F1–SS
Estimating fractions
This sheet shows how to use three spreadsheets to estimate fractions: Fraction line, Fraction
estimation, and Fraction circle.
Fraction line
When you open the spreadsheet you will see something a bit like this.
Scale from
22
to
3
Reset 0, go 9
Guess - num'tor
- denominator
7
0
10
9
You choose the denominator. Then a point is randomly drawn.
Your challenge is to estimate its position using a fraction.
If you do GREAT!, a new point will be drawn, otherwise, TRY AGAIN.
1
3
GREAT!
Result
0
0
•
•
•
•
•
1
1
9
2 120
3
4
1
1
5
6
7
8
9
10
The fraction is plotted on the line at the bottom.
You guess the fraction as a mixed number, typing the whole number and fraction part.
Type a new denominator; the spreadsheet will work only with fractions with that denominator.
You may have to use 0 for the numerator.
When you are correct, it says GREAT! and plots a new number. For example, the number on the
screen above is not 7 1--- ! It has plotted a new number for the next problem.
3
Fraction estimation
•
•
This is very similar. This time the number line runs from 0 to 1. Fractions will have denominators of
2, 3, 4, 5, 6, 8, 10 or 12. You have to decide which fraction it is.
Enter the numerator and the denominator. If you are GREAT! you will get a new fraction to estimate.
Fraction circle
•
•
Estimate the fraction
This time you estimate the of the circle marked.
fraction of a circle that is
2
TRY AGAIN
marked. The denominator is
9
given – you only have to
estimate the numerator. In
the example it is a number
of ninths, more than 2.
When you get it right a new
diagram is drawn, and you
are told the previous correct
answer.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F2–SS
Estimating decimals
This sheet is about how to use the spreadsheet Estimating decimals.
When you open it you will see something a bit like this.
Scale from
to
Accuracy ±
Reset 0, go 9
0
10
0.2
9
In this spreadsheet a point is randomly drawn.
Your challenge is to estimate its position using a decimal.
If you do GREAT, a new point will be drawn, otherwise, TRY AGAIN.
6.5
Guess
GREAT!
Result
44
0
6.6
1
0.1
2
3
4
1
9 5
1
61
7
8
9
At the bottom is a number line. A dot is plotted with a decimal value between 0 and 10.
• Your task is to estimate the number that is plotted.
• When you type it in you will be told either to TRY AGAIN, or that your answer is GREAT.
• If it is GREAT another number is plotted.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
10
F3–SS
Estimating ratios
This sheet is about how to use the spreadsheet Estimating ratios.
When you open it you will see something a bit like this.
Scale from 20
to 0
Accuracy ± 0.1
Green
Red
#REF!
0
In this spreadsheet two lines of random lengths are drawn from 0.
Your challenge is to estimate the ratio of the green line to the red line.
If you do GREAT!, new lines will be drawn, otherwise, TRY AGAIN.
= 0.16 TRY AGAIN
16
0
2
0.1
0.1
4
6
18
2
1
1
8
10
6
0
2.66666667
12
14
0.05
0.05
16
18
20
At the bottom is a number line. Above it two lines are drawn from 0. The top one is green, and the lower
is red. Their lengths are decimal values between 0 and 10.
•
Your task is to estimate the number the ratio of the green line to the red line.
If the green line is longer than the red line, how many times longer is it?
If the green line is shorter than the red line, what decimal fraction of the red line is it?
•
•
When you type your ratio you will be told either to TRY AGAIN, or that your answer is GREAT!
If it is GREAT! another pair of lines is drawn.
The ratio of green to red in the picture above is not 0.16. (It is actually about 2.7)
So you have to keep trying.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F4–SS
Ordering decimals
This sheet is about how to use the spreadsheet Ordering decimals.
When you open it you will see something a bit like this.
Choose a number of decimal places. Then put numbers 1 to 4 under
the decimals below to show their order, from smallest to largest.
If two or more are equal, press F9 to try again.
Number of decimal places
2
0.65
4
0.24
2
0.51
3
COOL!
0.07
1
Now clear your answers.
0.07
0
2
0.24
0 1
0.1
0.51
4
0.65
0 1
0.2
3
0 .02.45 1
0 1
0.3
1
0.07
0 1
0.65
0.4
0.5
0.6
0.7
•
•
You choose to work with numbers of a certain number of decimal places (1 to 4).
Then four numbers will appear, probably out of order.
