Transcript 3_erf_maths_l1

• Lesson 1
• Mathematical Literacy
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Mathematical literacy and basic
competences in science and technology
Mathematical Literacy
and basic competences
in science and
technology
• Definition:
– Mathematical literacy is defined in the Programme for
International Student Assessment (PISA) as the capacity to
identify, understand and engage in mathematics, and to make
well-founded judgements about the role that mathematics plays in
an individual’s current and future private life, occupational life,
social life with peers and relatives, and life as a constructive,
concerned and reflective citizen.
– Source Publication: Education at a Glance, OECD, Paris, 2002,
Glossary
.
• A skill which is used in everyday situations.
– Emphasis is on activity rather than knowledge.
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Mathematical literacy and basic
competences in science and technology
An introduction
• Definition:
–
It is an individual’s capability and capacity to
understand the role mathematics play in
the world, and be able to apply them in ways
that serve his everyday life (i.e. when
shopping, traveling, cooking (PISA).
• Although, basic mathematics were covered at
an early childhood, people need to be able to
use them in unstructured contexts were
directions are not clear and they need to
decide which knowledge should be applied in
each situation.
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Mathematical literacy and basic
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Mathematical Literacy
• What kind of knowledge you need to solve the
following problem?
– If the sales tax is 6% and a €10.00 purchase is made, the sales tax is
€ 10.00*6/100 =€ 0.60
• Required: knowledge of ratios and percentage
– The sum of 645 and 450
• Required: Mental math (estimating and rounding numbers). Mental
math are vital as they are used on an every day basis. No time to
think, no time for a calculator!
– Answer: 645 + 450= ?
– 645 is close to 600 and 450 is close to 500 answer is 1100 which
is close to 1095.
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Mathematical literacy and basic
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Mathematical Literacy
• Addition: 15+70=85
• Subtraction: 85-70=15
– If you add an amount then take it away again,
you will end up at the same place and vice
versa.
• A reminder about values
– Have a look at the number 623.
• 6 is the hundreds digit.
• 2 is the tens digit.
• 3 is the units digit.
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Mathematical literacy and basic
competences in science and technology
Computation methods
• Estimate the answer: Round 314 to
300 and 82 to 100.
– The total is 100+300= 400.
• Answer is close to 396
• Estimate the answer: 384-182
– 384 is rounded to 400 and 182 to 200. 400200=200
• answer is close to 202
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Mathematical literacy and basic
competences in science and technology
Computation methods
• Estimate the answer: Calculate the
sum of 974 and 117
– 974 is rounded to 1000 and 117 to 100.
1000+100=1100
• Answer is close to 1091.
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Mathematical literacy and basic
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Computation methods
• Other ways for addition:
–
Splitting the large numbers
into hundreds, tens and units.
• What happens in
subtraction
– If one of the columns has
a smaller number on top,
the number on top
borrows from the number
to its left.
– When working out the
units in this sum, as 2 is
less than 4, you have to
borrow 10 from the tens
column. So 2 becomes
12, and in the tens
column, 9 becomes 8.
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Mathematical literacy and basic
competences in science and technology
Addition and Subtraction
• Addition:
– plus, add, sum, altogether, increase,
total
• Subtraction:
– subtract, minus, decrease, difference,
less than, take away, fewer than,
decomposition, reduce
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communication reflects the views only of the author, and the Commission cannot be held
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Mathematical literacy and basic
competences in science and technology
Addition and Subtraction
glossary
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Mathematical literacy and basic
competences in science and technology
Multiplication tables
• Reverse the question
– If someone asks you what 3 x 8 is and
you're not sure of your 8 times table,
turn it around into 8 x 3.
• Use the facts you know well, like
10 times a number.
– If you need to work out 12 x 4, start
with 10 x 4 = 40 and add 2 more 4s to
give 48.
