Developing Thinking Skills Primary Maths CPD Course Spring 07.
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Transcript of Developing Thinking Skills Primary Maths CPD Course Spring 07.
Spilt InkSpilt Ink
I’ve knocked a paint pot over my homework and I can’t remember the number underneath the stain.
What number was it?
6 + 3 = 14
Developing ThinkingDeveloping Thinking
Find me a formula that has the value 7 when a = 2 and
b = 3a b = 7
What’s the Question?What’s the Question?
How much more than 3 is
10?
How old will my brother
be next week?
How many days are
there in 1 week?
Nine take away two
What is one quarter of
28?
What is 3 plus
4?
How many years until
you’re 13?
I have 1 square & 1 triangle.
How many sides are there
altogether?
The answer
is 7
A Question of BalanceA Question of Balance
6 + 2 = 4 + 3 + 13 + 2 = 6 − 1
6 ÷ 3 = 4 ÷ 2 6 = 3 × 4 ÷ 2
6 , 3 , 5 , 4 , 1 , 2
A visualisation activityA visualisation activityImagine a square-based pyramid, made out of plasticine, in the air in front of you …
What is 3 add 7? How many days are there in a week? How many centimetres are there in a metre? Is 31 a prime number?
Recalling factsRecalling facts
Tell me two numbers that have a difference of 12. What unit would you choose to measure the width of the table? What are the factors of 42? 8 x 6 = 48, so what is 8 x 60? … 16 x 6?
Applying factsApplying facts
Estimate the number of words on this page. If we did our survey again on Friday, how likely is it that our graph would be the same? Roughly, what is 51 times 38? How many crosses in the next diagram?
+ ++ +++ … and the next? … in the tenth? … hundredth?
Hypothesising or Hypothesising or predictingpredicting
How might we count this pile of sticks? How could you subtract 37 from 82? How could we test a number to see if it is divisible by 6? How could we find the 20th triangular
number? Are there other ways of doing it?
Designing and comparing Designing and comparing proceduresprocedures
So what does that tell us about numbers that end in 5 or 0? What does the graph tell us about the most common shoe size? So what can we say about the sum of the angles in a triangle?
Interpreting resultsInterpreting results
The seven coins in my purse total 23p. What could they be? In how many different ways can four children sit at a round table? Why is the sum of two odd numbers always even?
Applying reasoningApplying reasoning
Effective questionsEffective questions• Why is … an example of …?• How can we be sure that …?• What is the same & what is different about …?• Is it ever/always true/false that …?• Why do …, …, … all give the same answer?• How do you …?• How would you explain …?• What does that tell us about …?• What is wrong with …?• Why is … true?
The Effect of Changing a The Effect of Changing a QuestionQuestion
Instead of asking :
“Is 7 a prime number?”
what would be the effect of asking:
“Why is 7 an example of a prime number?”
Less effective questionsLess effective questions• What is 127 + 99, 25 + 201 and 198 + 28?• Where are the lines of symmetry on this shape?• What do the angles of a triangle add up to?• Sort these shapes into two groups• Are these triangles congruent?• What is 2/3 of 24?• What is 17 x 0.3?• Is 46 a multiple of 3?• What is the probability of drawing a red card
from a pack?• What is an odd number plus an odd number?
More effective questionsMore effective questions• How do we know that 127 + 99, 25 + 201 and
198 + 28 will all give the same answer?• Why is this picture an example of a shape that
has symmetry?• Explain the way you have sorted these shapes.• How do we know these triangles are congruent?• How do you find 2/3 of a number?• Is it always true that multiplying makes
numbers bigger?• Why is selecting a red card from a normal pack
an example of an event that has an even chance?
What is it about …What is it about …
… a cuboid that also makes it a prism?
… three quarters that tells you it’s bigger than a half?
… those numbers that tells you that they’re in the five times table?
… 3.689 that tells you that it lies between 3.6 & 3.7?
… this triangle that tells you it’s isosceles?
Shape & SpaceShape & SpaceSit back to back with your partner.
Look at the picture.
Don’t let your partner see the picture
Tell your partner how to draw the picture
Topic WebTopic Web
Angle
Turning
Types
Anticlockwise
Clockwise
Acute
Roamer
Obtuse
Measure Protractor
Degrees180
http://www.nrich.maths.org/public/viewer.php?obj_id=2005&refpage=monthindex.
php&part=index&nomenu=0
nrich examplenrich exampleOn a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Same? Different?Same? Different?
What is the same & what is different about …
… find the area of a rectangle with length 4cm & width 6cm.
… find the area of a
rectangle with length
4cm & perimeter
20cm.
GeneraliseGeneralise
If you are the 55th person in the queue then there are 44 people in front of you.
77:37 p.m. = 1919:37
73636 – 23636 = 50000
36 x 42 = 42 x 36
On your whiteboard …On your whiteboard …
Write down a number that’s bigger than 16 but less than 25.
Draw me a number line showing 43 + 21.Write down a fraction that’s bigger than ½
but less than ¾ .Draw me a picture to show 5/8 of a shape
Coloured red.