•
Your task is to put 1 below the smallest, 2 below the next largest, 3 below the next largest and 4 below
the largest of all.
•
•
If you are wrong, you will be asked to TRY AGAIN.
When you are right, you are told so, and the program will plot the four numbers on the number line.
•
To continue you must clear your answers. Select each cell in turn and delete. This will give you a new
set of numbers to try.
(At this stage you may choose a different number of decimal places.)
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F5–SS
1
2
Estimating percentages in a square
The squares below have 100 parts. Put xs into them in a pattern.
a 50% of the squares
b 25% of the squares
c
75% of the squares
Try the spreadsheet Percentage square.
When you open it you will see something a bit like this.
Estimate the percentage
of the square that is shaded.
%
56
COOL!
To be COOL! guess within 5%.
Each guess makes a
new problem.
It was
53 %
0.4
0 1
0 0
0 1
1 1
0 0
1 1
1 1
1 1
1 1
1 0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
The large square has 100 parts. Some of these are shaded (red). You guess (estimate) this percentage, or
count them if you really want.
•
If you are not within 5% of the correct answer, you will be told the correct answer, given another
problem, and told to keep trying.
In the example above the previous problem was 53% and not 56%.
The new problem presented is ready to answer.
•
If you are COOL! you will be told the correct answer and given a new problem.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F6–SS
1
•
•
•
•
•
Estimating percentages on a line
For each of the lines in the diagram below, there is a percentage.
Estimate that percentage of the distance from the left end of the line and put a small mark.
Check your answer by measuring the line and the distance to your mark in millimetres.
Use a calculator to divide the distance by the line length.
Round the answer to a whole number.
Compare your calculated answer with the number on the page. Find the difference.
a 72%
b 31%
c 96%
d 28%
e 58%
2
Try the spreadsheet Percentages on a line.
When you open it you will see something a bit like this.
Scale from
to
Accuracy ±
Reset 0, go 9
Guess
0%
100%
2%
9
33%
37
0
In this spreadsheet a point is randomly drawn.
Your challenge is to estimate its position using a percentage.
If you do GREAT!, a new point will be drawn, otherwise, TRY AGAIN.
Result
62%
10
20 62
0.1
30
0.1 40
TRY AGAIN
0.1
0.9 50
1
601
70
80
90
100
The number line runs from 0% to 100%.
• A point is plotted using a percentage. Type a percentage into the Guess. Use the % key.
• If you are wrong, as the example clearly is, you are told to TRY AGAIN.
• When you are correct you will be told so, and a new point will be plotted.
3
Here are four pictures of a flag being raised up a pole.
A
a
b
c
d
B
C
D
E
Put the pictures into the correct order.
Estimate the height of the top of each flag as a percentage of the pole height.
Check your answer by measuring, dividing and converting to a percentage.
It took 20 seconds to fully raise the flag, pulling at a constant speed. After how many seconds was
each picture taken?
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F7–SS
1
•
•
•
•
Estimating percentage quantities
The glasses below are partly filled with cordial.
Estimate each percentage
Measure the height of the drink and the glass
Calculate the correct percentage by dividing, rounding and converting to a percentage.
Score 2 if within 2%, 1 if within 5%.
a
2
b
c
d
e
f
Try the spreadsheet Percentage full.
When you open it you will see something a bit like this.
Estimate the percentage
of the container that is full.
38 %
COOL!
To be COOL! guess within 5%.
Being cool makes a
new problem.
It was
38
%
The container is partly full, somewhere between 0% and 100%.
•
•
•
Type a percentage.
If you are wrong you are told to KEEP TRYING.
When you are correct you will be told so, and a new percentage full will be drawn.
In the example above the previous answer was 38%, and was guessed exactly. The new problem is
more than 38%.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F8–SS
1
Estimating percentages in a circle
The circles below are shaded 25%, 50% and 75%.
Use a similar method to shade these circles as best you can.
a 20%
b 40%
c 60%
2
d 80%
Try the spreadsheet Percentage circle.
When you open it you will see something a bit like this.
Estimate the percentage
of the circle marked.
88
It was
COOL!
92%
The part of the circle that is marked with an arc is the part to watch.
You are to estimate the percentage of the circle that is marked.
•
•
If you are wrong you are told to KEEP TRYING.
When you are correct you will be told so, and a new percentage circle will be drawn.
