Mathematics in Indigenous Contexts
Gilgandra 2005
Artist: Errol Roberts
Artworks: Culcha Disc, Australian Indigenous Images Volume 1
Available from Keeaira Press www.kpress.com.au
Unit Outcomes
Number
NS3.2
Selecta and applies appropriate strategies for addition and subtraction with counting numbers
of any size
NS3.3
Selects and applies appropriate strategies for multiplication and division
NS4.1
Recognises the properties of special groups of whole numbers and applies a range of
strategies to aid computation
NS4.3
Operates with fractions, decimals, percentages, ratios and rates.
Measurement
MS3.1
Selects and uses the appropriate unit and devices to measures lengths, distances and
perimeters
MS4.1
Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and figures
composed of rectangles and triangles.
Space and Geometry
SGS2.2 (a)
Manipulates, compares, sketches and names two-dimensional shapes and describes their features
Working Mathematically
WMS3.1
Asks questions that could be explored using mathematics in relation to Stage 3 content
WMS3.2
Selecta and applies appropriate problem solving strategies including technological
applications in undertaking investigations
WMS4.2
Analyses mathematical or real life situations, solving problems using technology where appropriate
Units of Measure
MS3.1, WMS3.2, MWS4.2
Discussion Questions
1. Why do we need to have standard units of measure?
______
______
______
2. List 4 jobs where measurement is used and very important.
______
______
3. What unit of measure would YOU use to measure the following:
a) Your height ______
b) The length of a car ______
c) The length of a matchstick ______
d) The distance you travel to school ______
e) The length of a train ______
f) The length of a new born baby ______
Smallest mm millimetres
cm centimeter
s
m metres
km kilometre
Largest
Relationship between units
10 mm = 1 cm
100 cm = 1 m
1000 m = 1 km
A very Special Relationship: In the building industry
1000 mm = 1 m
km x 1000 m x 100 cm x10 mm
mm ¸10 cm ¸ 100 m ¸1000 km
MS3.1, WMS3.2, Reasoning
Outcome: To be able to draw intervals of a given length without a ruler
To improve my ability to estimate
Equipment Needed: Pencil and a straight edge without any markings on it
Exercise: Draw intervals of the given length
1. 10 mm
2. 20 mm
3. 5 mm
4. 50 mm
5. 3 cm
6. 10 cm
7. 1 cm
8. 2 cm
9. 3 ½ cm
10. 25 mm
11. 8 mm
12. 42 mm
13. 4.2 cm
14. 12 cm
15 120 mm
Now measure each interval accurately with a ruler writing the exact measurement along side each one
Exercise:
Estimate how long these intervals are:
Question 1 – 6 estimate in milimetres.
1. ______
2. ____
3. ______
4. ______
5. ______
6. ______
Question 7 – 12 estimate in centimetres
7. ____
8. ______
9. ______
10. ______
11. ______
12. ______
NOW MEASURE AND WRITE THE MEASUREMENT ALONGSIDE THE GIVEN INTERVAL
1. How close were you?______
______
2. Which was easiest to estimate: mm or cm?______
Why? ______
MS3.1,WMS3.2/4.2.ReasoningProcess
SNAKES
v Students makes ‘snakes’ using playdough
v Students estimate, measure, and label the length
written in a different form, eg 20 cm , 0.2 m …
v Order their snakes in terms of length and note the different
ways to record the same length
v Could you estimate, measure and record the length of your snake
v Did your recognize the length of your snake recorded
using a different unit of measure?
Record your measurement using decimal
notation to two decimal places?
Convert your measurement to
i) millimetres ______
ii) centimetres ______
MS3.1,WMS3.2/4.2
MEASUREMENT – SMALL OBJECTS
Investigation Exercise
Estimate and measure the length or width of a selection of small
objects to the nearest millimetre and record the results in the table
using millimetres and a combination of millimetres and centimetres
Estimate / Measurement in mm / Measurement in cm and mmWidth of pencil
Length of a pencil
Sharpener
Length of a paper clip
Thumb Nail
Stick of chalk
Pen lid
Watch Band
1. Which unit of measure was the best to use?
Why?
