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Decimals and Percentages

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Decimals and Percentages Marie Hirst, Numeracy Facilitator, m.hirst_at_auckland.ac.nz Mathematics Lead Teacher Symposium Waipuna Conference Centre September 2011 – PowerPoint PPT presentation

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Title: Decimals and Percentages


1
Decimals and Percentages
Marie Hirst, Numeracy Facilitator,
m.hirst_at_auckland.ac.nz Mathematics Lead
Teacher Symposium Waipuna Conference
Centre September 2011
2
To be a proportional thinker you need to be able
to think multiplicatively
  • How do you describe the change from 2 to 10?

Additive Thinking Views the change as an
addition of 8 Multiplicative Thinking Views the
change as multiplying by 5
3
Proportional Thinking
A sample of numerical reasoning test questions as
used for the NZ Police recruitment
4
  • ½ is to 0.5 as 1/5 is to
  • a. 0.15
  • b. 0.1
  • c. 0.2
  • d. 0.5

5
  • 1.24 is to 0.62 as 0.54 is to
  • a. 1.08
  • b. 1.8
  • c. 0.27
  • d. 0.48

6
  • If a man weighing 80kg increased his weight by
    20, what would his weight be now?
  • a. 96kg
  • b. 89kg
  • c. 88kg
  • d. 100kg

7
Developing Proportional thinking Fewer than half
the adult population can be viewed as
proportional thinkers And unfortunately. We do
not acquire the habits and skills of proportional
reasoning simply by getting older.
8
Objectives
  • Understand common decimal place value
    misconceptions and how to address these.
  • Develop content knowledge of how to add, subtract
    and multiply decimals.
  • Develop content knowledge of calculating
    percentages
  • Become familiar with useful resources

9
  • At what stage of the Number Framework are
    decimals first introduced to students?

10
(No Transcript)
11
Decimals
Decimals are special cases of equivalent
fractions where the denominator is always a power
of ten.
12
Misconceptions with Decimal Place Value How do
these children view decimals?
  • Bernie says that 0.657 is bigger than 0.7
  • (decimals are 2 separate whole number systems
    separated by a decimal point, 657 is bigger than
    7, so 0.675 is bigger than 0.7)
  • 2. Sam thinks that 0.27 is bigger than 0.395
  • (the more decimal places, the tinier the
    number becomes, because thousandths are really
    small)
  • 3. James thinks that 0 is bigger than 0.5
  • (decimals are negative numbers)
  • Adey thinks that 0.2 is bigger than 0.4
  • (direct link to fractional numbers , i.e. ½
    0.2, ¼ 0.4)
  • 5. Claire thinks that 10 x 4.5 is 4.50
  • (when you multiply by 10, just add a zero)

13
Addressing Misconceptions
14
Use materials to develop an understanding of
decimal tenths and hundredths place value
  • Use decipipes, candy bars, or decimats to
    understand how tenths and hundredths arise and
    what decimal numbers look like

3 5
15
3 chocolate bars shared between 5 children.

30 tenths 5 0 wholes 6 tenths each 0.6
0
6
16

Now try this 5 4
17
Connecting the Place Value
5 4 1 whole 2 tenths 5 hundredths
1
2
5
  • Understand how tenths and hundredths arise
  • express remainders as decimals

18
  • BIG IDEA
  • The CANON law in our place value system is that
    ONE unit must be split into TEN of the next
    smallest unit AND NO OTHER!

Read, Say, Make
19
Using Decipipes Book 7 p.38-41 (Understanding
how tenths and hundredths arise)
  • What is 1 quarter as a decimal?

View childrens response to this task (30.40
33.30 0r 34.40)
20
  • Make and compare decimals
  • Which is bigger 0.6 or 0.43?
  • How much bigger is it?

21
  • Add and subtract decimals
  • Rank these questions in order of difficulty.
  • 0.8 0.3,
  • 0.6 0.23
  • 0.06 0.23,

Exchanging ten for 1 Mixed decimal place
values Same decimal place values
22
Add and Subtract decimals (Stage 7)
Place Value
Tidy Numbers
1.4 - 0.9
Reversibility
Equal Additions
Standard written form (algorithm)
23
Add and Subtract decimals (Stage 7)
Place Value
Tidy Numbers
1.6 - 0.98
Reversibility
Equal Additions
Standard written form (algorithm)
24
(No Transcript)
25
Decimal Keyboard
26
  • When you multiply the answer always gets
    bigger.
  • True False

0.4 x 0.3 Which is the correct answer? 0.12
1.2 0.012
27
Multiplying Decimals by a whole number(Stage 7)
Tidy Numbers
Place Value

5 x 0.8
Proportional Adjustment
Convert to a fraction, e.g. x 0.25 ¼ of
Standard written form (algorithm)
28
Multiplying a decimal by a decimal (Stage 8)
using Arrays 0.4 x 0.3
0.3
0
1











0.4
Ww w

1
29
Using Arrays 0.4 x 0.3 0.12
0.3
0
1











0.12
0.4
Ww w

1
30
1.3 x 1.4
1
0.4




















1




















0.3
31
1.3 x 1.4
1
0.4




















1.82
1
0.4
1
0.3
0.12




















0.3
32
1.3 x 1.4
0.4
1
1
0.4
1
0.12
0.3
0.3
33
0.7 x 1.6
1
0.6
1.12
0.0
0
0
0.42
0.7
0.7
34
Why calculate percentages?
  • It is a method of comparing fractions by giving
    both fractions a common denominator i.e.
    hundredths.
  • So it is useful to view percentages as
    hundredths.

35
Applying Percentages
  • Types of Percentage Calculations at Level 4
    (stage 7)
  • Estimate and find percentages of amounts,
  • e.g. 25 of 80
  • Expressing quantities as a percentage
  • (Using equivalence)
  • e.g. What percent is 18 out of 24?

36
  • Estimate and find percentages of whole number
    amounts.
  • 25 of 80

Using common conversions halves, thirds,
quarters, fifths, tenths
35 of 80
Using benchmarks like 10, and ratio tables FIO
Pondering Percentages NSAT 3-4.1(p12-13)
37
Find __________ (using benchmarks and ratio
tables)
100











38
Find 35 of 80
100
80








80
39
Find 35 of 80
100
80










80
40
Find 35 of 80
100
80










41
Find 35 of 80
35 28
100
80










42
  • Now try this
  • 46 of 90

100
90
43
46 of 90
46 of 90
100 10 40 5 1 6 46
90 9 36 4.50 0.90 5.40 41.40
Is there an easier way to find 46?
44
Estimating Percentages
16 of 3961 TVs are found to be faulty at the
factory and need repairs before they are sent for
sale. About how many sets is that? (Book 8 p.26
- Number Sense)
About 600
45
Decimal Games and Activities
  • First to the Draw
  • Four in a Row Decimals
  • Beat the Basics
  • Decimal Keyboard Games
  • Target (Figure It Out)
  • Decimal Jigsaw
  • Percents
  • Decimal Sort

What is this game aimed at? How could you adapt
it to make it easier / harder?
46
http//mathsleadteachers.wikispaces.com/
http//teamsolutions.wikispaces.com/
47
  • Objectives
  • Understand common decimal place value
    misconceptions and how to address these.
  • Develop content knowledge of how to add, subtract
    and multiply decimals.
  • Develop content knowledge of calculating
    percentages
  • Become familiar with useful resources.

What do you know now that you didnt know
before? What parts of this workshop could you
share back with your staff?
48
Thought for the day
  • A DECIMAL POINT  
  • When you rearrange the letters becomes
  • I'M A DOT IN PLACE

49
Problem Solving from nzmaths
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