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iii© Didax® www.didax.com Math Skill Builders

CONTENTSTeacher Notes .......................................................................................................................................................................................... ivMeeting the NCTM Standards ...............................................................................................................................................................v

FOREWORD

NumberWriting Numbers .............................................................. 2–3Large and Small Numbers .............................................. 4–5Rounding ............................................................................ 6–7Decimals ............................................................................ 8–9Percents ......................................................................... 10–11Addition........................................................................... 12–13Subtraction .................................................................... 14–15Multiplication ................................................................ 16–17Multiplication Word Problems ................................... 18–19Mental Multiplication .................................................. 20–21Division ........................................................................... 22–23Mental Division ............................................................. 24–25Fractions ........................................................................ 26–27Money ............................................................................ 28–29Mixed Word Problems ................................................. 30–31Number Sentences and Patterns ............................... 32–33Special Numbers........................................................... 34–35Number Theory.............................................................. 36–37Rational Numbers ......................................................... 38–39

Geometry Lines and Angles .......................................................... 40–41 2-D shapes ................................................................... 42–43

3-D shapes ................................................................... 44–45 Angles in Polygons ..................................................... 46–47 Perspective and Transformations ............................ 48–49 Symmetry ...................................................................... 50–51 Reducing and Enlarging ............................................. 52–53 Ordered Pairs ............................................................... 54–55

Measurement Length ........................................................................... 56–57 Perimeter ...................................................................... 58–59 Circumference ............................................................. 60–61 Area of Triangles and Parallelograms ...................... 62–63 Volume and Surface Area of a Rectangular Prism ...................................................... 64–65 Mass .............................................................................. 66–67 Time ............................................................................... 68–69

Data Analysis and Probability Probability .................................................................... 70–71 Diagrams and Tables ................................................. 72–73 Graphs .......................................................................... 74–75 Measures of Central Tendency ............................... 76–77

Math Skill Builders is a series of books with a back-to-basics approach designed to support and reinforce the foundations of the math curriculum. It is a clear and comprehensive resource that covers number and operations, geometry, measurement, and data analysis and probability concepts for each year level. This series is ideal for:

• teaching a new concept• consolidation • homework• assessment• remediation

Titles in the series are:

Math Skill Builders – Grade K Math Skill Builders – Grade 1Math Skill Builders – Grade 2 Math Skill Builders – Grade 3Math Skill Builders – Grade 4 Math Skill Builders – Grade 5Math Skill Builders – Grade 6

Math Skill Builders www.didax.com © Didaxiv

TEACHER NOTES

The Format of the Book

Each book contains teacher notes and links to the NCTM standards. Four sections are included in each book:

• Number and Operations • Geometry • Measurement • Data Analysis and Probability

Each section covers a variety of concepts. The number of concepts covered varies from section to section.

Each student page in the book provides teachers with activities that relate to one mathematical concept. The activities increase in diffi culty as the student works through each section. In this way, teachers can use the activities to introduce a new concept and then reinforce knowledge and skills.

The student pages are supported by a corresponding teacher page.

Teacher Notes Page

Student Page

Since this series of books follows a set format, teachers may fi nd it helpful to use a preceding title to review a corresponding concept before new skills are introduced. Students who need extra assistance may also fi nd this a helpful way to revise material previously taught.

The name of the concept is given.

The name of the related strand is given.

Skills show the specifi c desired outcomes when completing the worksheet.

The concepts required for students to complete each page are provided.

Answers are given for all questions on the student page.

The name of the concept is given.

The name of the related strand is given.

Space is provided for each student to write his/her name on each worksheet.

