Buckle Down Louisiana
iLEAP 6 Mathematics
Lesson 1: Whole Numbers
Lesson 2: Integers
Lesson 3: Decimals
Lesson 4: Fractions
Lesson 5: Number Representations
Lesson 6: Ratio, Proportion, and Percent
Unit 2
Patterns, Relations, and Functions
Lesson 7: Patterns
Unit 3
Algebra
Lesson 8: Expressions
Lesson 9: Equations
Unit 4
Geometry
Lesson 10: Geometric Figures
Lesson 11: Geometric Concepts
Lesson 12: Solids
Unit 5
Measurement
Lesson 13: Length
Lesson 14: Geometric Measurement
Unit 6
Data Analysis, Probability, and Discrete Math
Louisiana
Lesson 15: Data Analysis
Lesson 16: Probability
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ENGLISH LANGUAGE ARTS • MATHEMATICS • SCIENCE
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Student Set LA02064S1
ISBN 0-7836-5133-3
5 1 2 9 5
Includes: Student Workbook, Form A
Practice Test, Form B Practice Test
Individual Products:
Student Workbook LA02064W1
Form A Practice Test LA02064A1
Form B Practice Test LA02064B1
9
780783 651330
6
iLEAP
Mathematics
6 MATHEMATICS
Number and Number Relations
Louisiana iLEAP
The cover image depicts a protractor.
This important tool for measuring
angles is also a useful instrument for
drafting and plotting.
Unit 1
TABLE OF CONTENTS
Introduction...................................................................................... 1
Test-Taking Tips................................................................... 2
Unit 1 – Number and Number Relations.................................... 3
Lesson 1: Whole Numbers................................................... 4
GLE: 1, 2, 3, 12, 14
Lesson 2: Integers.............................................................. 22
GLE: 6, 8
Lesson 3: Decimals............................................................. 28
GLE: 6, 7, 9, 10, 11
Lesson 4: Fractions............................................................ 42
GLE: 6, 9, 10
Lesson 5: Number Representations.................................. 53
GLE: 4, 5, 6
Lesson 6: Ratio, Proportion, and Percent......................... 61
GLE: 13, 20
Unit 2 – Patterns, Relations, and Functions............................ 73
Lesson 7: Patterns.............................................................. 74
GLE: 37, 38
Unit 3 – Algebra.............................................................................. 83
Lesson 8: Expressions........................................................ 84
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GLE: 15, 16
Lesson 9: Equations........................................................... 93
GLE: 15, 17
Unit 4 – Geometry.......................................................................... 99
Lesson 10: Geometric Figures......................................... 100
GLE: 26
Lesson 11: Geometric Concepts........................................ 115
GLE: 27, 28
Lesson 12: Solids.............................................................. 128
GLE: 24, 25
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Table of Contents
Unit 5 – Measurement................................................................. 135
Lesson 13: Length............................................................ 136
GLE: 18, 21, 31
Lesson 14: Geometric Measurement............................... 143
GLE: 19, 21, 22, 23, 31
Unit 6 – Data Analysis, Probability, and Discrete Math...... 157
Lesson 15: Data Analysis................................................. 158
GLE: 29, 30, 32, 33
Lesson 16: Probability...................................................... 174
To the Teacher:
Grade-Level Expectation numbers are
listed for each lesson in the table of
contents. The numbers in the shaded gray
bar that runs across the tops of the pages
in the workbook indicate the Grade-Level
Expectation for a given page (see example
to the right).
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GLE: 34, 35, 36
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Unit 1 – Number and Number Relations
GLE: 12
Lesson 1: Whole Numbers
Whole numbers are the counting numbers and zero. In this lesson, you will divide
whole numbers and review multiples, factors, prime factorization, perfect squares,
and square roots. You will also solve word problems with multiples and factors.
Dividing Whole Numbers
A quotient is the result of dividing one number by another number. The number to
be divided is called the dividend. The number you divide by is called the divisor.
The remainder (R) is the amount that is left over. It must always be smaller than
the divisor. A dividend is divisible by a divisor when the quotient has a remainder
of 0 (R  0). When a dividend is not divisible by a divisor, the quotient can be
written as either a decimal or a mixed number.
Example
Divide: 2,388 4 32
divisor
’
{ {
74.625 quotient
_________
32​ 2388.000 ​ dividend with additional zeros
 224 ‘
148
 128 ‘
20 0 { remainder is 20
 19 2 ‘
80
 64‘
160
 160
0
Therefore, 2,388  32  74.625.