In the example above the previous answer was 92%, and was guessed within 5%. The new problem is
less than 92%.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F9–SS
1
Fractions to percentages
To convert a fraction to a percentage on a calculator you divide the denominator into the numerator,
3
and then multiply the answer by 100. (So for --- you use 3 ÷ 4 × 100 = 75%.) When needed, the
4
answers may be rounded to the nearest whole number.
Practise this skill with these fractions.
3
a ---
3
b ---
2
5
c ---
8
5
5
d ------
9
12
To improve your ability to estimate the answers to these conversions, try the spreadsheet
Fractions to percentages.
When you open it you will see something a bit like this.
Choose a fraction
that you think is
close to the
percentage below.
1
10%
90%
32%
8
9
Fraction
80%
20%
is the same as
89%
It was
87%
NOT BAD!
30%
70%
60%
40%
50%
The spreadsheet gives you a percentage at the top of the left columns. In the example the new problem is
32%.
• You have to choose a fraction that you think is reasonably close in value to the percentage.
(‘Reasonably close’ means within 2%.)
8
In the example above the previous problem was 87%. I typed the fraction --- .
9
The computer worked out that this was 89%. It showed this on the circle diagram.
Because 89% is close to the problem (87%) it told me that this was NOT BAD! and posed a new
problem. (It is now asking for 32% as a fraction.)
Before you get it right, it kept the problem the same, and converts all your fractions to percentages so
you can see how close the answers are.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F10–SS
Fractions of money
This sheet tells you how to use the spreadsheet Fractions of money.
When you open it, you will see something like this.
Estimate the answer. When you are COOL! you will be shown the answer.
Then delete your answer to get a new problem.
5
1
2
Problem
5 of
Your estimate ->
0
$6.70
0
0
$0.00
0.00
0
0
$
2.681109567
$0.00
0.1
0.1
0.11
0.11
2.68
0
$1.00
1
2
3
4
5
6
7
$ 2 .80 0
3
$ 6.70
2
3
4
5
6
8
10
$
123 . 0 0
0
6.70
$4.00
$5.00
$6.00
$7.00
$8.00
•
•
•
A problem is presented, asking you to find a fraction of an amount of money under $10.
To help you estimate the amount is shown on a number line.
Type your estimate. If you are within 20% you are COOL! Then the correct answer is graphed so you
can see how close you were.
•
There is another sheet in the same program that does the same thing for mixed numbers. For these,
the answers will always be more than the amount shown.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F11–SS
Decimal multiplication and
Percentages of money
This sheet tells you how to use two spreadsheets.
Decimal multiplication
Estimate the answer. When you are COOL! you will be shown the answer.
Then delete your answer to get a new problem.
0
Problem
0.83
7.6
6
of
Your estimate ->
7.602348004
0
0
6.279056625
0
0
1
1
COOL!
0.1
0.1
0.1
0.1
2
6.28
6.279056625
4
3
5
6
7.60
7
8
You are presented with a problem. (The first decimal is less than 1, and the second is under 10.)
The second number is also graphed. This lets you think of the problem as a fraction of the second
number.
•
•
When you type your estimate, you will be COOL! if you are within 20% of the answer. If you are
COOL!, you will be shown the right answer.
In the example above, the estimate of $6 is within 20% of the rounded answer of $6.28.
If you are wrong you will be given more chances to estimate correctly.
Percentages of money
0 Type your estimate. When COOL! delete it for a new problem.
of $ 3 7 . 3 4
1
Problem 3 %
YOUR ESTIMATE ->
$1.11
$0.00
$37.34
0
0
$1.11
$5.00
1
COOL!
0.1
0.1
0.1
0.1
$10.00
$37.34
1.114618764
$15.00
$20.00
$25.00
$30.00
$35.00
$40.00
This is very similar, but the first number is presented as a percentage, instead of a decimal.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F12–SS
Converting decimals to fractions
Sometimes you can add several of the same decimal together and the answer is 1.
For example: 0.25 + 0.25 + 0.25 + 0.25 = 1.
1
How many of each of these decimals must you add together to get exactly 1 as the answer?
Decimal
0.25
Number
needed
4
Fraction
1
--4
2
0.1
0.2
0.5
0.125
0.05
0.04
0.02
0.01
0.0125
1
If 4 times the decimal makes 1, then the decimal must be --- . Use this idea to complete the last line of
4
the table.
Sometimes you can add several of the same decimal together and the answer is a whole number.
For example: 0.75 + 0.75 + 0.75 + 0.75 = 3.
3
How many of each of these decimals must you add together to get a whole number answer?