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Mathematical literacy and basic
competences in science and technology
Multiplication methods
• Doubling
– Doubling is a good trick. If you know
that 4 x 4 = 16, then you can work
out 8 x 4 by doubling 16, which gives
32.
• Separate and add up
– If you had to work out 25 x 5 you
could use:
10 x 5 = 50 plus another 10 x 5 = 50.
Then 5 x 5 = 25.
Added together 50 + 50 + 25 = 125
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Mathematical literacy and basic
competences in science and technology
Multiplication methods
• Tips
– To find out if a number is in the 2 times table, look at the digit at
the end.
• 1 357 318 is a multiple of 2 because the digit at the end is 8, which is
even.
– To find out if a number is in the 3 times table, add up the digits of
the number you want to find out about. If they add up to 3, 6, or 9,
then you know that it's in the 3 times table .
– All the numbers in the 4 times table are EVEN - they end with 0, 2,
4, 6 or 8 (116:look at last one digit).
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Mathematical literacy and basic
competences in science and technology
Multiplication tips
• Tips
Mathematical literacy and basic
competences in science and technology
Multiplication tips
– All multiples of 5 end in a 5 or a 0.
– All the numbers in the 6 times table are EVEN - they end with 0, 2,
4, 6 or 8. Additionally, they are all a multiple of 3, they can be divided
by 3.
– You can work out a 6 times sum by doubling the number and then
tripling it. 5 x 6 is the same as 5 x 2 = 10, then 10 x 3 = 30.
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• Tips
– There is no easy trick for finding out if
a number is in the 7 times table
– The numbers in the 8 times table are
always even. That means they can be
divided by 2 without remainder
– All the digits in the 9 times table add
up to 9.
18 = 1 + 8 = 9
27 = 2 + 7 = 9
36 = 3 + 6 = 9
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Mathematical literacy and basic
competences in science and technology
Multiplication tips (cont.)
Estimating:
– When you divide any numbers, it is a good
idea to estimate a rough answer first. Your
estimate can then be checked against your
actual answer.
92 ÷ 3 is approximately
90 ÷ 3 which is 30
143 ÷ 7 is approximately
140 ÷ 7 which is 20
994 ÷ 5 is approximately
1 000 ÷ 5 which is 200
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Mathematical literacy and basic
competences in science and technology
Division
• Divide 22972/4
– 4 into 2 won't go - so carry 2
– 4 into 22 (5 x 4 = 20) - so carry 2
7 x 4 = 28) - so carry 1
4 into 17 (4 x 4 = 16) - so carry 1
4 into 12, that will be 3 exactly
– 4 into 29 (
–
–
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Mathematical literacy and basic
competences in science and technology
Division
• Multiplication:
– multiply, multiple, times, sets of, lots of, groups of, product, factor,
prime numbers
• Division:
– divide, divisible, left over, remainder, share, groups
– Adapted from BBC: Skillwise
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Mathematical literacy and basic
competences in science and technology
Multiplication and division
• Algebra is all about:
– addition, division, multiplication, subtraction
and formulas
• Example: volume=width x height x depth
– Inequalities are also part of algebra
Symbol
Words
Example
>
<
≥
≤
greater than
x+3>2
less than
7x < 28
greater than or equal to
5≥x-1
less than or equal to
2y + 1 ≤ 7
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Mathematical literacy and basic
competences in science and technology
Algebra
Mathematical literacy and basic
competences in science and technology
Percentages
• To determine the percent of a number follow the steps:
– (eg calculate 87% of 68)
• Multiply the number by the percent (e.g. 87 * 68 = 5916)
• Divide the answer by 100 (Move decimal point two places to the left)
(e.g. 5916/100 = 59.16)
• Round to the desired precision (e.g. 59.16 rounded to the nearest
whole number = 59)
• ANSWER IS 59.16%
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Calculate the 20% of 100?
20
30
40
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Mathematical literacy and basic
competences in science and technology
Example
Calculate the 5% of 15?
