Mathematics: Number
THE NEW ZEALAND CURRICULUM EXEMPLARS
Fractions
LEVELS
1
TO
4
This set of exemplars describes a possible progression in number: the progression in students’ knowledge,
understanding, and use of fractions.
The progression in the development of students’ understanding of non-whole numbers (fractions, decimal numbers,
and percentages) tells us a lot about their development in number as a whole. Fractions of numbers play an
important role in our lives because not everything that needs to be expressed in number can be represented by
integers.
LEVEL 1
Identify half or quarter of a region
At this stage in the fractions progression, students are able to state what unit fraction of a region is
shaded and/or shade a stated unit fraction of a region.
LEVEL 2
Assign unit fraction symbols to regions
At this stage in the fractions progression, students are able to write the correct symbol to
represent a unit fraction.
LEVEL 3 i
Order unit fractions and fractions with like denominators
At this stage in the fractions progression, students are able to order unit fractions or fractions
with common denominators from smallest to largest.
LEVEL 3 ii
Order fractions with unlike numerators and denominators
At this stage in the fractions progression, students are able to identify equivalent
fractions and to order all fractions from smallest to largest.
LEVEL 4
Convert fractions, decimals, and percentages
At this stage in the fractions progression, students are able to convert fractions to
decimals or percentages and vice versa. They are able to use this ability to identify
equivalent fractions and to arrange all fractions in order of size.
Mathematics: Number
THE NEW ZEALAND CURRICULUM EXEMPLARS
Fractions
ACCESS THE MATHEMATICS EXEMPLARS ONLINE AT www.tki.org.nz/r/assessment/exemplars/maths/index_e.php
BACKGROUND TO THE TASK
The task chosen as a context for this set of exemplars gives the teacher sufficient scope to observe students’
knowledge, understanding, and use of fractions through levels 1 to 4.
The teacher asks the students to:
• complete a series of tasks requiring them to name fractions;
• arrange fractions in order from smallest to largest.
The teacher increases the difficulty of the task by altering the types of fraction provided according to the students’
level of development.
The task
The teachers asked the students whose work is shown in these exemplars to complete one (or more) of the following
tasks according to their level of development.
1 1
• Level 1: The teacher showed the students a region with a fraction shaded ( 4 , 2 ) and asked them to identify how
much of it was shaded. If they could identify this verbally, the teacher asked them to write down their answer.
• Levels 2, 3, and 4: The teachers gave the students some sets of fractions and asked them to order each set from
smallest to largest. The sets included:
1 1 1 1 1
1 2 4 5 6
– level 2: a set of unit fractions ( 10 , 8 , 4 , 3 , 2 ) and a set of fractions with a common denominator ( 4 , 4 , 4 , 4 , 4 );
2 7 2 2 6 3
– levels 2, 3, and 4: a mixed set of fractions ( 5 , 16 , 4 , 3 , 9, 4 );
– level 4: a set of percentages and decimals to include in the range (30%, 0.5, 0.6, 75%) if the students could
order the mixed set of fractions correctly.
Parallel tasks
This progression could be explored in the context of any kind of activity where students are required to use fractions.
REFERENCES
Department of Education (1985–1989). Beginning School Mathematics: Cycles 1–8. Wellington: School Publications.
Ministry of Education (1992). Beginning School Mathematics: Cycles 9–11. Wellington: Learning Media, Ministry of
Education.
Ministry of Education (1993). Beginning School Mathematics: Cycle 12. Wellington: Learning Media, Ministry of
Education.
Ministry of Education (2002). Figure It Out, Level 2. Wellington: Learning Media.
Ministry of Education (1999). Figure It Out, Levels 2–3. Wellington: Learning Media.
Ministry of Education (2000). Figure It Out, Level 3. Wellington: Learning Media.
Ministry of Education (2001). Figure It Out, Levels 3–4. Wellington: Learning Media.
Ministry of Education (2002). Figure It Out, Years 7–8. Wellington: Learning Media.
Note: Each level of Figure It Out consists of a set of student books, with an accompanying Answers and Teachers
Notes for each book.
Ministry of Education (1992). Mathematics in the New Zealand Curriculum. Wellington: Learning Media.
Ministry of Education (1996). Te Whàriki: He Whàriki Màtauranga mò ngà Mokopuna a Aotearoa/Early Childhood
Curriculum. Wellington: Learning Media.