This problem solving activity has a number (all operations) focus.
There is a special number in each of these envelopes.
When you get your envelope, open it and find out what your number is.
This number is the answer to a maths problem that YOU make up.
What is your problem?
- Use their mathematical knowledge to create their own addition and subtraction problems.
- Solve other students’ problems.
- Devise and use problem solving strategies to explore situations mathematically.
Students are challenged to create their own number problems. This can require a deeper understanding than solving a given problem.
Some students may simply suggest an equation such as 2 + 3 = ? Some may be able to confidently embed an equation in a story context, and other students might readily suggest contextual problems that involve more than one step.
This open problem has students use their imaginations to create word problems of their own and to apply the mathematics that they are learning. You can adjust the difficulty of the problem by changing the numbers you place inside the envelopes.
A series of similar problems span Level 1 to Level 5. These problems are Make Up Your Own, Number, Level 2; Invent-A-Problem, Number, Level 3; Create a Question, Number, Level 4; and Working Backwards, Number, Level 5.
You may find that this serves as a useful assessment task.
- Copymaster of the instructions (English)
- Copymaster of the instructions (Māori)
- Envelopes
- Numbers to go in the envelopes. Choose these as appropriate for your class, or get students to create them.
The Problem
There is a special number in each of these envelopes.
When you get your envelope, open it and find out what your number is.
This number is the answer to a maths problem that YOU make up.
What is your problem?
Teaching Sequence
- Write a number for all to see. For example 8. Explain that this is the answer to a problem.
- Ask the students what two numbers can add together to make the number. Record the students ideas. (1 + 7, 2 + 6 etc.)
- Tell a story about a pair of numbers. (2 children are on the mat and 6 more come along. How many altogether are on the mat now?)
- Highlight/List key words and symbols for students to use as they write their own problems (e.g. add, plus, together, =).
- Challenge children to work in pairs and suggest a number story (problem) of their own for the given number (8). Suggest what the problem could be about (children in the class, subjects of current interest).
- Share and record stories of interest. Have students check for that the solution for each problem is the given number (e.g. 8).
- Model and then challenge student pairs to make a problem that uses more than two addends (2 children + 1 child + 5 children = ? on the mat).
- Revisit the given problem and have students explain it in their own words.
- Have students work in pairs creating several word problems for their 'special number.'
- Support students with questions as they work on the problem.
- Students should return their special number to the envelope, keeping it secret, before sharing their problems for their classmates to solve.
Extension
Create subtraction problems for which the 'special' number is the difference.
Solution
The solutions depend on your class.