The Basics Of Seventh Grade Math On One Page

Don’t know what’s going on with your kid’s math? Let’s make this easy on you. Here is a resource page for parents who want to teach their kid some math. It covers the key stuff in your local grade 7 curriculum. Read through the sections and download the workbooks. The key to learning is to have fun with it. Make a schedule and offer rewards. Making the practice fun and challenging and you will see your child thrive!

Have they already mastered seventh-grade math? Check out our Grade 8 Math Curriculum resource page.  

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    Introduction To Math Education

    Like in constructing a building, there are no shortcuts to learning math. All new math is built an on existing math foundation. 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 new things by using other people’s work as a foundation. It is important that we make the foundation as solid as we can to make future studies more successful. Unlock your ability to learn math without frustration. Without a strong foundation anyone will find it difficult to follow along in later years. Like building a house, we should aim to have the most complete foundation we can. Cracks must get fixed 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.
    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 degree. A knowledge gap at the base cuts through to the top.

    Grade 7 Math Curriculum

    A one sheet summary of grade 7 math curriculum.
    A one sheet summary of grade 7 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: its school board. The school board issues a curriculum (or math standards) 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 from your school’s curriculum. You can expect to learn:

    • Negative numbers: addition and subtraction
    • Negative numbers: multiplication and division
    • Fractions, decimals, & percentages
    • Rates & proportional relationships
    • Expressions, equations, & inequalities
    • Geometry: triangles, polygons, and circles
    • Statistics and probability: theory and applications 

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    Grade 7 Math Curriculum Examples

    Introduction To Negative Numbers

    There’s 3 main things you need to know about negative numbers:
    1). How to think about them
    2). How to add and subtract them
    3). How to multiply and divide them
    Whenever you see the negative sign (-) that means “the opposite of”. -3 means “the opposite of 3”. What does that mean? It can mean a loss or deficiency of something. You can think of it as a debt. Debt is a negative asset.
    This video shows how negative numbers are just the opposite of numbers. You can think of them as numbers left of 0 on a number line.

    Adding A Negative Number

    In this video the concept of adding a negative number is explored. Adding a negative number is really the same as subtracting that number.

    Negative numbers can add the same way as positive numbers. The only difference is the sign. The negative numbers lay left of zero on the number line. Any number left of zero is a negative number.  

    Adding a negative number is exactly like subtracting that number. When you add a negative number you move to the left of the number line. 

    Adding two negative numbers is like adding two positive numbers except the movement goes left. For example (-3) + (-5) = -8. We start at position -3 on the number line. We move 5 to the left and land on -8. This makes sense because if you add two debts together, you’ll get a single bigger debt.

    Subtracting A Negative Number

    Two negative signs next to each other cancel each other out. That’s because the opposite of an opposite is the original thing. Since subtraction (-) is the same symbol as negative (-), subtracting a negative number really is adding that number.

    If a negative number represents a debt and you subtract that debt, then you are gaining credit. For example, -(-10) = 10. 

    Adding a negative number to a positive number is the same as subtracting from the positive number. For example 5 + (-3) = 5 – 3 = 2. This makes sense because if you have 5 cup cakes and you owe 3 cup cakes to you friend, then you have 2 cup cakes. 

    If the result of subtraction is negative, then the answer is a negative number. -5 – (-3) = -2. If we are talking about debt, think about having $5 debt, taking away $3 of debt, and having $2 of debt left.

    This video shows basic addition and subtraction with negative numbers. A number line illustrates how it makes sense.

    Multiplying Negative Numbers

    This Video Explains How Multiplication With Negative Numbers Works. There are 4 possibilities. Postive times positive equals positive. Negative times positive equals negative. Positive times negative equals negative. Negative times a negative equals positive.

