Mathematics in Indigenous Contexts Gilgandra 2005

Mathematics in Indigenous Contexts Gilgandra 2005

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

Students makes ‘snakes’ using playdough Students estimate, measure, and label the length written in a different form, eg 20 cm , 0.2 m … Order their snakes in terms of length and note the different ways to record the same length Could you estimate, measure and record the length of your snake

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 mm

Width 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.

Measurement Length 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

CONVERTING UNITS MILLIMETRES, CENTIMETRES METRES

smaller than 1 cm name of object length

bigger than 1 cm name of object length

bigger than 10 cm and smaller than 1m name of object length


Place the name of the object you selected and write the measurement in the different units.

Measurement In Metres In Centimetres In Millimetres Watch 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 Difference Height 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

How well do we expect the students to do the tasks we set? What do we want the students to learn? Why does it matter What are we going to get the students to actually do? When will they need to know this and why?

Suggested Outcomes

Selects and uses the appropriate unit and device to measure lengths Estimates, measures, compares and records lengths, distances in

centimetres an millimeters Converts between units of measures

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____________

Challenge: Determine for the wheel you have measured how many times it will go around on a trip from Gilgandra to Dubbo (65 km)


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 8 My 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

Radius Circumference 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 figures (to the nearest mm)and calculate the perimeter of each a) b) c)


8. Without using a measuring instrument estimate the length of the following intervals in mm a) __________ answer = _____ b) ______________ answer = ______ c) ____________________ answer = ______ d) ____ answer = _______ e) _____________ answer = ________ 9. Estimate the length of the following in centimetres (nearest) a) ___________________ answer =________ b) ________________________ answer = ________ c) _____ answer = ________ d) ___________ answer = _______ e) ____________________ answer = _______

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Mathematics in Indigenous Contexts Gilgandra 2005