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Transcript of Number Sense
Teaching for flexibility with number
"A maths classroom is the only place in the world where it is normal to buy 27 watermelons."
- What is 'number sense'?
- 'Number talks'
- Investigative learning of number
Mental Maths tests
Discuss on your tables: how can we use them in a way that promotes 'number sense'?
'Chocolate made out of nothing'
In your head:
18 x 5
- tell your table how you did it
- one person scribe all the ways and show using visuals or objects
"To learn maths is to do maths"
What number am I?
Ask people on your table questions that will allow you to deduce what number you have
No peeking at your number(!)
Olly the Octopus
Who am I?
odd or even?
You can verbally share the clues, but don't show them to each other
Record your thinking
Make up a version for your class
Try: Make an Olly for your Maths class
Teaching point: What do these activities all have in common?
"an ability and willingness to break number apart or decompose the numbers - and regroup them. This is an important foundational base from which all other mathematics builds."
What maths did we use to solve it?
Multiplication / division facts
Find the 9x table
on your reversed 100 square.
- What patterns can you see?
- How do the patterns help you predict further multiples?
- Can you make sense of any divisibility rules?
(How could this help for any other multiplication tables?)
Multiplication / division facts
- Mental maths questions give us a good chance to recap on different aspects of maths, but...
- Informal testing by itself does not raise attainment- learning experiences do.
- Better to spend time looking at the different ways of arriving at the answer and
Value All Responses.
- Have lots of
after the test to teach each other before going through an answer
- Have students explain at the board
- Emphasise conceptual understanding. Fluency comes from understanding.
- Stress inhibits learning. Are our tests done in a way that promotes or calms anxiety?
- Celebrate mistakes: e.g. an 'excellent mistakes' board.
- Have a Maths 'Help Wall'
understanding and fluency
each other's ideas
In your year groups, think of a topic in number that you will teach after xmas. How will you teach it in a way that will promote
- Keeping maths on the boil through more open-ended tasks (e.g. olly, who am I?, Guess the number)
- Number sense is about flexibility and creativity with number
- Procedures are fairly meaningless without conceptual understanding
- investigations are enjoyable and deep, so can be accessed on many levels ("low threshold/high ceiling")
- multiplication facts can be taught in a deeper way that reveals patterns and relationships
"The depressing thing about arithmetic badly taught is that it destroys a child's intellect, and to some extent, his integrity. Before they are taught arithmetic, children will not give their assent to utter nonsense; afterwards, they will."
Walter W. Sawyer
TES Maths Podcast
"Practical experience also shows that direct teaching of
is impossible and fruitless. A teacher who tries this usually accomplishes nothing but empty verbal- ism, a parrotlike repetition of words by the child, simulating a knowledge of the corresponding concepts but actually covering up a vacuum."
Maths is a creative and flexible subject
Countdown: the numbers game
- conceptual understanding
- multiplication as the inverse of division
- division as repeated subtraction
- related number facts
- factors and multiples ...
"A person who never made a mistake never tried anything new."
What were your experiences of learning maths at school?
How have these impacted on your view of maths as a subject?
Have they influenced where you put your statement on the wall?
By 2015, 60% of the new jobs being created will require mathematical skills held only by 20% of the population
PISA 2012/13 Results
Try with other multiplication tables:
- 3x, 6x, 9x (any relationship?)
- 2x, 4x, 6x
Without drawing, what will the 1x and 9x table pattern look like (and why)?
The new curriculum - September 2014
Just as people “see” things differently, there are often many ways to approach any mathematical problem.
Explaining one’s thinking clearly is important. This requires that students to retrace the steps of their answers and learn to use academic language, where possible, to describe what they did to solve the problem.
It is important for students not only to explain what they did, but why their process makes sense. In the case of dot card number talks, this involves where they “saw” the numbers they used. In the case of arithmetic operations, it involves understanding the mathematics that underlies any procedure that they use.
The teacher’s job is to ask questions that clarify
the students see rather than how they “should” see.
(not Just for KS1..)
- Write your name on the strip of paper
- Look at the statement. Put it up on the wall to show 夫とっto what extent you agree or disagree with it.
Do you agree...?