152_Fluency, Problem solving and Reasoning Maths for NQTs

Fluency, Problem solving and Reasoning Maths for NQTs Mark Hattersley Mark.hattersley@bradford.gov.uk @MarkAHattersley Philipa Varley Philipa.varley@bradford.gov.uk @philipav Aims • To develop an understanding of the new mathematics curriculum •To develop ideas for fluency, problem solving and reasoning Starter- Strike it out • How to play ‘Strike it out’ NRich Player 2+3 = Player Must start where player finished + 10 = 15 Player Must start where player finished 15 – is and so on The loser is the person who can not complete their go Play again collaboratively– can you use as many numbers as possible? Starter- Factors and multiples a collaborative game Rules of the game • Player chooses a number • Player must choose a number that is a factor or multiple of player 1’s number • Player must choose a number that is a factor or multiple of player 2’s number • And so on… How many numbers can you get in your sequence? NRich Minute task • What is important? What is important? What these mean? What does it look like? Estimation/ Range of answers Key stage example 63 + ? = 100 Discuss these “answers” using estimation to decide which could be right and which are wrong 47 46 37 36 Sometimes, always, or never true? •The difference between any two odd numbers is an even number •If you add three consecutive numbers together the answer is always even •The sum of three odd numbers is divisible by KS1 Sometimes, always, or never true? •When I add two numbers together I get an even answer •Adding 10 to a digit number changes both digits •When I add two lots of odd numbers, the answer is always odd Questioning techniques – right or wrong? Using your reasoning mat, discuss these sequences or number sentences 10, 8, 5, 1, -4 – 10 = -7 3, 6, 10, 16, 22, 29 – 10 = -3 KS Questioning techniques – right or wrong? Using your reasoning mat, discuss these sequences or number sentences 2, 4, 6, 8, 10 + = 11 5, 10, 16, 20, 23 – = 11 Doing and Undoing • Doing Find the area of these rectangles 6cm 8cm 2cm 4cm 7cm 8cm Doing and Undoing • The area of a rectangle is 48cm • What could the dimensions be? Doing and undoing KS1 • Doing + = Doing and undoing KS1 Undoing – How many teddies are hiding in each pot? + = Fluency, problem solving and reasoning every day • Look at the two examples of worksheets Which allows for problem solving and reasoning? • Closed, closed, open Where to go for ideas • • • • • • Opening up questions documents Pitch and Expectations (year group) Reasoning mat Levelopaedia Nrich Website NCETM Where to go for ideas • • • • Opening up questions documents Reasoning mat NCETM reasoning documents Levelopaedia Available on Bradford Schools Online New sample questions July 2014 Fluency Reasoning Problem Solving Fluency Reasoning Problem Solving New sample questions July 2014 Aims • To develop an understanding of the new mathematics curriculum •To develop ideas for fluency, problem solving and reasoning ... What does problem solving mean? • Does it mean word problems? Representing Word Problems Enquiring  plan  decide  organise  Interpret  reason  justify Problem solving and reasoning Reasoning...Aims • To develop an understanding of the new mathematics curriculum •To develop ideas for fluency, problem solving and reasoning Starter- Strike it out • How to play ‘Strike... NCETM – new curriculum resources What does reasoning mean? • Close your eyes and think of … I noticed a connection between This is true here because… Reasoning Mat I noticed that What if… This