Parent Workshop Fractions, Decimals & Percentages (Bar Modelling)

James Smyth Year 6 Teacher and Maths Coordinator Liz Martin Year 1 Teacher Charlotte Griffith Year 3 Teacher Ruth Scott Year 5 Teacher

Programme of Study – Year 1 & 2 - Number and Place Value - Addition and Subtraction - Multiplication and Division - Fractions - Measure - Geometry - Statistics

Programme of Study – Year 3 & 4 - Number, Place Value & Rounding - Addition & Subtraction - Multiplication & Division - Fractions & Decimals - Measure - Geometry - Statistics

Programme of Study – Year 5-6 - Number, Place Value & Rounding - Addition & Subtraction - Multiplication & Division - Fractions, Decimals & Percentages - Measure - Geometry - Statistics - Ratio & Proportion (Year 6 only)

Programme of Study (Website)

New Curriculum 2014 Focus on: - Fluency - Reasoning - Problem Solving

Fluency To be fluent in mathematics children should be able to… - grasp the fundamentals of mathematics - practice arithmetic skills - make connections - become more confident with written and mental methods - be confident with what they are doing and why - recall and apply their knowledge rapidly and accurately

Fluency Examples of fluency in fractions, decimals and percentages: - Find ½ of 8 (Year 1) - Find 1/3 of 30 (Year 2) - Find 2/5 of 45 (Year 4) - Find 5 equivalent fractions of ¾ (Year 5) - 4/7 ÷ 5 (Year 6) - 75% of £1340 (Year 6)

Reasoning Through reasoning problems children should… - be able to explain why an answer is right or wrong - follow a line of enquiry to a logical conclusion - prove theories using mathematical language Can be thought of as the ‘glue’ that helps maths makes sense.

Reasoning Examples - Which would you rather have, three quarters of £2 Reasoning Examples - Which would you rather have, three quarters of £2.40 or one quarter of £6? Explain your reasoning. (Year 4) - Sophie thinks 1.007 is bigger than 1.01 because 7 is bigger than 1. Do you agree? Explain why. (Year 5)

Problem Solving Children should be able to… - apply their mathematics to a variety of routine and non-routine situations - put maths into context - break down problems into a series of manageable steps This is fundamental to the mathematical development of all children

Problem Solving Examples: -Look at 20 toy cars Problem Solving Examples: -Look at 20 toy cars. Is it possible to find ½, 1/3 and ¼ of them without breaking any of them? (Year 2) - Find the smallest number that can be added to 92.7 to make it exactly divisible by 7. (Year 6)

Fluency Time -To support the basic arithmetic skills - Short sessions (5 minutes) alongside day-to-day maths lessons

Problem Solving Pineapple I’m here to set children mathematical problems and help them with their reasoning and problem solving.

Concrete – Pictorial - Abstract At Lindfield Primary Academy we believe that all students, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. This is why we work through a Concrete – Pictorial – Abstract approach

Concrete Students have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.

Concrete

Pictorial Students build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems.

Pictorial

Bar Modelling Using the bar model 4 11 ? 4 15 ? 4 ? ? 20 20 ? 20 ? 4 + 11 = ? 4 11 ? 15 - 4 = ? 4 15 ? 5 x 4 = ? 4 ? 20 ÷ 5 = ? ? 20 2 of 20 = ? 5 20 ? Share 20 in the ratio 2:3 20 ? Using the bar model

Early Years Using the bar model Aliya had 4 oranges, Alfie had 3 oranges. How many oranges did they have altogether? Using the bar model

Using the bar model

Using the bar model

Key Stage 1 Using the bar model

Key Stage 2 Using the bar model Pictorial Abstract 300 ÷ 5 = 60 Eats Matthew has a 300g block of cheese. He eats 2 5 of the cheese and puts the rest back in the fridge. How much cheese did Matthew put back in the fridge? Pictorial Abstract 300 ÷ 5 = 60 Eats Put back 60 3 x 60 = 180 Using the bar model

Abstract With the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.

Abstract

FDP Progression in School Halving of sets of objects begins as early as EYFS and Year 1. It is vital that children know halves and quarters must be equal in size. In Year 2 children begin to use ½, ¼, ¾ and 1/3 ; find simple fractions of amounts (½ of £12 = £6) and know equivalence of ½ = 2/4 .