    Here’s how to multiply negative numbers. There are two things about a number: 1). the sign (+/-) and 2). the size (called magnitude). Calculating the size of a number after multiplication works the same way with negative numbers as it does with positive numbers. The only difference is with negative numbers the sign will change. If you have a two negatives multiplied together, you get a positive number. This makes sense because “the opposite of the opposite” is just the original number.

    There are four possibilities:

    • Negative x Negative = Positive
    • Negative x Positive = Negative
    • Positive x Negative = Negative
    • Positive x Positive = Positive

    Dividing With Negative Numbers

    Dividing by a number is the same thing as multiplying by its reciprocal. A reciprocal is when you think of that number as a fraction and you flip the numerator and denominator. For example the reciprocal of 2 is 1/2. The reciprocal of 3 is 1/3. 

    Since dividing is the same thing as multiplying by its reciprocal, then the same rules of negative numbers applies from multiplication. So:

    • Positive / Positive = Positive
    • Positive / Negative = Negative
    • Negative / Positive = Negative
    • Negative / Negative = Positive

    It works the exact same way as multiplication works.

    This video shows how dividing a number is really the same as multiplying by it's reciprocal. Therefore the same rules of signs from multiplications applies to division. A negative divided by a negative equals a positive.

    Converting Decimals to Fractions And Fractions To Decimals

    This video shows how to convert decimal numbers into fractions. You will need to find the common denominator in this method.

    Recall that to add two or more fractions, convert them to the lowest common denominator of two fractions. Use the smallest common multiple of two numbers.

    To convert a decimal number into a fraction you can break it into place value parts and add them together. For example 2.75 has 3 digits. 2 as a fraction is 2/1 or just 2. 0.7 as a fraction is 7/10. 0.05 as a fraction is 5/100. Therefore 2.75 = 2 + 7/10 + 5/100. The lowest common denominator of 10 and 100 is 100. So to add 7/10 and 5/100, first we multiply 7/10 by 10 to have the lowest common denominator. So we have 70/100 + 5/100 = 75/100. 

    The same number can be represented different ways: decimal or fraction. There are infinite representations of a number with fractions, but there’s one that is in the simplest form. In this example we divide 75/25 and 100/25 to get 3/4 as the simplest form.

    Converting Fractions To Decimals

    To convert fractions to decimals you can do long division. Add zeros after the decimal point in the number that is bigger until the number of digits match. The answer of the long division will be the decimal form of the fraction.

    It’s important that the decimal is in the right place and that they numbers are neatly in columns. When it’s not possible to divide a number at least once, then you can write a zero for that column and carry over the remainder to the next column on the right.

    In this video you will see how to convert a fraction to a decimal by using long division to find the numbers. Divide the numerator (the number on top) by the denominator (the number on the bottom).

    Adding And Subtracting Any Rational Numbers

    This video shows how to add and subtract any rational number. Percentages can be converted to decimal and the vertical method of addition and subtraction can be used. Keep in mind that a negative times a negative equals a positive.

    There are a lot of rational numbers. Rational means that they can be written down exactly. 1/4 = 0.25 is a rational number. 1/3 = 0.333… is not rational because the 3’s continue forever right of the decimal. Percentages and fractions can represent rational and irrational numbers. Irrational numbers can sometimes be represented as fractions very well. 1/3 is a very nice way of saying 0.33333… (forever going to the right).


    Rates With Fractions

    A good way to solve problems is to use rates. The numerator and the denominator can represent different things. 

    The numerator can represent the amount of cleaning solution and the denominator can represent the area that gets cleaned from it. For example 1/3 of a bottle of cleaner cleans 3/5 of a bathroom.

    In this video we show how rates can be represented as a fraction which has a numerator representing one kind of measurement an the denominator representing another kind. In this example it is bottle per bathroom.

    Seventh Grade Math Problem Worksheets

    Are you looking for something you can hand to your second grader to start learning? Check out our free 7th grade math worksheets. 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 7 math today! If you don’t have a printer, open it with the iPad and play online. 

    We also love to write 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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