# Reasoning: Odd one out

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2 Reasoning: Odd one out For pupils Steps to success. Identify the odd one out from a set and explain why you have chosen it, with some mathematical justification.. Convince others of the reasons for your choice, perhaps changing their minds by your argument.. Justify your reasoning using correct mathematical language, both orally and using good written English. Bank of Odd one out questions a) product b) multiple c) square number d) factor e) prime a) b) b c) d) e) a) 0 b) Boys Girls 6 c) Gender Number Boys Girls 6 d) a) b) c) d) e) f) a) b) c) d) e) 6 a) b) c) 6 d) e) f) See the pupil activities with the icon on pages to 6 for topic-based practice of this strategy. 06 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.

3 Reasoning: Always, sometimes, never true Learning objective To decide if a statement is always, sometimes or never true by considering it from a number of standpoints. Links to year 6 problem solving and reasoning pupil target sheet Reasoning I can identify if a statement is always, sometimes or never true. I can explain my reasoning using clear sentence structures, calculations and diagrams. I can convince others by proving and justifying my answers, using further examples to back up my reasoning. I am beginning to use simple algebraic expressions to help explain my reasoning. Teaching notes Try to choose a statement that addresses a misconception, a common error or something that is intuitively always true or always false for example, doubling a whole number is always less than squaring it ( + > and + = shows this statement is sometimes true). Guide the pupils a little more than in some of the other reasoning sections, possibly through the use of What if? type questions. If, for example, the pupils believe that multiplication always makes numbers bigger, ask them to consider 6. Point out that you only have to find one thing that does not fit the statement for it to not be always or never true for example, prime numbers are odd numbers is sometimes true because is a prime number and it is even. As with all these reasoning skills, expect clear explanations using correct mathematical language. Example: The sum of two fractions is than their product. First ask if the sum of two positive whole numbers is than their product. Give the pupils opportunities to try some. Intuitively it might seem that this is never true for example, + <. Hopefully, someone will identify a calculation where it is for example, + >. In fact, if one of the numbers is, then it is always true ( + a > a when a > 0). Therefore, elicit from the pupils that the statement is sometimes true. Now pose the question about fractions. Let the pupils try some some pupils could work on fractions with the same denominator, some with numbers where one denominator is a multiple of the other and some where they need to find a common denominator. Display the results in a table like the one below. From this, the statement would appear to be always true. Fraction A Fraction B Sum Product Sum is than/less than/equal to the product 06 Keen Kite Books, an imprint of HarperCollinsPublishers Ltd. You may photocopy this page.

6 What is the same and what is different about these two ways of showing? Challenge Look at this sequence of calculations. 00 = 6 00 = 6 00 = What is the 0th term? Explain the pattern and your answer. Emma knows that 6 6 = She subtracts 6 from 6 She says: That is the answer to 6 Is she correct? Explain how you know. Challenge 6 Sahid thinks that 6 is a prime number. Is he correct? Explain how you know. Explain why you do not have to check for any factor bigger than 6 What are the missing digits in this long division? There are two possible answers How did you do?

7 Fractions Remember that a fraction expresses a ratio or a proportion. A fraction is also a number in its own right every fraction has a position on a number line. A fraction can be a calculation, for example = Example: Which is the larger fraction: or? Explain how you know. is less than and is less than is larger than because the denominator is smaller and the numerators are the same. Therefore, < Note: You could also write and as equivalent fractions to compare the numerators, e.g. = 6 and = 6 so is bigger. Getting started Which calculation is the odd one out in each row? a) 6 + b) c) 0 6

8 Are the following statements always, sometimes or never true? Explain why. a) of a pizza is more than of a pizza. b) The product of two fractions is than c) a b is bigger than b a d) If the numerator of a fraction is larger than the denominator, then the fraction is bigger than but smaller than e) If the highest common factor of the numerator and the denominator is equal to, then the fraction is in its simplest form. Challenge Find all the possible fractions between 0 and where the numerator and the denominator are prime numbers less than 0 and arrange them in order of size. The men s long jump world record is feet inches. Zoe says: That s over metres. Is she correct? Explain how you know. Challenge a) Explain the rule which gets you the next calculation in the sequence and find the next three terms.,,, 6 b) What will be the first calculation smaller than? Explain why. 0 6 Are the following statements always, sometimes or never true? Explain why. Give reasons to explain your answers. a) Between any two fractions there is another fraction. b) A unit fraction can be expressed as the sum of two different unit fractions, e.g. = + 0 c) a > How did you do?

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