SCITT Day 10 Fractions decimals percentage ratio and

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

Summer Term Visits by Gill End of day 9. 6 Tash & Jess Northwick Park Primary School Hockley 10. 6 Peter & Martin Brightlingsea Junior School & St Johns Colch 11. 6 Roxie & Amy Northwick Park Primary School Basildon 20. 6 Danielle & Tamsin Takeley P 23. 6 Sarah & Clare Bentfield & Henham+Ugley 24. 6 Laura Cold Norton Thurrock 25. 6 Tom & Adam Stebbing St Peters 26. 6 Katie Newnham Crofy Herts 27. 6 Candice & Louise Lyons Hall & White Notley 30. 6 Emma & Stefanie Copford & Heathlands Colch 1. 7 Rebecca & Jo Highwood & Moulsham Inf Chelmsfd 2. 7 Richard Water Lane Harlow 9. 7 Lucy & Tacita Felsted & Boreham Gt Easton & Thaxted 10. 7 Dan & Stacey

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.

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!

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.

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?

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?

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.

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

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

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)

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.

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.

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. ** **

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

1/5 of 2 4 x 1/10 ½ of 80% 40% 2 x 1/5 8/20 2/5 4 ÷ 10 4/10 2÷ 5 0. 400 4 x 0. 1

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

Would you Prefer to Calculate using Fractions, Decimals or Percentages? 1. 0. 5 x 40 2. 145% of 1000 3. Which is larger, 8/10 or 6/7?

Progression in Understanding 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 Where do your learners fit into this progression?

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

Defining terms 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 As a Proportion • “One in every four tiles is green” As a Ratio • “The ratio of green tiles to red tiles is 4 to 12 or 1 to 3” • or “ 1 green for every 3 red”

Proportion and Ratio

Proportion and Ratio

Proportion and Ratio

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

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

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

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

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

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

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?

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 5 (or 2 x 2 x 2 = 32) … 2(5 is covered!) Adaptations?

Calculator digits

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

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?

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

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

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

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?