Developing Thinking Skills Primary Maths CPD Course Spring 07

Spilt Ink I’ve knocked a paint pot over my homework and I can’t remember the number underneath the stain. What number was it? = 14

Hidden number What number am I hiding beneath my finger? + 1 = 13 2 x

Find the number - 2 = 19 3 x What number does stand for?

Developing Thinking Find me a formula that has the value 7 when a = 2 and b = 3 a b= 7

3421 Addition Wall

10 Addition Wall

Difference Pyramid Difference Pyramid (Primary Games Vol. 4)

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 Balance = = 6 − 1 6 ÷ 3 = 4 ÷ 26 = 3 × 4 ÷ 2 6, 3, 5, 4, 1, 2

Number Sequences with holes in

Puzzle? Maths?

From Answering to Thinking

Multiplication Facts

Sum Product Difference

Sum & Product

Two Numbers

A visualisation activity Imagine 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 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 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 predicting

 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 procedures

 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 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 reasoning

Effective 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 Question 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 questions What is , and ? 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 questions How do we know that , and 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 … … 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? … that tells you that it lies between 3.6 & 3.7? … this triangle that tells you it’s isosceles?

Shape & Space Sit 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 Web Angle Turning Types Anticlockwise Clockwise Acute Roamer Obtuse Measure Protractor Degrees 180

Graphic Organiser

nrich

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nrich example On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Pair Them Up

Pick Up Sets

Matching

Odd one out?

Odd one out?

Same? Different? What is the same & what is different about …

Same? Different? What is the same & what is different about …

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.

Generalise 5 4 If you are the 5 th person in the queue then there are 4 people in front of you :37 p.m. = 19: – 236 = x 42 = 42 x 36

On your whiteboard … Write down a number that’s bigger than 16 but less than 25. Draw me a number line showing 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?

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

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Speed Grid Challenge Speed Grid Challenge

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’

‘Guardians of the Rules’ Multiple of 3 Even Neither

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 boards

Two-Way Tables

Sorting quadrilaterals Parallelogram, Rhombus, Rectangle, Square, Kite, Arrowhead, Trapezium

Always? … Sometimes? … Never? If I double the length of the side of a square, the area is also doubled. To multiply a number by 10, you just add a nought at the end of it. When you cut a piece off a shape you reduce its perimeter. You can multiply a number by 4 by doubling it twice. The more digits a number has, the larger its value. The sum of two consecutive numbers is odd.

Hint Cards

Do You Agree? In January, fares went up by 20%. In August, they went down by 20%. Sue claims that: “The fares are now back to what they were before the January increase.” Do you agree?

Concept Cartoons What 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

Make 999 +

Four Dice Four dice made into a tower – can you make the total on all four sides of the tower the same total?

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 row

24 Game

Four 4s +-x+-x

Estimation Golf 2 nd Hole : Par < x 2 < st Hole : Par < 19 x b < 275

Millionaire £100 question … £1000 question … £32000 question … £ question …

0Studio/cfsmaths/NumBal/nbKS2.swf 0Studio/cfsmaths/NumBal/nbKS2.swf

Which Number Where?

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Queen Hatshepsut has ordered her Nubian general, Nehsi, to sail to the Land of Punt and obtain planks of the finest cut cedar wood for the gates and doors of her new temple. Each ship can carry planks of wood so how many ships will Nehsi have to take with him to transport all the wood back to Egypt?

Towers of Hanoi Towers of Hanoi

subtangent

“Starter of the Day”

Time Tunnel Alf, 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 Tunnel Alf 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 pennies

Strictly Maths Dancing

Forbidden Words Forbidden Words

ware/Trantunnels/default.asp ware/Trantunnels/default.asp

/games/othello/ /games/othello/

/games/solitaire/ /games/solitaire/

brain/brainers.html brain/brainers.html

/logicgames.html

/Logic_Games_2.html

Whodunnit?

Maths Puzzles for Able Pupils

Countdown

Nubble!

Su Doku

Mathematical versions

/starship/maths/index.shtml /starship/maths/index.shtml

Group Problem Solving

Problem Solving

Puzzles and Challenges

On the CDROM

“Real Life Graphs”

Cryptarithmetic O N E + T W O S I X

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