Y8 CORE AUTUMN TERM UNIT: Number and Algebra 1 – Numbers and Sequences TIME ALLOCATION: 6 Hours PRIOR KNOWLEDGE How to add and subtract negative integers Recognise negative numbers in contexts Recognise multiples of 2, 3, 4, 5, 6, 7, 8, 9 and 10 Describe what a prime number is. The square and triangle number sequences How to generate terms of a simple sequence KEY WORDS STARTER integer, negative, positive, sign, square, squared, square root, cube, cube root, power, factors, prime factors, HCF, LCM, multiples, BODMAS, product, sequence, term, nth term, consecutive, predict, rule, generate, continue, ascending, descending, symbol, index Sequences in words 1, 2, 3, 4 Find factor and multiples (choose easy) Sequences LEARNING OBJECTIVES LEVEL 5 To be able to find squares, square roots and cubes, and use appropriate notation. Recognise triangular numbers Be able to find highest common factors and lowest common multiples in simple cases Counting stick adding on Whiteboards or number fans ask pupils number facts e.g. first prime number, third multiple of 7 etc Get students to guess the rule, ask a pupil for a number you apply the rule keep repeating until pupils come up with the rule LEARNING OUTCOMES know the square numbers up to 12x12 and can find their square roots know that square numbers make square patterns of dots and triangular numbers makes triangles Find the lowest common multiple (LCM) of two numbers, such as 6 and 8; 6 times table: 6 12 18 24 30… 8 times table: 8 16 24 32… The lowest common multiple of 6 and 8 is 24. Find the highest common factor (HCF) of two numbers, such as 18 and 24; The factors of 18 are 1 2 3 6 9 18 The factors of 24 are 1 2 3 4 6 8 12 24 1, 2, 3 and 6 are common factors of 18 and 24, so 6 is the highest common factor of 18 and 24. To be able to add and subtract negative numbers. To be able to generate a sequence Start at 0 and count on in steps of 0.5. 0.5, 1, given a rule for finding each term from 1.5, 2, … Each term is a multiple of 0.5. its position in the sequence: Start at 41 and count back in steps of 5. 41, 36, 31, 26, … Each term is a multiple of 5 plus 1. LEVEL 6 To be able to add, subtract, divide and multiply positive and negative integers To be able to find the prime factor decomposition of a number To be able to describe in words the rule for the next sequence where the rule is linear To be able to find a rule for a linear sequence Extend patterns such as: 2+1=3 –3 – 1 = –4 2+0=2 –3 – 0 = –3 2 + –1 = 1 –3 – –1 = –2 2 + –2 = 0 –3 – –2 = –1 2 + –3 = –1 –3 – –3 = 0 ACTIVITIES Using matchsticks in pairs, one person starts a pattern can the other person continue it ICT RESOURCES www.mymaths.co.uk negative numbers 1 and 2 odds, evens, multiples multiples factors and primes sequences Multiple and Factors resources Generate a sequence from nth term (Excel) Negative number ladders Divisibility tests Product of prime factors nth term (Excel) Negative nth term and term to term (Excel) sequences term to term rule sequences and nth term nth term match –up game pupil interactive activity nth term (Excel) 4 different sequence activities FUNCTIONAL SKILLS and MPA OPPORTUNITIES NRich : Factors and Multiples Game, Factors and Multiples Puzzle Sequences from a practical context PLENARIES AND KEY QUESTIONS Which numbers less than 100 have exactly three factors? What number up to 100 has the most factors? Find some prime numbers which, when their digits are reversed, are also prime. There are 10 two-digit prime numbers that can be written as the sum of two square numbers. What are they? The answer to a question was –8. What was the question? The result of subtracting one integer from another is –2. What could the two integers be? The temperature is below freezing point. It falls by 10 degrees, then rises by 7 degrees. What could the temperature be now? Can you give me an example of a number greater than 500 that is divisible by 3? How do you know whether a number is divisible by 6? etc Can you give me an example of a number greater that 100 that is divisible by 5 and also by 3? Is there a quick way to check whether a number is divisible by 25? How do you go about finding the prime factors of a given number? What are the prime factors of 125? 81? 343? What do you notice? How do you go about finding the rule for a sequence of numbers? Where do you start? What do you look for? How many terms do you check before you are convinced you know the rule? 1, 2, 4. What could the next 2 terms be? Why ?