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Developing Understanding of Fractions in KS2

Enhance your understanding of fractions in KS2 and learn pedagogical approaches to teaching mathematics. Explore visual and practical methods to help students grasp the concept of fractions.

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Developing Understanding of Fractions in KS2

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  1. Aims of the Session • To build understanding of mathematics and it’s development throughout KS2 • To have a stronger awareness of when and how to progress from non-formal to formal methods at the appropriate stage for your pupils (and the pitfalls of formal methods) • To enhance subject knowledge of the pedagogical approaches to teaching mathematics

  2. Fractions Fractions have often been considered as one of the least popular areas of maths. Many children consider the concept of fractions as ‘difficult’ and too often children have had difficulty understanding why they are carrying out a particular procedure to solve a calculation involving fractions. “It has been said that ‘fractions’ have been responsible for putting more people off mathematics than any other single topic.” (Nuffield Maths 3 Teachers’ Handbook: Longman 1991) This is probably due to confusion caused by introducing calculations involving fractions too early, when certain children still require more experience with the visual and practical aspect of creating simple fractions of shapes in order to gain a more secure understanding of what a fraction actually is. Children need to have a firm understanding of what the denominator represents and the numerator represents through the use of visual (and kinaesthetic) resources.

  3. The mission must be to not go back to the experiences of generations before, even though the New National Curriculum risks the past problems being repeated (as it is now crammed full of calculations with fractions). Do be aware it doesn't take much work to find fractions "support" which reinforces misconceptions...

  4. Number and Measure

  5. Picture Frame What fraction of the whole is the picture frame?

  6. How many different ways can you fold an A4 sheet to represent a half?

  7. Build a dragon • Use cubes to make a dragon that is ½ red, 1/5 blue and the rest green. • What fraction is green? • Make a dragon that is twice the size • Describe the colours using fractions

  8. The Fractions Journey • Counting in Fractions • Finding a Fraction of an Amount • Equivalence of Fractions • Mixed Numbers and Improper Fractions • Number operations To be covered next session • Try to have consistent approaches across year groups.

  9. Counting in Fractions Year 2 Count up in ½and ¼ up to 10 (differentiation opportunity?) Year 3 Count up and down in tenths. Year 4 Count up and down in hundredths (huge differentiation opportunity) http://www.mathsisfun.com/numbers/number-line-zoom.html

  10. Finding a Fraction of an Amount Year 3 Recognise, find and write fractions of a discrete set of objects, unit fractions and non-unit fractions with small denominators. e.g. Find ½ of 16 Find ¼ of 12 Find of 15 Year 4 Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities including non unit fractions where the answer is a whole number) - main focus tenths and hundredths. e.g. Find of 30 Find of 28

  11. Reflection... Are circles the easiest shape to tackle fractions with?! What resources might help the pupils?

  12. Equivalence of Fractions Year 3 Recognise and show, using diagrams, equivalent fractions with small denominators. Year 4 Recognise and show, using diagrams, families of common equivalent fractions. Visually seeing http://www.mathsisfun.com/numbers/fraction-number-line.html

  13. Don’t forget Cuisenaire!

  14. Cuisenaire Rods • If the orange rod has a value of one, what is the value of the yellow rod? • Can you find a quarter family? How did you find it? Is there more than one way? • Can you find the value of all the other rods in relation to the orange rod?

  15. NCETM 2014(National Centre for Excellence in Teaching Mathematics) It is important that learners think about relationshipsbetween fractions, rather than just trying to memorise methods for processing them. The learning of fractions should include a strong emphasis on developing reasoning skills, comparingfractional amounts in a variety of contexts and exploring equivalence. https://www.ncetm.org.uk/resources/28795

  16. Equivalence of Fractions Year 5Compare and order fractions whose denominators are all multiples of the same number. Which are bigger than:

  17. Year 6 Use common factors to simplify fractions: Use common multiples to express fractions in the same denominator. Compare and order fractions (once previous is mastered!). Reflection - inequalities

  18. Mixed Numbers & Improper Fractions Year 5 Convert between the two. No "tricks" to be taughts. 4 Nice Example Poor Example

  19. Tangram Puzzle http://nrich.maths.org/1

  20. Aims of the Session • To build understanding of mathematics and it’s development throughout KS2 • To have a stronger awareness of when and how to progress from non-formal to formal methods at the appropriate stage for your pupils (and the pitfalls of formal methods) • To enhance subject knowledge of the pedagogical approaches to teaching mathematics

  21. Where now? • By the next meeting, I am going to trial/action... • * • * • Where next? • Progress in fractions, decimals and percentages

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