

This student scored well in the fi rst two parts of the test, but lower in the remaining

sections If these results are similar to other assessments, this student is likely to need

intervention materials and may fi nd the grade-level material too challenging without any

intervention The teacher should also note that the student scored particularly low in the

Geometry and Spatial Reasoning This student may require intensive intervention when

these skills are taught

Using Placement Tests for Diagnostic Purposes

These placement tests also provide valuable diagnostic information for classroom

teachers Reproducible learning-objective charts list the learning objective for each

test question and can be found before each test By marking each question the student

answered incorrectly, you can see which objectives the student has not mastered

Math Triumphs: Foundations for Algebra 1

Algebra 1 Strategic Intervention —See page Aix for materials list.

Glencoe Algebra 1

Placement Test

Scoring Guide

Student Name

Key: Consider this student for…

For each part, mark the box under the number of correctly answered questions.

Math Triumphs: Foundations for Algebra 1

Algebra 1 Strategic Intervention —See page Aix for materials list.

Glencoe Algebra 1

Placement

Test

Scoring Guide

Student Name

Key: Consider this student for…

For each part, mark the box under the number of correctly answered questions.

Geometry and Spatial Reasoning

Measurement

Probability and Statistics

Mark the total number correct below.

Approximate (mentally and with calculators) the value of irrational numbers as they arise from problems situations (such as π, √ 2 )

3 Express numbers in scientifi c notation, including negative exponents, in appropriate problems situations.

4 Express numbers in scientifi c notation, including negative exponents, in appropriate problems situations.

5 Select appropriate operations to solve problems involving rational numbers and justify the selections.

6 Select appropriate operations to solve problems involving rational numbers and justify the selections.

7 Use appropriate operations to solve problems involving rational numbers in problem situations.

8 Use multiplication by a constant factor (unit rate) to represent proportional relationships.

Geometry

and Spatial

Reasoning

14 Generate similar fi gures using dilations including enlargements and reductions.

15 Graph dilations, refl ections, and translations on a coordinate plane.

16

Use facts about the angles created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to fi nd unknown measures of angles

17 Use geometric concepts and properties to solve problems in fi elds such as art and architecture.

In the column on the left, mark the questions that the

student answered incorrectly.

Question Number Objective Geometry

and Spatial Reasoning

18 Use geometric concepts and properties to solve problems in fi elds such as art and architecture.

19 Locate and name points on a coordinate plane using ordered pairs of rational numbers.

Measurement

20

Find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models)

21

Estimate measurements and use formulas to solve tion problems involving lateral and total surface area and volume

22 Use the Pythagorean Theorem to solve real-life problems

23

Use proportional relationships in similar two-dimensional

fi gures or similar three-dimensional fi gures to fi nd missing measurements

24 Describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally.

Probability and Statistics

25 Find the probability of dependent and independent events

26 Use theoretical probabilities and experimental results to make predictions and decisions.

27

Select the appropriate measure of central tendency or range

to describe a set of data and justify the choice for a particular situation

28 Draw conclusions and make predictions analyzing trends in scatterplots.

29

Select and use an appropriate representation for presenting and displaying relationships among collected data including line plots, line graphs, stem and leaf plots, histograms, and Venn diagrams, with and without the use of technology

30 Evaluate methods of sampling to determine validity of an inference made from a set of data.

A Special Note About Intervention

When using diagnostic tests, teachers should always question the reason behind

the students’ scores Students can struggle with mathematics concepts for a variety

of reasons Personalized instruction is recommended for English language learners,

students with specifi c learning disabilities, students with certain medical conditions, or

for those who struggle with traditional instructional practice Teachers should always

consider the needs of the individual student when determining the best approach for

instruction and program placement.

Student

Performance

Level

Number of Questions Correct

Suggestions for Intervention and Remediation

Intensive

Intervention

0 –17 Use Math Triumphs: Foundations for Algebra 1 to

accelerate the achievement of students who are below grade level Students should follow a personalized remediation plan A variety of materials and instructional methods are recommended For example, instruction and practice should be provided in print, technology, and hands-on lessons

Strategic

Intervention

18–23 Use the additional Intervention and Remediation

materials listed on the next page This list of materials can provide helpful resources for students who struggle

in the traditional mathematics program Strategic intervention allows students to continue to remain in

the Glencoe Algebra 1 program, while receiving the

differentiated instruction they need Teaching Tips and other resources are also listed in the Teacher Edition

Algebra 1 24 or more Use Glencoe Algebra 1 This student does not require

overall intervention However, based on the student’s performance on the different sections, intervention may be required For example, a student who missed

3 or more questions in the Measurement section may require extra assistance as you cover these skills throughout the year.

$IAGNOSTIC

#HART

4EST 0LACEMENT

Algebra 1

Print Materials

Quick Review Math Handbook

A comprehensive reference of important mathematical terms and concepts

to help build math literacy Also available in Spanish

Study Guide and Intervention Masters

A brief explanation, along with examples and exercises, for every lesson in the Student Edition These masters are included in the Chapter Resource Masters

Skills Practice Masters

Additional practice in computational and application exercises for each lesson in the Student Edition These masters are included in the Chapter Resource Masters

Practice Masters

Additional practice in computational and spiral review exercises for each lesson in the Student Edition These masters are included in the Chapter Resource Masters

Study Guide and Intervention Workbook

A consumable version of the Study Guide and Intervention Masters for each lesson

Skills Practice Workbook

A consumable version of the Skills Practice Workbook Masters for each lesson

Homework Practice Workbook

This combines the exercises in the Skills Practice Masters and the Practice Masters into one workbook

Word Problem Practice Masters

This master closely follows the types of problems found in the Exercises section of the Student Edition and includes word problems Use as an additional practice option or as homework for second-day teaching of the lesson

and Test Manager for using disaggregated data to make informed curriculum and instruction decisions

Mathematics Super DVDs

Includes: MindJogger Plus, a chapter review provided in a new game-show format and more

Interactive Classroom A custom classroom teacher-tool incorporating a variety of assets including

Additional Examples, Check Your Progress, and 5-Minute Checks

B represents the area of the base of a solid fi gure

P represents the Perimeter of the Base of a three-dimensional fi gure.

