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Transcript
Investigative approach to number Consecutive numbers Take any 5 consecutive numbers, add them together, divide the answer by 5 and subtract 2 from the answer. What happens? Investigate. Does the rule hold for 6 consecutive numbers? … Digit sum Take a 3-digit number and write down all the possible 2 digit arrangements from them. Sum them. Can you predict this total from the original 3-digit number chosen? Extend. Generalise. Prove. Can you work out the sum of the first 100 counting numbers 1 + 2 + 3 + 4 + … + 99 + 100 = ? in less than 1 minute? Consecutive sums Some numbers can be written as the sum of two or more consecutive numbers. Investigate. Extensions: what happens if you include negative numbers? What about consecutive odd numbers? What happens if you sum the squares of consecutive numbers? Form a chain of numbers as follows: multiply the units digit by 9 add to it the tens digit and repeat eg 37 66 60 6 54 Investigate chains of this type. Consecutive numbers again! Take any three consecutive numbers, square the middle one and multiply the other two. Investigate. Products The product of any two consecutive numbers is a multiple of 2. The product of any three consecutive numbers is a multiple of 3. The product of any four consecutive numbers is a multiple of ? Investigate.