# Sixth Grade Math Curriculum (Examples, Worksheets and Games)

This is a resource page for parents who want to teach their sixth grade kid some 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!

Miss the grade 5 math fun? Check out our Grade 5 Math Curriculum resource page.  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.

## Introduction To Math Education

Like in constructing a building, there are no shortcuts to learning math. All new math is on existing math foundations. 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. 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 get fixed before construction can continue.

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.

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.

• Ratios, rates, & percentages: 6th grade
• Properties of numbers: 6th grade
• Variables & expressions: 6th grade
• Equations & inequalities introduction: 6th grade
• Data and statistics: 6th grade

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## Grade 6 Math Curriculum Examples

### Ratios

A ratio is a the number of one thing contained in the number of another thing. A good example is the ratio of water to rice. When you want to cook rice, you do not want to have too much water or it will be soggy. You also do not want too little water, or it won’t be soft. You need the right ratio, which is simple 1:1. You should add 1 cup of water and then 1 cup of rice when the water is boiling.

When comparing two things you can describe the relationship with a ratio. If you’ve got 6 apples and 9 oranges in your basket.

### Equivalent Ratios

A ratio can always turned in another one. How? By multiplying both numbers by a factor. These other ratios are equivalent. For example 2:3 is equivalent to 40:60 because 2 x 20 = 40 and 3 x 20 = 60.

In the previous rice example, supposed you want to cook 10 cups of rice instead of 1 cup. If you want to cook 10 cups of rice, you’ll need 10 cups of water because the ratio of 1:1 is equivalent to 10:10. How can you tell? Because you can multiply each number in the ratio 1:1 by 10 to get 10:10.

A ratio that cannot be smaller (reduced) than a smaller equivalent ratio is “in the simplest form” or lowest terms. In many math questions, students will have to put their answers ratios in their simplest terms on a test.

### Rates

A rate is a ratio between two numbers. The numbers also will be in different units. For example 60 miles per hour is the ratio of 60:1, where 60 represents 60 miles and 1 represents 1 hour.

A common kind of rate is a “per unit of time” rate. If you measure your heart rate, you’ll get heart beats per minute.

Another kind of rate is an exchange rate. For example the exchange rate of Canadian Dollar:U.S. Dollar is 1:0.78 at the time of this writing. What that means is that 1 Canadian dollar is equal to 0.78 U.S. Dollars.

### Percentage

A percent is a ratio expressed as a fraction of 100. The root of the word is ‘cent’ which is Latin for 100. For example 55% is  “fifty-five percent” is the same thing as 45/100, or the ratio 45:55.

If 50% of students are male, then that means in a class of 100, 50 are male. In a class of 10, 5 are male.

It is useful to think of things as a percentage. You can compare percentages of things together. Sales tax is percentage of the total sale. In Ontario, Harmonized Sales Tax (HST) is 13%. That means for every \$100 of stuff that you buy, add \$13 to the total which will go to the government.

### Percent As A Decimal

To make some calculations easier, you may want to convert percentage to decimal form. When calculating the percent of a percent, convert the percentage to fractions of 100. That is exactly the same as decimal form.

For example to calculate 40% of 50%, recognize that 40% is the same as 40/100 and 50% is the same at 50/100. Now, multiply 40/100 x 50/100. You can convert it to decimal form to make it easier. So, 50/100 = 0.5 and 40/100 = 0.4. We calculate that 0.4 x 0.5 = 0.2. Convert 0.2 to percentage form to get the final answer: 20%.

Adding decimal numbers is the same as adding whole numbers using the vertical method. It’s important to remember is that the decimals should line up exactly. The same kind of numbers should be  over each other. All the numbers in a column are representing the same place value or the vertical method will not work.

If on number has digits where the other one has none, write a zero in the number without a decimal. This will show the fact there is none of that number. Adding zero to a number will never change the number, so the answer will be correct.

### Subtracting Decimal Numbers

Subtracting two decimal numbers using the vertical method takes practice. The main difference from adding is that the “carry over” happens from left to right. What if the number you are subtracting from is smaller than the number you are subtracting? Wou will have to carry over one place value from the next largest number. If this is not possible, then the answer will be a negative number.

What is a negative number? Imagine if you have 10 dollars, but you owe 20 dollars. Then you have -10 dollars in you bank account. Negative number are not “natural numbers”. They only exist in our number system and not in nature. If you see a -10 walking around, please let me know!

### Word Problems With Decimal Numbers

Many math problems will asked with words. The key to solving these problems is to read the question and underline the numbers and write them down. When you have “extracted” the numbers from the sentences, then the puzzle is to figure out what to do with them. You will need to do some kind of operation. The operation could be addition, subtraction, multiplication, division. It could be some other trick you learned in class.

If the questions is asking for the “total” or “sum” You may have to add decimal numbers.  If the question is asking for the “difference” or “distance” you may have to subtract them.

Try to apply something that you learned in class to the problem and see if it makes sense.

### Multiplying Decimals

It’s hard to multiply sometimes. That’s why there are tricks to make it easy. When you learn the trick you can use it to solve questions. Many tricks depend on the fact of things being the same, but in a different form. For example, a decimal number is the same as a fraction, but in a different form. Also, you know that a fraction is the same as division. To figure out the answer, write out that decimal number as two whole numbers where one divide each other. Then you can multiply and divide whole number which may be easier. When you solve the problem, try to understand what is the trick you can use the next time to make it faster.