Ideas for using the 0-99 Grid

Transcription

1 Ideas for using the 0-99 Grid These activities are not presented in any particular order. Many of them can be adapted for children of different abilities and ages. Some of the activities can be carried out using different sized grids (e.g. 8 by 8) or grids with different numbers (eg , etc.) Jigsaw: Cut up into pieces to make a jigsaw for the children to reassemble. Increase the number of pieces to make it harder. Cut along the lines, not through the numbers. Cover-up: Child 1 covers up one or more squares using counters. Child 2 has to guess which numbers are hidden under the counters. Race to 100: Give the children a copy of a blank grid. Time how long it takes them to fill in the numbers. Repeat on a regular basis to see if they can improve on their time. Missing numbers: Provide children with pieces of the 0-99 grid with only some of the numbers filled in. They have to think about the patterns to fill in the empty spaces. Number swap: Using a 0-99 grid with pockets, swap over two of the numbers. Children have to spot the numbers in the wrong places. Make the activity more difficult by asking children to calculate the total of or the difference between the two swapped numbers. 4 in a row: (a game for 2 or 3 players) Throw three 0 9 dice. Use the numbers and any operation to make one of the numbers on the hundred square. If all the players agree that the calculation is correct, cover the number with one of your counters. The aim is to get four of your counters in a row. Squares: Draw a 2 by 2 square on the hundred square. Add the numbers in opposite corners. What do you notice? Is it the same for different 2 by 2 squares? Now multiply the numbers in opposite corners. What do you notice this time? Is it always true? Differences: Choose two 0 9 cards and write down the two 2-digit numbers you can make (with 3 and 7, you can make 37 and 73). Find the difference between your two numbers and colour your answers on a hundred square. Explain any patterns you can see. Predictions: Cover the multiples of 3 up to 30. Use the pattern to predict whether the number 52 will be in the sequence. Try predicting other numbers. How do you know? How could you check your answer? Repeat the activity using different multiples. Total 100: Find pairs of numbers on the grid that total 100. How many different pairs can you find? How could you organise your answers so that you know you have found all of the possible ways? Which are the two unhappy numbers because they do not have a partner. Digit sums: Use red counters to cover numbers on the hundred square whose digits add up to 10. Explain the patterns that you notice? Use a different colour counter to cover numbers whose digits add up to 9, 8, 7 etc. Can you explain what is happening each time? Consecutive numbers: Circle three numbers next to each other in a row. Find their total. Repeat for other groups of three consecutive numbers. What do all of the answers have in common? Try to explain why this happens. Make a track: Cut a hundred square into rows, and then stick it together as a number track. Can you decide where to cut it to turn it back into a hundred square? Explain why you know.

2 Hidden numbers: Cover the numbers 1 to 99 on the grid with counters. Spin two 0 9 dice and make a 2-digit number. Work out which counter the number is hidden under. If you are right, keep the counter. If you are wrong, put the counter back down. How many counters can you collect in 5 minutes? Play again and try to beat your record. Spirals: Fill in the numbers on a blank hundred square in a spiral pattern. Cover up some of the numbers. Can a partner tell you which numbers are covered? Can you make a different spiral pattern next time? L shapes: Draw an L-shape on the hundred square (3 down, 2 across). Find the difference between the two shaded numbers. Repeat with other L-shapes on the hundred square. What do you notice about the differences? Can you explain why? Palindromic Numbers: Colour the palindromic numbers on the grid (numbers the same backwards as forwards e.g. 55). Describe the pattern made. Can you explain why the pattern is diagonal? Is it diagonal on different 100 squares? Pathways: Use a grid with 1 to 10 on the bottom row. Choose a start and finish number. Write a list of instructions to move from the start number to the finish number e.g. Start on 17. Add 30, subtract 4, add 10, add 6. Read your instructions to a partner. Do they finish on the correct number? Can they tell you how to get back to the start number in just two moves? Square numbers: Predict how many square numbers you think there are on the grid. Circle them to find out how close your estimate is. Describe any patterns you see. Which two square numbers have a difference of 20, 40, 60? Do you think there is a pair of square numbers with a difference of 80? Coordinates: Each child needs a grid. Label the columns of the grid A H and the rows Child 1 puts crosses on their grid to make a letter or shape e.g. H, and they then read out the coordinates. Child 2 marks the squares with a cross. Check to see if the same pattern is made on both squares. Common multiples: Circle the multiples of 3 and cross the multiples of 4. What do you notice about the numbers that are circled and crossed? What do these numbers have in common? Do you know what the next few numbers in the pattern would be? Crosses: Draw a 3 by 3 cross on the grid. Add the four numbers around the edge. Can you see a relationship to the middle number? Repeat for other crosses. Explain what you have noticed to a friend. 24 Number puzzles: Devise a set of calculations. The answers (when covered on the grid) should make a shape or letter. Children complete the calculations and cover the answers. Teachers can quickly see whether the answers are correct. Can you make up a similar puzzle for your friend to complete? Favourite numbers: Choose your favourite number from the grid. Make up 5 statements about it e.g. it is a multiple of 5, it is a square number etc. Can someone else guess your number correctly? If not, let them ask a question to help them. 100 Ideas for using the 0-99 Grid 1. Cut up the grid and make it into a number line. 2. Colour all the even numbers and establish a rule for recognizing even numbers. 3. Find the multiples of Play a game in two s. Each picks a number between Add together the digits of that

