Mathematics Assessment Map – Sample at Level 4
Helping Silvana with division
Context
Students were asked to identify a common mistake (not considering place value) which students sometimes make when carrying out a division algorithm. Students identified which answers are correct and which are not, and then create other examples in which this error is likely to occur, as well as those in which Bert is unlikely to make the error. They are asked to provide advice on how to avoid the error in the future and explain a suitable checking strategy.
The elements of the Number standard addressed by the task are:
(Students) explain and use mental and written algorithms for the … division of natural numbers (positive whole numbers).
(Students) use estimates for computations and apply criteria to determine if estimates are reasonable or not.
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Sample
The following samples illustrate the kinds of responses that students typically produce when they have achieved the elements of the standard addressed by this task.
Sample A
Student responses to Questions 1–3
Question 2
Question 3
Sample B
Student response to Question 4
Question 4
Sample C
Student response to Question 5
Question 5
Sample D
Student response to Question 5
Question 5
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Annotation
Number – Level 4
Sample A
- The student correctly identifies those answers which are correct and gives correct answers for the last two, then creates an appropriate question, involving ‘carrying’, which Silvana is likely to get correct. The student correctly creates two problems where Silvana is likely to make an error. The student provides the answers that Silvana might give to these questions, as well as the correct answers.
Sample B
- The student indicates the use of the inverse relationship of multiplication with respect to division to provide a check on the original calculation.
Samples C and D
- The students justify why Silvana’s answer must be too small. In Sample C division facts are used with front end estimation, while in Sample D the inverse operation multiplicative relationship is used.
Elements of Number
(Students) explain and use mental and written algorithms for the … division of natural numbers (positive whole numbers).
(Students) use estimates for computations and apply criteria to determine if estimates are reasonable or not.
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