# Fractions, Place Value, Decimals & Percentages workshop 2 plac… · Decimals & Percentages Day...

### Transcript of Fractions, Place Value, Decimals & Percentages workshop 2 plac… · Decimals & Percentages Day...

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

• 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

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

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

• What resources do you use?

Reflection

4

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

Place Value, Decimals and Percentages Trajectory

Developmental Based on PSC

Concrete Pictorial Abstract

Linear

Area

Set

4 levels

ww

w.p

dst

.ie ICT

Suggested teacher

language

To be aware of

Consolidation Activities

Assessment Pack

Differentiation

Book Walk

ww

w.p

dst

.ie

Instructional Framework for Supporting & Developing Mathematical Thinking

Eliciting

ExtendingSupporting

P 11

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

Figure it Out

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

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

• Introducing Base Ten

Base 10pp. 30-36

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

Practical Activities

Nice or nasty

Win a one

Base 10 activity catalogue trail

Make 4.253

ww

w.p

dst

.ie

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

ww

w.p

dst

.ie

Counting (Appendix A)

• Sound of a number

• Fill the bag

• Rope activity

• Count around

ww

w.p

dst

.ie

Target Board

520 100 490 460 180

360 670 330 240 990

280 230 720 300 130

200 380 210 190 820

ww

w.p

dst

.ie

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

Assessment

ww

w.p

dst

.ie

• 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

ww

w.p

dst

.ie

• 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

ww

w.p

dst

.ie

Example• P. 91

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

ww

w.p

dst

.ie

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

change as a result of this workshop?

Reflection

25

ww

w.p

dst

.ie

Scoilnet Themepages Numeracy

• Decimals and Percentages

• Fractions

• Place Value