Progression in KS2 In Year 3 children begin to use the terms denominator and numerator in writing proper fractions. They recognise, find and write fractions of objects and begin to compare and order them. They begin to add and subtract them and solve problems. In Year 4 children read and write fractions, ordering them and recognising equivalent fractions. Children also find fractions of amounts (3/5 of 25Kg = 15Kg). They continue to add and subtract fractions and understand more equivalences, including tenths and hundredths.

Progression KS2 By Year 5 children simplify fractions. They relate fractions to decimals and percentages, and begin to multiply them. They begin to convert mixed numbers to improper and vice versa. In Year 6 we ask children to find common factors in numerators and denominators. They multiply and divide fractions and associate them with division. Children convert between F, D and P and recall and use equivalences.

Fractions - what are they? 1 2 Part of a whole. When an object or number is divided into a number of equal parts, then each part is called a fraction.

Fractions A fraction is a part of a whole Slice a pizza, and you will have fractions: 1/2 1/4 3/8 (One-Half) (One-Quarter) (Three-Eighths) The top number tells how many slices you have The bottom number tells how many slices the pizza was cut into.

The denominator is downstairs! Parts of a Fraction Numerator 2 5 How many parts you have. Denominator The number of parts the whole is divided into (total). The denominator is downstairs!

Lowest Common Denominator Language of fractions Language of fractions is used all around children, “here’s my half.” “I’ll cut this cake into equal parts for the four of us.” etc We would encourage correct use of terms from early on - not “My half is bigger than yours!” Mixed Number Simple Fraction Equivalent Fraction Lowest Common Denominator Improper Fraction Simplifying

Equivalent fractions Equivalent fractions are fractions that are equal in size but have different denominators or numerators. 1 = 2 2 4 There are many more! We use a fraction wall as well as lots of images and models to aid understanding.

Fractions, Decimals and Percentages Decimals, Fractions and Percentages are just different ways of showing the same value: A Half can be written...     As a fraction: 1/2 As a decimal: 0.5 As a percentage: 50%

Fraction terminology Numerator: the number on the top of a fraction showing the number of equal parts in the fraction eg 3/4 Denominator: the number on the bottom of the fraction showing the total number of equal parts in the whole eg 3/4 Proper fraction: the numerator is less than the denominator eg 2/3 Improper fraction: the numerator is larger than the denominator indicating that the parts come from more than one whole (top-heavy fractions) eg 9/5 Mixed fraction: has a whole number and a fraction eg 8 ½ Equivalent fraction: the same fraction written in different ways so each one gives the same answer in a calculation, even though they look different eg ½ and 3/6 Common denominator: a number that can be divided by the denominators of all of the fractions eg 2/3 5/8 7/12 all the denominators divide into 24 so 2/3 becomes 16/24, 5/8 becomes 15/24, 7/12 becomes 14/24. So 24 is the lowest common denominator as this is the smallest number that 3, 8 and 12 will divide into.

End of Key Stage Assessment For Year 2 children – SATs - Arithmetic Paper - Reasoning & Problem Solving Paper For Year 6 children – SATs - Arithmetic Paper (30 mins) - Two Reasoning & Problem Solving Papers (40 mins)

Academy Website – Maths Section - Year Group Overviews - Times table challenge support - Calculation Policy - Key Vocabulary - Maths Websites

Maths Websites Super Maths World Supermathsworld (Username:1010lpa) My Maths My Maths - https://www.mymaths.co.uk/   USER NAME: lindfieldps PASSWORD: nine

Times Tables Rockstars - https://ttrockstars.com Times Table Rockstars Times Tables Rockstars - https://ttrockstars.com

Books Maths for Mums and Dads Maths on the Go Rob Eastaway and Mike Askew Maths on the Go Rob Eastaway and Mike Askew

Pupil Demonstrations Key Stage 1: Jumaima Choudhury Jess Tingley Millie Farbrother Year 3: Charlie Kell David Boyer Finley Piddington

Pupil Demonstrations Year 4: Charlotte Smith Sam Mercer Ava Burnage Year 5: Ellie Martin Beth Simmons Alice Anderson Year 6: Hannah Bryan Tess Marshallsay Martha Gibson Maria Forrest

Any questions please feel free to talk to any of us afterwards