Decimal
Answer
0.75
3
Number
needed
4
Fraction
3
--4
4
0.3
0.4
1.5
1.2
1.25
0.375
0.08
0.15
0.06
3
If 4 times the decimal makes 3, then the decimal must be --- .
4
Use this idea to complete the last line of the table.
5
A TI graphics calculator does exactly what you have been doing above. To ask it to convert a decimal
to a fraction, enter the decimal and press MATH 1 ENTER . It will produce a single fraction, which may
be improper (numerator greater than denominator) .
6
The spreadsheet Decimal to fraction does the same thing.
Delete the decimal and enter to get 0/1.
Then type a new decimal and enter.
For repeating decimals type at least 15 decimal digits.
23
8
2.875
= 2 78
To convert a repeating decimal to a fraction you will need to type several repeats. For example,
1
0.142857142857142857 gives --- . But 0.142857 does not. In fact it gives up after trying all the
7
denominators up to 1000.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F13–SS
Ratio on a spreadsheet
This sheet is about using the spreadsheet Ratio on a number line. When opened it looks a bit like this.
Mauve =
2
Ratio red : blue =
Ratio red : mauve =
Ratio blue : mauve =
red
0
0.5
x
0
1
2
2
1
0
mauve
dot =
1
1
1
1
: 1
: 2
: 2
y
0
0 blue
0
-0.1
1.5
-0.1
unit ratios
=
=
=
1
: 1
0.5 : 1
0.5 : 1
2
2.5
There are three coloured lengths along a number line.
• the mauve length,
• the red (as far as the black dot) and
• the blue (from the dot to the lend of the mauve line).
The spreadsheet compare the lengths of these in pairs, using ratios. For example, above,
- the red and blue lines are equal, so the red to blue ratio is 1 : 1.
- the red line is half the mauve line, so the red to mauve ratio is 1 : 2.
- the blue is half the mauve line, so the blue to mauve ratio is 1 : 2.
You can change the lengths using the boxes at the top of the screen. The ratios change instantly.
The unit ratios are simply the first length compared to 1. This is like a fraction with a denominator of 1.
The first number will often be a decimal. It will be shortened to only a few decimal places.
Here are some things to try on this spreadsheet.
1
Make a list of the mauve and dot numbers that make a red : blue ratio of 1 : 1.
2
Make a list of the mauve and dot numbers that make a red : blue ratio of 1 : 2.
3
Make a list of the mauve and dot numbers that make a red : blue ratio of 2 : 1.
4
What happens if the mauve and dot numbers are equal? Why?
5
How can you make the red : blue ratio and the red : mauve ratio equal?
6
How can you make the blue : mauve ratio equal to 1 : 1?
7
Sometimes some unit ratios become blank. When does it happen? Explain why.
8
Is it possible to make all three ratios equal? Explain your answer.
9
Explain how this program can convert fractions into decimals.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F14–SS
Ratios in a right-angled triangle
This activity refers to the spreadsheet Right-angled triangles. When opened it looks like this.
a
2
b
1
c
6
d
3
Enter any
lengths you
wish for a, b, c.
Figure out the
missing length
for d.
2
1
6
2
=
=
6
?
3
0
?1
11
0
2
5
5
0
2
0
0
0
6
0
2
6
0
6
GREAT!
6
2
1
?
Think of it as two poles in the sunshine.
The horizontal lines at the bottom are their shadows.
For example, in the picture above the short pole (2 m high) has a shadow of 1 m.
The other pole is 6 m high. However we do not know its shadow length.
Once you have entered a, b and c, the computer draws the picture.
Your task is to figure out the shadow length of the pole on the right, d.
You can use ratios to help. There are two ratios you could use.
Use a ratio to compare each pole to its shadow. These ratios are equal.
2
In the example, each pole is twice as high as its shadow. This is written as --- .
1
The missing number must be 3, so that 6 is twice as high as 3.
You could have used the ratio to compare the heights of the two poles.
The ratio of the two shadows (in the same order) will be the same.
The right pole is three times the left pole.
So the right shadow length must be three times the left shadow.
1
2
You should choose the simpler of these two ratios.
The table below has some examples of numbers you could use for a, b and c. Find the missing d.
a
2
2
2
2
2
3
3
3
3
4
4
4
4
3
5
6
b
2
2
3
4
4
4
5
6
7
3
3
6
6
2
10
3
c
4
5
4
3
5
6
6
4
6
8
6
6
10
6
2
10
d
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F15–SS
Proportion
This sheet refers to the spreadsheet called Proportion.
