OpenStax-CNX module: m31873
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Grade 10 Maths Curriculum SHAWCO
∗
SMART
James MBewu
This work is produced by OpenStax-CNX and licensed under the
†
Creative Commons Attribution License 3.0
Abstract
SHAWCO SMAR maths curriculum 2009
1 Lesson 1 - Distance, speed and time.
Lesson outcomes:
•
•
•
•
Learners understand that the same measurement can be expressed in dierent units
Learners can convert between dierent units
Learners can convert to SI units
Learners can calculate average speed
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Problem for the week:
A cyclist rides at 20 km/h for 40 km, and then rides at 40 km/h for the next 20 km. What is the cyclist's
average speed for the whole journey?
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Measuring
Start by asking the learners how tall they think a person is (in meters or cm, avoid using feet and inches).
Go round your group and let everybody give an answer. Ask them to vote on the most reasonable answer.
Then use a ruler to measure how tall an ordinary-height person is. See if the answer is close to the answer
that they guessed. Then do the same for the length of a hand.
Units
Ask the learners what we were measuring. (Distance) Ask them what units we can use for measuring
distance.
Get as many answers as they can come up with.
(Include non-metric units).
Make sure they
include km, m, cm and mm. Once you have a whole list (maybe write it down somewhere so they can see)
say that for school they will only need those four.
Ask them what the standard unit for measuring distance is. (m) Now ask individual people how many
km's, cm's and mm's go into a metre. Don't be harsh if they don't know, just ask someone else.
The useful to remember units goes like this:
King Henry died a Miserable death Called Measles
kilometre metre centimetre millimetre
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1.1: Sep 2, 2009 9:08 pm -0500
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It goes down in powers of 10. Ask them to learn it or make up their own one. They only need to know
km, m, cm and mm, so tell them that the other words are just place-holders. Make sure that they notice all
the words end in metre just with a dierent prex. Show them how to use it to work out that a kilometre
is 1000 times bigger then a metre, a metre is 100 times bigger than a centimetre and a centimetre is 10 times
bigger than a millimetre.
Converting Units
For example:
1cm =
1
100
m
or
1km = 1000m
or
6mm = 6 × 1mm = 6 ×
1
1000
m=
6
1000
m
Now ask them what the standard unit for measuring time is. (seconds). Ask them how many seconds
are in a minute and how many minutes are in an hour. Then ask them if they can gure out how many
seconds in an hour.
See if anybody can give you a precise denition of speed. (Speed is a ratio of distance and time, or speed
is distance divided by time, they must know both.) Using this denition, ask them what the standard unit
for speed is (m/s). Ask for another unit of speed (km/hour). Work through an example of converting 10m/s
to km/hour. (10 m/s = 600 m/min = 36 000 m/hour = 36 km/hour). It's is easy we think of it as a fraction
as such.
10m
1sec
=
10m
60 min
1
=
60×10m
1min
=
600m
60 hours
1
=
60×600m
1hour
=
1
36000× 1000
km
1hour
=
36km/hourMake sure that they under-
stand each step so that they will be able to convert any units. Ask them what a normal speed for a car
should be, in built up areas. (60 km/hour). To test them ask them to convert this to km/hour.
Average Speed
Ask them if they know what average speed means. Give them the example of walking to school in the
morning and ask them how they would go about calculating their average speed. They would rst have to
estimate the distance and then estimate the time taken. Then use the following equation
Average speed = (distance travelled)
÷
(time taken)
Ask them what this number means. (It is the speed at which the learner walk if she walked at a constant
speed, i.e. without stopping of running)
The standard units used in science are called SI units. This means that for distance there is only one SI
unit (metres). The same goes for time (seconds) and speed (metres per second (m/s)). See if the learners
2
know of any others such as force (newtons (N)), acceleration (metres per second per second (m/s )) and
momentum (kilogram metres per second (kg.m/s)).
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Answer to the Problem for the Week
We know that speed = distance
÷ time.
Rearranging this equation we nd that time = distance
÷ speed.
Using this we know that the rst 40 km takes
(40km
÷
20km/h) = 2 hours
and the next 20 km takes
(20km
÷
40km/h) =
½
hour.
So the cyclist rides 60 km in 2
(60km
÷
2
½hours)
½
hours, for an average speed of
= 24 km/h.
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Mathematical Regions of Africa - The Lebombo Bone
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Figure 1
SwazilandThe oldest mathematical object known to us was found in Border Cave in the Lebombo Mountains between South Africa and Swaziland. A small piece of a baboon's bone was found here that had 29
clearly dened lines engraved into it.
This bone is about 37000 years old.
The bone is very similar to
calendar sticks that are still used by Bushmen clans in Namibia today.
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Worksheet 1 Questions - Distance, speed and time
Part one
1. Convert the following into the standard units (metres and seconds):
(a) 3 km (b) 37 cm
(c) 12 600 mm (d) 3 minutes
2. Convert the following distances into the units in brackets:
(a) 23 m (km) (b) 0,5 cm (mm)
(c) 3 000 000 mm (km) (d) 9 m (cm)
3. Convert the following times into the units in brackets:
(a) 300 s (min) (b) 9 hours (min)
(c) 750 min (hours) (d) 1 day (s)
4. Thando can run at 8 m/s. Write this in km/h.
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Pop Quiz
1. Convert 7 300 mm into the standard units (metres)
2. Convert 75m into kilometres (km)
3. Convert 23m/s into km/h
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Part Two
5. A small car can top speed at 180 km/h. Write this in SI units (m/s).
6. A taxi drives 360km in 4 hours.
(a) What is it's average speed?
(b) How long will it take to drive 540km at the same speed?
Worksheet 1 Solutions Distance, speed and time
Part One
1. Convert the following into the standard units:
(a) 3 km = 3 000 m (b) 37 cm = 0,37 m
(c) 12 600 mm = 12,6 m (d) 3 minutes = 180 s
2. Convert the following distances into the units in brackets:
(a) 23 m (km) = 0,023 km (b) 0,5 cm (mm) = 5 mm
(c) 3 000 000 mm (km) = 3 km (d) 9 m (cm) = 900 cm
3. Convert the following times into the units in brackets:
(a) 300 s (min) = 5 min (b) 9 hours (min) = 540 min
(c) 750 min (hours) = 12,5 hours (d) 1 day (s) = 24 hours = 1 440 min
= 86 400 s
4. Thando can run at 8 m/s. Write this in km/h.
8 m/s = 480 m/min = 28 800 m/h = 28,8 km/h.
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Pop Quiz
1. Convert 7 300 mm into the standard units (metres)
7300mm
= 7300 ×
1
1000
m = 7.3m
1. Convert 75m into kilometres (km)
75m
= 75 ×
1
1000
km
= 0.075km
(1)
1. Convert 23m/s into km/h
23m/s
=
1
× 1000
km
=
1
1 × 60×60 h
23
23
× 3600
1000
km/h
= 82.8km/h
(2)
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Part Two
5. A small car can top speed at 180 km/h. Write this in SI units.
180 km/h = 30 km/min = 0,5 km/s = 500 m/s.
6. A taxi drives 360km in 4 hours.
(a) What is its average speed? 360 km
÷
4 hours = 90 km/h
(b) How long will it take to drive 540km at the same speed?
540 km
÷
90 km/h = 6 hours.
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