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TOPIC 12 Strand: Strand unit: 517 518 519 Identify simple prime and composite numbers. Identify square and rectangular numbers. Identify factors and multiples. 1. This strand unit is introduced into the curriculum for the first time at 5th class level. 2. The children should have acquired an understanding of odd and even numbers from their previous work on number patterns and sequences. 1. Applying and problem-solving: Applying the concept of multiples to everyday contexts. 2. Integrating and connecting: Using diagrams and symbols to solve problems in number theory. 3. Reasoning: Searching for and investigating mathematical patterns in the context of number shapes. 4. Implementing: Using a calculator to investigate number patterns. 5. Understanding and recalling: Understanding and recalling the new terminology and concepts of number theory. Geoboards, calculators Even, odd, factor, product, multiple, prime, composite, square number, rectangular number, divisible, divisor The are several new terms and concepts in this unit that will be new to students 1. Factors, products and multiples are introduced for the first time 2. Prime and composite numbers are introduced for the first time 3. Square and rectangular numbers are introduced for the first time 58 Fans: Show the first 4 prime numbers. Revise tables looking for the product and the factors of different numbers. Target board 2: How many odd numbers in the first row, column, etc? How many even numbers in each row and column? State whether each number is a prime or a composite number. Show the first 4 triangular numbers. Target board 1: How many square numbers on the page? How many triangular numbers on the page? 1. 2. 3. 4. 5. Using a calculator find all the square numbers up to 10,000. Using a calculator find all the rectangular numbers up to 10,000. Investigate triskaidekaphobia, which is fear of the number 13. Investigate tetraphobia, which is fear of the number 4. Investigate the history of house numbering and find out if house numbering methods vary from country to country. Which number? 1. This is the 13th odd number. (25) 2. This is the 2nd odd number. (3) 3. This number is even but 2 of its 3 digits are odd. (914) 4. This odd number is divisible by 13. (481) 5. This even number is 76 years before Columbus sailed the Atlantic ocean. (1416) 6. This odd number is 31 times greater than 3. (93) 7. This odd number is 11 times 11. (121) 8. This even number is perfectly divisible by 50, 10 and 5. (150) 9. This is the 3rd odd number. (5) 10. This odd number has 3 odd digits. (535) Lower attainers: Photocopiable has extra practice on multiples, factors, prime numbers, composite numbers and square numbers. Higher attainers: 1. Photocopiable has vocabulary activities and short revision activity on prime and composite numbers. It also has a very challenging activity based on multiples. 59 2. ‘Challenge Yourself’ activity on page 81 and Activity B on page 83, which is an investigative activity that will require a whole-class discussion. Topic Topic 12 12 1. List six multiples for each of the following numbers. 1. Write a sentence to show your understanding of the following terms. (a) 2 (b) 3 (c) 5 (a) factor (d) 8 (e) 10 (f) 12 (b) multiple (c) product 2. List three pairs of factors for each of these numbers. (a) 18 (b) 28 (c) 32 (d) 40 (e) 56 (f) 60 2. Write out all the prime numbers between 1 and 50. 3. Write out all the composite numbers between 51 and 100. 3. Put a circle around all the prime numbers in this list. 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25 4. (a) The first square number is ___. (b) ___ is the third square number. (c) The fifth square number is ___. (d) The seventh square number is ___. (e) 100 is the ___ square number. 4. Put an X on all the composite numbers in this list. 26 31 36 41 46 27 32 37 42 47 28 33 38 43 48 29 34 39 44 59 30 35 40 45 50 5. (a) Mary wears her jacket every 4 days and her hat every 5 days. If she wears her jacket and hat on March 8th, what is the next date she will wear both her jacket and hat? (b) Greg goes swimming every 3 days. Sive goes swimming every 4 days. If they both go swimming on 10th October, what is the next date on which they will both go swimming? (c) Three bells toll together and then toll again at intervals of 4, 5 and 6 seconds. After how much time will they toll together again? (d) If oranges in a supermarket were arranged in groups of 3, 4, 6 or 9 and none were left out what 5. How many square numbers are there between 1 and 100? Use this 100 square to help you. is the least number of oranges there could have been? (e) Gordon and Tom go jogging at 7am. Gordon stops for a rest every 10 minutes and Tom stops for a rest every 12 minutes. What time will it be when they stop for a rest at the same time? Name: _______________________________________ Date: ___________________ © Folens Photocopiables Date: ___________________ © Folens Photocopiables There are ___ square numbers between 1 and 100. Name: _______________________________________ 134 Rules and Properties: Number patterns and sequences 2D Shapes: Square and rectangular numbers Number: Operations – Multiplication and division of whole numbers SESE Geography: House numbering in the built environment SESE History: Exploring patterns of historical dates At the end of this unit children should exhibit an understanding if the following terms and concepts: Prime and composite numbers; factors and multiples, square and rectangular numbers. Children should be encouraged to examine number patterns in their environment, for example: 1. Examine patterns of street numbering in the locality. 2. Examine the presence/absence of a 13th floor in high-rise buildings. 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