Example
Divide: 2,796  23
{ quotient
divisor ’ 23​ 2796 ​ { dividend
 23 ‘
121
_____
49
 46‘
36
 23
13 { remainder
13
23
Therefore, 2,796  23  121​ ___ ​.
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Lesson 1: Whole Numbers
GLE: 12
Practice
Directions: For Numbers 1 through 6, divide and write each quotient as a decimal.
1. 1,401 4 25 5 ____________
4. 4,203 4 45 5 ____________
2. 3,120 4 64 5 ____________
5. 2,601 4 36 5 ____________
3. 2,350 4 80 5 ____________
6. 3,031 4 56 5 ____________
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Directions: For Numbers 7 through 12, divide and write each quotient as a mixed
number.
7. 3,825 4 91 5 ____________
10. 2,208 4 47 5 ____________
8. 1,739 4 64 5 ____________
11. 2,643 4 35 5 ____________
9. 3,293 4 82 5 ____________
12. 4,262 4 51 5 ____________
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Unit 1 – Number and Number Relations
GLE: 2, 3
Multiples
Multiples of a number are the products that result from multiplying the number by
each of the whole numbers (0, 1, 2, 3, 4, and so on).
Example
What are the first five multiples of 6?
Multiply 6 by each of the first five whole numbers.
6•050
6•16
6 • 2  12
6 • 3  18
6 • 4  24
The first five multiples of 6 are 0, 6, 12, 18, and 24.
A number that is a multiple of two or more numbers is a common multiple of
those numbers. (Zero is not considered a common multiple.) The smallest common
multiple of two or more numbers is called their least common multiple (LCM).
Example
multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, . . .
multiples of 8: 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, . . .
The numbers 24 and 48 are the first two common multiples of 6 and 8. The
least common multiple of 6 and 8 is 24.
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What is the least common multiple of 6 and 8?
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Lesson 1: Whole Numbers
GLE: 2, 3
Practice
Directions: For Numbers 1 through 5, list the first 10 multiples.
1. multiples of 4 __________________________________________________________
2. multiples of 7 __________________________________________________________
3. multiples of 9 _________________________________________________________
4. multiples of 12 ________________________________________________________
5. multiples of 16 ________________________________________________________
6. What is the least common multiple of 4 and 7? __________
7. What is the least common multiple of 7 and 9? __________
8. What is the least common multiple of 9 and 12? __________
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9. What is the least common multiple of 12 and 16? __________
10. What is the least common multiple
of 10 and 15?
11. What is the least common multiple
of 3 and 13?
A. 30
A. 13
B. 50
B. 26
C. 60
C. 39
D. 90
D. 52
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Unit 1 – Number and Number Relations
GLE: 2, 3
Factors
Factors of a number divide that number evenly (remainder of 0). A number is
divisible by all its factors.
Example
What are the factors of 24?
Find the numbers that divide 24 evenly.
24  1  24
24  2  12
24  3  8
24  4  6
24  6  4
24  8  3
24  12  2
24  24  1
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Example
What is the greatest common factor of 24 and 42?
factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24
factors of 42: 1, 2, 3, 6, 7, 14, 21, and 42
The numbers 1, 2, 3, and 6 are the common factors of 24 and 42. The
greatest common factor of 24 and 42 is 6.
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A number that is a factor of two or more numbers is a common factor of those
numbers. The largest common factor of two or more numbers is called their
greatest common factor (GCF).
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Lesson 1: Whole Numbers
GLE: 2, 3
Practice
Directions: For Numbers 1 through 5, list all the factors.
1. factors of 5 ______________________________________________________________
2. factors of 10 ___________________________________________________________
3. factors of 17 ___________________________________________________________
4. factors of 102 __________________________________________________________
5. factors of 110 _________________________________________________________
6. What is the greatest common factor of 5 and 10? __________
7. What is the greatest common factor of 10 and 17? __________
8. What is the greatest common factor of 17 and 102? __________
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9. What is the greatest common factor of 102 and 110? __________
10. What is the greatest common factor
of 44 and 52?
11. What is the greatest common factor
of 39 and 78?
A. 1
A.  1
B. 2
B.  3
C. 4
C. 13
D. 6
D. 39
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Unit 1 – Number and Number Relations
GLE: 2, 3
Solving Problems with Multiples and Factors
You can use common multiples and common factors to solve real-world problems.
Example
Todd and Amy volunteer at a local nursing home. Todd volunteers every
5 days and Amy volunteers every 4 days. If Todd and Amy both volunteer
today, in how many days will they volunteer together again?
