Using the worksheetsFor parents and teachers
FractionsGrades 3–7
Fractions from Grade 3 to Grade 7
Fractions become easier to handle when each step stays tied to equal parts. This guide moves from comparing simple fractions to choosing an operation, with a paper-strip technique that works at the kitchen table or in class.
On Tuesday after dinner, my younger brother Sam pointed to 1/8 and 1/6 on his homework. He chose 1/8 as the greater fraction because eight is greater than six. Then he frowned and asked, “How can eight make a smaller piece?”
Why a fraction can look misleading
Sam was treating the top and bottom numbers as separate whole numbers. In a fraction, they have different jobs. The numerator is the top number and tells how many parts are counted; the denominator is the bottom number and tells how many equal parts make the whole.
A larger bottom number means the same whole has been cut into more pieces. Each piece is therefore smaller. This comparison only makes sense when the wholes are the same size and the pieces are equal.
Grade 3: Compare the size of equal parts
At the kitchen table, Sam says 1/8 is greater than 1/6 because 8 is greater than 6. Which fraction is greater?
- Take two paper strips of the same length.
- Fold one strip into six equal parts. Fold the other into eight equal parts.
Show step 3
Shade one full section on each strip. One sixth is longer than one eighth.Show step 4
Both fractions count one part, so compare the size of that part. Splitting the same whole into fewer parts makes each part larger.
Answer: 1/6 is greater than 1/8.
Grade 3: Find a fraction of a number
For 3/4 of 20, first find the size of one quarter. Share 20 into four equal groups to get 5 in each group. Then take three groups: 5 + 5 + 5 = 15.
If the written work says 20 × 3 = 60 and stops, the error is stopping before dividing by 4. Ask, “What is one quarter of 20?” before returning to three quarters.
Grade 4: Use equivalent names for the same amount
Equivalent fractions give the same amount a different name. For example, 2/3 becomes 4/6 when both numbers are multiplied by 2. A paper strip can confirm that four sixths covers the same length as two thirds.
For 2/6 + 3/6, the pieces are already the same size. Count the pieces to get 5/6. Adding both top and bottom numbers produces 5/12 because 2 + 3 = 5 and 6 + 6 = 12, but that working changes sixths into twelfths without cutting the pieces again.
Back at the kitchen table
Sam put the sixths strip beside the eighths strip and corrected his first answer. Then he tried 3/4 and 5/8. He renamed 3/4 as 6/8, so he could see that 6/8 is greater than 5/8.
The paper strips gave him a reason for the rule. The shared bottom number then made the written comparison quick.
Grade 5: Make the parts match before adding
For 1/3 + 1/4, thirds and quarters are different-sized parts. Rename both fractions in twelfths: 1/3 = 4/12 and 1/4 = 3/12. The sum is 7/12.
Mixed numbers add one more choice. For 1 1/2 + 3/4, change 1 1/2 to 3/2, meaning three halves. Then 3/2 = 6/4, so 6/4 + 3/4 = 9/4, or 2 1/4.
Grades 4–7: Choose a method for +, −, ×, ÷, comparison or ordering with two fractions
1. If either number is a mixed number, first change it to one fraction, such as 1 1/2 = 3/2. Does the problem use + or −?
- Yes: go to question 2
- No: go to question 3
2. Do the bottom numbers match?
- Yes: Add or subtract the top numbers as shown, and keep the shared bottom number. Reduce the answer if both numbers have a common factor.
- No: Rename both fractions with a shared bottom number. Then add or subtract the top numbers and reduce the result when possible.
3. Does the problem use ×?
- Yes: Multiply the top numbers. Multiply the bottom numbers. Then reduce the result when possible.
- No: go to question 4
4. Does the problem use ÷?
- Yes: If the second fraction is not zero, keep the first fraction, turn the second fraction upside down, change ÷ to ×, and multiply. Division by zero has no answer.
- No: For comparison or ordering, give the fractions a shared bottom number and compare their top numbers.
Grade 6: Keep multiplication and division separate
For multiplication, 2/3 × 3/5 becomes 6/15, which reduces to 2/5. The parts do not need matching bottom numbers because the operation is multiplication.
For division, consider 3/4 ÷ 1/2. Turn only the second fraction upside down: 3/4 × 2/1 = 6/4 = 3/2, or 1 1/2. If the first fraction is flipped instead, the work becomes 4/3 × 1/2 = 4/6 = 2/3, so that wrong answer follows directly from flipping the wrong fraction.
Grade 7: Mixed operations are review
A mixed set tests the choice of method as well as the calculation. Before writing any numbers, circle the operation sign and say the first move. For + or −, check the bottom numbers; for ×, multiply top by top and bottom by bottom; for ÷, check the second fraction is not zero, then turn it upside down and multiply.
A mixed set has 2/3 + 1/6 and 2/3 ÷ 1/6. First problem: the sign is +, so match the bottom numbers: 4/6 + 1/6 = 5/6. Second problem: the sign is ÷, so turn the second fraction upside down and multiply: 2/3 × 6/1 = 12/3 = 4.
Keep mixed practice until after each operation has been practised alone. Otherwise, an incorrect answer may come from choosing the wrong method rather than carrying out the chosen method badly.
What to avoid
Avoid comparing bottom numbers as though they were scores. A larger bottom number describes more pieces in the whole, not a larger piece.
A drawing can also mislead if the wholes have different sizes or the sections are uneven. Use equal-length strips and mark equal sections. When making an equivalent fraction, multiply the top and bottom by the same whole number greater than 1 to make an equivalent fraction. When reducing a fraction, divide both by the same number that divides each exactly to make the numbers smaller.
When to talk to the teacher
Talk to the teacher if short practice keeps stopping at the same point, even after the problem has been shown with equal parts. Bring two examples of the written working. One correct attempt and one stuck attempt give the teacher something clear to discuss.
It also helps to ask which form is being used in class, such as paper strips, number lines or written equations. The teacher can then suggest whether to revisit equal parts, equivalent fractions or the operation itself.
Sam explains the difference
Before packing away his homework, Sam looked again at 1/8 and 1/6. He pointed to the strips and said that one sixth is larger because the same whole has been split into fewer parts. When he compared 3/8 and 3/5, he used the same idea and chose 3/5.
The useful change was asking what the bottom number says about part size before choosing a written rule.
Grade 3 quick review
1Which is greater: 1/4 or 1/7? Explain using the size of one part.
1/4 is greater. A same-sized whole split into four equal parts has larger pieces than one split into seven equal parts.
1. Which is greater: 1/4 or 1/7? Explain using the size of one part.
Answer: 1/4 is greater. A same-sized whole split into four equal parts has larger pieces than one split into seven equal parts.
2What is 1/3 of 12?
4. Share 12 into three equal groups.
2. What is 1/3 of 12?
Answer: 4. Share 12 into three equal groups.
3What is 2/5 + 1/5?
3/5. The parts are already fifths, so count three fifths.
3. What is 2/5 + 1/5?
Answer: 3/5. The parts are already fifths, so count three fifths.
From KidosLab
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