Properties of Numbers
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1 Properties of Numbers Level 3/4 Number of practice sheets: 10 MathSphere
2 Booster: KS2: Properties of Numbers 3/4 Page 2 Notes Calculators may be used on more difficult questions. You should push the children to do as much in their heads or on paper as they can as this gives very good practice. Obviously, there comes a point when use of a calculator becomes desirable. Some answers are more open ended and have many possibilities. We have tried to show patterns of possible answers where this is feasible. The I m Thinking of a Number game pages may be read out to save paper if you do not wish to repeatedly photocopy them. A good knowledge of odd, even, square, triangle and prime numbers is required for this work and children should be regularly tested to see if they know these. Calculation of factors and multiples is also required. They should also be familiar with the tests for divisibility and how to combine them. The following simple tests should be well known. Divisibility by 10: Number ends in 0 Divisibility by 5: Number ends in 0 or 5 Divisibility by 3: Sum of digits is divisible by 3 Eg is divisible by 3 because digits total 27 which is divisible by 3. Divisibility by 9: The above test for divisibility for 3 may be extended to 9. Number is divisible by 9 if sum of digits is divisible by 9. Divisibility by 2: Number ends in even digit. Divisibility by 4: Last two digits of number are divisible by 4. Combining divisibility tests: To test if a number is divisible by 6, for instance, we note that 6 = 2 3, so number must be even and divisible by 3. Eg is divisible by 6 because it is even and digits add up to 30, which is divisible by 3. This idea may be extended indefinitely. Eg to test if a number is divisible by 45 apply the divisibility for 5 and for 9 tests.
3 Booster: KS2: Properties of Numbers 3/4 Page 3 Here s a practice page to see if you know all the types of numbers you need to know. 1. a) Write down the first 10 odd numbers, beginning with 1. b) Write down the first 10 even numbers, beginning with 2. c) Write down the first 10 square numbers, beginning with 1. d) Write down the first 10 triangle numbers, beginning with 1. e) Write down the first 10 prime numbers, beginning with 2. f) Write down the first 10 multiples of 6, beginning with 6. g) Write down all the factors of 12.
4 Booster: KS2: Properties of Numbers 3/4 Page 4 You may like to look at your lists of numbers to help with this page. 1. What could the missing numbers be? a) An even number greater than 21. b) An odd number between 16 and 24. c) A square number between 40 and 50. d) A prime number less than What could the missing numbers be? a) A multiple of 7 that is greater than 50. b) A factor of 30 that is greater than 10. c) A multiple of 12 between 40 and 50. d) A multiple of 9 less than Write down all the factors of 20 and circle the ones that are odd. 4. Write down all the factors of 24 and circle the ones that are even.
5 Booster: KS2: Properties of Numbers 3/4 Page 5 I hope you are revising your square, prime and triangle numbers. 1. What could the missing numbers be? a) An even number between 17 and 23. b) An odd number less than 13. c) A square number between 73 and 90. d) A prime number greater than What could the missing numbers be? a) A multiple of 12 that is greater than 70. b) A factor of 48 between 10 and 15. c) A multiple of 30 greater than 100. d) A factor of 28 more than Write down all the factors of 28. Add them all up (except 28). 4. Write down all the factors of 32 and circle the ones that are odd.
6 Booster: KS2: Properties of Numbers 3/4 Page 6 Hi, guys and gals. Let me introduce you to my old friend the Venn Diagram. You need to put two sets of numbers on this diagram. Numbers in the first set but not in the second set go in here. Numbers in both sets go in here. Numbers in the second set but not in the first set go in here. Numbers in neither set go in here. Put these numbers on this Venn Diagram: of 5 of 3
7 Booster: KS2: Properties of Numbers 3/4 Page 7 Transfer the numbers in the double box to each Venn Diagram. a) of 7 of 4 b) Even numbers Odd numbers c) of 4 of 5 d) of 3 of 9 Nice man, Mr Venn, giving you all this lovely work to do!
8 Booster: KS2: Properties of Numbers 3/4 Page 8 A woman phoned her local radio to tell them she had sixteen children. The reporter was a bit deaf and said, Please repeat that. Not blooming likely! said the woman. a) Square numbers of 4 b) of 10 Triangle numbers c) Factors of 12 Factors of 20 d) of 5 Factors of 30 Good joke, but did you hear the one about the high wall? Don t worry, you ll never get over it! Ha, Ha!!!!!!!!
