FRACTIONS, DECIMALS, PERCENTAGE, RATIO AND PROPORTION (FDPRP) SCITT Maths Day 5 FRACTIONS, DECIMALS, PERCENTAGE, RATIO AND PROPORTION (FDPRP)

Another go… Talk your way through these examples… 42 x 7 = 243 x 6 = 57 ÷ 3 = 62 ÷ 4 = 125 ÷ 3 = 324 ÷ 12 =

Group Reading D Haylock ‘Mathematics Explained for Primary Teachers’ Chapters 14 and 16 SEARCH Nrich ‘Understanding Fractions’ ‘Teaching Fractions with Understanding: Part-whole Concept’

Today we will…. Consider the differing mathematical concepts involved with fractions Explore the relationships between different representations FDPRP Consider how this adds to developing understanding in properties of number Associated issues for teaching How do fractions link with other aspects of mathematical learning? Errors and misconceptions and their role in learning mathematics

…as a learner …as a teacher SELF-AUDIT What do you know now? What do you understand? Opportunities for clarification? Questions to answer through the day? …as a learner …as a teacher

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

Starters What could you learn about a pupil’s understanding of fractions? What fractions can you make with digit cards 1, 8, 2 and 4? 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) Are all the fractions different? Choose a way / some ways of sorting the fractions into groups. Explain your thinking. If this is half the house, can you make the whole?

Written representations… ‘Three quarters’ ¾ 6/8 12/16 75/100 75% 25% + 25% + 25% 0.75 ¼ + ¼ + ¼ ½ + ¼ …

What’s the same? What’s different? Images from NRICH www.nrich.org “Say what you see; see what is said” NCETM Primary Magazine Issue 74: Maths in the Staff Room

What do you know about…? 7 3

Pick three numbers from… 2, 3, 4, 5, 6, 7, 8, 9 Introduce the term integer

Start your number line at zero Mark the position of your fractions on the Number Line with crosses (X). 1 2 Start your number line at zero Check understanding of number line. Decide on level of accuracy required. Discuss strategies – paper folding, decimals etc.

FDP equivalences Draw a number line 0% 100% 0 1 Mark as many points on the line as you can and label these points as fractions, decimals and percentages. (How will you ensure accuracy?) 50% 0.5 ½

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

Reasoning Questions

Halving means divide by 2…? Apply it… ⅓ x ¼ = ⅔ x ½ = ⅓ ÷ 2 = ¼ ÷ 4 = 6 ÷ ¼ = 12 ÷ ⅔ = Sharing? Counting? Grouping? Halving means divide by 2…? Commutativity?

NCETM ‘Teaching for Mastery’ What examples are given for fractions? What are the Big Ideas? Do the maths! Master it yourself. What would the learners need to be successful? Could you use ideas to assess learning? Starters? Use common misconceptions? Challenge thinking?

Defining terms ‘Proportion’ 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 ‘Ratio’ So, 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”

KS2 ii

MATHS TASK 4 Reflective Log Outcomes: Carrying out the assessments gives you information about the learners after one term of teaching (evidence of impact) You experience what formal and informal evidence of learning. You discuss whole-school assessment systems for tracking progress ST/MT/LT. Track progress of learners with your mentor (3 identified learners at different stages of understanding) using the school’s assessment system to support judgements. Look at a range of informal and formal ‘mathematical evidence’ (observations, books, group work…) and use this to assess levels of understanding (mastery). Analyse your findings with reference to age- appropriate NC expectations and any other assessment materials your school uses. Reflective Log