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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