AC9M4N04 • Year 4 Maths
Count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines.
Fractions are numbers that can be counted and located on a continuous number line. An improper fraction and a mixed numeral can represent the same point, such as 7/4 = 1 3/4.
Learning routine: Choose step size → Partition each whole equally → Count beyond one → Rename → Locate and compare
Every interval represents one quarter. Crossing a whole does not change the step size or denominator.
Count how many complete denominator-sized groups fit in the numerator, then keep the remainder over the same denominator.
Worked explanation: For 7/4, separate one group of four quarters and three quarters more: 7/4 = 4/4 + 3/4 = 1 3/4. For 2 2/3, two wholes contain six thirds, and two more thirds give 8/3.
These are different names for the same number-line positions, not multiplication of the whole and fractional parts.
Start at 1 1/4 and move left by quarters: 1 1/4, 1, 3/4, 1/2, 1/4, 0. Think of 1 as 4/4 when you cross it. The step is still one quarter.
Quick check: One third before 2 is 1 2/3 because 2 can be renamed as 1 whole and 3 thirds.
The whole unit from 2 to 3 has three equal intervals. Point P is two thirds after 2, so it is 2 2/3 = 8/3. The left endpoint is 2; it must not be relabelled as zero.
Look for: Students count spaces, not tick marks, and use the given whole-number labels.
Content description: count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines.
The following teaching examples cover the curriculum elaborations.
Cut or draw two identical paper strips in quarters. Lay down the pieces one at a time: one quarter, two quarters, three quarters, four quarters or one whole, five quarters or one and one quarter. Continue to eight quarters or two wholes.
Check: Six quarters are 1 2/4 = 1 1/2. Students should show one complete whole and the remaining parts.
Draw three aligned number lines with the same 0, 1 and 2. Partition each whole into halves, quarters and thirds. The common point at 1 is 2/2 = 4/4 = 3/3, and the point at 2 is 4/2 = 8/4 = 6/3.
On the halves and quarters lines, 1/2 = 2/4 and 1 1/2 = 3/2 = 6/4 align too. Halfway points fall between the third-ticks; they are not whole numbers of thirds.
Mark 5/4 on a quarter number line: four steps reach 1, and the fifth reaches 1 1/4. Label the same point with both names. Reverse the process for 2 2/3: two wholes contain 6 thirds, then another 2 thirds give 8/3.
Check: The value and position stay unchanged when the number is renamed.
Partition a line from 0 to 2 into ten equal intervals per whole. Count 8/10, 9/10, 10/10 = 1, 11/10 = 1 1/10, 12/10 = 1 2/10. Count backwards over the same points.
Check: One tenth before 1 is 9/10, and one tenth after 1 is 1 1/10. The denominator remains 10.
Mark equal quarter intervals on a floor number line and stand at 3/4, 5/4, 1 1/2 and 9/4.
Check the positions: A = 3/4; B = 5/4 = 1 1/4; C = 1 1/2; D = 9/4 = 2 1/4.
Count by thirds from 0 to 3, recording improper fractions and mixed numerals at every whole and beyond.
Use interval size and neighbouring labels to identify missing fractions on partially labelled number lines.
Answers: A = 1 1/4 and B = 2 3/4. Use the quarter-intervals and the labelled whole numbers.
Core idea: Fractions are numbers that can be counted and located on a continuous number line. An improper fraction and a mixed numeral can represent the same point, such as 7/4 = 1 3/4.
Before this lesson: Students recognise unit fractions and equal partitions. Support: Use physical half and quarter strips alongside a line from 0 to 2. Core: Count forwards and backwards across wholes; locate and draw fractions, mixed numerals and matching improper fractions. Extend within this code: Read a line beginning at 2 or count jumps of 2/3 or 3/4 while keeping the unit intervals fixed.
Boundary: Renaming supports counting and number-line representation. Formal algorithms for adding unlike fractions are not the target.
Use the Topic Guide, then project the Classroom View. Complete the written worksheet tasks before Practice and Test. Drawing tasks need an adult to inspect equal intervals, the whole-number scale and actual labelled points.
Mastery evidence: Students keep equal spacing on the number line and can rename between improper fractions and mixed numerals without changing the value.
Project the Classroom View and open one teaching section at a time.
Open Classroom View| Australia | Australian Curriculum v9.0 | AC9M4N04 |
| Victoria | Victorian Curriculum F–10 | Year 4 Number: fractions on number lines. |
| NSW | NSW Curriculum | Stage 2 Mathematics: fractions. |
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
Math Antics — Place fractions between and beyond whole numbers.
As you watch: Why must the intervals between marked fractions be equal?
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Try it: Draw a number line from 0 to 2 and mark every quarter, including mixed numerals.
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Mapped skill: count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M4N04 · Year 4 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M4N04 · Level 4 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA2-PF-01 · Stage 2 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 4 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 4 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 5, Key Stage 2 |
| India | NCERT / CBSE — Mathematics | Class 4 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M4N04 — AC9M4N04: Count by fractions and mixed numerals
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