Fifth Grade Math Curriculum (Examples, Worksheets and Games)

This is a resource page for parents who want to teach their child some sixth grade math. It covers the content of an average grade 6 curriculum. Read through the sections and download the workbooks provided. Remember to keep practice fun and challenging, and your child will thrive!

Mastered fifth-grade math? Check out our Grade 6 Math Curriculum resource page.  We also love to write fun and resourceful blogs about learning, check out our blog on 6 free back to school math activities to get to the next level.

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    Introduction To Math Education

    Like in constructing a building, there are no shortcuts to learning math. All new math is based on existing math concepts. Sir Isaac Newton, the famous scientist and mathematician once wrote: “If I have seen further, it is by standing on the shoulders of giants.”. This means that we discover truth by building on previous discoveries. Therefore it is important that we learn the foundation the best we can. This will unlock the math that we have yet to learn. Without a strong foundation we will find it difficult to follow along with the class in later years. Like building a house, we should aim to have the most complete foundation we can. Cracks must be mended before construction can continue.

    A diagram showing a pyramid of educational learning with the foundation being Elementary School Math and the Pinnacle being a pHD. A knowledge gap at he base cuts through to the top.

    These 2 pyramids represent educational learning with the foundation being Elementary School Math. The Pinnacle being a pHD. A knowledge gap at the base cuts through to the top.

    Grade 5 Math Curriculum

    It is very important for parents to be aware of what their child is learning in school. Your school gets its direction from a governing body. The school board issues a curriculum (or math standard) for schools to follow. The curriculum varies across the world. For example. in Russia, the multiplication table starts in Grade 1, while in Ontario it starts in Grade 3. That means your school’s curriculum differs from what you may find online. In this article we cover an estimation of what you can expect your school’s curriculum to contain.

    • Decimal place value: 5th grade
    • Add decimals: 5th grade
    • Subtract decimals: 5th grade
    • Add and subtract fractions: 5th grade
    • Multi-digit multiplication and division: 5th grade
    • Multiply fractions: 5th grade
    • Divide fractions: 5th grade
    • Multiply decimals: 5th grade
    • Divide decimals: 5th grade
    • Powers of ten: 5th grade
    • Volume: 5th grade
    • Coordinate plane: 5th grade
    • Algebraic thinking: 5th grade
    • Converting units of measure: 5th grade
    • Line plots: 5th grade
    • Properties of shapes: 5th grade

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    Grade 5 Math Curriculum Examples

    Decimal place value: 5th grade

    We use “Arabic Numerals”. The way numbers work is that each digit has a position. There’s a 1’s position. There’s a 10’s position. There’s a 100’s position.  This is useful because it lets a number represent something very big. Think about the number 973. The 9 represents 9 hundreds, the 7 represents 7 tens, and the 3 represents 3 ones. You add all those together and you will get (9 x 100) + (7 x 10) + (3 x 1) = 973. That’s how you represent big things. In fact you can keep going up forever in place value forever!   The same way also allows a number to represent something very small. Let’s see how.
     
    When you write a number, you can think about each digit as being multiplied by a place value factor for each position. What if that place value factor was 0.1? This is how 1 tenths of a number can be written. For example 1.1 =(1 x 1) + (1 x 0.1). 2.2 = (2 x 1) + (2 x 0.1).  Do you see how it works the same way as when the number is big? Think about the number 0.973. The 9 represents 9 tenths, the 7 represents 7 hundredths, the 3 represents 3 thousands. You add all those together  and you will get (9 x 0.1) + (7 x 0.01) + (3 x 0.001). That’s how you can represent small things. In fact you can keep going down in place value forever!
     
     
    An example of 6 digit number. 3 digits before the decimal and 3 digits after the decimal. The number is 973.973
    The picture shows a whiteboard example of transfroming the common fractions 1/4 and 1/5 into decimal form.

    Common Fractions In Decimal Form

    In math there are many forms of the same things. A lot of the time, you can rewrite a fraction in decimal form. Doing a calculation one way may be so hard that it would be easier to transform that number into something else to make the calculation easy.

    Fractions can be transformed into decimal form if you can find the right factor to multiply it by. For example the fraction 1/5 can be transformed into 0.2 by multiplying the numberator and the denominator by 2. Then when the fraction is written as 2/10, you can recognize that it is the same as having 2 in the tenths place in the decimal form. So you can write 2/10 = 0.2.