When you open the spreadsheet you will see something like this.
run
6
2
x
y
rise
0
6
1
0
0
2
0
12
1
1
0
run
12
4
x
y
rise
0
0
1
1.2
1
1
1.2
0
0
1
1
1
1
0
2
2
1
1
0
2
2
2.2
OTHER
equal ratios
0
6
0
12
0
0
2
0
4
0
0
rectangles x
0
2
2
0
0
4
4
0
13.2
0
12
4
6
2
y
Multn: b = 1 so
0 Divn: d = 1, so
0 Direct proportio
6 Inverse propor
0
0
0
12
0
12
12.6
0
6
2
4
You may change the three coloured numbers. (Here they are 6, 2 and 4).
The black number will change ‘in proportion’.
The diagram shows that the triangles are similar.
(The ratios of height to base, often called rise to run, are the same for each.)
Note that the scales are usually not the same for the vertical and horizontal directions.
The ratios in the top corner are other ways of showing the proportion. These ratios compare the two
heights and the two bases, and you can see that these are also equal.
Change any or all of the three coloured numbers and observe what happens.
Try making predictions. ‘If I change this number to ___, the black number will change to ___.’
For more detailed use of this spreadsheet, see F19.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F19–SS
Create a wage sheet on a spreadsheet
This page will help you create a wage sheet on an Excel spreadsheet.
• You will be able to use it to learn the total number of hours one person has worked.
• You will be able to find their pay at the regular rate, for up to 35 hours per week.
• You will be able to find their overtime hours, and the pay earned, for hours over 35 in the week.
1
2
Open a spreadsheet.
a In cell A1, type ‘Name’.
b
In cell A2 type ‘Wage rate =’.
Create a table for entering starting and finishing times, and calculating time worked. (See below.)
Here is what you will now have.
1
2
3
4
5
6
A
Name
Wage rate =
Day
Time in
Time out
Time worked
B
Mon
C
Tues
D
Wed
E
Thurs
F
Fri
G
TOTAL
3
In cell B6, type ‘=B5–B4’. Tap ENTER. This will find the time worked by subtraction.
4
To use the same formula for the other weekdays, first select cells B6 to F6.
a In the Edit menu, find Fill.
b Choose Fill right.
5
To find the total time worked, type ‘=’ then click in cells B6, C6, D6, E6 and F6. Tap ENTER.
6
You will need to use hours and minutes in the cells in rows 4 and 5. This is best done by using the
correct format. Select the cells B4 to F5.
a Choose Format and select Cells.
b Under Number, choose Time, 13:30. (This is 24-hour time, in hours and minutes. You have to
type a colon (:) between hours and minutes.) Save the spreadsheet.
7
Check that the spreadsheet is working.
a In B4, type ‘9:00’ and in B5 type ‘16:00’. This is 7 hours. B6 should say 7.00. It may use more
decimal places. This does not matter.
b Add times for the other days, and check that the subtractions work and the total works.
8
The calculations require more formulas. First type the words (see below). Save the spreadsheet.
9
In cell 10, type ‘=if(G6>35,35,G5). This says
that the value will be 35 if the total hours
are over 35, but otherwise will show the total.
10 In cell B10 type ‘=B2’. This uses the value
you will enter in B2.
11 In C10, type ‘=A10*B10’. This multiplies to
find the regular wage. Save the spreadsheet.
8
9
10
11
12
13
14
B
C
D
A
Regular wage calculation
Regular hours
x rate = regular wage
Overtime wage calculation
Overtime hours x rate = overtime wage
Gross pay for week
12 In cell A13, type ‘=if(G6>35,G6-35,0)’. This will find the amount over 35 for any overtime hours.
13 In cell A13, type ‘=B2*1.5’. This is the ‘time and a half rate’ for overtime.
14 In C10, type ‘=A13*B13’. This multiplies to find the overtime wage.
15 In cell C14, type ‘=C10+C13’.
16 Finally use Format: Cells to use Currency for cells B2, B10, C10, B13, C13 and C14. Save the
spreadsheet.
