Maths investigations

1. NETW10RK Maths investigations

2. NETW10RK Aims To support the teaching of mathematical investigations. To provide resources to support mathematical investigations.

3. Mathematical reasoning 'Pupils rarely investigate open-ended problems which might offer them opportunities to choose which approach to adopt or to reason and generalise. Most lessons do not emphasise mathematical talk enough; as a result, pupils struggle to express and develop their thinking.' Understanding the score, Ofsted (2008) ‘Learners should be taught to apply their mathematics to both routine and non-routine problems, including breaking down more complex problems into a series of simpler steps.’ New Draft Curriculum 2013

4. Purposes of problem solving and investigating. Problem-solving activities or investigations: • are effective (natural) strategies for learning; • are active approaches to learning; • give children responsibility for their learning What are the benefits of problem solving and investigating?

5. Building blocks • It is not possible to teach pupils how to solve every possible calculation but we can equip pupils with an awareness of the pattern in number and a range of efficient strategies to draw from. • - If children are not secure with their basic number understanding they cannot apply it to solve problems/investigations. • Once they are secure, children need to be given a range of opportunities to talk about and solve problems. • Lessons should include modelled teaching of investigative methods which children can then apply to problem solving.

6. Success Criteria to solve maths problems/investigations. What skills do the children need ?

7. 7 Steps to Solve a Problem • Read the question. • Underline key words that help you to solve the problem. • Decide which operation to use. • Write down the calculation you are going to do. • Work out the approximate answer. • Decide if you will use a calculator. • Do the calculation and interpret the answer. • Refer to question. Does the answer make sense?

8. Teaching strategies. http://www.schoolsworld.tv/node/3371 With the curricular targets in mind, consider a lesson from a recent unit of work. Identify an opportunity for problem solving. Discuss in small groups how to introduce the problem and the type of questions that could be asked to support learning. Discuss how the plenary could be used and what type of questions could be asked to find out what the children understood about solving problems. http://www.ofsted.gov.uk/resources/good-practice-film-heversham-st-peters-cofe-primary-school-cumbria-mathematics

9. You need to ‘teach’ children how to go about solving problems using stepped prompts to guide their thinking. • Children may attempt problem solving on their own but most often they will benefit from working in pairs or small groups. • You may wish to encourage the children to: • Accept a challenge which at first might seem difficult to them. • Have the confidence to make reasoned ‘guesses’ and try to find a solution. • Realise that you can fail to find a solution without being a failure. • Recognise there is almost always more than one way to solve a maths problem* • Interact efficiently with classmates without teacher intervention. • *Children will become better problem • solvers if they can think of 'another way' to solve a problem. • This will help them to check their answers and become more confident • in them, whilst encouraging them beyond the old 'safe and secure'.

10. Setting tasks for children • These need to be realistic and appropriate – here are a few examples: • Order a meal from a Chinese takeaway menu. How much change will you get from £ 40 etc. • Complete the number pattern 2,4,_,_,_, in three different ways. • Write down a price list for a shop and write out various problems for your classmates. • Decide what the largest number you can write is… • Solve tasks that ask for the process – not the solution • Give solutions – identify the question (work backwards) • Work as a group – give each member a different piece of information • Identify operations required through key words • Consider … will the answer be bigger or smaller? Bigger may indicate + or x , smaller – or ÷ • Introduce problem of the day… investigation of the week. • Familiarity and practice = confidence and progress. • Build it in ….don't just bolt it on

11. Resources Story books to use as a starting point The Greedy Triangle by Marilyn Burns Published by Scholastic Paperbacks (ISBN 0590489917) The story of a bored and unhappy young triangle. He visits his local ‘Shape Shifter’, who gives him another side and another angle, magically transforming him into a quadrilateral. The Shape Shifter continues giving him more angles and sides, so begins a visual journey through polygons. 365 Penguins by Jean-Luc Fromental and Joelle Jolivet When a box containing a penguin arrives anonymously on New Year’s Day, a family of four is puzzled, but as they continue to receive one penguin each day their problems — and food budget, and storage issues — are multiplied. Christchurch libraries book list. Can you think of any more?

12. Maths and counting books

13. www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=255682&ResourceID=3548149www.school-portal.co.uk/GroupDownloadFile.asp?GroupId=255682&ResourceID=3548149

14. Provides PowerPoints of questions for maths investigations. http://www.thegrid.org.uk/learning/maths/ks1-2/framework/investigations/#y1

15. Sparky teaching http://www.sparkyteaching.com/resources/thinkingskills/reallifemaths.php

16. No.20 A half-time pie and a cuppa Where is the most expensive ground to feed yourself at half-time? And the cheapest? What’s the average price? Does your local team charge more or less than the average? Does the cost of a half-time pie and a cuppa seem to depend on how good the team is? Find each club on a map. Are the cheapest pies in certain parts of the country?

17. Websites http://www.transum.org/Software/SW/Starter_of_the_day/index.htm NRich http://nrich.maths.org/public/leg.php?code=-333&cl=2&cldcmpid=636 http://www.problempictures.co.uk/examples/op06.htm

18. http://primarytopics.co.uk/maths/uanda/uanda.htm Video questions http://www.youtube.com/watch?v=BnDgLVL3N90

19. Plenaries. In the plenary, the teacher may use a problem-solving or investigative activity to: • assess the children’s understanding of the objectives being taught; • prepare children for the next lesson or series of lessons; • provide opportunities for the children to communicate their different approaches to the specific problem-solving activities and to address any misconceptions. ‘How many ways can four different books be placed on a bookshelf?’ Try using five books, ten books and any number of books.