Class time using rounding and compensating to solve addition problems
Class time solving multiplication word problems
Class time using multiplication bracket notation
- This exemplar homework sheet is designed to extend the work done in class, not simply repeat it. As such large numbers of carefully graded questions that slowly increase in difficulty are not required.
- Students are being encouraged to think more, rather than simply follow algorithms, so the sheet should encourage independent thought and action.
Comments on the Exercises
Word problems – many students find word problems difficult, and these form the core of many NCEA assessments. Consequently practice with them is continually needed. Here the focus is also on setting out and explaining what is being done at each step, as this is also a maths based skill required for NCEA. This could have been the focus of a lesson at some stage in the past, then simply be part of the regular homework – or it may be a way of starting the next lesson where this aspect of mathematics is the teaching point for the day.
The word problems follow a format that is common in NCEA achievement standards assessment – with a bit more scaffolding. It requires students to explain what they are calculating at each step.
Question 4 could be used to prove students have actually done their homework – and good questions are a source of further worksheets for next year.
Rounding and compensating. This exercise revises a strategy and when it works – but over both domains rather than within a single domain. Be aware that this particular strategy works for +/-/?, but not division. (A very good extension problem is to ask students why it does not…) Getting students to look at decimals may be revision for some – or it may be an extension piece that is making student really think. In either case, the focus is on explanation rather than simple computation. This also means that question 13 is an extension problem that may not be used with all students.
The decimal problems should be collected and marked, if this is set, as it may bring to light a number of understanding issues around both decimals and the strategy
Multiplication without the sign – introduces a small piece of knowledge that would otherwise take lesson time. It is also serving as part of the bridge from number to algebra and the development of the distributive law. One concern with this exercise is that it has only a few problems to support new learning, so may need follow up in group time.
The exercise can be followed up by using the notation in this format in group teaching sessions.
Notes on marking homework
Checks that homework has been completed can be run very quickly at the start of the period, while someone is running the starter.
- Actual marking for a lot of numeracy homework could be done by students using a calculator at the start of independent work time. Alternatively, the answer sheet could be made available at the start of independent work time, with students self-marking this way. In other words it can be part of students’ responsibilities so does not have to be a teacher responsibility.
- Handing in word questions is a good way of developing a bank of student-centred practical contexts for word problems. It is also a way of quickly monitoring that students are actually doing their homework and making sense of it without too much marking.
- With wall displays and project work, students can be given the task of marking (or peer reviewing) work. This not only removes the need for the teacher to mark, but also gives students a clearer idea of what quality work looks like, and how it is identified.
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