3 number and move that many spaces. The winner is the first person who is closest to Find the square roots of the numbers to the nearest whole number. 6. Pick 10 numbers and treble them. 7. Make a Lucas Sequence, e.g Find all the cubic numbers. 9. Investigate all the numbers and find the numbers where the digits add up to Pick a number between 1 and 9 and keep adding 10 until you get to the end of the number square. 11. Find all the numbers whose digits add up to Make your own 100 square. 13. Choose 10 numbers from the square and subtract them from Find two consecutive numbers which add up to a square number, e.g. 12 and 13 = Pick numbers and reverse the digits and add them together, is the answer different from adding the digits without reversing. 16. Find all the numbers containing a digit Find all the prime numbers. 18. Are there any prime triples? (Three prime numbers in a row with an even number between each) 19. Go to a prime number add 1 and divide by Divide any number by Reverse the number, read the new number. 22. Find any palindromes - numbers which are the same forwards and backwards e.g Make a spiral hundred square. 24. Pick a number and add the number above or below it. 25. Find the square numbers. 26. Pick a number and halve it. 27. Think of a number pattern, use a cut up grid to make it, remove some of the numbers and get your friend to fill in the missing numbers or finish the pattern. 28. Find all the triangular numbers. 29. Pick a number, double it, add 1. Explain how to get back to your original number. 30. Make a 0-99 grid beginning in the middle. 31. From a cut up 0-99 grid make a calendar for the month of your birthday. 32. Find all the multiples of Pick a number and find the next multiple of Make a zigzag 0-99 grid, e.g goes from left to right, next row from right to left, etc. 35. Find the multiples of Find your age. 37. Find numbers where the digits add up to Pick a number which is greater than 10, double the units digit and add it to your original number. 39. Use your 0-99 grid to draw some snakes and ladders and play the game with a dice. 40. Find the multiples of Find the twin prime numbers, two consecutive prime numbers with an even number between them. 42. Pick a number, double an odd number and subtract 10, halve an even number and add 1, keep repeating, can you get back to 1? Make your own rules. 43. Find your house number. 44. Pick a number, subtract 4 then subtract 3, keep repeating. How many sums until you reach 1? 45. Can you make a rectangular spiral?

4 46. Start making a spiral from Pick a number, subtract the number below. Try for 10 different numbers, what do you notice? 48. Put some coloured counters on a number series. How many different series can you find? 49. Make a Fibonacci series. 50. Find the factors of Add the ages of all the people in your family and find that number. 52. Find 2 numbers which when 53. Pick a number, add 100, is the answer a prime number? 54. Find some squares within the hundred square, add the corners together. 55. If A=1, B=2, etc., what numbers are your initials? What is the value of your name? 56. Form a circle of numbers. 57. Pick a number and add the next odd number. Find a rule about adding odds and evens. 58. Pick a number, shut your eyes, what numbers are either side of your number? 59. Find the age of your eldest brother or sister. 60. Pick a number, can you make your number by adding 2 consecutive numbers? Are there any impossible numbers? 61. Pick 2 numbers, find the difference. 62. Pick a number, shut your eyes, what numbers are above and below your number? 63. Pick a number, add 7, subtract 3, how many sums do you do to reach 100? What was the 5th answer in your sequence? 64. Pick a number, multiply the units digit by 5, and add the tens digit to the answer. 65. Draw some rectangles on your 0-99 grid, add up the numbers around the edge of each rectangle. 66. Find numbers which can be divided by both 2 and Using your cut up square, make a 7 x 7, or 8 x 8 number square. What is the last number in this square? 68. Pick a number, find 2 numbers which add up to your number, are there any other pairs of numbers which make the same total? 69. Find a number with a prime number above and below it. 70. Using the cut up square, make a hollow number square. How many numbers have you used? 71. Pick a number, make a sequence by adding 5 each time. 72. Find a number with a digit 2 in it. 73. Pick a number, subtract the digits. 74. Pick three numbers and add 2 of the numbers and subtract the third number. 75. Pick a number and divide it by 7. Is there a remainder? 76. In pairs, pick a number each and put a counter on that number. Using a knight s move, (2 forward and 1 to the side) can you move to 0 or 99? 77. Pick a number, find its multiples. Is there a rule to move from one multiple to another? 78. In pairs, one person gives the first three numbers of a sequence, play hangman to guess the sequence to Find a number which can be divided by the sum of its digits. 80. Find all the multiples of Find the year of your birth, Pick a number; if the number is even, halve it, if it is odd, add 1 and double. Can you get to 100? 83. Design your own rules for investigations to Find pairs of numbers which add up to Find 3 numbers which total Use the 0-99 to fill in a multiplication square. Which numbers are never used, which numbers do you need several times?

5 87. Using the knight s move, which is the fastest way of travelling from 0 to Find the multiples of Make a magic square. 90. Make a number sequence using 10 numbers. Turn over the numbers so your partner can t see them. Turning one number at a time, in any order, how many do you turn over until they guess the correct sequence. 91. Choose your favourite number and say why it is special. 92. Find two numbers which have a difference of Find two numbers which add up to Pick 10 pairs of numbers and multiply them together. 95. Combine three prime numbers. Is the answer always odd? 96. Combine two prime numbers. Is the answer ever odd? 97. Pick 4 numbers, using +, -, x, only once each, what is the biggest number you can make? The smallest? 98. Start on any number, divide by 2 and add the remainder. Do you always reach 1? 99. In pairs, each put a counter on 1. Each must follow one of the following instructions. Square the number then add 1, or add 1 and square the number. Move your counter to the answer and then repeat. What happens? Who gets nearest to 100 first? Pick a different starting point, does the result change? 100. Make a Fibonacci sequence, add the previous 3 numbers. If you were to finish at 100, where would you start?