ILLUSION CONFUSION! - MEASURING LINES -

ILLUSION CONFUSION! - MEASURING LINES - WHAT TO DO: 1. Look at the line drawings below. 2. Without using a ruler, which long upright or vertical line looks the longest or do they look the same length? SOME THINGS YOU COULD INVESTIGATE: 1. Use a ruler to measure the actual length of both long vertical lines. 2. Why not try to re-draw the illusion in a different way to see what happens? For example, you could change the length of one or both of the vertical lines; change the size and angles of the wings or arrow-fins at either end of the lines; and change the distance between the two vertical lines. Remember to only change one thing at a time to make it a fair test. 3. What do you think is going on? 1

ILLUSION CONFUSION! - COMPARING CORNERS - WHAT TO DO: 1. Look at the two thick dark corner lines in the drawing below. 2. Without using a ruler, which thick dark line looks the longest or do they look the same length? SOME THINGS YOU COULD INVESTIGATE: 1. Use a ruler to measure the actual length of both dark corner lines. 2. Why not try to re-draw the illusion in a different way to see what happens? For example, you could change the length of one or both of the thick dark lines; change the position of one or both of the thick dark lines on the grid ; or change the other lines of the grid itself in some way. Remember to only change one thing at a time to make it a fair test. 3. What do you think is going on? 2

ILLUSION CONFUSION! - CURIOUS CURVES - WHAT TO DO: 1. Look at the two arcs or curves drawn below. 1. Without using a ruler, which curve looks the longest or do they look the same length? SOME THINGS YOU COULD INVESTIGATE: 1. Use a ruler to measure the actual size of both curves. Better still, why not copy and cut out the two curves and compare them against each other that way? 2. Using cut-out copies of the curves, what is the effect of directly swapping around their positions, with the white curve now beneath the grey curve? 3. Using cut-out copies of the curves, what is the effect of changing the position of one curve to the other in other ways, such as moving the curves further apart or have one curve bending one way and the other the opposite way back to back? 4. Why not try to re-draw one or both curves a different size or with a different bend to see the effect? 5. What do you think is going on? 3

ILLUSION CONFUSION! - MEASURING SQUARES - WHAT TO DO: 1. Look at the square patterns below. 2. Without using a ruler, which black square looks the largest or do they look the same size? SOME THINGS YOU COULD INVESTIGATE: 1. Use a ruler to measure the actual size of both black squares. 2. Why not try to re-draw the illusion in a different way to see what happens? For example, you could change the size of one or both of the black squares; change the size of one or both sets of the white squares; draw the white squares not touching the black squares; change the distance between the two groups of squares; and change the squares to other shapes. Remember to only change one thing at a time to make it a fair test. 3. What do you think is going on? 4

ILLUSION CONFUSION! - MEASURING CIRCLES - WHAT TO DO: 1. Look at the circle patterns below. 2. Without using a ruler, which white circle looks the largest or do they look the same size? SOME THINGS YOU COULD INVESTIGATE: 1. Use a ruler to measure the actual size of both white circles. 2. Why not try to re-draw the illusion in a different way to see what happens? For example, you could change the size of one or both of the white circles; change the size of one or both sets of the black circles; draw the white circles at a different distance from the black circles; change the distance between the two groups of circles; and change the circles to other shapes. Remember to only change one thing at a time to make it a fair test. 3. What do you think is going on? 5

ILLUSION CONFUSION! - MEASURING BLOCKS - WHAT TO DO: 1. Look at the flat tops of the rectangular blocks draw in 3-D below. 2. Without using a ruler, which flat top looks the widest, which looks the longest or do they look all the same? SOME THINGS YOU COULD INVESTIGATE: 1. Use a ruler to measure the actual size of each flat top. 2. Maybe try to draw a similar illusion for yourself, without actually measuring the distances. First draw one of the blocks and then try to draw the other so that both flat tops look the same shape and size. Remember not to measure any of the distances as you draw the blocks. Once you ve drawn the two blocks, only then use a ruler to measure whether you drew them the same size and shape or not. 3. Why not try to re-draw the shape of the blocks in a different way to see what happens? For example, you could draw them to look thinner or thicker, or just draw the two tops so that they look like thin sheets rather than blocks. Remember to only change one thing at a time to make it a fair test. 4. What do you think is going on? 6