17 Now test it. Put a wage rate in B2, and it should calculate a weekly pay. If in doubt, check.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F16–SS
Proportion with negatives
Spreadsheet: Proportion
Open the spreadsheet and create this situation by entering two negative numbers. The spreadsheet does
not show raised signs.
run
-6
-2
x
y
rise
0
- 6
1
0
0
- 2
0
12
1
1
0
rise
run
0
0
1
0.857142857
1
1
0.857142857
0
0
1
1
x
- 0
- 0
0
0.7
0.7
- 0
- 0
0
0.7
0.7
0.7
12
4
OTHER
equal ratios
y
0
- 6
0
12
0
0
- 2
0
4
0
0
rectangles x
0
- 2
- 2
0
0
4
4
0
13.2
0
-2
12
4
-6
-2
y
Multn: b = 1 so
0 Divn: d = 1, so
0 Direct proportio
- 6 Inverse propor
0
0
0
12
0
12
12.6
0
4
-6
Here we see that the triangle on the left has a negative rise (–6) and a negative run (–2). However the ratio
(–6 to –2) is still positive 3, because it is equal to the ratio 12 to 4!
1
Explore other examples of a negative rise and a negative run.
2
Explore cases of two negative runs.
3
Explore cases where only one of the three numbers you can change is negative.
4
Explore cases where all three of the numbers you can change are negative.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F17–SS
The AFL football ladder 1999
Here are the results a the end of the 1999 home-and-away matches. For later ladders, try the AFL web side:
www.afl.com.au/ladder.
Wins
Losses Draws
For
Against
Adelaide
8
0
1903
2232
Brisbane
16
0
2422
1671
Carlton
12
0
2088
2028
Collingwood
4
0
1973
2326
Essendon
18
0
2400
1905
Fremantle
5
0
1981
2403
Geelong
10
0
2328
2454
Hawthorn
10
1
1858
1943
Melbourne
6
0
1850
2293
Kangaroos
17
0
2483
2129
Port Adelaide
12
0
1851
2054
Richmond
9
0
1977
2170
St Kilda
10
0
1978
2021
Sydney
11
0
2184
2128
West Coast
12
0
2068
1937
Western Bulldogs
15
1
2363
1993
%
Points
Position
1
Complete it.
To find the Position use the AFL rules: Teams with equal points are ranked on percentage.
Teams with high points are above teams with lower points.
2
For AFL results at the end of the home-and-away seasons for each year from 1991, see the databasespreadsheet ‘AFL ladders’. Start with 1991.
a This gives the results in the same form as above. However it also gives you formulas to make the
spreadsheet do all the calculations. The formulas are in cells E4, I4 and J4. Look at them and
understand what they do.
• E4 takes the total number of matches played (C4), and subtracts the number of wins (D4) and
the number of draws (F4) to get the number of losses (=C4–D4–F4).
• I4 finds the percentage, by dividing points for (G4) by points against (H4) and multiplying by
100. (The spreadsheet uses * for multiply.) This makes =G4/H4*100
• J4 calculates the points: 4 for each win and 2 for each draw.
So the formula is = 4*D4 + 2*F4.
b To make the formula do the right thing in each cell:
• in column E, select the cells from E4 to E18 and choose Edit: Fill, then Down.
• in column I, select the cells from E4 to E18 and choose Edit: Fill, then Down.
• in column J, select the cells from E4 to E18 and choose Edit: Fill, then Down.
c You can now use the AFL rules to decide the order of the final ladder. Teams with equal points
are ranked on percentage. Teams with high points are above teams with lower points.
d For other years, type in the same formulas into cells E4, I4 and J4, and fill down in the same way.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F18–SS
Interest — simple and compound
When you are paid simple interest you receive the same percentage of the same amount each year. The
money is usually paid into a different bank account.
A common example are term deposits. No matter for how long the term deposit runs (the term) the
interest paid will be the same each year. It is always the fixed percentage of the original amount invested.
That is why you can just multiply by the number of years to get the total amount of simple interest.
Compound interest is similar, but different. This time the interest is paid into the amount invested, so
that gets bigger in regular steps. And because the interest is the fixed percentage of the amount that is
growing, the interest also grows! You get interest on the previous interest!
You can compare these by using the spreadsheet Interest. When you open it you will see this.
years
Simple Simon
Simple Sally
Compound Chris
0
$1,000
$1,000
$1,000
1
$1,200
$1,150
$1,110
2
$1,400
$1,300
$1,232
3
$1,600
$1,450
$1,368
4
$1,800
$1,600
$1,518
5
$2,000
$1,750
$1,685
6
$2,200
$1,900
$1,870
7
$2,400
$2,050
$2,076
8
$2,600
$2,200
$2,305
9
$2,800
$2,350
$2,558
10
$3,000
$2,500
$2,839
The green curve uses compound interest. The others use simple interest.