9 Booster: KS2: Properties of Numbers 3/4 Page 9 1. Put a circle around all the numbers that are multiples of Explain how you knew which ones to circle. 2. Put a circle around all the numbers that are multiples of Explain how you knew which ones to circle. 3. Put a circle around the prime numbers in this list Explain what a prime number is. 4. Put a number in the box that is A square number and a multiple of 3 5. Put a number in the box that is A prime number and an even number
10 Booster: KS2: Properties of Numbers 3/4 Page 10 You may find a calculator useful for some of these questions. Me? I just use my pencil. 1. a) Which of these numbers can be divided by 3 with no remainder? Put a circle around them b) Which of these numbers can be divided by 7 with no remainder? Put a circle around them c) Which of these numbers can be divided by 3 with no remainder and by 8 with no remainder? Put a circle around them Complete this three digit number to make it a multiple of Complete these three digit numbers to make them multiples of I expect you ll need something delicious to eat after that. How about a piece of cheese? Oh dear, I ve just bumped my head!
11 Booster: KS2: Properties of Numbers 3/4 Page 11 I m Thinking of a Number (1) Multy thinks of a number. Divvy tries to guess it.. Can you help Divvy? a) Divvy Is it greater than 30? Is it less than 40? Is it a square number? Multy What is the number? b) Is it a prime number? Is it more than 20? Is it greater than 10? Is it a factor of 66? What is the number? No c) Give me a clue, please. It s a multiple of 9 Is it an odd number? No Is it less than 50? Is it a square number? No What is the number?
12 Booster: KS2: Properties of Numbers 3/4 Page 12 I m Thinking of a Number (2) Divvy thinks of a number. Multy tries to guess it.. Can you help Multy? a) Multy Can you tell me anything? Is it less than 30? Is it an odd number? Is it a multiple of 7? Divvy It s a triangle number No What is the number? b) How many factors does it have? 2 How many digits does it have? 2 Is it more than 20? No What is it a factor of? 51 What is the number? c) Give me a clue, please. It s more than 100 Another clue? It s a square number What is the total of its digits? 4 Is it 400? No, good try. What is the number?
13 Booster: KS2: Properties of Numbers 3/4 Page 13 Answers Page 3 1. a) 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 b) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 c) 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 d) 1, 3, 6, 10, 15, 21, 28, 36, 45, 55 e) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 f) 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 g) 1, 2, 3, 4, 6, 12 Page 4 1. a) One of 22, 24, 26 etc b) One of 17, 19, 21, 23 c) 49 d) One of 2, 3, 5, 7, a) One of 56, 63, 70 etc b) Either 15 or 30 c) 48 d) Either 9 or
14 Booster: KS2: Properties of Numbers 3/4 Page 14 Answers (Contd) Page 5 1. a) One of 18, 20, 22 b) One of 1, 3, 5, 7, 9, 11 c) 81 d) Any prime greater than 30 such as 31, 37, a) Any multiple of 12 greater than 70 such as 72, 84, 96.. b) 12 c) Any multiple of 30 greater than 100 such as 120, 150,. 300, 3000 d) Either 14 or = Page of 5 of
15 Booster: KS2: Properties of Numbers 3/4 Page 15 Answers (Contd) Page 7 of of 4 Even numbers Odd numbers of 4 of of of 9
16 Booster: KS2: Properties of Numbers 3/4 Page 16 Answers (Contd) Page 8 Square 3 10 numbers 4 of of 10 Triangle numbers Factors Factors 7 of 12 of of Factors of Page 9 1. of 5: 15, 20, 25, 40, 45, 620 Last digit is 5 or 0 2. of 3: 3, 12, 18, 72, 111 Total of digits is divisible by 3 3. Primes: 2, 3, 5, 13, 17 (A prime number is a number that has just two factors, 1 and the number itself) 4. Any of 9, 36, 81, 144 etc 5. 2
17 Booster: KS2: Properties of Numbers 3/4 Page 17 Answers (Contd) Page a) 3, 18, 138, 357, 450 b) 644, 868 c) 24, 72, 216, or 456 Middle digit can Middle digit can be 0, 3, 6 or 9 be 2, 5 or 8 Last two digits First two digits Last two digits must be a must be a must be a multiple of 6 multiple of 3 multiple of 6 less 2 eg 126 plus 2 eg 216 eg 402, 414 Page 11 a) 36 b) 11 c) 18 Page 12 a) 28 b) 17 c) 121 (other possibilities such as 40000, 12100)
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