**Sixth Grade Math**

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

Whole Numbers, Operations with Whole Numbers, Decimals, Integers, Graphing, Fractions, Measurements, Functions and Probability, Geometry, 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 section of this book may also be purchased individually by searching for the section and “For Sixth Graders."

Whole Numbers, Operations with Whole Numbers, Decimals, Integers, Graphing, Fractions, Measurements, Functions and Probability, Geometry, 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 section of this book may also be purchased individually by searching for the section and “For Sixth Graders."

## Print Copy: Sixth Grade Math

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**Excerpt**

Whole Numbers

Whole numbers are the base numbers for all the mathematics learned beginning essentially when a child first starts counting things. Whole numbers do not include fractions, decimals, or negative numbers. However, whole numbers are used throughout our society daily.

When we go shopping at the grocery store, we purchase whole portions of items such as loaves of bread, bags of chips, bottles of soda pop, boxes of crackers and cereal, fruits and vegetables, and a variety of other goods. The same concept can be applied to our purchases of several other goods like clothing, cars, houses, furniture, etc. Whole numbers are the core of how we function using math.

Addition Addition is the first type of mathematical equation students learn in school. First, adding single whole numbers is taught followed by adding double-digit numbers and single numbers, then double-digit numbers to each other. Finally, adding triple-digit numbers to single numbers, to double-digit numbers, and to triple-digit numbers is taught. The concept of carrying the one and adding multiple numbers are also covered in sixth grade math.

The final answer calculated after adding whole numbers together is referred to as the Sum. The Sum is always larger than any of the numbers being added together (addends) unless the equation includes the Sum being added to zero.

Adding single-digit numbers involves applying mental math by sixth grade. By learning fact families, students will be better able to remember the sums of single-digit addends and perform better on timed math tests. After studying fact families, some patterns begin to emerge that both students and parents can use to their advantage.

One such pattern involves the equations including nine. Learning the sums of equations with ten is easy because students just replace the zero in the ten with the number being added. If students can remember than nine is just one less than ten, then the sum will be one less than the sum with ten. So, if the student knows 10 + 4 = 14, then 9 + 4 = 13, just one less than the equation with the ten.

Another pattern involves the addition of the number to itself. If the student can remember 5 + 5 = 10, then adding one less to five would have the sum of 9, and adding one more to five would have the sum of 11.

Subtraction Subtracting whole numbers is defined as finding the Difference between numbers. When finding the difference, the smaller number is subtracted from the larger number. Finding the difference between whole numbers is a mathematical operation that most of us perform several times daily.

For example, whenever we calculate someone’s age, we are finding the difference between the person’s birth year and the current year. For example, if someone was born in 1968 and it is now 2013, their current age is 2013 – 1968 = 45, so the person is 45-years-old.

Subtraction is also used for calculating a variety of comparisons. Some common comparisons are finding the distance between points, figuring out which locations are closer or farther from each other, and calculating whether a specific point is closer to one location of another.

For example, when calculating the distance traveled during a car trip, the difference between the starting odometer value and ending odometer value is calculated. If, the odometer reading at the start of the trip is 13,478 miles and the odometer reading at the end of the trip is 13,623 miles, the distance traveled is 13,623 miles – 13,478 miles = 145 miles.

After another car trip, the odometer reads 13,789 miles, so the distance traveled is the difference between 13,789 miles and 13,623 miles. In equation form, the difference is expressed as 13,789 – 13,623 = 166 miles.

From these two calculations, it can be determined that the distance of the second car trip was longer than the first, the second location was farther from the first than the first was from the original start point, and the original start point was closer to the first location than the second location was to the first. This information can be important when planning a trip for the purposes of time management, cost of gas, and determining how far the destinations are from the start point and from each other.

In sixth grade, students will use the difference between numbers to interpret their location on a number line relative to each other and relative to other specific values and points. Differences between numbers will also be taught in story problems.

A story problem using the difference between two numbers is presented below:

The students of a sixth grade class held a bake sale. The girls baked cupcakes and the boys made cookies. 127 cupcakes were sold and 213 cookies were sold during the sale. How many more cookies were sold than cupcakes?

To find the answer, the difference between what the boys sold and what the girls sold needs to be calculated. The difference between 213 and 127 is 86. So, the boys sold 86 more cookies than the girls sold cupcakes.

Multiplication The answer to a multiplication problem is defined as the Product. Whether we realize it or not, multiplication is used constantly throughout out daily routines. One example is how we are cooking a meal or baking desserts, we multiply how many servings we need to prepare to be sure everyone gets a proper portion.

For example, 18 people are attending a dinner party. How many desserts does the chef need to prepare if each guest is going to get three? The multiplication equation would be 18 x 3 = 54. The chef will need to prepare 54 desserts for the dinner party.

A school-related example involves the distribution of books. If the entire sixth grade class needs new math and science books and there are 64 students in the sixth grade, how many books total need to be ordered? The factors are 2 and 64 and the product is the multiplication of 2 and 64. The equation is 64 x 2 = 128. A total of 128 books will be ordered for the sixth grade.

Division Division is also used on a daily basis by most of our society. The answer to a division problem is called the Quotient. To take a quantity and break it up into equal evenly distributed parts requires division. Dealing cards during a card game, distributing money earned during a fundraising event, splitting up birthday favors to be sure each child gets the same amount of each prize, etc. are all examples of using division.

