Mathematics Assessment Map – Sample at Level 2
How old are they?
Context
Students were asked to solve a simple worded problem about the total age in years of two students. They were able to use a calculator to check their working.
The elements of the Working mathematically standard addressed by the task are:
(Students) make and test simple conjectures by finding examples …
(Students) use a four-function calculator … to check the accuracy of … solutions to simple number sentences …
Stimulus
Teachers gave students the following problem and explained it verbally.
- Gino is in Grade 2 and his friend Carl is in Grade 3.
- When they add their ages (in years) together they get a total of 17 years. How old (in years) could Gino and Carl be?
- Explain how you obtained your answers and check them using a calculator.
Sample
The following sample illustrates the kind of response that students typically produce when they have achieved the elements of the standard addressed by this task.
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Annotation
Working mathematically – Level 2
Sample A
- The student tries several different combinations (7 and 8, 7 and 9) using trial and error before obtaining the combination of 8 and 9. Checks the calculations using finger counting. In each case Gino has been assigned the smaller of the two ages.
Sample B
- The student initially identifies Gino as 9 years old and Carl as 8 years old and then reverses these answers to account for the fact that Gino is in Year 2 and is likely to be the younger of the two children.
Sample C
- The student uses a calculator to try 7 + 9 , with Gino having the smaller (younger) age value, but realises the answer, 16 was too small. Then checks 8 + 9 = 17 and accepts this as the answer. While the ‘=’ sign has been used, this has not been expressed using the conventional form of writing a number sentence.
Sample D
- The student uses a combination of words, numbers and arrows (representing the ‘+’ symbol) to express their working as two addition sums.
Samples A–D
- The problem was posed as an open question, and students were not directed to present their solutions in a particular form such as … + … = ….
- They have used a variety of notations to record their working. Students usually assigned Gino the younger age, or rejected examples where he was older by crossing out. Combinations such as 7 + 8 = 15 and 7 + 10 were rejected, and the related reasoning explained through discussion with the teacher. Related working was typically checked by finger counting and/or four-function calculator. The feasible (if less likely) possibilities 9 + 8 = 17 and 7 + 10 = 17 were generally not accepted.
Elements of Working mathematically
(Students) make and test simple conjectures by finding examples…
(Students) use a four-function calculator … to check the accuracy of … solutions to simple number sentences …
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