2. Which is was the more accurate mm or cm ? Why?
MS3.1,WMS3.2/4.2,Reasoning Process
APPROPRIATE MEASURE
PROBLEM
1. Jacob needs to measure the length of his eraser.
What measuring device and unit of measure do you suggest
be best for him to use? ______
______
______
2. He now needs to measure the length of his desk, the room and
the playground.
What measuring device and unit of measurement would you suggest
he uses? ______
______
______
______
3. Measure these things and record your answer in the table.
MeasurementLength of desk
Length of room
Length of playground
INVESTIGATION
You are to locate (find), measure and records the lengths of THREE
objects of which one is
i) smaller than 1cm
ii) bigger than 1 cm
iii) bigger than 10 cm and smaller than 1 m
Place the name of the object you selected and write the measurement
in the different units.
Measurement / In Metres / In Centimetres / In MillimetresWatch Band Width / 0.018 / 1.8 cm / 18mm
What measuring device did you use? ______
Why did you select this device? ______
______
______
What unit did you use to record your measurements initially?
______
______
How did you convert your measurements to
a) millimetres
b) centimetres
c) metres?
MS3.1,NS3.2,NS4.1,NS4.3
MY PERSONAL PROFILE
Name ………………………..
Age ……………………………
Estimate / Actual / DifferenceHeight
Hand Span
Elbow to the tip of middle finger
Arm Length
Arm Span (both)
Foot Length (right)
Foot Length ( Left)
Length of Thumb
Distance Around Head
Pace
Key Points Used in Planning/Writing Units
v How well do we expect the students to do the tasks we set?
v What do we want the students to learn?
v Why does it matter
v What are we going to get the students to actually do?
v When will they need to know this and why?
Suggested Outcomes
v Selects and uses the appropriate unit and device to measure lengths
v Estimates, measures, compares and records lengths, distances in centimetres an millimeters
v Converts between units of measures
v Describes the limits of accuracy of measuring instruments
MS3.1,NS4.1,NS3.2,NS4.3,WMS3.2/4.2,SG2.2
Boomerang Activity
Given the outline of a boomerang and a selection of strings
of various lengths- some loose , some in packets rolled up
examine the boomerang-
select from the loose strings which one would around it
select from those in packets which one would around it
measure the distance around the boomerang
compare the actual with the ones you have chosen
which was the easiest – the loose string /or the one in packet
why/why not
THE BOOMERANG
Investigation Activity
1. You are to study the outline of the boomerang on the given sheet of paper
2. Estimate the distance around it , and complete the sentence ;
I estimated the distance around it to be ______
( You have to decide what units of measure you use)
3. Now examine the loose pieces of string. Without actually measuring
determine which piece would go around it.
I have chosen the piece labelled ______
4. Now carefully examine the pieces of string enclosed in the plastic bags.
Choose which bag contains the piece of string you think will go around
the boomerang.
I have chosen bag labelled ______
5. Carefully measure around the boomerang to determine the actual
distance around it.
The actual distance around it is ______mm
______cm
RESULTS
How close in length was your chosen piece of string to the actual
distance around the boomerang
______
What was the difference in these two measurements?______
How close was the string in the bag to the actual distance.
______
What was the difference in these two measurements?______
Which was the easiest to use to estimate: the loose string or the
one in the bag?______
Why______
______
Has your ability to estimate improved since starting this unit of work?
______
6. You are to do a SYMMETRICAL design on the boomerang
and colour it in.
MS3.1,MS4.1,NS3.3,WMS3.1/4.2
TYRES
Investigation and Discovery
1. Use a piece of string (or something similar) and measure
the circumference of a bike or car wheel. Circumference is
the distance around the outside.
Estimate the distance around the tyre ______cm
______mm
______m
2. Measure the string to determine the distance travelled in
in one revolution ( one turn)
Record the measurement in mm ______
cm ______
m ______
3. Calculate the distance travelled in
5 revolutions ______
1000 revolutions______
MS3.1,NS3.2,NS4.1,NS4.3,WMS3.2/4.2
How far does a Bullroarer travel?
