Homework sheet: stage 6 – 7, Revision of add-sub and mult-div 2

Prior knowledge

Background

1. 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.
2. 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

Mixed problems – students are often fine when told exactly what to do when solving a class of problems, but cannot identify when each strategy to use when left to their own devices. This is especially true for students taught algorithmically. Bringing a range of problem types together and forcing the choice is an essential learning experience. Spending time marking such an exercise is a valuable use of group time. Students need to practice communicating their solution methods correctly using mathematical symbols. This may not come easy to some as can be shown in the following example.
“I did 25 + 9 by taking 25 and adding 5 to it to make 30, then I added 4 to make 34”
This when recorded literally is 25 + 5 = 30 + 4 = 34, which of course is running arithmetic. This exercise could therefore be part of a series whereby students experiment with written recording that avoid producing mathematically incorrect statements.

Solving equations – here number skills have been pushed into low-level algebra – CL3. Again the focus is on developing understanding of a new notational form, tying it to existing knowledge. The later problems require more that instant recall of known facts, and require some understanding of how to rearranging equations to form equivalent statements. This could be used as an introduction to the formal study of opposite operations and their use to solve equations.

This exercise seeks to exploit the tendency of students to look for their own meaning and create their own mathematics (much in the way that our numeracy shills have developed even when they have not been identified, taught or valued in class). It also seeks to build a rationale for equation solving strategies (of which there are a few) for when the numbers are too hard to deal with. Such an exercise would probably lead on to a teaching session.)This exercise involves some algebraic thinking. It looks beyond getting the answer into looking at process. Some understanding of opposite and inverse operations would assist with the latter problems.
It may pay to discuss the process of “explaining” in mathematics, whereby using a mix of symbols with a few words is all that is needed – rather than an English essay!
Marking this exercise in the group would provide a good teaching session, though it could also be collected in and marked.

Notes on marking homework

1. Checks that homework has been completed can be run very quickly at the start of the period, while someone is running the starter.
2. 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.
3. 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.
4. 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.