$3,500
Amounts
rate
20%
15%
11%
$3,000
20%
11%
$2,500
15%
$2,000
$1,500
$1,000
$500
$0
0
1
2
3
4
5
6
7
8
9
10
11
Years
•
•
•
•
The spreadsheet compares the investments of three fictional people: Simon and Sally who use simple
interest, and Chris, who uses compound interest.
In the example above they all invest $1000. You may give them different amounts by changing the
numbers in cells C2, C3 and C4.
They can all use different interest rates. Change these in cells B2, B3 and B4.
The total amount they have, including their interest, is shown in the table and on the graph.
1
Compare the two simple interest people. Sally invests $1000 at 10%, but Simon can only invest at
5%. What amount must Simon invest to get the same interest each year? Compare the graphs.
2
Make the compound interest for Chris and simple interest for Simon have the same amount and same
rate. You will see that the compound interest quickly climbs away from the simple interest.
3
Choose a compound interest rate — say 10%. Find the simple interest rate that gives the same
amount after 10 years. Try it for a different rate. Compound interest needs a lower rate.
4
Choose the same rate for compound and simple interest — say 10%. Then $1000 will reach $2000 in
10 years. Find, by trial and eror, the amount for compound interest that will also give $2000 after 10
years. Compound interest needs a lower amount.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F19a–SS
Proportion on a spreadsheet
1 of 2
This sheet assists you to use the spreadsheet program Proportion. For a simpler page see F13.
On the worksheet you will see a proportion with three coloured numbers and one black one. You can
put new numbers in place of the coloured numbers, but not the black one.
3
orange
rise
run
black
1
2
rise
run
blue
1
3
6
rise
red
run
2
6
The diagram is a pair of triangles. The height (rise) and base length (run) of each is given a number from
the proportion in the worksheet. Whenever you change the worksheet numbers it changes the shape of the
triangles. The numbers from the worksheet also appear on the diagram.
1
Try it. Put different coloured numbers into the worksheet and see the effect on the diagram.
However both triangles will be the same shape. They are both right-angled, and the other angles are also
the same. The triangles are ‘similar’, and the corresponding sides are proportional.
rise
rise
1
The fraction -------- measures the gradient, or slope of the side of the triangle. (The fraction -------- is --- in the
run
run
2
diagram above.) Both triangles will have the same gradient. In the first four questions you will keep the
gradient the same and change the red number.
2
2
Make the first ratio --- . Now change the red number from 1 to 2, 3, 4, 5, and
6
1
2
so on. (The example shows the ratio --- and red number 3. The black number
1
is 6.)
a Explain what happens to the diagram. Does the gradient stay the
same?
b What happens to the values of the black number? Describe the
numbers you get.
c Can you work out a short cut for finding the black number from
the others?
3
2
1
3
3
Make the first ratio --- .
1
a Change the red numbers from 1 to 2, 3, 4, 5, and so on. Describe the black numbers you get.
b Check that your short cut still works.
4
3
Make the first ratio --- . Change the red numbers from 1 to 2, 3, 4, 5, and so on. (This time you will get
2
some decimal fractions for the black number.)
a Change the red numbers from 1 to 2, 3, 4, 5, and so on. Describe the black numbers you get.
b Check that your short cut still works. You may have to change your short cut.
5
1 2 3 5
3
Try other scale factors, such as --- , --- , --- , --- and --- . Try to get a good idea of how the equal ratios look.
2 3 4 2
5
a For each fraction you try, change the red numbers from 1 to 2, 3, 4, 5, and so on.
b Check that your short cut still works.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F19b–SS
Proportion on a spreadsheet
2 of 2
Use Proportion.
2.5
If the two triangles are different in size,
then a scale factor relates their side lengths.
orange
black
1
2
rise
run
1
2.5
5
rise
run
blue
rise
red
5
2
run
5
For example, the scale factor in this diagram is the ratio 5 : 2, or the fraction --- or the number 2 1--- .
2
2
In the next questions you will set up the scale factor by fixing the red and blue numbers (the runs). These
are the denominators of the ratios. Change the rise of one triangle (the orange number) only.
6
3
Make the two runs blue 1 and red 2.
2
This means that the scale factor is --- = 2.
1
1.5
Now change the orange number from 1 to 2, 3, 4, 5, and so on.
