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Fractions, Decimals, Percentage, Ratio and Probability

This session focuses on understanding the relationship between fractions, decimals, percentage, and ratio, as well as exploring probability through predicting and testing activities. Homework and other learning opportunities outside the classroom will also be discussed.

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Fractions, Decimals, Percentage, Ratio and Probability

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  1. SCITT Day 10 Fractions, decimals, percentage, ratio and probability

  2. Summer Term Visits by Gill

  3. We will… • understand the relationship between fraction, decimal, percentage and ratio; • explore probability as an extension of activities with predicting and testing; • discuss homework and other associated learning outside the classroom.

  4. Associated issues for teaching • Extending the number line to include all real numbers. • Consider the role of mathematical games in the classroom. • Finding relevant homework activities. • Probability as “making decisions”, a key life skill. • & CALCUALTORS!

  5. Sessions 1. Homework and FDPRP 2. Calculators in the Primary Classroom 3. Games to consolidate learning 4. What / where next? Identifying your next steps for mathematics learning and teaching.

  6. Homework • What is your school policy for homework? • What have you seen as examples of homework? • How COULD homework be used? • What could maths in the home look like? • What role could games play at different ages?

  7. Issues to consider 1.Manageability 2.Parents – info and support 3.Timings? 4.Variety 5.Use of existing scheme/books to provide materials. 6.Use of games? 7.Investigations? 8.Staff meeting provision… 9.Open evening/meeting?

  8. Fractions Identifying the language, models, images and experiences children need in order to have an understanding of fractions; Considering the different concepts involved in fractions; Reviewing a range of materials which can support the learning of fractions.

  9. Mental Oral Starters What could you learn about a pupil’s understanding during these activities?

  10. This is half the house.Can you make the whole?

  11. Halving • Create an array of counters 3 x 4. • Can you put a line through the array to show half? • How many different ways can you find? • Choose another array, try placing 1, 2, 3…. lines. Talk about what’s happening! • (Use language of x, ÷ or fractions)

  12. What fractions can you make with 1, 8, 2 and 4? Are all the fractions different? Choose a way / some ways of sorting the fractions into groups. Explain your thinking.

  13. How might ¾ be represented? With your partner, generate as many different representations of ¾ as you can. Draw each ‘ ¾ ’ on a different post-it. Compare your representations with others.

  14. Part – Whole Fractional Models • Area: The whole is split in to equal parts. • Linear: The size of the fraction is modeled by the length of the line. 0 ¼ ½ ¾ 1 • Set: The set of objects is the whole and we split in to equal subsets. ** ** ** **

  15. Fractions Should be Thought of as… • Part of a whole (proportion) • A relationship between two separate things (ratio) • A division operation ÷

  16. Percentages How would you express 7/8 as a percentage? How would you express 85% as a fraction?

  17. Would you Prefer to Calculate using Fractions, Decimals or Percentages? 0.5 x 40 145% of 1000 Which is larger, 8/10 or 6/7?

  18. Progression in Understanding Where do your learners fit into this progression? Fractions are… 1. Part of whole – region split in two or more parts 2. Part of the set 3. Numbers on the number line 4. An operator (division) 5. A ratio

  19. Misconceptions • Fractions are less than 1 • The bigger the denominator the bigger the size of the fraction • The smallest number always goes on top • If I split any shape into 2 pieces, they are two halves • ½ = 2/3 = ¾ = 4/5 … • 2/3 + 2/3 = 4/6 • represents 1/3

  20. As a Fraction “¼ of the tiles are green” As a Decimal “0.25 of the tiles are green” As a Percentage “25% of the tiles are green” Defining terms

  21. As a Proportion “One in every four tiles is green” As a Ratio “The ratio of green tiles to red tiles is 4 to12 or 1 to 3” or “1 green for every 3 red” Defining terms

  22. Proportion and Ratio

  23. Proportion and Ratio

  24. Proportion and Ratio

  25. Games to support FDPRP • 0 – 10 line: Decimal Digit cards • Calculator Fish • Domino Fractus!

  26. Probability Scale What is the probability of… Flipping a coin and it landing on ‘heads’?

  27. Probability Scale What is the probability of… Rolling a ‘5’ on a normal dice?

  28. Probability Scale What is the probability of… Choosing a Jack from a pack of cards?

  29. Probability Scale What is the probability of… Picking a red counter from a bag with 3 blues, 2 yellows and 4 red counters?

  30. Number Spinners ITP • …it’s on the disk!

  31. Games for thinking Target 24 – in Pairs • Use any numbers from 1 to 10 (once and once only) to add cumulatively. • The player that makes ‘24’ wins. Ideas for adaptations?

  32. Games for thinking Turn over 2 digit cards. Use any maths you know to make as many ‘solutions’ as you can…e.g. Player 1 turns over 2 and 5… Cover: • 2 and 5 • 25 and 52 (Place value) • 3, 7, 10 (using 3 of the 4 operations) • 2 (or 2 x 2 x 2 x 2 x 2 = 32) … (5 is covered!) Adaptations? 5 2

  33. Calculator digits

  34. Getting to know your calculator • How does the memory work? • How does the constant facility work?

  35. Calculators as a teaching tool • Press the following sequence of buttons • 5 + + = 0 • Now press = 3 times • What happens? • What if I press it 3 times more? • How many presses to get to 50? • What about - - or x x?

  36. Try this • 9 + + = • Now enter 12 and ask the question • “ What number is 9 more than 12?” • Press =

  37. Constant function • Some are: • Start no + + step size = = = • Others are • Step size + + start number = = = • What have you got? • Try 24 ++ 5 =========

  38. Mathematical Games Share your games… • What was the intended learning objective? • Does the game support that learning intention? • How could the game be adapted?

  39. Did we…? • understand the relationship between fraction, decimal, percentage and ratio? • explore probability as an extension of activities with predicting and testing? • discuss homework and other associated learning outside the classroom? • Extending the number line to include all real numbers? • Consider the role of mathematical games in the classroom? • Finding relevant homework activities? • Probability as “making decisions”, a key life skill? • & CALCULATORS?

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