Step 1:Determine whether you will use common multiples or common
factors to solve the problem.
The solution will be larger than 5 and 4, so use common multiples.
Step 2: Write the multiples of each number.
multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, . . .
multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, . . .
Step 3: Find the nonzero multiples that are common.
multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, . . .
multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, . . .
The least common multiple is 20. Todd and Amy will volunteer together
again in 20 days.
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Step 4: Find the LCM.
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Lesson 1: Whole Numbers
GLE: 2, 3
Example
The math class is making fruit baskets to donate to charity. The class has
collected 24 oranges and 36 apples. The teacher wants the same number of
oranges in every basket. The teacher also wants the same number of
apples in every basket. What is the greatest number of baskets the class
can make?
Step 1: D
etermine whether you will use common multiples or common
factors to solve the problem.
The solution will be smaller than 24 and 36, so use common factors.
Step 2: Write the factors of each number.
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 3: Find the common factors.
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The class can make 1, 2, 3, 4, 6, or 12 baskets.
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Step 4: Find the GCF.
The greatest common factor is 12. The greatest number of baskets the
class can make is 12, each holding 2 oranges and 3 apples.
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Unit 1 – Number and Number Relations
GLE: 2, 3
Practice
Directions: For Numbers 1 through 4, first determine whether you will use
common multiples or common factors to solve the problem. Then, solve the problem.
1. One species of cicada hatches every 13 years. Another species hatches every
17 years. If both species hatch this year, how many years will it be before both
species hatch at the same time again?
Will you use common multiples or common factors to solve the problem?
_______________
How many years will it be before both species hatch at the same time again?
_______________
Will you use common multiples or common factors to solve the problem?
_______________
What is the greatest number of books Paul can assemble? _______________
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2. Paul is assembling books. He has 42 color pages and 77 black and white pages.
Each book must have the same number of color pages and the same number of
black and white pages. What is the greatest number of books Paul can
assemble?
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Lesson 1: Whole Numbers
GLE: 2, 3
3. Susie is making cakes at her bakery. She has 8 cups of flour and 12 eggs. Each
cake must have the same number of cups of flour and the same number of eggs
in it. What is the largest number of cakes Susie can make?
Will you use common multiples or common factors to solve the problem?
_______________
What is the greatest number of cakes Susie can make? _______________
4. At Sunnydale Middle School, the sixth graders have mashed potatoes every
10 days and pudding every 6 days. If the sixth graders have mashed potatoes
and pudding today, how many days will it be before they have both on the same
day again?
Will you use common multiples or common factors to solve the problem?
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_______________
How many days will it be before the students have mashed potatoes and
pudding on the same day again?
_______________
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Unit 1 – Number and Number Relations
GLE: 1
Prime and Composite Numbers
A prime number has only two factors: 1 and the number. A composite number
has at least three factors. Remember, 0 and 1 are neither prime nor composite
numbers.
Examples
The number 3 has only two factors: 1 and 3. Therefore, 3 is a prime
number.
The number 4 has three factors: 1, 2, and 4. Therefore, 4 is a composite
number.
The number 6 has four factors: 1, 2, 3, and 6. Therefore, 6 is a composite
number.
Practice
1. Is 8 a prime number or a composite number? _____________________________
2. Is 11 a prime number or a composite number? ____________________________
3. Is 15 a prime number or a composite number? ____________________________
___________________________________________________________________________
5. List all the composite numbers between 20 and 30.
___________________________________________________________________________
6. Which is a prime number?
7. Which is a composite number?
A. 37
A. 43
B. 45
B. 59
C. 51
C. 61
D. 63
D. 77
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4. List all the prime numbers between 20 and 30.
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Lesson 1: Whole Numbers
GLE: 1
Prime Factorization
Prime factorization is a way of expressing a composite number as the product of
prime numbers. The fundamental theorem of arithmetic states that every
counting number is either prime or can be decomposed (broken down) into its prime
factorization. You can use a factor tree to find the prime factorization of a number.
Example
What is the prime factorization of 504?
Write the number 504. Write a prime factor under the left branch and
circle it. Write the nonprime factor under the right branch. Repeat this
process under each composite number until you have two prime numbers
at the bottom of the tree. The prime factorization is the product of all the
circled numbers.
504
2
252
126
2
2
63
21
3
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3
7
The prime factorization of 504 is 2 • 2 • 2 • 3 • 3 • 7 or 23 • 32 • 7.