Questions or activities relating to each concept are given with suffi cient space provided for students to write answers.

v© Didax® www.didax.com Math Skill Builders

MEETING THE NCTM STANDARDS

Num

ber and Operations

Understand num

bers, ways of representing num

bers, relationships among num

bers, and number system

s

Work fl exibly w

ith fractions, decimals, and percents to solve problem

s

Com

pare and order fractions, decimals, and percents effi ciently and fi nd their

approximate locations on a num

ber line

Develop m

eaning for percents greater than 100 and less than 1

Develop an understanding of large num

bers, and recognize and appropriately use exponential, scientifi c, and calculator notation

Use factors, m

ultiples, prime factorization, and relatively prim

e numbers to solve

problems

Understand m

eanings of operations and how they relate to one another

Understand various m

eanings of addition and subtraction of whole num

bers and the relationship betw

een the two operations

Understand the effects of adding and subtracting w

hole numbers

Understand situations that entail m

ultiplication and division, such as equal groupings of objects and sharing equally

Writing Numbers, pp. 2–3

Large and Small Numbers, pp. 4–5

Rounding, pp. 6–7

Decimals, pp. 8–9

Percents, pp. 10–11

Addition, pp. 12–13

Subtraction, pp. 14–15

Multiplication, pp. 16–17

Multiplication Word Problems, pp. 18–19

Mental Multiplication, pp. 20–21

Division, pp. 22–23

Mental Division, pp. 24–25

Fractions, pp. 26–27

Money, pp. 28–29

Mixed Word Problems, pp. 30–31

Number Sentences and Patterns, pp. 32–33

Special Numbers, pp. 34–35

Number Theory, pp. 36–37

Rational Numbers, pp. 38–39

Math Skill Builders www.didax.com © Didaxvi

MEETING THE NCTM STANDARDS

Num

ber and Operations (cont.)

Com

pute fl uently and make reasonable estim

ates

Select appropriate methods and tools for com

puting with fractions and decim

als from

among m

ental computation, estim

ation, calculators or computers, and paper

and pencil, depending on the situation, and apply the selected methods

Develop and analyze algorithm

s for computing w

ith fractions, decimals, and

integers and develop fl uency in their use

Develop and use strategies to estim

ate the results of rational-number

computations and judge the reasonableness of the results

AlgebraU

nderstand patterns, relations, and functionsRepresent, analyze, and generalize a variety of patterns w

ith tables, graphs, words,

and, when possible, sym

bolic rules

Writing Numbers, pp. 2–3

Large and Small Numbers, pp. 4–5

Rounding, pp. 6–7

Decimals, pp. 8–9

Percents, pp. 10–11

Addition, pp. 12–13

Subtraction, pp. 14–15

Multiplication, pp. 16–17

Multiplication Word Problems, pp. 18–19

Mental Multiplication, pp. 20–21

Division, pp. 22–23

Mental Division, pp. 24–25

Fractions, pp. 26–27

Money, pp. 28–29

Mixed Word Problems, pp. 30–31

Number Sentences and Patterns, pp. 32–33

Special Numbers, pp. 34–35

Number Theory, pp. 36–37

Rational Numbers, pp. 38–39

vii© Didax® www.didax.com Math Skill Builders

MEETING THE NCTM STANDARDS

Lines and Angles, pp. 40–41

2-D Shapes, pp. 42–43

3-D Shapes, pp. 44–45

Angles in Polygons, pp. 46–47

Perspective and … , pp. 48–49

Symmetry, pp. 50–51

Reducing and Enlarging, pp. 52–53

Ordered Pairs, pp. 54–55

Length, pp. 56–57

Perimeter, pp. 58–59

Circumference, pp. 60–61

Area of Triangles and … , pp. 62–63

Volume and Surface Area, pp. 64–65

Mass, pp. 66–67

Time, pp. 68–69

Probability, pp. 70–71

Diagrams and Tables, pp. 72–73

Graphs, pp. 74–75

Measures of … , pp. 82–83

Geometry

Analyze characteristics and properties of tw

o- and three-dimensional geom

etric shapes and develop mathem

atical arguments about geom

etric relationships

Precisely describe, classify, and understand relationships among types of tw

o- and three-dim

ensional objects using their defi ning properties

Understand relationships am

ong the angles, side lengths, perimeters, areas, and

volumes of sim

ilar objects

Specify locations and describe spatial relationships using coordinate geometry and other representational system

