BRINGING IT ALL TOGETHER Use of Rich Tasks

What is a Rich Task? Accessible to all levels Provides an opportunity to explore mathematics Involves testing, proving, explaining, reflecting and interpreting Encourages discussion Encourages collaboration Encourages creativity Encourages deeper thinking Encourages independence Involves pupils in making decisions Enjoyable

Symmetry Task Is this a Rich Task Why?

Is the task richer ?

Lower Order Questions or Higher Order Question? A. Draw the lines of symmetry on these pictures B. Divide into groups of 4 each with a loop of string. Make a quadrilateral with one line of symmetry...two lines...three lines A. Complete these multiplications B. Choose four multiplications, one that is easy, one that is difficult and two which are neither easy or difficult. Explain your choices.

Bloom’s Taxonomy

Involvement of Pupils Presentation of problem Grouping Encouragement of participation Encouragement of discussion Asking of questions

Mathematical Processes and Applications Solve problems, explore and investigate in a range of contexts. Representing Analysing (reasoning) Analysing (procedures) Interpreting and Evaluating Communicating and Reflecting

PLTS – Personal, Learning and Thinking Skills ‘The programme of study requires pupils to work on open and closed tasks in a variety of contexts ’ Creative Team workers Self managers Effective participators Reflective Independent

Independent enquirers The programme of study requires pupils to work on open and closed tasks in a variety of contexts that allow them to select the mathematics to use. The key concept of competence requires pupils to process and evaluate information, applying mathematics to familiar and unfamiliar contexts. Pupils plan what to do, selecting the most appropriate methods, tools and models when representing situations or problems.

Creative thinkers The key concept of creativity requires pupils to combine understanding, experiences, imagination and reasoning to construct new knowledge. They are also expected to use existing mathematical knowledge in novel contexts. By adopting a questioning approach they develop their own lines of enquiry and convincing arguments to support their decisions and conclusions. When deciding on how to use mathematics to model a situation or solve a problem pupils need to think creatively, drawing on their knowledge and understanding of mathematics and identifying the mathematical features that are important.

Team workers The mathematics programme of study provides opportunities for pupils to work collaboratively as well as independently to solve mathematical problems in a range of contexts. Knowing about the history of mathematics and the mathematics of different cultures encourages and supports pupils to listen to, and be sensitive to, different views and broadens their perspective on the subject.

Self-managers Pupils are expected to work independently on extended tasks that bring together different aspects of mathematical content, using several of the key processes. They will make decisions autonomously while working towards goals, showing initiative, confidence, commitment and perseverance.

Effective participators Pupils’ use of mathematical ideas and models to explore issues or problems is mediated through the key concept of critical understanding. When interpreting and evaluating, pupils should be able to develop convincing arguments to influence others and take part in discussions. Working on problems that arise in other subjects and outside school helps pupils understand how mathematics is relevant in all areas of life.

Reflective learners Pupils will be expected to evaluate their own and others' work and respond constructively. The key process of analysing requires them to work logically towards results and solutions, and to value feedback and learn from mistakes.

Pilot Project While some exercises and worksheets may provide some evidence of pupil achievement, teachers in the pilot project found that open-ended, less scaffolded tasks and activities allowing pupils to demonstrate more independent understanding were a richer source of evidence.

Gifted and Talented Standards High priority is given to the development and effective deployment of resources to extend, inspire and fully provide for the needs of gifted and talented mathematicians. Learners research an area of mathematics that interests them, pushing beyond the boundaries of the curriculum.

Scheme of Work

'Squares in Rectangles' A 2 by 3 rectangle contains 8 squares. Can you see how? A 3 by 4 rectangle contains 20 squares. Can you see how? A 4 by 6 rectangle contains 50 squares. Can you see how? What size rectangle contains exactly 100 squares? Is there more than one? Can you find them all? Can you prove that there are no more?

Setting the Scene Year 7 class of 33 pupils Set 1 Level 5 on entry First Investigation What is the role of the teacher?

Share your thoughts. Process skills Assessment criteria PLTS Role of Teacher

NRICH

The Way Forward Development of Schemes of Work with more rich tasks More tasks? Variety – first, last Grouping Use of ICT