Another example involves a school bake sale. If the students want to earn at least 400 dollars and they have 200 cookies to sell, how much should they charge for each cookie? The equation is 400 ÷ 200 = 2, so the students should charge 2 dollars per cookie to earn 400 dollars for their bake sale.

Whole numbers are the base numbers for all the mathematics learned beginning essentially when a child first starts counting things. Whole numbers do not include fractions, decimals, or negative numbers. However, whole numbers are used throughout our society daily.

When we go shopping at the grocery store, we purchase whole portions of items such as loaves of bread, bags of chips, bottles of soda pop, boxes of crackers and cereal, fruits and vegetables, and a variety of other goods. The same concept can be applied to our purchases of several other goods like clothing, cars, houses, furniture, etc. Whole numbers are the core of how we function using math.

Addition Addition is the first type of mathematical equation students learn in school. First, adding single whole numbers is taught followed by adding double-digit numbers and single numbers, then double-digit numbers to each other. Finally, adding triple-digit numbers to single numbers, to double-digit numbers, and to triple-digit numbers is taught. The concept of carrying the one and adding multiple numbers are also covered in sixth grade math.

The final answer calculated after adding whole numbers together is referred to as the Sum. The Sum is always larger than any of the numbers being added together (addends) unless the equation includes the Sum being added to zero.

Adding single-digit numbers involves applying mental math by sixth grade. By learning fact families, students will be better able to remember the sums of single-digit addends and perform better on timed math tests. After studying fact families, some patterns begin to emerge that both students and parents can use to their advantage.

One such pattern involves the equations including nine. Learning the sums of equations with ten is easy because students just replace the zero in the ten with the number being added. If students can remember than nine is just one less than ten, then the sum will be one less than the sum with ten. So, if the student knows 10 + 4 = 14, then 9 + 4 = 13, just one less than the equation with the ten.

Another pattern involves the addition of the number to itself. If the student can remember 5 + 5 = 10, then adding one less to five would have the sum of 9, and adding one more to five would have the sum of 11.

Subtraction Subtracting whole numbers is defined as finding the Difference between numbers. When finding the difference, the smaller number is subtracted from the larger number. Finding the difference between whole numbers is a mathematical operation that most of us perform several times daily.

For example, whenever we calculate someone’s age, we are finding the difference between the person’s birth year and the current year. For example, if someone was born in 1968 and it is now 2013, their current age is 2013 – 1968 = 45, so the person is 45-years-old.

Subtraction is also used for calculating a variety of comparisons. Some common comparisons are finding the distance between points, figuring out which locations are closer or farther from each other, and calculating whether a specific point is closer to one location of another.

For example, when calculating the distance traveled during a car trip, the difference between the starting odometer value and ending odometer value is calculated. If, the odometer reading at the start of the trip is 13,478 miles and the odometer reading at the end of the trip is 13,623 miles, the distance traveled is 13,623 miles – 13,478 miles = 145 miles.

After another car trip, the odometer reads 13,789 miles, so the distance traveled is the difference between 13,789 miles and 13,623 miles. In equation form, the difference is expressed as 13,789 – 13,623 = 166 miles.

From these two calculations, it can be determined that the distance of the second car trip was longer than the first, the second location was farther from the first than the first was from the original start point, and the original start point was closer to the first location than the second location was to the first. This information can be important when planning a trip for the purposes of time management, cost of gas, and determining how far the destinations are from the start point and from each other.

In sixth grade, students will use the difference between numbers to interpret their location on a number line relative to each other and relative to other specific values and points. Differences between numbers will also be taught in story problems.

A story problem using the difference between two numbers is presented below:

The students of a sixth grade class held a bake sale. The girls baked cupcakes and the boys made cookies. 127 cupcakes were sold and 213 cookies were sold during the sale. How many more cookies were sold than cupcakes?

To find the answer, the difference between what the boys sold and what the girls sold needs to be calculated. The difference between 213 and 127 is 86. So, the boys sold 86 more cookies than the girls sold cupcakes.

Multiplication The answer to a multiplication problem is defined as the Product. Whether we realize it or not, multiplication is used constantly throughout out daily routines. One example is how we are cooking a meal or baking desserts, we multiply how many servings we need to prepare to be sure everyone gets a proper portion.

For example, 18 people are attending a dinner party. How many desserts does the chef need to prepare if each guest is going to get three? The multiplication equation would be 18 x 3 = 54. The chef will need to prepare 54 desserts for the dinner party.

A school-related example involves the distribution of books. If the entire sixth grade class needs new math and science books and there are 64 students in the sixth grade, how many books total need to be ordered? The factors are 2 and 64 and the product is the multiplication of 2 and 64. The equation is 64 x 2 = 128. A total of 128 books will be ordered for the sixth grade.

Division Division is also used on a daily basis by most of our society. The answer to a division problem is called the Quotient. To take a quantity and break it up into equal evenly distributed parts requires division. Dealing cards during a card game, distributing money earned during a fundraising event, splitting up birthday favors to be sure each child gets the same amount of each prize, etc. are all examples of using division.

Another example involves a school bake sale. If the students want to earn at least 400 dollars and they have 200 cookies to sell, how much should they charge for each cookie? The equation is 400 ÷ 200 = 2, so the students should charge 2 dollars per cookie to earn 400 dollars for their bake sale.