Grades 7 and 8 math in Ontario: integers, ratios and starting algebra

Your child isn't bad at math. Grades 7 and 8 are where math starts to look like high school math: negative numbers, letters standing for numbers, and problems with several steps. A child who has quietly been going along since Grade 4 can run out of road here. That is a reason to look closely, not a reason to worry.

What Grades 7 and 8 cover

These grades follow Ontario's 2020 math curriculum for Grades 1 to 8. In the lessons we teach, the two years include:

• Grade 7: adding, subtracting, multiplying and dividing integers; fractions; order of operations (BEDMAS); ratios, rates and unit rates; percent change, discounts and tax; algebraic patterns, expressions and equations; circles, area and volume; data; and probability of one and two events.
• Grade 8: rational numbers, exponents and square roots; the Pythagorean theorem; circles, prisms and cylinders; ratios, rates and proportions; percent; expanding and simplifying algebra; solving equations with the variable on both sides; linear relations and slope; scatter plots; compound probability; and transformations on a grid.

Grade 8 is the doorway to Grade 9, so what is shaky here tends to show up there.

Where children get stuck

Negative numbers. Children memorize "two negatives make a positive" without a picture, and the rule falls apart under pressure. They mix up −4 − 6 and −4 − (−6).

Proportional reasoning. A recipe uses 2 cups of flour for 5 muffins. How much for 15? Children who guess "add 10" get 12 cups, which is far too many. Proportional thinking means multiplying by the same number on both sides: 15 is 3 times 5, so the flour is 3 times 2, or 6 cups.

Letters as numbers. In 2x + 5 = 17, x is a number that is hiding. The equation is a balance, and you can undo the steps in reverse. Subtract 5 to get 2x = 12, then divide by 2 to get x = 6. Check it: 2 × 6 + 5 = 17.

Multi-step work. A longer problem asks children to keep several ideas in mind. One shaky step causes the whole answer to fall over, and they conclude they are bad at it. That is almost never true.

Children rarely ask for help here. By this age, asking feels weak and they don't want to be left out. One bad week can lead them to give up on the rest of the course, so noticing early matters.

A worked example: subtracting a negative on a number line

The key is helping them visualize it. Draw a number line first, and decide three things in order: where you start, which way you are heading, and how far.

Compare −4 − 6. There is one negative in the middle, so we head left from −4. Six steps left lands on −10.

Try this at home tonight

You need a long strip of paper or a piece of masking tape on the floor, and a marker.

• Mark a number line from −10 to 10 with 0 in the middle.
• Ask your child to stand on −4. Say, "Walk 6 steps to the right." Where do they land?
• Now ask, "What if I say add 6?" Same thing. Then, "What if I say subtract negative 6?" Ask them to predict, then walk it.
• Try three more with different starting points, such as 3 − 5 or −2 − (−7).
• Finish by asking them to explain to you, in their own words, how to decide which way to walk.

This takes about ten minutes, and a child who can explain it understands it.

Next steps

The free 15-question check-in shows where your child stands in Grade 7 or 8 math. There is no mark, and it points to what is solid and what needs practice. The free math games are.

For live help with the hardest ideas of each grade, see our Toughest Topics courses. We find out where your child is first, and I don't want to take your money if they don't need it. For students ready to work ahead of their grade, see our Go Further group.