Fractions …all the parts! Presented by D & A

Learning Outcomes  To link fractions with addition/subtraction and multiplication/division strategies.  To make sense of fractions and decimals using equipment  To look at BSM and FIO activities related to fractions.

Fractions  Draw one half on a piece of paper.  The trapezium is one quarter of a shape what does the shape look like?

Regions and Sets Continuous (length/region) Discrete (sets) Part to whole This Cuisenaire rod is two thirds of a length. How long is the length? Here are two lollies. They are one-quarter of a bag. How many lollies are in the bag? Whole to part Cut this circle into quarters Here are 12 lollies. If you eat one-quarter of them how many do you get?

Fractional Misconceptions  No acceptance of the existence of numbers between numbers Share 5 biscuits between 4 children …. You can’t do it!

Fractional Misconceptions  The numerator relates to the whole ½ is 1 shared between 2 ¼ is 1 shared between 4

Fractional Misconceptions  The symbol can be either way up  You can’t have fractions greater than 1 4 = 6 never been challenged 6 4 if fractions greater than 1 haven’t been explored

Fractional Framework Regions Knowing how many parts make a whole Number Recognising the symbol Knowing where half lives on a number line Sets Using half as an operator on other numbers

Stage 2/3 RegionsNumberSets Know half is 2 equal parts. Know quarter is 4 equal parts. Recognise symbol ½ Recognise symbol ¼ Doubles and halves

Stage 4 RegionsNumberSets 1 half, 2 halves, 3 halves 1 quarter, 2 quarters, 2 quarters, 3 quarters 4 quarters 5 quarters 5 quarters Place of ½ on a number line. Place of 2 halves 3 halves etc. Find half and quarter of a set by equal sharing.

Using the Teaching Model Materials  Give half of these Smarties to Courtney and the other half to Kieran Imaging  Half of the cake has 4 Smarties. How many on the whole cake? Number Properties  I had 8 Smarties and I ate half of them. How many did I have left?

Stage 5 RegionsNumberSets Comparison and ordering of unit fractions by region. ½ > ¼ > ⅛ Extend knowledge to other fractions: Thirds, fifths, tenths etc. Meaning of – ths Identify symbols for fractions including those greater than 1 Place of ½ on a number line 2 x ½ = 1 4 x ½ = 2 Link to repeated addition for multiplication. Comparison and ordering of unit fractions by sets of ½ of 12 = 6 ¼ of 12 = 3 Link to repeated addition and commutativity of multiplication. ½ x 12 = 12 x ½ = 6

Stage 6 RegionsNumberSets Order unit fraction Recognising equivalence using materials Building decimals, using pipe numbers Place of all unit fractions on the number line Particular attention to tenths Decimal notation for tenths Position of hundredths on number line. Decimal notation for hundredths Extend to thousandths. Solving fractional problems using division. ¼ of 28 from 28 ÷ 4 = 7

Stage 7 RegionsNumberSets Order non unit fractions Fractions out of 100 Percentages Order decimals to 3 decimal places Conversion between fractions, decimals and percentages. Solving fractional problems using knowledge of equivalence ¼ of 64 by ½ 64 = 32 ½ 32 = 16 Solve fractional problems using multiplication and division. ⅜ of 64 = 64 ÷ 8 = 8 8 x 3 = 24

Stage 8 RegionsNumberSets Solve percentages, comparing ratios and proportions

Visit 4  Observation of a lesson which includes warm up, one strategy group and a warm down.  Numpa – retesting of children. Data on line by 15 th November.