What’s my rule?What’s my rule?This pair of numbers is connected by a simple rule.
Suggest another pair of numbers that satisfies the same rule.
If you think you know the rule, don’t say what it is. Just provide further examples to confirm your conjecture.
2 , 8
‘‘Guardians of the Rules’Guardians of the Rules’
1116
9
14
8
4
19
10
1
7
3
28
34
61
Multiple of 3
Even
Neither
100
12
15
66
1818
1717
33
1212
1616
A 2-digit
number A multiple of
5 An even
number
Between 10
and 16 An odd
number Less than 10
More than 19 Even and
more than 16 Between 6
and 12
Problem solving target boardsProblem solving target boards
2020
1010
1515
Sorting quadrilateralsSorting quadrilateralsParallelogram, Rhombus, Rectangle, Square, Kite,
Arrowhead, Trapezium
Always? … Sometimes? … Always? … Sometimes? … Never?Never?
If I double the length of If I double the length of the side of a square, the the side of a square, the area is also doubled.area is also doubled.
To multiply a number by To multiply a number by 10, you just add a nought at 10, you just add a nought at the end of it.the end of it.
When you cut a piece When you cut a piece off a shape you reduce off a shape you reduce its perimeter.its perimeter.
You can multiply a number You can multiply a number by 4 by doubling it twice.by 4 by doubling it twice.
The more digits a The more digits a number has, the larger number has, the larger its value.its value.
The sum of two consecutive The sum of two consecutive numbers is odd.numbers is odd.
Do You Agree?Do You Agree?In January, fares went up by 20%.In January, fares went up by 20%.In August, they went down by 20%.In August, they went down by 20%.
Sue claims that:Sue claims that:““The fares are now back to what they The fares are now back to what they were before the January increase.”were before the January increase.”
Do you agree?Do you agree?
Concept CartoonsConcept CartoonsWhat shape is the window?
I’d say it’s a parallelogra
m
It’s a square because it’s got 4 right
angles
I think it’s called a polygon
Don’t you mean a
quadrilateral – a polygon’s got 5 sides
I think it’s a rhombus
Four DiceFour Dice
Four dice made into a tower – can you make the total on all four sides of the tower the same total?
31 14 20 16
24 6 5 25
30 29 18 36
11 7 13 1
14 20 21 34 39 45 50
Choose two numbers from the row of numbers above the grid.
Find the difference between these numbers.
If the answer is on the grid, cover that number with a counter.
Three in a rowThree in a row
MillionaireMillionaire
£100 question …
£1000 question …
£32000 question …
£1000000 question …
http://www.csfsoftware.co.uk/MILL_info.htm
http://www.crick.northants.sch.uk/assets/Flash%20Studio/cfsmaths/NumBal/nbKS2.swf
http://www.bbc.co.uk/bbcfour/tvsites/mindgames/
http://www.eyelid.co.uk/numbers.htm
Queen Hatshepsut has ordered her Queen Hatshepsut has ordered her
Nubian general, Nehsi, to sail to the Land Nubian general, Nehsi, to sail to the Land
of Punt and obtain planks of Punt and obtain planks
of the finest cut cedar wood for the gates of the finest cut cedar wood for the gates
and doors of her new temple. and doors of her new temple.
Each ship can carry planks of Each ship can carry planks of
wood so how many ships will Nehsi have wood so how many ships will Nehsi have
to take with him to transport all the wood to take with him to transport all the wood
back to Egypt?back to Egypt?
http://www.thelighthouseforeducation.co.uk/interactive/towersofhanoi.htm
Towers of HanoiTowers of Hanoi
http://www.puzzlemania.org.uk/Default.htm
http://www.subtangent.com/maths/ig-leapfrog.php
http://www.subtangent.com/maths/jugs.php
http://www.vtaide.com/png/puzzles.htm
““Starter of the Day”Starter of the Day”
http://www.transum.org/Software/SW/Starter_of_the_day/index.htm
Time TunnelTime TunnelAlf, Betty, Colin and Dewi have to walk through a long dark tunnel. They only have one torch between them so a maximum of two people can go through the tunnel at any one time.
Each person takes a different amount of
time to get through the tunnel and if two
people walk together they must walk at the
rate of the slowest.
Time TunnelTime TunnelAlf takes 2 minutes to walk through,Betty takes 5 minutes,Colin takes 9 minutes,Dewi takes 11 minutes.
What is the least amount of time for all four to walk through the tunnel?
All four begin at the same end of
the tunnel.The torch must be walked
back through the tunnel by at least
one person, it cannot be thrown.
The answer is less than 29 minutes!
http://www.transum.org/http://www.transum.org/software/Trantunnels/software/Trantunnels/
default.asp default.asp
http://www.bbc.co.uk/http://www.bbc.co.uk/schools/starship/maths/schools/starship/maths/
index.shtml index.shtml
http://www.standards.dfes.gov.uk/thinkingskills/?http://www.standards.dfes.gov.uk/thinkingskills/?view=getview=get