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