sU

se coordinate geometry to represent and exam

ine the properties of geometric

shapes

Apply transform

ations and use symm

etry to analyze mathem

atical situations

Describe sizes, positions, and orientations of shapes under inform

al transform

ations such as fl ips, turns, slides, and scaling

Examine the congruence, sim

ilarity, and line or rotational symm

etry of objects using transform

ations

Use visualization, spatial reasoning, and geom

etric modeling to solve problem

s

Draw

geometric objects w

ith specifi ed properties, such as side lengths or angle m

easures

Use tw

o-dimensional representations of three-dim

ensional objects to visualize and solve problem

s such as those involving surface area and volume

Measurem

entU

nderstand measurable attributes of objects and the units, system

s, and processes of measurem

entU

nderstand both metric and custom

ary systems of m

easurement

Understand relationships am

ong units and convert from one unit to another

within the sam

e system

Math Skill Builders www.didax.com © Didaxviii

MEETING THE NCTM STANDARDS

Measurem

ent (cont.)A

pply appropriate techniques, tools, and formulas to determ

ine measurem

entsSelect and apply techniques and tools to accurately fi nd length, area, volum

e, and angle m

easures to appropriate levels of precision

Develop and use form

ulas to determine the circum

ference of circles and the area of triangles, parallelogram

s, trapezoids, and circles and develop strategies to fi nd the area of m

ore-complex shapes

Develop strategies to determ

ine the surface area and volume of selected prism

s, pyram

ids, and cylinders

Data Analysis and ProbabilityForm

ulate questions that can be addressed with data and collect, organize, and display relevant data to answ

er them

Select, create, and use appropriate graphical representations of data, including histogram

s, box plots, and scatterplots

Select and use appropriate statistical methods to analyze data

Find, use, and interpret measures of center and spread, including m

ean and interquartile range;

Discuss and understand the correspondence betw

een data sets and their graphical representations, especially histogram

s, stem-and-leaf plots, box plots, and

scatterplots.

Understand and apply basic concepts of probability

Use proportionality and a basic understanding of probability to m

ake and test conjectures about the results of experim

ents and simulations

Com

pute probabilities for simple com

pound events, using such methods as

organized lists, tree diagrams, and area m

odels

Lines and Angles, pp. 40–41

2-D Shapes, pp. 42–43

3-D Shapes, pp. 44–45

Angles in Polygons, pp. 46–47

Perspective and … , pp. 48–49

Symmetry, pp. 50–51

Reducing and Enlarging, pp. 52–53

Ordered Pairs, pp. 54–55

Length, pp. 56–57

Perimeter, pp. 58–59

Circumference, pp. 60–61

Area of Triangles and … , pp. 62–63

Volume and Surface Area, pp. 64–65

Mass, pp. 66–67

Time, pp. 68–69

Probability, pp. 70–71

Diagrams and Tables, pp. 72–73

Graphs, pp. 74–75

Measures of … , pp. 82–83

© Didax® www.didax.com Math Skill Builders

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1. Write these numbers in words.

(a) 44

(b) 909

(c) 8,765

(d) 2,840

(e) 20,000

(f) 2,987,304

2. Write each as a numeral.

(a) eighty-seven (b) one hundred one

(c) one thousand ten

(d) sixteen thousand seventeen

(e) two hundred fi fty thousand

(f) fi ve million

3. Order these groups of numbers from smallest to largest.

(a) 77; 707; 7; 7,000; 777; 177

(b) 462; 442; 642; 246; 624; 264

(c) 82; 28; 888; 2,828; 8,888; 2,282

(d) 55,050; 55,550; 55,005; 55,505; 55,555; 55,515

(e) 111; 1; 1,001; 1,111; 1,101; 1,110

4. Order these groups of numbers from largest to smallest.

(a) 3,033; 3,333; 333; 33,033; 33; 33,333

(b) 987; 978; 9,987; 9,978; 1,978; 9,098

(c) 100; 100,000; 1,000; 10,000; 1,010; 101,010

(d) 6,006; 6,000,000; 6,660; 6,060; 66,060; 6,606

(e) 2,000,002; 2,200,200; 2,020,020; 2,222,000; 2,202,202

5. Write the number that is 100 less and 100 more.

(a) 100 (b) 1,100 (c) 5,000

(d) 6,900 (e) 10,125

(f) 2,045,045

6. (a) Write your birth date using eight numerals (for example, 05 22 1995).