2
In the example shown, the scale factor is --- and the orange number is 1.5.
1
The black number is 3.
a Explain what happens to the diagram as the numbers change.
Does the gradient stay the same?
b What happens to the values of the black number?
c Can you work out a short cut for finding the black number from the others?
7
2
1
3
Change the runs to blue 2 and red 3. This gives the scale factor --- = 1.5.
2
a Change the red numbers from 1 to 2, 3, 4, 5, and so on. Describe the black numbers you get.
b Check that your short cut still works.
8
1 2 3 5
3
Try other ratios, such as --- , --- , --- , --- and --- .
2 3 4 2
5
a
For each fraction you try, change the red numbers from 1 to 2, 3, 4, 5, and so on.
Describe the black numbers you get.
b Check that your short cut still works.
9
Keep the blue run number at 1. Change either the orange or red numbers, or both. How could you
work out the black number from the orange and red numbers?
Extension: Negative numbers
10 This spreadsheet will also allow you to enter
negative numbers. Make the blue number 1 again.
a Try 2 for the red number, and change the
orange number from 2 to 1, 0.5, 0.1, 0, –0.1, –
0.5, –1, –2. What happens to the diagram?
How could you work out the answer?
b Repeat part a, but with –2 for the red number.
c Try different combinations of negative and
positive numbers for the coloured numbers in
the worksheet.
10a
1
-0.5
2
-1
10b
1.5
-2
1
-3
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.
F20–SS
Create a wage sheet on a spreadsheet
This page will help you create a wage sheet on an Excel spreadsheet.
• You will be able to use it to learn the total number of hours one person has worked.
• You will be able to find their pay at the regular rate, for up to 35 hours per week.
• You will be able to find their overtime hours, and the pay earned, for hours over 35 in the week.
1
2
Open a spreadsheet.
a In cell A1, type ‘Name’.
b
In cell A2 type ‘Wage rate =’.
Create a table for entering starting and finishing times, and calculating time worked. (See below.)
Here is what you will now have.
1
2
3
4
5
6
A
Name
Wage rate =
Day
Time in
Time out
Time worked
B
Mon
C
Tues
D
Wed
E
Thurs
F
Fri
G
TOTAL
3
In cell B6, type ‘=B5–B4’. Tap ENTER. This will find the time worked by subtraction.
4
To use the same formula for the other weekdays, first select cells B6 to F6.
a In the Edit menu, find Fill.
b Choose Fill right.
5
To find the total time worked, type ‘=’ then click in cells B6, C6, D6, E6 and F6. Tap ENTER.
6
You will need to use hours and minutes in the cells in rows 4 and 5. This is best done by using the
correct format. Select the cells B4 to F5.
a Choose Format and select Cells.
b Under Number, choose Time, 13:30. (This is 24-hour time, in hours and minutes. You have to
type a colon (:) between hours and minutes.) Save the spreadsheet.
7
Check that the spreadsheet is working.
a In B4, type ‘9:00’ and in B5 type ‘16:00’. This is 7 hours. B6 should say 7.00. It may use more
decimal places. This does not matter.
b Add times for the other days, and check that the subtractions work and the total works.
8
The calculations require more formulas. First type the words (see below). Save the spreadsheet.
9
In cell 10, type ‘=if(G6>35,35,G5). This says
that the value will be 35 if the total hours
are over 35, but otherwise will show the total.
10 In cell B10 type ‘=B2’. This uses the value
you will enter in B2.
11 In C10, type ‘=A10*B10’. This multiplies to
find the regular wage. Save the spreadsheet.
8
9
10
11
12
13
14
B
C
D
A
Regular wage calculation
Regular hours
x rate = regular wage
Overtime wage calculation
Overtime hours x rate = overtime wage
Gross pay for week
12 In cell A13, type ‘=if(G6>35,G6-35,0)’. This will find the amount over 35 for any overtime hours.
13 In cell A13, type ‘=B2*1.5’. This is the ‘time and a half rate’ for overtime.
14 In C10, type ‘=A13*B13’. This multiplies to find the overtime wage.
15 In cell C14, type ‘=C10+C13’.
16 Finally use Format: Cells to use Currency for cells B2, B10, C10, B13, C13 and C14. Save the
spreadsheet.
17 Now test it. Put a wage rate in B2, and it should calculate a weekly pay. If in doubt, check.
ACTIVE LEARNING by Ian Lowe. This page may be reproduced for classroom use.