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Fractions, Place Value, Decimals & Percentages

Day One: Fractions

http://www.pdst.ie/number

Follow this link for slides and related resources

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Day Two: Place Value, Decimals & Percentages

Overview

• pre-base 10 activities

• 100 square

• problem solving

• counting

• assessment

Day One: Fractions

• instructional framework

• PDST manual

• CPA approach

• Area, linear and set models

• benchmarking and estimation

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• to provide opportunities to reflect on current practice

• to explore the multiple formats that can be used to represent fractions

• to support teachers in developing pupils’ conceptual understanding of fractions

Session One Objectives

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Key Messages

By constructing ideas and communicating

them to others, pupils develop mathematical

concepts

A variety of learning experiences enhances the

understanding of mathematical concepts/skills

and allows for differing abilities and learning styles

Mathematical thinking is developed by eliciting,

supporting and extending children’s mathematical

ideas

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Reflection

• What is your current practice in relation to fractions?

• What resources do you use?

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Fractions Trajectory

Developmental Based on PSC

Concrete Pictorial Abstract

Linear

Area

Set

5 levels

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ICT

Suggested teacher language

To be aware of

Counting in Fractions

Assessment Pack

Consolidation Activities

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Concrete – Pictorial - Abstract

Concrete

Pictorial

Abstract

Differentiation

Learning Trajectory

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Concrete – Pictorial - Abstract

Concrete

Pictorial

Abstract

• cuisenaire• bears• vehicles• cubes• pie pieces• lollipop sticks• geoboards• counters• paper folding

• dotted paper• number lines• empty number

lines• pupil

representations

• fractional notation• numbers written in

words or digit form• mathematical

symbols

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Models for Fractions

Length Set

P62

• ENL• paper strips• string• cuisenaire rods• lolly sticks• distance

• geoboards• pie or rectangular

pieces• hundredth

wheels• paper strips• dotted paper

• vehicles• bears• buttons• counters• cubes• coloured

lollipop sticks

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Eliciting

Supporting

Extending

Instructional Framework for supporting and developing mathematical thinking

Child-centred

Teacher as Facilitator

Language-based

Revoicing

Strategy-sharing

Higher-order

skills

Teacher not

sole validator of

mathematical

knowledge

Pupil self-

reflection

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Level A.1, A.2, B.1 and B.6

• Find half or a quarter of a set or shape

• Compare, order, count and identify fractions and equivalent fractions

Denominators 2, 4,

Denominators 8, 10

Denominators 3, 5, 6, 9, 12

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Activities

Paper Strips

Linear Model

Cuisenaire Activity Geoboards

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• fractional notation

• addition of fractions

Set Model

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Level C.3: Construct algorithms for equivalent and simplified fractions

Slicing squares activity

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Benchmarking and Estimation

• Benchmarks are helpful for pupils to develop their number sense in relation to fractions

• Estimation is central to applying benchmarks. Pupils need lots of opportunities to compare fractions to benchmarks

• The most important reference points or benchmarks for fractions are 0, ½ or 1

• Ideally children should work in groups to identify sensible benchmarks

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Level D.3 Multiply a fraction by a whole number

6 ×

• Represent this equation concretely or pictorially

• Transfer your learning to an empty number line

• How does this support the understanding of the algorithm?

4

3

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How will your experiences from this workshop impact on your teaching of

fractions?

Reflection

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Focus for day 2

AssessmentPlace Value Decimals Percentages