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Developing Mathematical Thinking in Addition and Subtraction. Pupils discussing mathematics. Homework. - PowerPoint PPT Presentation
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Developing Mathematical Thinking in Addition and
Subtraction
Pupils discussing mathematics
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
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
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 Glow
Embedding problem solving
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
Embedding problem solving
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?
Embedding problem solving
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)
5 10 (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
Embedding problem solving
How many games are there if there are 6 teams in a league ?How many lines between 20 teams?Rule?Number of teams
Games Played Number of games
2 a v b 1
3 a v b b v ca v c
3 (2+1)
4 a v b b v c c v d a v c b v d a v d
6 (3+2+1)
5 10 (4+3+2+1)
20 ?
n n x (n-1) 2
Any similarity with the previous
questions?
What if the teams play home and
away?
Triangular NumbersAny similarity
with the previous
questions?
What other number patterns can you investigate?
Supporting mathematical thinkingTo 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?
Next stepsWhat
informationwillyou
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?