Transcript Embedding problem solving

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
How could this be
adapted to be less /
more challenging?
Competitive aim – stop your partner from
going
Collaborative aim – cross off as many as
possible
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
Used by Mike Askew, Kings College, during CPD sessions in
Scotland
How have you
gone about
tackling this?
Explain your
colleagues
approach.
Have you all
the same
solution?
Explain
your
approach.
Embedding problem solving
What are
possible
contexts?
How many cans if 10 in base?
How many cans if 100 in base?
Rule?
Any similarity with the
previous question?
Find the rule – what
approach?
Embedding problem solving
Mystic Rose
How many lines between 6 points?
How many lines between 1000 points?
Rule?
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 Games Played
teams
Number of
games
2
avb
1
3
avb bvc
avc
3 (2+1)
4
avb bvc cvd
avc bvd
avd
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 Numbers
Any similarity
with the previous
questions?
What other number patterns can you investigate?
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?
Next steps
What might you
or your staff do
differently in the
classroom?
What impact will this
have on your practice?
What else can you do as to
improve learning and teaching
about number
What
information
willyou
share with
colleagues?