Diagnostic and Placement Test

1 Which set of numbers is ordered from least to greatest? 1

A 38 ; 12 ; 1; √ 2 ; 4 C 4; √ 2 ; 1; 12 ; 38

B 38 ; 12 ; √ 2 ; 1, 4 D 12 ; 38 ; 1; 4; √ 2

2 The area of a square is 8 square meters Which of these is 2

closest to the length of one side of the square?

3 Light travels at a speed of about 2.998 × 10 8

Express this number in standard notation.

4 A thunderstorm cloud holds about 6,200,000,000 raindrops 4

Which of the following shows this number in scientifi c notation?

5 Jake goes to the grocery store and buys 3 apples, 2 cans of 5

soup, and 1 box of cereal The apples cost $0.89 each; the

soup costs $2.98 per can; and the box of cereal costs $4.99

Write an equation that represents the total cost c of Jake’s purchases.

This test contains 30 multiple-choice questions Work each problem in the

space on this page Select the best answer Write the letter of the answer on

the blank at the right.

6 Mr Thomas wants to buy a boat He must make 48 monthly 6

payments to pay back the amount he borrowed, plus interest

His monthly payment is $161.85 What other information is necessary to determine the amount of money Mr Thomas borrowed from the bank?

7 Barb walked 1.3 miles to her friend’s house and then 7

8 On average, a dog runs 5.5 times faster than a child 8

Which equation can be used to fi nd s, the speed of a dog, given r, the speed of the child?

B s = 5.5 _

5.5

9 Ricky jogs 5 laps around a track in 8 minutes Which of 9

the following would be the same number of laps per minute?

10 What is the slope and y-intercept of the equation 10

11 Aleta went to dinner The bill was $36 She gave the 11

waiter a 15% tip What was the total amount Aleta spent on the food and the tip?

12 What is true concerning the lines graphed by the system of 12

equations shown below?

⎧

⎫ 8x 12x + 6 = 2y - 3 = 3y

13 Which algebraic expression can be used to fi nd the 13

nth term in the following sequence?

14 A photo with a length of 3 inches and a width of 5 inches is 14

enlarged to poster size The poster and the photo are similar

The length of the poster is 21 inches What is the width of

-2 -7-6-5-4-3-2

A

B

15

grid to the right Which of the following graphs

represent the translation of Rectangle ABCD

x

7 6 5 4 4 2 1

-2 -7-6-5-4-3-2

-2 -7-6-5-4-3-2

-2 -8-7-6-5-4-3-2

-2 -7-6-5-4-3-2

16 A rectangle is cut along its diagonal The measure of ∠A is 55° 16

A

B

17 A farmer wants to fence in part of her land so that her 17

chickens will have their own little area If she only has

28 feet of fence, what is the area of the largest pen that she can build?

18 Jason is experimenting with different ramps to replace 18

the stair step into his house The table below shows the

measure of a given angle m and its complement.

Measure of ∠m Measure of Complement ∠m’s

Based on the table, which of the following statements is true?

Diagnostic and Placement Test

19 Robin’s neighborhood is mapped out on the graph below 19

y

x

5 4 3 2 1

-3 -4 -5 -5-4-3-2

Park

School

Library

HomeDiner

Which ordered pair shows the location of the library?

20 The fi gure below is a net of a rectangular prism with a 20

length of 14 yards, a width of 12 yards, and a height of 4 yards.

14 yd

12 yd

4 yd

What is the surface area of the prism?

21 A cylindrical water tower is 24 feet high and has a diameter 21

of 20 feet Approximately how many cubic feet of water could

the tower hold?

22 The delivery ramp at the Corner Café is a right triangle 22

The hypotenuse is 4 meters long One leg is 3 meters long

What is the length of the other leg?

1073.25 cm 2 Area

713.25 cm 2 Area

533.25 cm 2Based on this pattern, what will be the area of the next fi gure?

because the next fi gure will decrease in area

by 1 2 the previous fi gure.

25 Four cards numbered 1, 5, 8, and 9 are placed in a bag A card 25

is drawn at random and then replaced Then a card is drawn

at random again What is the probability that both cards drawn have the number 9?

26 Twelve members of a band purchased one beverage each during a 26

break at practice Exactly 5 of the 12 members bought bottled

water At this rate, how many band members would you expect

to buy bottled water, if all 168 band members purchase a beverage?

27 A company has fi ve employees Their annual 27

earnings, in dollars, are shown below.

Which of the following measures best represents the typical

annual earnings of an employee of the company?

28 The scatter plot below shows the yearly advertising 28

expenditures and the relative sales for a small

company What can be concluded from this data?

250 225 200 175 150 125 100 75 50 25

Advertising Expenditures (in dollars)

1500

NAME DATE

Diagnostic and Placement Test

29 Last month, Enrico gave 25% of his salary to charity, 29

put 25% into savings, spent 20% on food, spent 20%

on rent, and spent the remaining amount on vacation

Which pie graph best shows how Enrico used his salary last month?

A

Food Rent

Savings

30 A survey is taken to determine which type of vehicle is 30

most popular The data is shown in the bar graph below.

0 5 10 15 20 25 30

Men Women

Type of Vehicle

What can you conclude about the survey?