Mathematics Assessment Map – Sample at 1.75
Caterpillars
Context
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The Maths Caterpillar Investigation is a variation on a number chain (pattern).
The teacher related this story to the class.
‘The maths caterpillar is a rare species of caterpillar. Each caterpillar is born with just a head, with a number on its face. It grows according to two rules:
- If the number is EVEN then the next segment is HALF that number
- If the number is ODD then the next segment is ONE MORE than that number.’
The teacher then drew some caterpillars on the board to illustrate this. She added ‘all caterpillars stop growing when they grow a segment with a 1 on it’.
The teacher then asked the students to draw at least five different caterpillars and find the longest caterpillar under 20, under 50 and under 100. The students were also asked to write any patterns they noticed and to describe why these were the longest.
This context is also used in Working mathematically Level 2, Level 3 samples and Number Level 2 samples.
The elements of the Number standard addressed by the task are:
(Students) model the place value of the natural numbers from 0 to 1000.
(Students) form patterns … based on simple criteria such as odd and even numbers.
(Students) add and subtract one- and two-digit numbers by counting on and counting back.
(Students) mentally compute simple addition and subtraction calculations involving one- or two-digit natural numbers, using number facts such as … doubles.
Sample
The following sample illustrates the kind of response that students typically produce at 1.75 as they progress towards the Level 2 standard.
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Annotation
Number – 1.75
- The student identifies odd and even numbers and correctly applies the arithmetic rules of adding and halving to produce four complete patterns.
- Chooses to use starting numbers up to ninety nine and demonstrates facility with using numbers in this range.
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