Grade 4 math in Ontario: multi-digit multiplication and fractions

Grade 4 is where many parents first hear, "I don't get fractions", or "I forgot how to multiply big numbers." Your child isn't bad at math. Two big ideas arrive in the same year, and both of them build on facts from Grade 3. If a fact wasn't practiced enough, the new lesson wobbles.

What Grade 4 math covers

Grade 4 follows Ontario's 2020 math curriculum for Grades 1 to 8. In the lessons we teach, the year includes:

• Adding and subtracting four-digit numbers, including across zeros.
• Multiplying by a one-digit number, and then a two-digit number by a two-digit number.
• Dividing by a one-digit number, including division with remainders.
• Fractions: equivalent fractions, comparing fractions, mixed numbers and improper fractions, and adding and subtracting fractions with the same denominator.
• Decimals: tenths and hundredths, and decimals with money.
• Area and perimeter of rectangles, angles, number patterns, and elapsed time.

Where children get stuck: multiplying bigger numbers

When children first meet 23 × 14, they often try to do everything at once and lose track of place value. A common slip is forgetting that the 2 in 23 is really 20, so the answer comes out far too small.

A way out is the area model. Break each number into tens and ones, draw a box, and multiply the pieces. The answer comes from adding four easy products, so the child can check each piece for sense.

Where children get stuck: fractions

Fractions are confusing, and that's okay. It is a whole new idea. Until now, numbers counted things. A fraction describes a part of a thing. Children have usually met halves and fourths, but not formally, so Grade 4 is where the rules start.

The main stumbling blocks:

• Equivalent fractions. 1/2 and 4/8 are the same amount written differently. This is hard to believe unless you can see it.
• Comparing. Is 3/4 bigger than 5/8? You can't tell by looking at the numbers. You need the same size pieces.
• Mixed numbers. 7/4 and 1 3/4 are two names for the same quantity.

All three get easier when children can fold paper and see it. Visualizing is the key. Once they have seen that 2 of 4 equal parts fills the same space as 4 of 8, they have already got the idea; the symbols are just the way of writing it.

A worked example: 23 × 14

Children who can explain the four parts out loud usually understand the standard written method later, when they see it as a shortcut for the same work.

Try this at home tonight

You need three strips of paper of the same length and a pencil.

• Fold the first strip in half and shade one half.
• Fold the second strip into fourths and shade two parts. Put it under the first strip. Ask, "What do you notice?" They are the same length.
• Fold the third strip into eighths and shade four parts. Ask your child what they think before they lay it down.
• Write the three fractions side by side: 1/2, 2/4 and 4/8. Ask what is the same about them.
• Now ask, "Which is bigger, 3/4 or 5/8?" Shade 3/4 on the fourths strip and 5/8 on the eighths strip, and let them compare. (6/8 is more than 5/8, so 3/4 is bigger.)

Ten minutes is plenty. Let them do the folding. The more they handle it, the more it sticks.

A note on practice

Understanding a fraction on a strip isn't too hard. Keeping that picture in mind a month later is the challenge. A few minutes with a strip, or a game that asks "which is bigger?", will keep it ready for Grade 5.

Next steps

If you want to see where your child stands in Grade 4 math, the free 15-question check-in is. It has no mark and it shows what is solid and what needs practice. The free math games give extra practice.

For live help with the toughest ideas of Grade 4, including multi-digit multiplication 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.