Fractions lesson by grade, 3 to 6: what each grade teaches (unit fractions and the number line, equivalence and comparing, adding and subtracting, multiplying and dividing), a twenty-minute lesson plan for each with the model, the guided practice and the check, the CBSE class it matches, the misconceptions to catch, and a printable worksheet with answers

"Fractions lesson" is searched by parents and tutors who need to teach one tonight, by teachers planning a unit, and by students who were absent for the lesson the rest of the class had. Fractions are taught across four grades, and the reason a child is stuck in grade 6 is nearly always a lesson from grade 3 or 4 that did not land; so this page gives one lesson per grade, each in the same twenty-minute shape, so you can start at the grade the child needs rather than the grade they are in. Each has the model with its picture, the guided questions, the check question that exposes the misconception, and the CBSE class it matches. The printable has the four plans and a twenty-question worksheet with answers.

Download the fractions lesson plans and worksheet (PDF) (the four twenty-minute plans with the model and the check question, the misconceptions to listen for, and twenty questions by grade with answers; two pages, free).

Before the first lesson: what a fraction is

A fraction is one number, not two. 3/4 is three of the number 1/4, and 1/4 is what you get when 1 is cut into four equal parts. The denominator names the size of the piece; the numerator counts the pieces. Every lesson below starts by making that visible, with a bar or a number line, before any rule; and every misconception in the table at the end comes from losing it.

Grade 3 (CBSE Class 3 to 4): fractions as numbers

The goal: a fraction is a point on the number line; unit fractions are the building blocks; two fractions can name the same point.

I do (5 min). Draw a bar, cut it into four equal parts, shade one: that is 1/4, "one of four equal parts". Shade three: 3/4, three of the 1/4 pieces. Draw a number line from 0 to 1, mark it into quarters, and place 1/4, 2/4, 3/4, 4/4 on it. Say aloud: 4/4 is the same point as 1.

We do (10 min). 1) Shade 2/3 of a bar cut in thirds. 2) Put 1/2 on a number line from 0 to 1. 3) Cut a bar into eighths; shade 3/8; which is bigger, 3/8 or 3/4, and why (the pieces are bigger)? 4) Mark 2/2 and 3/3 on a line: where are they? 5) Shade 1/2 of one bar and 2/4 of another the same length: what do you notice?

You do (5 min). Shade 5/6 of a bar. Then the check: which is bigger, 1/8 or 1/4? A child who says 1/8 "because 8 is bigger" has not yet got the idea; draw both.

Grade 4 (CBSE Class 4 to 5): equivalence, comparing, adding like denominators

The goal: equivalent fractions by splitting the pieces; comparing by common denominator or benchmark; adding and subtracting when the denominators match; a fraction times a whole number as repeated addition.

I do (5 min). Shade 1/2 of a bar; cut each half into two: now it is 2/4, the same amount, more pieces. Cut again: 4/8. So 1/2 = 2/4 = 4/8, and the rule appears: multiply top and bottom by the same number. Then add 2/5 + 1/5 on a bar: three fifths, because you are counting fifths; the denominator does not change.

We do (10 min). 1) Write three fractions equal to 1/3. 2) Which is bigger, 2/3 or 3/4? Rewrite both over 12. 3) 3/8 + 4/8. 4) 7/10 − 3/10. 5) 3 × 2/5 as 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5.

You do (5 min). 5/6 + 1/6 (= 6/6 = 1). Then the check: 1/4 + 1/4. A child who writes 2/8 is adding the denominators; go back to the bar: two quarters is a half.

Grade 5 (CBSE Class 5 to 6): unlike denominators, multiplying fractions

The goal: add and subtract by rewriting over a common denominator; multiply fractions as "a part of a part"; divide a unit fraction by a whole number.

I do (5 min). 1/2 + 1/3: the pieces are different sizes, so first make them the same: sixths. 1/2 = 3/6, 1/3 = 2/6, so 5/6. Then 1/2 × 1/3 on a square: shade half, then a third of that half, and count: one of six parts, so 1/6. The rule (multiply tops, multiply bottoms) comes from the picture.

We do (10 min). 1) 2/3 + 1/4 (= 8/12 + 3/12 = 11/12). 2) 5/6 − 1/2 (= 5/6 − 3/6 = 2/6 = 1/3). 3) 2/3 × 3/4 (= 6/12 = 1/2); shade it. 4) 4 × 3/8 (= 12/8 = 1 1/2). 5) 1/3 ÷ 4: a third shared among four people is 1/12 each.

You do (5 min). 3/4 + 1/6 (= 9/12 + 2/12 = 11/12). Then the check: 1/2 × 1/2. A child who says 1 ("half times half") has not seen that a part of a part is smaller; draw the square.

Grade 6 (CBSE Class 6 to 7): dividing fractions, and fractions as ratios

The goal: divide a fraction by a fraction by asking "how many of these fit?", then by the rule (multiply by the reciprocal) once the picture has explained it; see ratios and unit rates as fractions.

I do (5 min). 3/4 ÷ 1/8: how many eighths fit in three quarters? Draw the bar in eighths: three quarters is six eighths, so six. Then show the rule: 3/4 × 8/1 = 24/4 = 6. The rule works because dividing by 1/8 is the same as asking how many eighths, and there are 8 in each whole.

We do (10 min). 1) 1/2 ÷ 1/4 (= 2). 2) 2/3 ÷ 1/6 (= 4). 3) 5/6 ÷ 2/3 (= 5/6 × 3/2 = 15/12 = 1 1/4). 4) 3 ÷ 1/2 (= 6: how many halves in 3?). 5) A recipe uses 3/4 cup of sugar for 6 biscuits; how much per biscuit? (3/4 ÷ 6 = 1/8 cup.)

You do (5 min). 4/5 ÷ 2/5 (= 2). Then the check: is 1/2 ÷ 1/4 bigger or smaller than 1/2? A child who says smaller "because you divided" is applying the whole-number rule; dividing by a number less than 1 makes the answer bigger, and the bar shows why.

The misconceptions to listen for

Where each lesson sits

The full grade content is in the grade 4 math syllabus and grade 6 math syllabus; the five methods for putting fractions in order are in ordering fractions.

Download the fractions lesson plans and worksheet (PDF)

Where to get help

A 1-on-1 online maths class with a tutor who holds a master's in mathematics, for grades 3 to 6 and CBSE Class 3 to 7: the lesson started at the grade the child's gap is in, not the grade they are in; bars and number lines on the shared whiteboard before any rule; the check question in every class; the school's own worksheet worked together. The recording and notes after every class, the same tutor all year, US$10 to $13 an hour. The grade 4 math page has the units; the free 30-minute first class is a real fractions lesson, and it will show you which grade's lesson the child needs.

Questions parents ask

See how we teach this, 1-on-1 online →