(Circumference of a Circle)
Let’s guess how far different BIG bullroarers would travel, if the length of cord was different numbers of steps. How many steps around the circle would the bullroarer travel?
1 One person will stay in the centre standing still and holds the end of the string. The walker stands beside the centre person, and then takes 4 paces, letting out the string.
If the walker keeps walking forward hanging onto the string, what path will they make?
2 How many paces do you think the walker will take around the circle with radius 4 steps?
(Write your guess in the table below)
3 Now count the steps to complete a circle and write in the actual number of Steps.
4 Next write in your guess for a radius of 7 steps and then find its circumference and continue for the rest.
Let’s go back to the room!
5 Divide yours steps by the radius for each one correct to 1 decimal place.
Radius / 4 / 7 / 6 / 10 / 8My Guess
Steps
Steps¸Radius
6 Describe a relationship between the distance around the circle, and the radius?
(If it exists)
7 Does the relationship work with other members of your group? ______
8 Distance around a circle = x
(circumference)
How far does a Bullroarer travel? Extension Worksheet
(Circumference of a Circle)
The distance around the circle is one of the following, guess now then do the activity.
A Just less than 6 times the radius.
B Exactly 6 times the radius.
C Slightly more than 6 times the radius.
The following activities may help you to decide.
1 Which radius would better help you decide?
If you repeated the walking activity, which radius,
a 2-pace radius, or 10 pace radius would better help?
2 Do the circle-walking activity using heel-to-toe paces
Be as accurate as possible, don’t let the centre move, and Keep the string tight
RadiusCircumference
6 x radius
3 Try using a trundle wheel
Tie one end of the string to a stake in the centre and the other to the handle of the trundle wheel, near the axle. Enter your measurements in the table above.
Conclusion: The distance around a circle is times the radius.
Pre-Test
Name …………………
1. What do these abbreviations stand for:
a) m ______
b) mm ______
c) cm ______
d) km ______
2. Circle which is the largest measure in the following
a) 12 mm or 2 cm
b) 1m or 120 cm
c) 300cm or 3.1 m
d) 3cm or 37 mm
3. Estimate the length of the following objects:
a) the height of the door ______
b) the height of your teacher ______
c) the width of the blackboard ______
d) the length of the piece of chalk ______
d) the width of the watch band ______
4. Complete the following
a) 2 cm = _____ mm
b) 3 m = _____ cm
c) 30 mm = _____ cm
5. Measure the following lines in millimetres
a) ______
b) ______
c) ______
d) _____
6. Draw intervals, given there length in centimetres
a) 4cm
b) 6 cm
c) 3.5 cm
d) 5.2 cm
Post Test
Name
1. What do these abbreviations stand for:
a) cm ______
b) m ______
c) mm ______
d) km ______
2. Which of the following measuring instruments :
ruler, tape measure, trundle wheel, dressmaker’s tape
would you select to measure the following:
a) your height ______
b) the distance around your desk ______
c) the distance (circumference) around your head ______
d) the perimeter of the school ______
e) the length of a piece of chalk ______
f) the length of your classroom ______
d) the thickness of a DVD ______
3. For each of the following circle which is the largest reading:
a) 90 mm or 9.1 cm
b) 250 cm or 2 m
c) 3.25 m or 330 cm
d) 2 cm or 18 mm
e) 2000m or 1.8 km
4. Complete the following conversions:
a) 20 mm = ______cm
b) 3 cm = ______mm
c) 2 m = ______cm
d) 1 m = ______mm
e) 25 mm = ______cm
f) 500 cm = ______m
g) 2.5 cm = ______mm
h) 300 mm = ______cm
i) 75 cm = ______m
j) 0.3 m = ______cm
5. Using the appropriate equipment draw intervals the following
lengths
a) 5 cm
b) 80 mm
c) 8 ½ cm
d) 38 mm
e) 58 mm
f) 7.5 cm
6. In each of the following sets of measures, circle the measurements
that are equal.
a) 300 cm , 30 m, 3 m , 3000 mm
b) 25 mm, 25 m, 2.5 cm, 25 cm
7. Using your measuring equipment , measure the sides of the following