# Mathematics NISPLAN Day 2 Afternoon Session. "The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas.

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Mathematics NISPLAN Day 2 Afternoon Session

"The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver." I. N. Herstein

“It’s not how many answers students know. It’s how they behave when they don’t know that counts.” Alistair Smith (2003) Leading Learning

Challenge How would you do the following questions?

Re -ordering Counting on / back Partitioning Rounding & adjusting Inverse operations Factors Equivalence

Mathematical concepts are made up of three components:

Mathematical Language What words do you use? Sometimes words sound the same but have different meanings

Working in pairs try to list as many definitions of ‘right’ you can think of. Right angle Turn right or right-hand side Right meaning correct Right meaning good or OK Right in terms of health Right wing or right-handed Right meaning deserved ‘Write’ down using a pen or pencil

What can you do to help a pupil’s understanding?

It is important that pupils are given the opportunity to explore and share different strategies for calculating, and through discussion, to conclude that some are more efficient than others. Such sharing of thinking is essential to consolidate understanding. For all pupils, reflecting on and explaining how a calculation has been worked out is a powerful way of learning. The teacher’s role is to encourage thinking, discussion and explanation in order to foster in pupils a willingness to listen to the strategies used by their peers, and consequently to evaluate their own strategies. Pupils, their parents and teachers should be aware that there can be a number of valid ways to arrive at an answer.

To help learners to adopt more active approaches towards learning Engage learners in discussing and explaining ideas, Challenging and teaching one another, Creating and solving each other's questions Working collaboratively to share methods and results.

One day the teacher was reading the story of Chicken Little to her class. She came to the part where the chicken warns the farmer. “ … and Chicken Little went up to the farmer and said, “The sky is falling!” The teacher then asked the class. “And what do you think the farmer said?” One little girl raised her hand and said, I think he said: “Holy Sh*t a talking chicken!” The teacher was unable to teach for the next 10 minutes

Multiplication http://www.teachertube.com/viewVideo.php?video_id=46231

The wall of maths mastery Mahesh Sharma Application Abstract Pictorial Intuitive Concrete Communication LinguisticConceptual Procedural

Application Abstract Pictorial No layers above so what supports further building? No solid foundation below so what’s going to happen? Text Book The wall of maths mastery

Developing Cognitive Strategies Ask a considerable number of questions Use a great deal of concrete experiences

Concrete Multiplication

Pictorial Multiplication 25 x 36 20 6 5 30 600 150 120 30 900 600 120 150 30

Algebra … Abstract?? Have you tried Algebra Tiles to keep the area model going?

Using your Algebra Tiles Show 3(x + 1) = 3x + 3

Using your Algebra Tiles Show (x + 2)(x + 3) equals x² + 5x + 6

Procedural As the number of minutes to be subtracted is bigger. (You have to subtract 45 mins which is bigger than 30 mins) Convert both times into minutes 11 hours 30 minutes is 11 x 60 + 30 = 690 minutes 4 hours 45 minutes is 4 x 60 + 45 = 285 minutes Subtracting them gives 690 - 285 = 405 minutes To change this into hours divide by 60 405 ÷ 60 = 6 with 45 left over The answer is 6 hours and 45 minutes. What is eleven hours and thirty minutes take away four hours and forty-five minutes? 26

Procedural What is eleven hours and thirty minutes take away four hours and forty-five minutes? 11.307.307.006.45 - 4 hrs - 30 mins- 15 mins 27

http://nlvm.usu.edu/en/nav/vlibrary.html

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