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Mathematics Assessment Map – Sample at Level 3

Mathematics
Samples
0.5
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
5.25
5.5
5.75
6

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Samples are available for the following tasks:

Representing fractions

Context

The sample is a collection of AIM 2003 – 2007 Year 3 items that require students to identify concrete representations of fractions in terms of sets and area.

The element of the Number standard addressed by the task is:

(Students) develop fraction notation … using physical models.

Sample 1

The following sample illustrates the kinds of responses that students typically produce when they have achieved the elements of the standard addressed by this task.

1.1 AIM 2003 Year 3 Mathematics Test 1

$AIM 2003 Year 3 Mathematics Test, Representing fractions - Question 18$

1.2 AIM 2003 Year 3 Mathematics Test 1

$AIM 2003 Year 3 Mathematics Test, Representing fractions - Question 32$

1.3 AIM 2004 Year 3 Mathematics Test 1

$AIM 2004 Year 3 Mathematics Test, Representing fractions - Question 32$

1.4 AIM 2005 Year 3 Mathematics Test 1

$AIM 2005 Year 3 Mathematics Test, Representing fractions - Question 8$

1.5 AIM 2005 Year 3 Mathematics Test 1

$AIM 2005 Year 3 Mathematics Test, Representing fractions - Question 24$

1.6 AIM 2005 Year 3 Mathematics Test 1

$AIM 2005 Year 3 Mathematics Test, Representing fractions - Question 33$

1.7 AIM 2006 Year 3 Mathematics Test 1

$AIM 2006 Year 3 Mathematics Test, Representing fractions - Question 12$

1.8 AIM 2007 Year 3 Mathematics Test 1

$AIM 2007 Year 3 Mathematics Test, Representing fractions - Question 13$

1.9 AIM 2007 Year 3 Mathematics Test 1

AIM 2007 Year 3 Mathematics Test, Adding and subtracting with money - Question 30

1.10 NAPLAN Numeracy Year 5, 2008

Representing 1.10 Number Level 3 Work sample

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Annotation

Number – Level 3

Questions 1.2, 1.4 and 1.6 require students to identify simple fractions of the form 1/x in relation to small ordered and unordered sets.
Questions 1.1, 1.5 and 1.8 require students to interpret simple fractions in relation to contexts which involve, or can be related to circular shapes or a near-circular cross section(face of a clock, an apple, a pizza).
Questions 1.3, 1.7 and 1.9 require students to identify simple fractions (including those with numerator greater than 1) with respect to representation using a rectangular grid or cross-section of a cylindrical container.
Question 1.10 requires students to determine a fraction represented on a figure and then to express the fraction in simplest form. (The second part of this is a Level 4 skill).

If students were also able to complete similar variations of these questions, they would be working at Level 3 with respect to the key element of the standard described below. In particular such students do not confuse the value of the denominator of the fraction being modelled, with simple counting of the number of elements in a row of an array or grid, as shown in Questions 1.2, 1.3 and 1.6.

Element of Number

(Students) develop fraction notation … using physical models.