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

Hidden numberHidden number

What number am I hiding beneath my finger?

+ 1 = 132 x

Find the numberFind the number

- 2 = 193 x

What number does stand for?

Developing ThinkingDeveloping Thinking

Find me a formula that has the value 7 when a = 2 and

b = 3a b = 7

34 21

Addition WallAddition Wall

10

Addition WallAddition Wall

Difference PyramidDifference Pyramid(Primary Games Vol. 4)

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

Number Sequences with Number Sequences with holes inholes in

Puzzle? Maths?Puzzle? Maths?

From Answering to Thinking

From Answering to Thinking

From Answering to Thinking

Multiplication Facts

Sum Product Difference

Sum Product Difference

Sum & Product

Two Numbers

A visualisation activityA visualisation activityImagine a square-based pyramid, made out of plasticine, in the air in front of you …

Possible visualisations

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

Graphic Organiser

nrichnrich

http://www.nrich.maths.org.uk/public/index.php

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?

Pair Them UpPair Them Up

http://www.csfsoftware.co.uk/PTU_info.htm

Pick Up SetsPick Up Sets

MatchingMatching

Odd one out?Odd one out?

16

11 5

Odd one out?Odd one out?

Odd one out?Odd one out?

Odd one out?Odd one out?

Same? Different?Same? Different?

What is the same & what is different about …

Same? Different?Same? Different?

What is the same & what is different about …

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 It Worth?What’s It Worth?

Fruit BoxFruit Box(Maths Pack 3)(Maths Pack 3)

http://www.mathplayground.com/

Algebra_Puzzle.html

Speed Grid Challenge

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

‘‘Guardian of the Rule’Guardian of the Rule’15

16

9

14 812

4

19

10

17

3

34

10061

28

11

‘‘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

Two-Way TablesTwo-Way Tables

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.

Hint CardsHint Cards

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

http://www.conceptcartoons.com/http://www.conceptcartoons.com/index_flash.htmlindex_flash.html

Make 999Make 999

+

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

24 Game24 Game

Four 4sFour 4s

+ - x

Estimation GolfEstimation Golf

2nd Hole : Par 5

160 < x2 < 162

1st Hole : Par 4

273 < 19 x b < 275

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

Which Number Where?

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

subtangentsubtangent

http://www.subtangent.com/maths/index.php

http://www.subtangent.com/maths/rushhour.php

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!

Car Supermarket

Targets

15 pennies15 pennies

Strictly Maths DancingStrictly Maths Dancing

Forbidden WordsForbidden Words

http://www.transum.org/http://www.transum.org/software/Trantunnels/software/Trantunnels/

default.asp default.asp

http://http://www.mathsyear2000.org/www.mathsyear2000.org/

games/othello/ games/othello/

http://http://www.mathsyear2000.org/www.mathsyear2000.org/

games/solitaire/ games/solitaire/

http://http://www.pedagonet.com/www.pedagonet.com/brain/brainers.html brain/brainers.html

http://www.mathsnet.net/puzzles.html

http://www.mathplayground.com/

logicgames.html

http://www.mathplayground.com/

Logic_Games_2.html

Whodunnit?Whodunnit?

Maths Puzzles for Able Pupils Maths Puzzles for Able Pupils

Countdown Countdown

Nubble!

http://www.virtualimage.co.uk/html/nubble.htm http://www.virtualimage.co.uk/html/nubble.htm

Su DokuSu Doku

http://www.websudoku.com/

Mathematical versionshttp://www.killersudokuonline.com/

http://www.kakuro.com/

http://www.bbc.co.uk/schools/numbertime/ http://www.bbc.co.uk/schools/numbertime/

http://www.bbc.co.uk/schools/http://www.bbc.co.uk/schools/digger/ digger/

http://www.bbc.co.uk/http://www.bbc.co.uk/schools/starship/maths/schools/starship/maths/

index.shtml index.shtml

www.counton.org.ukwww.counton.org.uk

http://www.ictgames.com/http://www.ictgames.com/resources.htmlresources.html

Group Problem Solving

Problem SolvingProblem Solving

Puzzles and ChallengesPuzzles and Challenges

On the CDROM

““Real Life Graphs”Real Life Graphs”

CryptarithmeticCryptarithmetic

O N E

+ T W O

S I X

http://www.standards.dfes.gov.uk/thinkingskills/?http://www.standards.dfes.gov.uk/thinkingskills/?view=getview=get