**Third Grade Math**

This book, with over 250 problems, covers the following topics:

Addition and Subtraction, Multiplication and Division, Fractions and Decimals, Money, Patterns, Metric System, Perimeter, Transformations and Symmetry, and more!

If you are home schooling (or if you are just trying to get extra practice for your child), then you already know that math workbooks and curriculum can be expensive. Home School Brew is trying to change that! We have teamed with teachers and parents to create books for prices parents can afford. We believe education shouldn’t be expensive.

Each topic of this book may also be purchased separately.

Addition and Subtraction, Multiplication and Division, Fractions and Decimals, Money, Patterns, Metric System, Perimeter, Transformations and Symmetry, and more!

If you are home schooling (or if you are just trying to get extra practice for your child), then you already know that math workbooks and curriculum can be expensive. Home School Brew is trying to change that! We have teamed with teachers and parents to create books for prices parents can afford. We believe education shouldn’t be expensive.

Each topic of this book may also be purchased separately.

## Print Copy: Third Grade Math

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**Excerpt**

Number Theory

Numbers are used throughout our society every day. Writing out a grocery list, balancing a checkbook, measuring windows to be fitted for curtains, figuring out someone’s age, and calculating how much time a project may take are all examples of how we use math. During Third Grade students will learn about whole numbers, ordinal numbers, even and odd numbers, comparing numbers (greater than, less than, equal), and Roman Numerals.

Whole Numbers and Place Values Whole numbers are all numbers that are greater than or equal to one. The smallest whole numbers hold the “Ones” place value and are the following: 1, 2, 3, 4, 5, 6, 7, 8, and 9. The sequence of whole numbers and their place values are determined by the number of places or columns they hold to the right of the “ones” place. The table below shows you the layout of the places to the right and their values. You can see that zero, although not considered a whole number, plays an important role in the base name as a placeholder.

To be able to work with Whole Numbers, the students need to learn how to name them based on how many "places" are occupied. For example, the number one hundred (100) is named as such because it has numbers occupying the ones, tens and hundreds places. The table below shows the place values and basic names for Whole Numbers up to Ten Thousand:

Naming Writing Numbers

· One Hundred (100) is named for the (1) in the hundreds place.

· Two Hundred (200) is named for the number two (2) and its placement in the hundreds place.

· Five Thousand (5,000) is named for the number five (5) and its placement in the thousands place.

· Eleven Thousand (11,000) is named for the number eleven (11) its placement in the ten thousands place.

To make naming numbers more interesting, the following examples include numbers in the various places instead of zeros:

· 15,156 Name: Fifteen thousand, one hundred fifty-six

· 2,124 Name: Two thousand, one hundred twenty-four

· 357 Name: Three hundred fifty-seven

· 17 Name: Seventeen

When zeros are used as place markers, they are NOT part of the name:

· 108 Name: One hundred eight

· 8,052 Name: Eight thousand, fifty-five

Expanded Whole Numbers Whole numbers can be “expanded’ into their separate “place” parts to make understanding places and naming easier for the students.

An example of an expanded number is presented below:

327 = 300 + 20 + 7

The number is broken down into hundreds, tens and ones to show the value of each number in Three hundred twenty-seven. The (3) is three hundreds, the (2) is two tens and the (7) is seven ones.

Based on the above information, students will be able to name the place a specific number occupies and the value of a digit based on its place.

For example, students will have to answer the following-type questions:

1. What is the place value of the (7) in 207? Answer: ones

2. What is the place value of the 3 in 3,021? Answer: thousands

3. Which number shows the 2 with a value of 200: 124, 3,257, or 12? Answer: 3,257

4. Which number shows the number 8 with the value of 80: 38, 1,328, or 287? Answer: 287

Another naming process for numbers is using the numbers themselves as place markers. These number names are used for ranking items, ordering number placements in a list, or indicating where numbers are located on a number line relative to each other.

