Children should be given every opportunity to solve problems to apply the skills, concepts and procedures they are learning, and also to allow them to reason and think mathematically. Make use of the old Numeracy Strategy problem-solving documents and resources such as Challenging More Able Children which most schools will have. The Association of Teachers of Mathematics (ATM) also has some excellent problem-solving booklets, such as Primary Points of Departure, and, of course, Nrich is full of great starting points for problems. Spending some time adapting these problems to fit your planning is the important thing and I go through the following simple steps when deciding on problems to use.
1. Start with your maths focus
Read through the objectives, the expected outcomes and the small steps of progression to work out the appropriate level for groups in your class. (These are the sections on my planning templates, but if you're not using them, the same information is needed and should be on your long-term or medium-term plans).
2. Gather problem-solving activities and investigations
It is well worth spending a little time trawling through your books, resources and favourite websites for ideas that may be useful for the 2-week unit.
3. Choose your theme
Your theme might come from another curriculum subject, the maths activities you have collected or it could be based on a stand-alone context. This won't be used for every maths lesson, but it will draw together some of the lessons, putting the maths in context to help make sense of it for your children.
4. Adapt the problems to fit the theme.
There may be one or two large problems to solve over a period of time or smaller problems to solve on different days.
For these examples I've used Unit 2 Addition and Subtraction from my scope and sequence (those of you using my planning package may be teaching this now). I found two small problems which I have adapted for two different themes.
Our playing field
This theme might pull together a popular science topic about living things and a geography topic looking at the local area.
(KS1) A square playing field has an oak tree in each corner and 5 ash trees on each side. How many trees are there altogether?
(KS2) In a survey of wildlife on the field some spiders and ants are collected. There were more ants than spiders and 16 heads and 104 legs were counted. How many of each were there? The next day some spiders and ants had escaped, now only 84 legs in total were counted. How many of each could there be?
Celebrations
This theme might link to different religious festivals, PE (dance) or an art project.
(KS1) A dance starts with everyone standing on the sides of a square. There is an adult in each corner and 5 children standing on each side. How many dancers are there altogether?
(KS2) Balloons and hats are needed for a party for 30 children. Sam has a total of 104 hats and balloons. The balloons are in packs of 6 and hats are in packs of 8. There are more balloons than hats. Are there enough hats for each person? How many spare hats are there?
This is just a small example of making starting points for problems fit the context. The maths focus is the key though - look at the best way for children to make sense of the specific learning objectives and the skills and concepts they need to work on, and then use problems to give the children the opportunity to reason and think mathematically.
