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Mathematics Subject Leader. Summer 2010. Agenda. Fractions Steps to Success Girls’ mathematics – update Mathematics outside the classroom VAK. Creative Mathematics A conference for primary heads, mathematics subject leaders and teachers. Keynote speaker – Rob Eastaway
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Mathematics Subject Leader Summer 2010
Agenda • Fractions • Steps to Success • Girls’ mathematics – update • Mathematics outside the classroom • VAK
Creative Mathematics A conference for primary heads, mathematics subject leaders and teachers Keynote speaker – Rob Eastaway Date: Friday 22nd October 2010 Venue: Rheged, Penrith
Session One Fractions
Aims • To explore teaching and learning of fractions with a focus on images, talk and notation • Progression of fractions through the school • To consider children’s errors and misconceptions
A half Numerator - the number of the parts Denominator – name of each part 1 2
Half of a square recombined recombined
A fraction becomes ‘a bit’ less than a unit, it splits a unit into parts and we have smaller units grouped to make a larger unit. So the number notation 7/10 in using 7 out of 10 a pair of numbers and comparison between quantities – one part of a whole
Talking fractions What do we here children saying: • Harf, harving, kwarter • ½ reads ‘one line two’ • ¼ reads ‘one line four’ Do we stress as teachers: one equal part Changing out of – to – out of every . . .
Key Stage Two SATs question Question 10: Fraction pyramid Shade 1/5 of this shape.
Find ¼ of each of these . . . • Part of a paper circle • A potato • Twelve counters • A piece of string • A two pound coin • A jug of water • Three paper equilateral triangles • Four cubes • Seven matchsticks
Which is bigger? Without using equivalents identify which is the larger in these fractions: 4/11 or 4/13 2/3 or 3/4 2/5 or 1/4 4/9 or 2/5
Division and fractions • I divide 29 pencils equally between 6 people. How many pencils does each person get? • 29 people are going on a journey. Each car holds 6 people. How many cars are needed? • You collect 29 CD tokens. You get a CD for every 6 tokens. How many CDs can you get? • 6 people win £29 and divide it equally between them. How much does each person get? • Divide 29 cakes equally between 6 people. • 6 people go out for a meal. The bill is £29. how much do they pay each? • Work out 29 ÷ 6 correct to 3 decimal places.
I don’t get fractions. I thought a quarter was less than one. I suppose it can be different on different days. How do you know which day means which? Can you work out a quarter of twelve? A quarter is three. Excellent! Three
Common Misconceptions • Fractions are always part of one, never bigger • Fractions are parts of shapes and are not numbers in their own right • A fraction such as ¾ is always seen as ‘three lots of a quarter’, without recognition that it can also be ‘a quarter of three’ • Decimals with more digits are bigger • Percentages can never be bigger than 100%.
Ordering fractions Draw a line like this. 0 0.5 1 Take turns to choose two numbers from 12 3 4 5 6 7 8 9 10 11 12 to make a fraction. Use your calculator to convert the fractioninto a decimal. Mark the decimal on the line and label it with your initial. Try to get three of your marks in a line without anyone else’s marks in between.
½ Resources 0.375 Counting sticks Blank card and peg Washing line Elastic Dominoes Flapjacks Circle pies Guess the fraction Dice – table and OHT Fraction strips Large Coins (decimal money notation) Follow me cards Chocolate and bags of sweets 37.5% ⅜ 1½ 1⅝ 0.75
Train Display The information display on a train shows letters by illuminating dots in a rectangular 5 x 8 array. In the letter 't' shown, what fraction of the dots in the array is illuminated?
Session Two Steps to Success
Booklet pages 4-7 which set out the ‘story’ of making use of the different elements of the resource to support planning and teaching the short description of each of the components the case studies providing examples of school-based use of the overcoming barriers materials which form the heart of the compendium
Discussion: whole-school implementation What are the implications of the availability of the compendium as a whole-school resource? How can you ensure that head teachers and senior leaders are aware of the compendium and steer its use across the school? What opportunities are there to review the whole-school approach to assessment and intervention? How will you distribute the compendium and convey key messages?
