Understand the idea.
Count spaces, not tick marks
First find the interval representing one whole, such as from to . Count its equal spaces, not its tick marks. Four equal spaces make quarters; the five marks include both ends of the whole interval.
Start at zero and count the spaces you travel to reach a point. Each space contributes one fraction-sized jump. Three quarter-sized jumps reach , so the numerator counts distance in those equal jumps.
Keep the scale past one
Continue the same scale beyond one whole. A quarter-sized jump after reaches . The distance between neighbouring ticks stays unchanged, so the denominator stays four on both sides of one.
On a number line, a point farther right represents a larger number. To compare fractions with different denominators, rename them with matching parts or place both accurately on one line. For example, halves can be renamed as quarters before comparing.
See the method in action.
Read a point
The whole interval is split into four equal spaces. What is A?
Worked solution
- 1
Read the size of each interval.
Four equal spaces from one whole number to the next make quarters.
- 2
Count six jumps from zero to A.
The point is six quarter-sized spaces from zero, including those beyond one.
- 3
Group four quarters into a whole.
Four of the six quarters make one whole and two quarters remain.
- 4
Rename the leftover part.
Two quarters cover exactly one half of a whole.
Compare two positions
Which is farther right: or ?
Worked solution
- 1
Give both amounts quarter-sized units.
Equivalent fractions let both positions use the same jump size.
- 2
Compare the numbers of quarter-jumps.
Three quarter-jumps travel farther from zero than two quarter-jumps.
- 3
Identify the point farther right.
It lies one extra quarter-jump to the right of one half.
Try it yourself.
Check your understanding
A line has three equal spaces from 0 to 1. What fraction is the second tick after 0?
Show answer & reasoning
Three equal spaces make thirds. The second tick after zero is two jumps away, so its value is . The zero tick is the start, not a jump.
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- Read point A.1 mark
- Read B as a fraction and a mixed number.2 marks
- Mark on the supplied line.1 mark
- Order from smallest to largest.2 marks
- The line is labelled . Between which two neighbouring marks does lie?1 mark
- Mark and explain how you chose its position.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Read point A.1 mark
Four equal spaces fill one whole; A is one space from zero.
- Read B as a fraction and a mixed number.2 marks
B is seven quarter-sized jumps from zero. Four quarters make one whole, leaving three quarters.
- Mark on the supplied line.1 mark
Each space is one third, so count two spaces from zero.
The second tick after 0. - Order from smallest to largest.2 marks
They equal two, five and six quarters.
- The line is labelled . Between which two neighbouring marks does lie?1 mark
The landmarks are six quarters and eight quarters.
and - Mark and explain how you chose its position.2 marks
Divide the zero-to-one interval into five equal spaces and count three spaces.
The third tick after 0.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Equivalence; counting beyond one; mixed numbers; number lines.
Official curriculum source ↗