Grade 6 math in Ontario: ratios, fractions and percent

Your child isn't bad at math. Grade 6 asks children to use ideas from the last three years, fractions, decimals and multiplication, in new combinations, and to do it with real-life numbers like sales and recipes. If one older idea is shaky, it shows up here.

What Grade 6 math covers

Grade 6 follows Ontario's 2020 math curriculum for Grades 1 to 8. In the lessons we teach, the year includes:

• Decimals: multiplying and dividing.
• Fractions: adding and subtracting with different denominators, mixed numbers, and multiplying and dividing fractions.
• How fractions, decimals and percent connect, and percent in real situations such as discounts and sales tax.
• Ratios and rates: writing, simplifying and comparing ratios, and finding unit rates and best buys.
• Order of operations, equations, patterns and rules.
• Area of triangles and parallelograms, volume of prisms, and angles.

Ontario students also write the provincial EQAO assessment in Grade 6. It is one snapshot. What helps most is steady understanding of the ideas above.

Where children get stuck

Dividing fractions. "Flip and multiply" is a rule many children memorize without knowing why. A picture helps: 1/2 ÷ 1/4 asks, "How many fourths fit in one half?" The answer is 2.

Ratios as fractions. A ratio of 2 red to 3 blue compares two parts. A fraction compares a part to the whole. It is easy to mix them up: 2 red out of 5 total is 2/5, not 2/3.

Percent as a rule, not a number. Children who can say "percent means out of 100" often still struggle to find 15% of something. The building blocks help: 10%, 5%, 1%, 25% and 50% are easy to find and can be combined.

Unit rates. If 3 notebooks cost $2.40, one costs 80 cents. Children can do that division but forget why it is useful: it lets them compare different-sized packages fairly.

Most children won't say they are confused. They would rather go along than be left out, and asking for help feels weak. A friendly conversation at home, using real numbers, makes it easier.

A worked example: a sale price with tax

Percent shows up in shops, so it is a good way to practice. Ontario's sales tax is 13% HST.

Notice that no step is hard. Percent is a few easy pieces put together, and a child who builds the pieces can check each one.

Try this at home tonight

You need a grocery flyer, a receipt or two products from the cupboard, and a pencil.

• Pick two sizes of the same food. For example, 500 g of pasta for $2.00 and 750 g for $2.85.
• Ask, "Which one is the better buy?" Let your child guess first.
• Find the price for 100 g of each. For the first, 500 g is five lots of 100 g, so $2.00 ÷ 5 = $0.40. For the second, 750 g is 7.5 lots of 100 g, so $2.85 ÷ 7.5 = $0.38.
• Compare: 38 cents is less than 40 cents, so the larger bag costs less per 100 g.
• Ask your child to find a second pair in the kitchen and explain their choice.

Ten minutes is enough, and it turns a chore into a game.

Practice a little at a time

Understanding ratios is not too hard. Keeping the idea ready is the challenge. A short question at the grocery store, a few times a week, does the work.

Next steps

The free 15-question check-in shows where your child stands in Grade 6 math. There is no mark, and it points to what is solid and what needs practice. The free math games are there for extra practice.

For live help with the toughest ideas of Grade 6, including fractions, ratios and percent, see our small-group course. We find out where your child is first, and I don't want to take your money if they don't need it. For children who are comfortable and ready to look ahead, there is also.