The number line above shows whole numbers from One to Twenty-Five. Ordinal naming of the numbers on this number line looks like the following:

Using the number line and Ordinal placement names, the following tasks can be performed:

1. What number is the 3rd to the right of 20?

2. If Lisa came in 3rd in the running race, what were the places that came in before?

3. Which number place comes after 36th place?

4. Which place is five places to the left of 14?

Even and Odd Numbers Even numbers are all multiples of the number two. Or, they are all divisible by two. If a number cannot be divided completely by two (into two equal halves), it is NOT an even number.

Counting by even numbers always results in the next number in line also being even. The following examples are counting using even numbers:

Two’s: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Four’s: 4, 8, 12, 16, 20, 24, 28, 32, 36

Sixes: 6, 12, 18, 24, 30, 36, 42, 48, 54

If a number cannot be completely dived into two equal parts, it is an odd number. In other words, if it is not even, it is odd.

Students will learn how to answer questions similar to the following:

1. Which odd number comes right after 45?

Since the number right after 45 is 46, which is even, 47 is the next odd number after 45.

2. Is the answer to 95-12 equal to an odd number or an even number? Since 95-12 is 83, and 83 is odd, then 95-12 produces an odd number.

Roman Numerals Roman Numerals are used for a variety of purposes. They are seen on buildings and on analog clocks and are used sometimes as volume numbers for written works that have more than one book.

There are five Roman Numerals that are used most often by themselves and in combination with each other to form larger numbers. They are as follows with their whole number equivalents:

I = One V = 5 X = 10 L = 50

When the numbers are presented in ascending order, they are added to produce the larger number. When a smaller number is placed to the left of a larger number, it is subtracted to get the smaller number.

Number combinations and their whole number equivalents are present below:

Based on this table, name the following Roman Numerals:

IV = Four = V – I = 5 – 1 = 4

VI = Six = V + I = 5 + 1 = 6

VIII = Eight = V + I + I + I = 8

XII = Twelve = X + I + I = 12

LIX = Fifty-nine = L + (X – I) = 50 + (10 – 1) = 59

CCXLI = Two hundred forty-one = (C + C + (L – X) + I = 100 + 100 + (50 – 10) + 1

Using Expanded Numbers, write the following numbers in Roman Numerals:

Twenty-four = (10 + 10 + 4) = X + X + (V – I) = XXIV

Thirty-eight = 10 + 10 + 10 + 5 + 1 + 1 + 1 = X + X + X + V + I + I + I = XXXVIII

Sixty-five = 50 + 10 + 5 = L + X + V = LXV

Ninety-nine = (100 – 10) + (10 – 1) = (C – X) + (X – I) = XCIX

One hundred sixty =100 + 50 + 10 = C + L + X = CLX

Numbers are used throughout our society every day. Writing out a grocery list, balancing a checkbook, measuring windows to be fitted for curtains, figuring out someone’s age, and calculating how much time a project may take are all examples of how we use math. During Third Grade students will learn about whole numbers, ordinal numbers, even and odd numbers, comparing numbers (greater than, less than, equal), and Roman Numerals.

Whole Numbers and Place Values Whole numbers are all numbers that are greater than or equal to one. The smallest whole numbers hold the “Ones” place value and are the following: 1, 2, 3, 4, 5, 6, 7, 8, and 9. The sequence of whole numbers and their place values are determined by the number of places or columns they hold to the right of the “ones” place. The table below shows you the layout of the places to the right and their values. You can see that zero, although not considered a whole number, plays an important role in the base name as a placeholder.

To be able to work with Whole Numbers, the students need to learn how to name them based on how many "places" are occupied. For example, the number one hundred (100) is named as such because it has numbers occupying the ones, tens and hundreds places. The table below shows the place values and basic names for Whole Numbers up to Ten Thousand:

Naming Writing Numbers

*Writing Names*are given according to the number of “places” the number occupies. For example, 10 is named “ten” because the biggest place it occupies is the tens place.· One Hundred (100) is named for the (1) in the hundreds place.

· Two Hundred (200) is named for the number two (2) and its placement in the hundreds place.

· Five Thousand (5,000) is named for the number five (5) and its placement in the thousands place.

· Eleven Thousand (11,000) is named for the number eleven (11) its placement in the ten thousands place.

