Developing Conceptual Understanding of Fractions in Years 3 and 4

Aims To review and further develop personal subject knowledge relating to teaching fractions and consider progression from KS1 to Y3 and Y4 To consider how children learn about fractions and misconceptions that may arise. To explore effective pedagogies - models and images to support conceptual understanding of fractions

Task Look at the progression in fractions. What do you think are the prerequisite skills pupils learn in Y1 & Y2 that are key to pupils understanding fractions in Y3 and Y4?

Multiple Representations Sort the cards into families so that each family shows the same fraction in different ways

Can you locate a fraction in between them? Exploring Misconceptions: ‘Fractions are part of shapes, not numbers in their own right’ Provide regular opportunities to count forwards and backwards in fractions Locate fractions on a number line, e.g. and     Can you locate a fraction in between them?

Use structured apparatus to support understanding of Fractions and the link with decimals 1 10                   This highlights relationship between tenths and dividing by ten   0.5

Comparing, ordering and equivalence

Paper Folding: Equivalence Compare and order fractions whose denominators are all multiples of the same number Paper activity 1 – A4 paper Paper activity 2 – strips paper **link to fractions of amounts*** Folding fractions

Fraction Wall

Fractions ITP FRACTIONS ITP Need to secure understanding around equivalent fractions Build on the work undertaken in Y3 and Y4 using diagrams (fraction walls and Fractions ITP paper folding and numicon shapes) Seeing the images is improtant in pupils understanding of the concept adding fractions

Equivalent Fractions What do you notice about the equivalent fractions?  

Exploring the tangram http://nrich.maths.org/1 Determine the fractional value of each piece if the square is 1? each large triangle = each small triangle = medium triangle = square = parallelogram = 1 4 16 8 Pose the question “If the whole area is 1, what is the area of different bits?”

Comparing and ordering Fractions with the same denominator        

To order fractions, learners also need to see them as points on a number line and convert to decimals.. Use bead bar or bead strings to locate decimals, fractions and percentages and highlight relationships between them: If you get 50% put it over 100 as this is 100% This is the type of activities you would be doing in your basic skills sessions If you have 17/25 as a comparison fractions – easily converted into 68/100 (scaling) This is fluency in making connections between numbers – seeing we can use knowledeg of equivalence and scaling up of and 20th s 25ths to 100ths helping to make comparisions of fractions  

Using measuring equipment: Y3 Count up and down in tenths Y4 hundredths, Y4 recognise hundredths arise when dividing an object by one hundred Y3 and dividing tenths by ten Using measuring equipment:     Talk about ml in terms of medicine spoon – small amounts CLICK for ARROW TO APPEAR Convert 600ml to litres = 600ml children feel like they need to x by 1000 – but the proportion we have is smaller than the whole so the answer will be 0.6 litres

Use structured apparatus on a place value chart to highlight relationships… If children struggling with the concept of fractions and decimals take them back to place value ….. This links perfectly to all the work you have already done on place value – (x and dividing by 10 100 and 1000) REPRESENTATION HEALTH WARNING When the representation becomes 1 (but shows 100 – base 10 flat) Use the multiplicative language 10 times bigger 100 times smaller etc

Use money on a place value chart to highlight relationships…

Introduce ‘pixie deines’ to highlight the relationship between each of the decimal places:

Calculating with Fractions

Raised Expectations Year 3 add and subtract fractions with the same denominator within one whole Year 4 add and subtract fractions with the same denominator

Calculating Fractions with Structured Apparatus = Missing Number Box: + =           Bridging through 1: =     1  

Adding and Subtracting Fractions Potential misconception: When adding (or subtracting) fractions, pupils add (or subtract) both the numerators and the denominators 0.2 & 20% 0.5 & 50% 0.7 & 70% Using a range of representations can support understanding

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The picture should now look like this: Simplify the fraction Look for the greatest common factor of both 3 and 6 = 3

Application     In this question we have the missing box and application of the skills Equivalence 5/15 is orange 6/15 apple juice Answer 3/15 is lime or simplified 1/5

 

Always, sometimes, never  

KS2 Sample Arithmetic paper 2016

Sample KS2 Reasoning Papers 2016