Note: There is more than one way to make a factor tree. In the first step of
this example, you could have divided by 3 or 7 instead of by 2. The order in
which you find the prime factors does not matter. However, when you list
the prime factors in your answer, list them in order from least to greatest.
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Unit 1 – Number and Number Relations
GLE: 1
Practice
1. Draw a factor tree for 45.
What is the prime factorization of 45? _____________________________
What is the prime factorization of 120? ______________________________
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2. Draw a factor tree for 120.
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Lesson 1: Whole Numbers
GLE: 1
3. Draw a factor tree for 1,260.
What is the prime factorization of 1,260? _____________________________
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4. Draw a factor tree for 800.
What is the prime factorization of 800? _____________________________
17
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Unit 1 – Number and Number Relations
GLE: 14
Perfect Squares and Square Roots
The square root of a number, n, is a number which, multiplied by itself, gives you
__
the original number. The square root of a number is denoted by a radical sign (​√ d ​).
A perfect square is the product of a number multiplied by itself.
Example
___
The model below can be used to find √
​ 25 ​ ​ . It can also be used to show that
25 is a perfect square.
The square has been
___ divided into 25 smaller squares, so 25 is a perfect
square. To find ​√ 25 ​, count the number of smaller squares that make up
each side of the larger square. Each side of the larger square is made up of
5 smaller squares.
___
​√ 25 ​​ ​  5
5 • 5  52  25
Practice
___
1.​√ 16 ​  _______________
Directions: For Numbers 7 through 12,
determine if the given number is a
perfect square.
7. 105 _______________
__
2.​√ 9 ​  _______________
8. 36 _______________
__
3.​√ ​4 ​  _______________
9. 64 _______________
___
4.​​√ ​49 ​ ​  _______________
10. 72 _______________
___
5.​​√ ​81 ​​  _______________
11. 88 _______________
____
6.​​√ ​144 ​ ​  _______________
12. 121 _______________
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Directions: For Numbers 1 through 6,
calculate each square root.
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Lesson 1: i LEAP Practice
iLEAP Practice
1. What is the greatest common factor
(GCF) of 72 and 84?
A.
6
A.
72
B.
8
B.
144
C.
12
C.
216
D.
18
D.
432
2. What is the prime factorization of
60?
5. What is the prime factorization of
350?
A.
5•6
A.
2 • 52 • 7
B.
2 • 33
B.
22 • 3 • 9
C.
3•4•5
C.
2 • 5 • 35
D.
22 • 3 • 5
D.
5 • 7 • 10
3. Tristan handed out markers and
crayons to the class. He shared
46 markers and 69 crayons equally.
If there are more than 10 but fewer
than 35 children in the class, how
many children are in Tristan’s class?
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4. What is the least common multiple
(LCM) of 18 and 24?
6. Josie’s computer saves its files
every 6 seconds. The computer
checks for computer viruses every
10 seconds. How many times, in
60 seconds, does the computer
save its files and check for viruses at
the same time?
A.
12
B.
23
A.
0
C.
28
B.
1
D.
34
C.
2
D.
30
i LEAP Practice
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Unit 1 – Number and Number Relations
7. What is the prime factorization of
184?
11. Which of the following is a
composite number?
A.
8 • 23
A.
89
B.
2•4
​ • ​23​
B.
51
C.
22
C.
23
• 3 • 23
D.​2​3​• 23
D.  2
____
8. ​√ 121 ​ 5
12. Which of the following is a perfect
square?
A.
10
B.
11
A.  10
C.
12
B.  27
D.
13
C.  64
D.
13. What are the common factors of 32
and 56?
A.
27, 36, 63
B.
24, 45, 54
A.
1, 2, 6
C.
18, 36, 44
B.
1, 2, 4, 8
D.
36, 54, 75
C.
1, 2, 8, 16
D.
1, 2, 3, 5, 6
10. Which of the following is a prime
number?
A.
27
B.
49
C.
79
D.
91
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14. Divide: 4,126 4 43
31
43
A.
93 ​ ___ ​ ​
B.
94 ​ ___ ​ ​
C.
95 ​ ___ ​ ​
D.
96 ​ ___ ​ ​
84
43
41
43
31
43
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9. Which of the following are multiples
of 9?
128
i LEAP Practice
1/18/07 3:19:57 PM
Lesson 1: i LEAP Practice
15. A.
Draw factor trees for 900 and 240.
B. Write the prime factorizations of 900 and 240.
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C. Write all the factors of 900 and 240.
D.
Find the greatest common factor of 900 and 240.
i LEAP Practice
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