To make naming numbers more interesting, the following examples include numbers in the various places instead of zeros:

· 15,156 Name: Fifteen thousand, one hundred fifty-six

· 2,124 Name: Two thousand, one hundred twenty-four

· 357 Name: Three hundred fifty-seven

· 17 Name: Seventeen

When zeros are used as place markers, they are NOT part of the name:

· 108 Name: One hundred eight

· 8,052 Name: Eight thousand, fifty-five

Expanded Whole Numbers Whole numbers can be “expanded’ into their separate “place” parts to make understanding places and naming easier for the students.

An example of an expanded number is presented below:

327 = 300 + 20 + 7

The number is broken down into hundreds, tens and ones to show the value of each number in Three hundred twenty-seven. The (3) is three hundreds, the (2) is two tens and the (7) is seven ones.

Based on the above information, students will be able to name the place a specific number occupies and the value of a digit based on its place.

For example, students will have to answer the following-type questions:

1. What is the place value of the (7) in 207? Answer: ones

2. What is the place value of the 3 in 3,021? Answer: thousands

3. Which number shows the 2 with a value of 200: 124, 3,257, or 12? Answer: 3,257

4. Which number shows the number 8 with the value of 80: 38, 1,328, or 287? Answer: 287

__Ordinal Names__Another naming process for numbers is using the numbers themselves as place markers. These number names are used for ranking items, ordering number placements in a list, or indicating where numbers are located on a number line relative to each other.

The number line above shows whole numbers from One to Twenty-Five. Ordinal naming of the numbers on this number line looks like the following:

Using the number line and Ordinal placement names, the following tasks can be performed:

1. What number is the 3rd to the right of 20?

2. If Lisa came in 3rd in the running race, what were the places that came in before?

3. Which number place comes after 36th place?

4. Which place is five places to the left of 14?

Even and Odd Numbers Even numbers are all multiples of the number two. Or, they are all divisible by two. If a number cannot be divided completely by two (into two equal halves), it is NOT an even number.

Counting by even numbers always results in the next number in line also being even. The following examples are counting using even numbers:

Two’s: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

Four’s: 4, 8, 12, 16, 20, 24, 28, 32, 36

Sixes: 6, 12, 18, 24, 30, 36, 42, 48, 54

If a number cannot be completely dived into two equal parts, it is an odd number. In other words, if it is not even, it is odd.

Students will learn how to answer questions similar to the following:

1. Which odd number comes right after 45?

Since the number right after 45 is 46, which is even, 47 is the next odd number after 45.

2. Is the answer to 95-12 equal to an odd number or an even number? Since 95-12 is 83, and 83 is odd, then 95-12 produces an odd number.

Roman Numerals Roman Numerals are used for a variety of purposes. They are seen on buildings and on analog clocks and are used sometimes as volume numbers for written works that have more than one book.

There are five Roman Numerals that are used most often by themselves and in combination with each other to form larger numbers. They are as follows with their whole number equivalents:

I = One V = 5 X = 10 L = 50

When the numbers are presented in ascending order, they are added to produce the larger number. When a smaller number is placed to the left of a larger number, it is subtracted to get the smaller number.

Number combinations and their whole number equivalents are present below:

Based on this table, name the following Roman Numerals:

IV = Four = V – I = 5 – 1 = 4

VI = Six = V + I = 5 + 1 = 6

VIII = Eight = V + I + I + I = 8

XII = Twelve = X + I + I = 12

LIX = Fifty-nine = L + (X – I) = 50 + (10 – 1) = 59

CCXLI = Two hundred forty-one = (C + C + (L – X) + I = 100 + 100 + (50 – 10) + 1

Using Expanded Numbers, write the following numbers in Roman Numerals:

Twenty-four = (10 + 10 + 4) = X + X + (V – I) = XXIV

Thirty-eight = 10 + 10 + 10 + 5 + 1 + 1 + 1 = X + X + X + V + I + I + I = XXXVIII

Sixty-five = 50 + 10 + 5 = L + X + V = LXV

Ninety-nine = (100 – 10) + (10 – 1) = (C – X) + (X – I) = XCIX

One hundred sixty =100 + 50 + 10 = C + L + X = CLX