    Another example is how you can rewrite the fraction 1/4 as 0.25. First try to think of a number that will transform 4 into 100 when you multiply it. The number 25 will do it. Multiply both the numerator and the denominator by 25 to get 25/100. Now, recognize that it is the same thing as having 2 in the tenths place and 5 in the hundredths place, so 25/100 = 0.25

     

    Add decimals: 5th grade

    Adding decimals is almost the same as adding whole numbers. The key is to add the same value holding digits together. When adding the number 8 and 2, both numbers have the same place value 1. So you can say 8 + 2 = 10. When adding the numbers 0.8 and 0.2, both numbers have the same place value 0.1. So you can say 0.8 + 0.2 = 1.0. The carry over always happens when you reach 10 of that place value.  That’s how it works for single digit addition.

    For adding multiple digits, repeat the same process as you would add single digit. Start from the smallest place value and work your way up. For example when adding 8.8 and 2.2, start by adding 0.8 and 0.2 which equals 1.0. Now carry 1 over to the next place value. So you will have 8 and 3. 8 + 3 = 11. So you know that 8.8 + 2.2 = 13. Practice makes perfect!

    This picture shows a whiteboard example of adding 0.9 to 0.3 to get 1.2.
    This is a video showing how the vertical method of adding numbers works. It works for decimals too.

    Addition Vertical Method

    One way to add number is by using the vertical method. You put two number on top of each other. Then starting from the smallest digits, add them up. Carry over a 1 for every time that the two digits is more than 10. This works great for decimal number or whole numbers. This method take a lot of steps, but its only adding two 0-9 digits. Still, it takes many hours of practice to get fast at doing it. The best way to learn is by doing.

    Subtraction With Decimals Vertical Method

    You can use the vertical method previously shown to do subtraction of two numbers. The only difference is that the carry over happens in reverse. When the digit you are subtracting from is smaller, carry over 1 of next highest place value and “break” it into 10. This will make the number you are subtracting from big enough. The difference will be positive. Decimals work the same way as numbers, we just keep in mind that they are a lot smaller place value.

    This is a movie that shows step by step how to do vertical subtraction of two decimal numbers.
    This video shows how to do multidigit multiplication using the vertical method with an example 234x321

    Multidigit multiplication

    The amazing things about multiplication is that the order that you do it in does not matter. Just like outcome of brushing your teeth and then flossing is the same as the outcome flossing and then brushing: You get clean teeth! The same is with numbers. So 2 x 3 is the same as 3 x 2. That means you can make calculations easier by rearranging the order! When we have to multiply many digits like 234 x 321, that’s hard. As always, there is a trick. Recognize that 234 = 2 x 100 + 3 x 10 + 4  and that 321 = 3 x 100 + 2 x 20 + 1. So 234 x 321 is ((2 x 100) + (3 x 10) + 4 ) x (3 x 100 + 2 x 10 + 1). Rearranging we have 2 x 3 x 100 + 3 x 2 x 10 + 4 + 1. We know 2 x 3 = 6 and so is 3 x 2. Then we have 6 x 100 + 6 x 10 + 14 which is 600 + 60 + 14. Simplify and your answer is 674. 

    We can also do the vertical method!

    Multidigit Division

    When dividing two large number we can use the vertical method, but instead of going starting from the smallest place value, we start at the largest place value. We break the problem into easier problems by asking how many times the divisor can be contained in a digit. We then subtract the total contained to get a remainder. We divide that remainder with the next smallest placeholder digit. We repeat this process until we have no more digits to divide.

    In this video we show long division using the example of 1946 divided by 2 using the vertical method.
    In this video 3 examples of multiplying fractions are given.

    Multiplication Of Fractions

    When multiplying two or more fractions, simply multiply the numerators (top numbers) and denominators (bottom numbers). You should also put the fraction in the lowest commons terms. For example if the numerator and denominator are both even numbers, then divide them both by 2 to cut them in half. Keep going until the fraction is in it’s simplest form.

    Division Of Fractions

    What you have to understand is that fractions and division are the same thing.  That means that dividing a fraction is the same thing as multiplying by a fraction. Lets suppose we want to divide 5/3 by 3. Then we will multiply 5/3 x 1/3. Using the technique of multiplication of fractions, we have 5/3 x 1/3 = 5/9. That means that 5/3 divides into three equal parts of 5/9. This video shows how to divide fractions and how it is the same as multiplying the reciprocal.

    This video shows how to divide fractions and how it is the same as multiplying the reciprocal.

    Fifth Grade Math Problem Worksheets

    Are you looking for something you can hand to your second grader to start learning? Check out our free 6th grade math worksheets which you can download or try out our math problem generator to learn online.  You can make a copy, download, and print these problems. Make it an exciting game and start learning Grade 6 math today! If you don’t have a printer, open it with the iPad and play online. 

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