BRAIN STRETCHERS 1! 1. A man has to get a fox, a chicken and a sack of corn across a river. He has a small rowing boat but it can only carry him and one other thing. If the fox and the chicken are left alone together, the fox will eat the chicken. If the chicken and the corn are left together, the chicken will eat the corn. How does the man get them all across the river? CLUE: Remember that the boat can carry things both ways across the river 2. Two children and one adult need to get across a river. They have a boat but the boat can only carry one adult OR two children. How do they all get across? CLUE: Remember that the boat can carry things both ways across the river 3. If today is Monday, what is the day after the day before the day before tomorrow? CLUE: It might be easier to work through the sentence backwards a break it into segments 4. A shop bought a painting for 70, sold it for 80, bought it back for 90, and sold it again for 100. How much profit did the shopkeeper make? CLUE: Start off with some money in the till, say, 100 5. If 2 hours ago it was as long after one o clock in the afternoon as it was before one o clock in the morning, what time would it be now? CLUE: As long after as it was before is the same as saying halfway between. 6. Mr. & Mrs. Plum have six daughters and each daughter has one brother. How many people are in the plum family? CLUE: Not as many as you might at first think. 7

BRAIN STRETCHERS 1! ANSWERS 1. Man carries chicken across, man leaves chicken and comes back; man then carries fox across, man leaves fox and carries chicken back; man leaves chicken and carries corn across, man leaves fox and corn together and goes back to fetch the chicken. 2. Both children row over together; one child rows the boat back again; that child gets out of the boat and lets the adult row over; adult gets out and lets other child row back again to pick up the remaining child. 3. Monday 4. 20 5. 9.00 p.m. 0r 21.00 6. There are nine Plums in the family. Since each daughter shares the same brother, there are six girls, one boy and Mr. & Mrs. Plum; that makes nine. 8

PUZZLING PUZZLES 1! Below is a stick-picture of a glass with an object inside. Without touching the object inside, how can you move only TWO sticks so that it all ends up looking like the object is outside the glass but the glass remains exactly the same shape? 9

PUZZLING PUZZLES 2! By moving only THREE coins how can you make the triangle of coins look like it points downwards instead of upwards? 10

PUZZLING PUZZLES 3! By moving only ONE stick how can you: 1. Make it look like the house faces the other way? 2. Make the stick picture below look like two houses? 11

PUZZLING PUZZLES 4! By moving only TWO sticks how can you change the three equal size squares to look like: 1. four equal size rectangles? 2. four equal size triangles? 3. five squares? 4. two equal size triangles and two equal size squares? 5. one large square and one smaller square? 6. three triangles? 12

PUZZLING PUZZLES 5! By moving only FOUR sticks how can you change the four equal size squares to look like: 1. Three equal size squares? 2. Eight equal size squares? 3. Six equal size triangles? 4. Eight equal size triangles? 13

PUZZLING PUZZLES 6! PART A In an equilateral triangle, all the sides are exactly the same length. By using SIX identical sticks how can you: 1. Make one equilateral triangle? 2. Make two equilateral triangles? 3. Make four equilateral triangles? PART B How can you arrange SIX identical sticks on the table so that each stick touches ALL the other sticks? PART A CLUE : To answer question 1 and 2 you need to think in 2D, and for 3 in 3D with steady hands! PART B CLUE : You will needs to very carefully arrange the sticks in two layers, so think in 3D again! 14

PUZZLING PUZZLES: ANSWERS NOTE: Dotted lines show the sticks or coins that are moved. PUZZLING PUZZLES 1 PUZZLING PUZZLES 2 PUZZLING PUZZLES 3 1. 2. PUZZLING PUZZLES 4 1. 2. 3. 4. 5. 6. 15

PUZZLING PUZZLES: ANSWERS NOTE: Dotted lines show the sticks that are moved. PUZZLING PUZZLES 5 1. 2. 3. 4. PART A PUZZLING PUZZLES 6 PARTS A & B 1. 2. 3. 3. To make four equilateral triangles using SIX sticks you would need to make a 3-dimensional shape called a TETRAHEDRON, or triangular pyramid. Looking down from above, it would look something like this: PART B You will need to carefully arrange the six sticks in two layers as shown for each stick to touch ALL the others: (the sticks are coloured black and white here to make the layers easier to see) 16

