Skip to content Skip to navigation

Connexions

You are here: Home » Content » Grade 10 Maths Curriculum SHAWCO SMART Lesson 1

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • FETMaths display tagshide tags

    This module is included inLens: Siyavula: Mathematics (Gr. 10-12)
    By: Siyavula

    Review Status: In Review

    Click the "FETMaths" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
Download
x

Download module as:

  • PDF
  • EPUB (what's this?)

    What is an EPUB file?

    EPUB is an electronic book format that can be read on a variety of mobile devices.

    Downloading to a reading device

    For detailed instructions on how to download this content's EPUB to your specific device, click the "(what's this?)" link.

  • More downloads ...
Reuse / Edit
x

Module:

Add to a lens
x

Add module to:

Add to Favorites
x

Add module to:

 

Grade 10 Maths Curriculum SHAWCO SMART Lesson 1

Module by: James MBewu. E-mail the author

Summary: A SHAWCO SMART lesson for Grade 10

Lesson 1 - Distance, speed and time

Lesson outcomes:

  • Learners understand that the same measurement can be expressed in different units
  • Learners can convert between different units
  • Learners can convert to SI units
  • Learners can calculate average speed

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?

Lesson

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

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 different prefix. 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:

Example 1

1cm=1100m1cm=1100m size 12{1 ital "cm"= { {1} over {"100"} } m} {} or 1km=1000m1km=1000m size 12{1 ital "km"="1000"m} {} or 6mm=6×1mm=6×11000m=61000m6mm=6×1mm=6×11000m=61000m size 12{6 ital "mm"=6 times 1 ital "mm"=6 times { {1} over {"1000"} } m= { {6} over {"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 figure out how many seconds in an hour.

See if anybody can give you a precise definition of speed. (Speed is a ratio of distance and time, or speed is distance divided by time, they must know both.) Using this definition, 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.

10 m 1 sec = 10 m 1 60 min = 60 × 10 m 1 min = 600 m 1 60 hours = 60 × 600 m 1 hour = 36000 × 1 1000 km 1 hour = 36 km / hour 10 m 1 sec = 10 m 1 60 min = 60 × 10 m 1 min = 600 m 1 60 hours = 60 × 600 m 1 hour = 36000 × 1 1000 km 1 hour = 36 km / hour size 12{ { {"10"m} over {1"sec"} } = { {"10"m} over { { {1} over {"60"} } "min"} } = { {"60" times "10"m} over {1"min"} } = { {"600"m} over { { {1} over {"60"} } ital "hours"} } = { {"60" times "600"m} over {1 ital "hour"} } = { {"36000" times { {1} over {"1000"} } ital "km"} over {1 ital "hour"} } ="36" ital "km"/ ital "hour"} {} (1)

Make sure that they understand 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 first 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 know of any others such as force (newtons (N)), acceleration (metres per second per second (m/s2)) and momentum (kilogram metres per second (kg.m/s)).

Solution to Problem for the Week

We know that speed = distance ÷ time. Rearranging this equation we find that time = distance ÷ speed. Using this we know that the first 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 ½ hours, for an average speed of

(60km ÷ 2 ½hours) = 24 km/h.

Mathematical Regions of Africa - The Lebombo Bone

Figure 1
Figure 1 (.png)
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 defined” 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.

Worksheet 1 Questions - Distance, speed and time

Part one

  1. Convert the following into the standard units (metres and seconds):
    1. 3 km
    2. 37 cm
    3. 12 600 mm
    4. 3 minutes
  2. Convert the following distances into the units in brackets:
    1. 23 m (km)
    2. 0,5 cm (mm)
    3. 3 000 000 mm (km)
    4. 9 m (cm)
  3. Convert the following times into the units in brackets:
    1. 300 s (min)
    2. 9 hours (min)
    3. 750 min (hours)
    4. 1 day (s)
  4. Thando can run at 8 m/s. Write this in km/h.

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

Part Two

  1. A small car can top speed at 180 km/h. Write this in SI units (m/s).
  2. A taxi drives 360km in 4 hours.
    1. What is it’s average speed?
    2. 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 (metres and seconds):
  1. 3 km = 3 000 m
  2. 37 cm = 0,37 m
  3. 12 600 mm = 12,6 m
  4. 3 minutes = 180 s
  1. Convert the following distances into the units in brackets:
  1. 23 m (km) = 0,023 km
  2. 0,5 cm (mm) = 5 mm
  3. 3 000 000 mm (km) = 3 km
  4. 9 m (cm) = 900 cm
  1. Convert the following times into the units in brackets:
  1. 300 s (min) = 5 min
  2. 9 hours (min) = 540 min
  3. 750 min (hours) = 12,5 hours
  4. 1 day (s) = 24 hours = 1440 min = 86400s
  1. 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.

Pop Quiz

  1. Convert 7 300 mm into the standard units (metres)

7300 mm = 7300 × 1 1000 m = 7 . 3m 7300 mm = 7300 × 1 1000 m = 7 . 3m size 12{"7300" ital "mm"="7300" times { {1} over {"1000"} } m=7 "." 3m} {}

  1. Convert 75m into kilometres (km)

75 m = 75 × 1 1000 km = 0 . 075 km 75 m = 75 × 1 1000 km = 0 . 075 km size 12{"75"m="75" times { {1} over {"1000"} } ital "km"=0 "." "075" ital "km"} {}

  1. Convert 23m/s into km/h

23 m / s = 23 × 1 1000 km 1 × 1 60 × 60 h = 23 × 3600 1000 km / h = 82 . 8 km / h 23 m / s = 23 × 1 1000 km 1 × 1 60 × 60 h = 23 × 3600 1000 km / h = 82 . 8 km / h size 12{"23"m/s= { {"23" times { {1} over {"1000"} } ital "km"} over {1 times { {1} over {"60" times "60"} } h} } = { {"23" times "3600"} over {"1000"} } ital "km"/h="82" "." 8 ital "km"/h} {}

Part Two

  1. A small car can top speed at 180 km/h. Write this in SI units (m/s).

180 km/h = 30 km/min = 0,5 km/s = 500 m/s.

  1. A taxi drives 360km in 4 hours.
  1. What is it’s average speed? 360 km ÷ 4 hours = 90 km/h
  2. How long will it take to drive 540km at the same speed? 540km ÷ 90 km/h = 6 hours

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Reuse / Edit:

Reuse or edit module (?)

Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.