0.33
0.75
7.5
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Mathematical literacy and basic
competences in science and technology
Example
• Ratios tell how one number is related to another
number.
– A ratio may be written as A:B or A/B or by the phrase "A to B".
– A ratio of 1:2 says that the second number is two times as large as
the first.
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communication reflects the views only of the author, and the Commission cannot be held
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Mathematical literacy and basic
competences in science and technology
Ratios
• Example:
– Determine the value of B if A=6 and the ratio of A:B = 2:5
15 (6/B=2/5B=6*5/2=30/2=15)
• A more detailed explanation
– Determine how many times the number A is divisible by the
corresponding portion of the ratio. (6/2=3)
– Multiply this number by the portion of the ratio representing B
(3*5=15)
– Therefore if the ratio of A:B is 2:5 and A=6 then B=15
• Adapted from:http://www.aaamath.com/rat62ax2.htm
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Mathematical literacy and basic
competences in science and technology
Ratios
• Percent Ratios are used in several situations:
– Commissions- A sales person receiving 10% commission on sales
• If sales is equal to 2000 then commission is 10/100* 2000=200
– Discounts
• During sales an item that costs €200 has a 20% discount. Therefore
discount equals to 20/100*200=40 and therefore price now is
• 200-40=160
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Mathematical literacy and basic
competences in science and technology
Percent Ratios
• Tax- eg VAT
– Vat in Cyprus is 15%.
• If price excluding VAT is 100 then price including VAT is 115
• Interest
– When money is borrowed, interest is charged for the use of that
money for a certain period of time.
• Interest = Principal * Rate * Time.
– If €100 was borrowed for 2 years at an interest rate of 10%, the
interest would be € 100*10/100*2 = € 20. The total amount that
would be due would be € 100+ € 20= € 120.
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Mathematical literacy and basic
competences in science and technology
Percent Ratios
• Graphs
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Mathematical literacy and basic
competences in science and technology
Graphs
• Formulas
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Mathematical literacy and basic
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Formulas
• Statistics
– Statistics is the study of the collection, organization, and
interpretation of data. It deals with all aspects of this, including the
planning of data collection in terms of the design of surveys and
experiments.
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Mathematical literacy and basic
competences in science and technology
Statistics
• Standard Deviation
– Standard deviation is a widely used measurement of
variability or diversity used in statistics and probability
theory. It shows how much variation or "dispersion" there is
from the average (mean, or expected value). A low standard
deviation indicates that the data points tend to be very close to
the mean, whereas high standard deviation indicates that the
data are spread out over a large range of values.
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Mathematical literacy and basic
competences in science and technology
Statistics Example
• A line is one of the basic terms in geometry. It extends
in both directions forever
• Points are also used in geometry and are marked by a
letter.
• Intersection is when lines, rays or figures meet
• Examples
– Line 1 meets the square at points N and M
– Line 2 intersects the circle at point P
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Mathematical literacy and basic
competences in science and technology
Geometry
• Line segment are simply named as segment AB or
segment HG.
• Rays are used to show the direction of segments
• Example:
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Mathematical literacy and basic
competences in science and technology
Geometry
• Angles: use this symbol < to
indicate the way that points
are allocated. Example:
<PBW, <CBP, and <WBA
• Tip: Angles C and B have the
same degrees
• Degrees
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Mathematical literacy and basic
competences in science and technology
Geometry
– In the right triangle, the hypotenuse has
length 5. According to the Pythagorean
Theorem 16 (4*4)+ 9 (3*3) = 25 (5*5) ή
42*32=25 (52)
– Area of a Triangle= h*b*1/2
– Area of a Circle =3.14*r2 (or π*r2)
• 3.14*52
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Mathematical literacy and basic
competences in science and technology
Geometry
Area of a Rectangle= A*B
Area of a Parallelogram= b *h
Area of a Trapezoid= 1/2 × h × (a + b)
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Mathematical literacy and basic
competences in science and technology
Geometry
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Mathematical literacy and basic
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