Mad mental maths! TRY THIS: 1. Think of a number 2. Add 4 to it 3. Multiply that answer by 2 4. Add another 6 5. Divide that answer by 2 6. Subtract the number you first thought of 7. WHAT DO YOU GET? 8. Now try again with other numbers and see what you get. AND TRY THIS: 1. Think of a number. 2. Add 7. 3. Multiply by 3. 4. Subtract 9. 5. Divide by 3. 6. Subtract 4. 7. What do you get? 8. Try for other numbers. NOW TRY THIS: 1. Think of a number. 2. Add 5. 3. Double the result. 4. Take away 8. 5. Halve the result. 6. Take away the number you first thought of. 7. What do you get? 8. Try for other numbers. Look carefully through the instructions of each of the mental maths tricks above. See if you can spot any clues about how these tricks work. 17

Shrinking coins or stretching holes? Take a sheet of paper (or a sheet of soft plastic from a shopping bag) and VERY CAREFULLY draw circles around a 1p, 2p and a 5p coin as shown below. Make sure that you use a sharp pencil or fine pen and draw your circles as closely around the edge of each coin as you can. Now use a small pair of sharp scissors nail scissors are good and VERY CAREFULLY AND SLOWLY cut around each of the circles you have drawn. CUTTING HINT: This cut is a little easier to do if you fold the sheet accurately on the dotted line shown above. This creates three half or semi-circles to cut around but you must fold accurately. You should end up with three holes in the sheet of paper (or plastic), each hole about the same size as a 1p, 2p and a 5p coin. You should be able to carefully push the 2p coin through the 2p-size hole, without damaging or stretching the paper or plastic sheet. Try this for yourself if you are not sure. Can you push the 2p coin through the 1p-size hole? (without damaging or stretching the paper or plastic sheet) Can you push the 2p coin through the 5p-size hole? (without damaging or stretching the paper or plastic sheet) CLUE : Holding the sheet of paper or plastic, rest the 2p coin in the 1p-size hole and very carefully bend the hole around the coin in two different directions. 18

Shrinking coins or stretching holes? (ANSWER) Rest the 2p coin in the 1p-size hole as shown in the picture below. Holding the sheet at corners E and F with the thumb and first two fingers of both hands, VERY CAREFULLY bend the sheet around the coin, as shown below, bending edge AB towards and close to edge CD Then bend the corners E and F outwards and upwards away from each other, as suggested by the two big arrows in the picture below. The 2p coin should drop straight through the hole! Q. How could you find out the smallest size hole through which a 2p could fit? CLUE : You could carry on cutting out smaller and smaller holes (though drawing and cutting them could be difficult), or you could find out about the relationship between the diameter of a circle (or widest width across it) and the circumference of a circle (or distance around the outside). 19

CUNNING CARD TRICK! 1. Take 15 playing cards and share them out FACE-UP onto a table into three lines in the number pattern shown below. You MUST be able to see what each card is. LINE 1 LINE 2 LINE 3 Card 1 Card 4 Card 7 Card 10 Card 13 Card 2 Card 3 Card 5 Card 6 Card 8 Card 9 Card 11 Card 12 Card 14 Card 15 2. Ask a friend to choose one card and remember it. They MUST NOT tell you what the card is. Just tell them to point to the LINE their chosen card is in - LINE 1, 2 or 3; 3. Carefully slide together each line of cards into three neat piles of cards; 4. Pick up the three piles of cards, placing the pile of cards they picked in between the other two (like a sandwich) you should now be holding all fifteen cards piled in your hand; 5. Repeat steps 1 to 4 again 2 MORE TIMES, but stay with the same chosen card. 6. Finally, count through the pile of fifteen cards until you reach the EIGHTH card this eighth card should be the card they chose. AMAZING! SOME THINGS TO INVESTIGATE: 1. In step 2, chose a card on the end of a line. How does the position of the card in the line change when you lay out the cards the second and third time? 2. Can you do the same card trick using different numbers of cards? 20

CUNNING CARD TRICK! To work out how to do the same card trick but using different numbers of cards GOOD CLUES: 1. On the first card trick you started with a pack size of 15 cards which you shared out into three lines and each line had the same number of cards. 2. The eighth card was the answer card, which is the middle card in a pack of 15 cards. REALLY GOOD CLUES: Try writing your ideas in a table like the one below, replacing the question marks with a number: (the numbers for the card trick you have already tried is filled in for you) Number of Cards Number of Cards Position of the in the pack in each line answer card??? 15 5 8?????????????????? Can you see any number patterns in the table of numbers you have calculated? (CLUE: Look down the columns of numbers) Does the card trick always work using the different pack sizes you have calculated? Do you always have to deal out the cards three times? If a card is chosen at the end of a line, how does the position of the card in the line change when you lay out the cards the second and third time? 21

