Developing Understanding of Multiplicative Reasoning Lesson Study Project 2017

3 5 − 1 3

a capacity to work flexibly and efficiently with an extended range of numbers (for example, larger whole numbers, decimals, common fractions, ratio and percent) an ability to recognise and solve a range of problems involving multiplication or division including direct and indirect proportion the means to communicate this effectively in a variety of ways (for example, words, diagrams, symbolic expressions and written algorithms).

Fractions as a division of a whole into equal parts

A fraction as a quotient 2 5 2 ÷5

A fraction as a number.

A Fraction as an Operator multiplying by 1 2 v. dividing by 2! Which would win in your school?

4 5 28 35 7 = 7 7 7 7

2 5 2 ÷ 5 =

1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5 1 5

‘Knowledge of fractions at age 10 will predict algebra knowldege and overall mathematics achievement in high school at age 16’ Early Predictors of High School Mathematics Achievement R Siegler et al. 2012

For our foundation Students 3x + 2 = 17 3x + 2 = 18 OR

For our higher students

Which group gets the most food each, per teacher?

Lesson study principals Teachers learn best from and improve their practice by seeing other teachers teach. Knowledge and experience is shared with colleagues It takes place in the moment of teaching and learning. Its focus is teaching not teachers, children working not children’s work.

Lesson study principals Provides teachers with opportunities to observe in a spirit of mutual development It is a collective effort and non-judgmental . It is about ‘guiding pupils to understand’ It is built round a ‘research question’

Draw a picture to show how you would share out the sandwiches in group A Write down how much each teacher in group A will get Find a different way to share out the sandwiches in group A. (Again draw a picture and write down how much each teacher will get)

To improve students understanding of multiplicative relationships Overarching aim: To improve students understanding of multiplicative relationships Lesson focus: • How do students make use of visual images to reason and justify their arguments? • What issues did your students reveal relating to ‘what is the whole’? • How flexible are students in finding alternative ways of sharing the sandwiches? • How much did students refer to the sandwich context to reason and justify their arguments? • Where students use formal procedures, can they explain why they work?

KS2 project - Lesson study Lesson Planning KS2 project - Lesson study Project school - Twynham School Stage 1 Pre teaching planning activity Date: Class year Unit: Lesson: Range of ability Lesson study group   Learning objectives of lesson: Lesson study focus: Key points identified from the lesson plan to pay careful attention to in relation to the focus Anticipated responses pupils are likely to make Possible teacher responses Further notes:

Draw a picture to show how you would share out the sandwiches in group A Write down how much each teacher in group A will get Find a different way to share out the sandwiches in group A. (Again draw a picture and write down how much each teacher will get)

‘Three fifths is more like a fraction’

Draw pictures to show ways of sharing out the sandwiches between the teachers in the other groups. In each case write down how much each person gets.

. The project has opened our eyes to using more open ended problems to understand what the children need to learn rather than my preconceived ideas about what I need to teach them. In the future we would incorporate more opportunity to use concrete resources and real life scenarios in our mathematics teaching to help deepen understanding of concepts. St. Katharine’s Primary School, Bournemouth As primary school teachers, the experience has influenced our teaching and understanding of children’s misconceptions and will encourage us to use a more investigative approach in future. When faced with the challenges (which we would not have previously attempted in these particular sets), the children rose to the occasion and were freer to use and question their own mathematical knowledge. Stourfield Junior School, Bournemouth