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Fractions, Place Value, Decimals & PercentagesDay Two: Place Value, Decimals & Percentages

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• to provide opportunities to reflect on current practice

• to engage participants in activities that can be used to develop the concepts of place value, decimals and percentages

• to explore journals and learning logs as a form of assessment

Session Two 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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• How do you currently teach the concepts of place value, decimals and percentages?

• What resources do you use?

Reflection

4

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Large Numbers

What is a million?

What is a billion?

What is a trillion?

Working in pairs, represent these amounts using numbers and symbols.

p.14

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Place Value, Decimals and Percentages Trajectory

Developmental Based on PSC

Concrete Pictorial Abstract

Linear

Area

Set

4 levels

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Suggested teacher

language

To be aware of

Consolidation Activities

Assessment Pack

Differentiation

Book Walk

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Instructional Framework for Supporting & Developing Mathematical Thinking

Eliciting

ExtendingSupporting

P 11

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Concrete – Pictorial - Abstract

Concrete

Pictorial

Abstract

• base 10• lollipop sticks• cubes• straws• counters• geoboards• paper folding

• dotted paper• number lines• empty number

lines• pupil

representations

• number fans• arrow cards• record sheet• decimal notation• numbers written in

words or digit form• mathematical

symbols

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Multiple Representations

Length Set

• paper strips• string• cuisenaire rods• empty number

lines

• geoboards• pie or rectangular

pieces• hundredth wheels• decimal fraction mat• paper strips• dotted paper

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

lollipop sticks

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Place Value

• The understanding of place value requires pupils to group by tens.

• This requires procedural knowledge regarding how these groups are recorded in our place-value system. This takes time.

• Before introducing base 10, pupils should be given opportunities to exchange in lots of bases

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Figure it Out

124 in base 8 stands for what number in our base 10 system?

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Level A.1 Explore, identify and record place value 0-99

Exchanging:

Ring is King

• Play in base 4

• Dice: 1, 2, 3

• First grouping: counters

• Second grouping: straw

• Third grouping: rings

pp. 25-29

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• Introducing Base Ten

Base 10pp. 30-36

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100 Square Activities Interactive 100 Squares

The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013

P37-41

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Level A.1, A2, B.1, B.2 C.1, C.2, C.4, C.6 and D.4

• Explore, identify and record place value 0-99, 0-199 and 0-999.

• Read, write and order 3 and 4 digit numbers

• Explore, express and identify place value in decimal numbers to two places and three places

• Solve problems involving decimals

• Explore and calculate simple interest, profit, loss and VAT

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Practical Activities

Nice or nasty

Win a one

Base 10 activity catalogue trail

Make 4.253

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Appendix C p.99

Area Model

• Level B.5: Make, order, compare and count decimals

• Level D.3: Compare and order fractions, percentages and decimals

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Counting (Appendix A)

• Sound of a number

• Fill the bag

• Rope activity

• Count around

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Target Board

520 100 490 460 180

360 670 330 240 990

280 230 720 300 130

200 380 210 190 820

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Assessment in the Primary School Curriculum: Guidelines for Schools (2007)

Assessment

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• to provide a vehicle for writing about thinking as a way of learning

• to provide a record of students’ thinking• identify challenges students are facing in their

learning which may help direct future instruction

• to increase student’s awareness of how they learn and remember

• to provide a context for recalling previous learning and summarising present learning

The purpose of Journal Writing

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• open-ended questions

• talk and discussion N.B prior to writing

• writing should be in pupils’ own words but incorporate appropriate maths vocabulary

• pupils need to know their audience

• allow for a variation of responses

• writing prompts

• model the process

• feedback from the teacher.

Using Journals in Mathematics

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Example• P. 91

Working in your group, brainstorm journal prompts for your given category.

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How will your teaching of the concepts of place value, decimals and percentages

change as a result of this workshop?

Reflection

25

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Scoilnet Themepages Numeracy

• Decimals and Percentages

• Fractions

• Place Value