STRANGE STRUCTURES! 1. Study carefully the hypersquare 3D-shape drawn below. It can be cut and folded from one sheet of paper or card. This flap should stick straight up in the air These parts of the shape should lie flat on the table 2. Try to make the above 3D-structure. Use only a single sheet of paper or card and a pair of scissors. You MUST NOT use any sticky tape or glue. 22

Shaping stars! 1 2 : Fold a sheet of thin A4 paper in half - thin paper is easier to fold and cut (dotted lines show where the folds should appear) 2 3 : Fold the corner A upwards to ½-way along the top edge BC 3 4 : Fold edge DE upwards to line up with edge AD 4 5 : Fold edge BD down (around edge AD) to line up with edge DF 5 6 : Cut along the dotted line shown and unfold both pieces to find two stars! 23

HOLEY PAPER! OR HOW TO CUT A HOLE IN A SHEET OF PAPER BIG ENOUGH TO FIT YOUR WHOLE BODY THROUGH! 1 2 3 : Fold a sheet of paper in half and then in half again the other way, bringing edge AB up to edge CD (see figures 2 & 3) (dotted lines show where the folds should appear) 3 4 : Fold the paper in half again, bringing edge EF up to edge AB 4 5 : Fold the paper in half once more, bringing edge GH up to edge EF SEE THE NEXT PAGE FOR FINAL INSTRUCTIONS 24

HOLEY PAPER! MORE INSTRUCTIONS 5 6 : From figure 5, unfold the paper back to where it has only one fold, as shown in figure 2 on the previous page. You should see seven creases, as shown by the seven horizontal dotted/dashed lines in figure 6 below: 6 7 : Make all eight cuts shown by the dark-dashed lines in figure 6 below: NOTE: FIRST make the cut IJ very close to the still folded edge AC. This cut should run between the two end creases, shown as 1 & 7. Then cut along the creases 1 to 7 in alternate directions, making sure that your cuts stop before they reach the opposite edge of the paper. Finally, VERY CAREFULLY unfold and open up the paper to reveal a hole large enough to fit your whole body through! THINGS TO TRY 1. Take another sheet of paper of the same size. Fold it in the same way as before but this time, when you reach step 5, make one more fold in half in the same direction. When you unfold the paper as asked in step 6, you should now see 15 creases. Similar to before, cut between the two end creases close to the folded edge AC and then make alternate-direction cuts along all the 15 creases. Is the size of the hole different to the first hole you made? 2. Try to find out what is the smallest piece of paper you can fold and cut, and still fit your whole body through. 25

MAGIC NUMBER CARDS! 1. Ask a friend to look at the number cards below. 2. Ask them to think of a number between 1 and 15. 3. Ask them NOT to tell you the number they have chosen. 4. Ask them to tell you ALL the cards where they can see their number. 5. You then ADD together the first numbers you can see on each of the cards they named. (NOTE: the first number on Card A is 1, B is 2, C is 4, and D is 8) The answer you get is the number they first thought of! Card A 1 3 5 7 9 11 13 15 Card B 2 3 6 7 10 11 14 15 Card C 4 5 6 7 12 13 14 15 Card D 8 9 10 11 12 13 14 15 6. What would be the first number on cards E, F & G (if you had them)? 7. What other number patterns can you see in each of the above cards? 8. Can you see any differences in the number patterns between cards? 26

LOSING LINES! Take a piece of paper and using a pencil and ruler very carefully draw THIRTEEN thick parallel lines, as shown in the picture just below. Draw the lines 10cm long and 1cm apart. (The lines will be easier to draw if you draw on squared- or graph-paper) Then draw a thin diagonal line AD from one corner of the block of lines to the opposite corner and extend the line to the edge of the paper. Now carefully cut along the line AD. Carefully place the two pieces of paper together again on a table and slowly slide the triangular sheet ACD along the cut until the lines line up again as shown below. Now count the thick drawn lines. You should now count only twelve lines! Can you see how this illusion works? Why not try the illusion with different measurements? Does it always work? 27