Grade 5 math in Ontario: decimals and fractions made clear

Your child isn't bad at math. In Grade 5, two ideas that felt separate (fractions and decimals) turn out to be the same thing written two ways, and that connection is where many children lose the thread. If it didn't land in Grade 4, Grade 5 can feel like a new language.

What Grade 5 math covers

Grade 5 follows Ontario's 2020 math curriculum for Grades 1 to 8. In the lessons we teach, the year includes:

• Decimals: place value, the powers of ten, adding, subtracting and rounding, and multiplying and dividing by a whole number.
• Multiplying large whole numbers, and long division with remainders.
• Fractions: equivalent fractions, comparing, mixed numbers, and adding and subtracting with different denominators.
• Multiplying a fraction by a whole number, and finding a fraction of an amount.
• How fractions, decimals and percent connect: 3/4 = 0.75 = 75%.
• Order of operations, simple equations, area of triangles and parallelograms, volume, and averages.

Where children get stuck with decimals

"A longer decimal is bigger." Some children think 0.45 is bigger than 0.5 because 45 is bigger than 5. Whole numbers trained them that more digits means more. With decimals it is the opposite. 0.5 is the same as 0.50, which is more than 0.45.

Lining up. In 3.4 + 0.25, children line up the right-hand digits instead of the decimal points. Writing 3.40 + 0.25 (adding a zero to hold the place) fixes that.

Place value after the point. Tenths, hundredths, thousandths: each place is one-tenth the size of the one on its left. It helps to say it aloud, "four tenths", rather than "point four".

Where children get stuck with fractions

Adding the tops and the bottoms. A common slip is 1/2 + 1/3 = 2/5. It looks reasonable, but 2/5 is less than a half, so it can't be right. The pieces have to be the same size first. 1/2 becomes 3/6 and 1/3 becomes 2/6, and then 3/6 + 2/6 = 5/6.

Fractions of an amount. Finding 3/4 of 20 asks children to divide first (20 ÷ 4 = 5) and then multiply (3 × 5 = 15).

Children often go along with this because they don't want to feel left out, and few of them ask for help.

A worked example: is 3/4 bigger than 0.7?

A hundred grid (10 rows of 10 squares) lets you see both numbers on the same picture.

Once children see this picture, 3/4 = 0.75 = 75% stops being something to memorize.

Try this at home tonight

You need a few coins. Canadian quarters are perfect, because 4 quarters make a dollar.

• Put 4 quarters on the table. Say, "This is one whole dollar."
• Take away 1 quarter. Ask, "How many fourths are left?" (3/4.) "How much money is that?" (75 cents, or $0.75.)
• Put out 7 dimes. Ask, "Is that more or less than the quarters?" (7 dimes is 70 cents, so it is $0.70, a little less.)
• Ask your child to say out loud which is more, 3/4 of a dollar or 0.7 of a dollar, and how they know.
• Try another: 1/2 of a dollar or $0.45?

Take about ten minutes. If they race through it, ask them to explain the picture, not just the answer.

Next steps

The free 15-question check-in shows where your child stands in Grade 5 math. There is no mark, and it points to what is solid and what needs practice. The free math games are a good way to keep decimals and fractions fresh.

For live help with the hardest ideas of Grade 5, including decimals and fractions, 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.