(b) Arrange the numerals to make the largest possible number.

(c) Write this number in words.

(d) Write the number that is 100 less and 100 more.

WRITING NUMBERSNUMBER AND OPERATIONS

4Math Skill Builders www.didax.com © Didax

LARGE AND SMALL NUMBERS

TEACHER INFORMATION

Skills

Recognizes and demonstrates place valueIdentifi es and represents different forms of the same number

Concepts Required

Whole number place value to the billionsDecimal place value to the thousandths

Expanded notation

Answers

1.

2. (a) 2,460,282,321 (b) 63,010,535,392 (c) 0.281 (d) 13.496

3. (a) 1 ! 1,000,000,000 + 8 ! 100,000,000 + 1 ! 10,000,000 + 9 ! 100,000 + 9 ! 10,000 + 1,000 + 2 ! 100 + 4 ! 10 + 7

(b) 4 ! 10,000,000,000 + 2 ! 1,000,000,000 + 1 ! 100,000,000 + 7 ! 10,000,000 + 7 ! 1,000,000 + 8 ! 100,000 + 5 ! 10,000 + 6 ! 1,000 + 2 ! 100 + 8 ! 10 + 2

(c) 9 ! 1 + 8 ! 0.1 + 1 ! 0.01 + 7 ! 0.001

(d) 7 ! 0.1 + 5 ! 0.01 + 2 ! 0.001

4. (a) two billion, seven hundred fi fty-eight million, four hundred ninety-three thousand, forty one

(b) fi fty-nine billion, fi fty-two million, seven hundred twenty thousand, one hundred eighty-fi ve

(c) seven and two hundred nine thousandths

(d) three thousandths

NUMBER AND OPERATIONS

Number Place Value Value (a) 65,271,094,922 hundred million 200,000,000 (b) 47,608,417,933 ten billion 40,000,000,000 (c) 283,507,122,414 hundred million 500,000,000 (d) 1,819,370,628 ten million 10,000,000 (e) 0.665 thousandths 0.005 (f) 2.109 tenths 0.1 (g) 0.981 hundredths 0.08 (h) 7.548 thousandths 0.008

© Didax® www.didax.com Math Skill Builders

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LARGE AND SMALL NUMBERS

1. Complete the table for the boldface digit.

Number Place Value Value

Example: 23,068,185,186 billion 3,000,000,000

(a) 65,271,094,922

(b) 47,608,417,933

(c) 283,507,122,414

(d) 1,819,370,628

(e) 0.665

(f) 2.109

(g) 0.981

(h) 7.548

2. Write the numbers in standard form.

(a) 2 ! 1,000,000,000 + 4 ! 100,000,000 + 6 ! 10,000,000 + 2 ! 100,000 + 8 ! 10,000 + 2 !

1,000 + 3 ! 100 + 2 ! 10 + 1 =

(b) 6 ! 10,000,000,000 + 3 ! 1,000,000,000 + 1 ! 10,000,000 + 5 ! 100,000 + 3 x 10,000

+ 5 ! 1,000 + 3 ! 100 + 9 ! 10 + 2 =

(c) 2 ! 0.1 + 8 ! 0.01 + 1 ! 0.001 =

(d) 1 ! 10 + 3 ! 1 + 4 ! 0.1 + 9 ! 0.01 + 6 ! 0.001 =

3. Write the numbers in expanded form.

(a) 1,810,991,247 =

(b) 42,177,856,282 =

(c) 9.817 =

(d) 0.752 =

4. Write the numbers in words.

(a) 2,758,493,041 =

(b) 59,052,720,185 =

(c) 7.209 =

(d) 0.003 =

NUMBER AND OPERATIONS