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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
STU
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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
STU
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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
Recommended