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Developing Mathematical Thinking in Addition and Subtraction

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Pupils discussing mathematics

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Homework Homework provides rich opportunities for children and young people to demonstrate, extend and explore learning through a variety of exciting and enjoyable activities. Homework is one piece of the teaching- learning picture and in best practice is connected to what happens in the classroom. Quality homework tasks allow learners to practise or process information, introduce them to material that will be discussed in the future, or provide feedback to teachers so they may check for understanding. HMIE, Learning Together in Mathematics, 2010

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Talking the talk Talking is central to teaching mathematics formatively and providing opportunities for students to express, discuss and argue is essential. Through exploring and unpacking maths, students can begin to see what they know and how well they know it. Jeremy Hodgen and Dylan Wiliam, Mathematics inside the black box, 2006

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6 + 4 = 10 10 take away 9 makes 1 1……. Score the numbers out you use. Circle the numbers you end on. Then score these out as you start with them for the next calculation Competitive aim – stop your partner from going Collaborative aim – cross off as many as possible 6 + 4 = 10 10 take away 9 makes 1 1……. Score the numbers out you use. Circle the numbers you end on. Then score these out as you start with them for the next calculation Competitive aim – stop your partner from going Collaborative aim – cross off as many as possible How could this be adapted to be less / more challenging? What mathematical skills, knowledge are being developed here? Challenging Able Young Mathematicians Pack (CAYM) Section 2a, Page 4 (MNU 1-02a) CAYM available on GlowCAYM available on Glow

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Embedding problem solving What number will be in the units column in this calculation ? 1 + 2 + 3 + 4 +... + 95 + 96 +97 What number will be in the units column in this calculation ? 1 + 2 + 3 + 4 +... + 95 + 96 +97 How have you gone about tackling this? Explain your approach. Explain your colleagues approach. Have you all the same solution? Used by Mike Askew, Kings College, during CPD sessions in Scotland

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Mathematical Conversations Mathematical, dialogic language. Teacher guided but learners firmly engaged Pose - a question to a group Pause - wait time – discussion as pairs. Share with another pair Pounce - ask a group Bounce - ask another group to explain the previous explanation

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Embedding problem solving How many cans if 10 in base? How many cans if 100 in base? Rule? How many cans if 10 in base? How many cans if 100 in base? Rule? What are possible contexts? Any similarity with the previous question? Find the rule – what approach?

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Embedding problem solving How many lines between 6 points? How many lines between 1000 points? Rule? How many lines between 6 points? How many lines between 1000 points? Rule? Mystic Rose Number of points Number of Lines 2 1 3 3 (2+1) 4 6 (3+2+1) 510 (4+3+2+1) 6? n? Any similarity with the previous questions? Is there a link between the number of points and number of lines

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Embedding problem solving How many games are there if there are 6 teams in a league ? How many lines between 20 teams? Rule? How many games are there if there are 6 teams in a league ? How many lines between 20 teams? Rule? Number of teams Games PlayedNumber of games 2a v b 1 3a v b b v c a v c 3 (2+1) 4a v b b v c c v d a v c b v d a v d 6 (3+2+1) 510 (4+3+2+1) 20? nn x (n-1) 2 Any similarity with the previous questions? What if the teams play home and away?

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Triangular Numbers Any similarity with the previous questions? What other number patterns can you investigate?

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Supporting mathematical thinking To what extent are your pupils encouraged to... pursue their own ideas and strategies? explore their own ways of expressing and recording their findings in a variety of ways? explain and illustrate their approach and their thinking? pose further questions and look for further challenges linked to the original problem?

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Next steps What information willyou share with colleagues? What might you or your staff do differently in the classroom? What else can you do as to improve learning and teaching about number What impact will this have on your practice?

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