Make Up Your Own
Use their mathematical knowledge to invent problems;
Solve other students' problems.
Devise and use problem solving strategies to explore situations mathematically.
When you look at the Copymasters, you will realise that this problem could be used twice during the year on two different types of numbers, whole numbers and fractions. Alternatively you might want to mix up the two sets of answers and use the problem towards the end of the year.
To be able to make up a problem from scratch like this, requires a deeper understanding of the problem than just being able to solve it. Hence this problem will give you both a means of assessing a student’s knowledge of the recent maths that they have done and a way of delving deeper into the subject.
It is likely that students who haven’t been given an exercise like this before will do no better than produce a sum such as 32 + 43 = 75, where 75 is the answer required. There are two directions that you can work from here. The first is to see what other sum they can make that has the answer 75. This gives them the opportunity to explore the number 75, it helps to cement their basic number facts, and it gives them a chance to use all of the four arithmetic operations. The second direction is to get them to embed the sum in a story. So you could ask them to put the problem into an actual situation with, say, cakes or money or clothes.
Mathematically weaker students may need to be prompted to help them produce a sum. You may need to recall for them what sums they have done so far. Try to lead them on to word problems. They will probably only be able to mimic these problems. But even that is a start towards deeper learning and understanding.
More able students might be extended to problems that need more than one step or might be challenged to produce a problem with an answer such as ‘Mary’.
This open problem allows the students to use their imagination. It should give them the chance to invent some interesting word problems and to put the mathematics that they have learned so far together in creative ways.
If you plan to assess a particular area of mathematics using this problem, then it should probably not be used until the students have become confident in handling that area.
Finally you might like to note that this problem is one of a series of problems that extend from Level 1 to Level 6. It might be useful for you to see how the problems develop. The lessons are You Be The Teacher, Level 1, Invent-A-Problem, Level 3, Create a Question, Level 4, Cart Before The Horse, Level 5 and Working Backwards, Level 5.
The Problem
The teacher has some sealed envelopes. Make up a problem. Your answer should be the number you find in the envelope.
Teaching sequence
There are several ways to approach this problem. If you think that this problem can be tackled easily by many of your class, then adopt Method A. This way you give little in the way of hints to the class as a whole. However, you may need to help some of them individually.
Method B is for a class that needs more help and it begins with a short session on the mat to remind the class of some of the things that they have done so far.
Method A:
Start with all the students together on the mat.
Tell them that today they are going to be the teacher and make up some maths problems. There is only one restriction. That is, the answer has to be the one you are going to give them in a sealed envelope. The problems that they make up can be anything they like.
- Let the students work on the problem together or on their own. Help the ones who are having trouble. Those students who finish quickly could be asked to make up another problem using another envelope.
- When a student has finished a problem put it into a sealed envelope. When you have collected enough problems the envelopes could be given to other students to solve either straight away or later on.
Method B:
Start with all the students together on the mat.
- Tell them that you would like them to make up some problems of their own today. So, in a way, they will be the teacher. Ask them what problems they can remember working on.
- Ask the students to give you a number. Then try to get them to make up a problem using that number as the answer. (It may be necessary to make up a sum first that has the required number as the answer.)
- Now say that you have some answers in sealed envelopes. You want them to make up a problem that has that number as the answer.
- Let them work singly or in groups to come up with some problems of their own. If they can only produce a sum rather than a problem then you could get them to find other sums that make up that number or you could help them to produce a word problem.
- You may need to write down their questions for them. These problems could also go into an envelope for later use.
- Those students who finish quickly might like to try to write another problem or solve someone else’s problem.
- On the mat, pose some of the students’ problems that they have put into sealed envelopes, for the class to solve.
- You might like to keep some of these problems to use with the class over the next few weeks.
Solution
The solutions here will depend on your class.
| Attachment | Size |
|---|---|
| MakeUpYourOwn.pdf | 38.6 KB |
| MakeUpYourOwnMaori.doc | 40 KB |
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