Session Three Mathematics Outside the Classroom
“We believe that every young person should experience the world beyond the classroom as an essential part of learning and personal development, whatever their age, ability or circumstances.” Such experiences “help us to make sense of the world around us by making links between feelings and learning. They stay with us into adulthood and affect our behaviour, lifestyle and work. They influence our values and the decisions we make. They allow us to transfer learning experienced outside to the classroom and vice versa”. “Learning Outside the Classroom” manifesto
Learning mathematics outside the classroom is not enrichment, it is at the core of empowering an individual’s understanding of the subject. “Learning Outside the Classroom” manifesto
Getting out of the classroom facilitates authentic or experiential learning (the engagement of learners with the world as they actually experience it) and gives better access to the main pathways to learning (Visual, Auditory and Kinaesthetic). Pupils not only experience mathematics in concrete and novel settings, but can be liberated from the sometimes restrictive expectations of the classroom. “Learning Outside the Classroom” manifesto
“Learning Outside the Classroom can take place a few feet from the classroom or a few thousand miles from the school. At the Foundation Stage it could be part of a regular ‘expedition’ across the school field to a wooded corner of the site as part of a Forest Schools programme. These experiences are as challenging and exciting to younger children as organising a Duke of Edinburgh Award Silver expedition trip is to older pupils”. “Learning Outside the Classroom” manifesto
“Learning outside the classroom takes place in many locations - from a school allotment or local library to a place of worship, art gallery or visit to the seaside. By themselves these will be exciting and stimulating activities. However, their true value lies in the learning that comes from the experience and how it is applied throughout the rest of the curriculum. In this sense, learning outside the classroom should be a seamless part of learning inside the classroom and not separate from it.” “Learning Outside the Classroom” manifesto
‘The overwhelming majority of educational visits are carried out safely and responsibly by teachers who take the time and effort to get things right. The benefits of such trips to pupils can be immense. Exposure to well managed risks helps children learn important life skills, including how to manage risks for themselves. The Learning Outside the Classroom Manifesto aims to ensure that all young people have a variety of high quality learning experiences outside the classroom environment.’ Martin Smith Chairman of the Outdoor Advisors Panel
Even the most modest of school grounds offer opportunities to discover the exciting world of mathematics in a safe and easily accessed environment, from tessellating patterns in brickwork, to dendrochronology and other cross-curricular activities such as wild-life surveys. The grounds also provide space to act out the otherwise 2-dimensional and abstract limitations of the whiteboard into meaningful 3-dimensional representations involving pupils in a creative and active way.
Discussion Time What opportunities do you give your children to do mathematics in the outdoors?
Have you thought of… • A maths trail? • Shape and number spotting? • Working with big measures (playground dimensions, girth of tree, height of plants, amount of water in rain barrel, etc)? • Co-ordinates and grid work? • Area and perimeter (of leaves as well as buildings)? • Scale drawings? • Estimation (blades of grass on football pitch)? • Average rainfall calculations?
Year three I wanted the children in my class to understand the importance of mathematics and to come to the realisation that it is all around them and is a fundamental part of their everyday life in and out of school. I asked for their help in organising our class trip to St. Nicholas’ Cathedral in Newcastle-upon-Tyne which was coming up in a few weeks time. I put the onus on them to plan every detail of the outing, which gave them ownership of their learning and fully engaged them in the mathematical processes involved in the preparation of such an activity. I wanted them to experience mathematics in a true-to-life, not a contrived context and take their mathematical learning out of the class text books and into the real world.
Planning a visit to the Cathedral (Grand Day Out) A Y3 trip Timetable problems Traffic survey Budgeting for the trip Distance activities on the yard Time and distance The maths trail Videos available on https://www.ncetm.org.uk/resources/7545#
Year Three of Corbridge Primary School began their project with a trip to the Prudhoe ‘Badger’. They walked its perimeter, estimated its area, saw it from a variety of viewpoints exploring ideas of perspective and distance and came back to school with drawings, sketches and measurements and tried to accurately reproduce the form on squared paper asnear as they could to scale.
