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• GETIntPhaseMaths

This module is included inLens: Siyavula: Mathematics (Gr. 4-6)
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# Decimal fractions in the context of measurement

Module by: Siyavula Uploaders. E-mail the author

## DECIMAL FRACTIONS IN THE CONTEXT OF MEASUREMENT

Activity 1:

• To recognise and use decimal fractions in the context of measurement [LO 1.5]
• To estimate, measure, record, compare and order two-dimensional shapes and three-dimensional objects using S.I. units [LO 4.5]
• To estimate, measure, record, compare and order two-dimensional shapes and three-dimensional objects using S.I. units [LO 4.7]

1. Measuring Mass: grams and kilograms: 1 000 g = 1 kg

Hands on: practical work

You may work in pairs or groups for this work. You will need to look at a new box of 100 tea bags and you will need a kitchen scale, one tea bag to work with, a box of cornflakes, a packet of margarine and a brick. You will also need a bathroom scale and a weight-watcher’s scale if possible (so work in a group and each one can bring two items of the above).

1.1 Estimate the mass of the box of tea bags. Pass it around the group. Did some clever person look at the outside of the box? Yes, they have to write the MASS on the outside.

1.2 Now pass the box of cornflakes around.

1. a) What is its mass? .
2. b) Which is larger: a box of tea bags or a box of cornflakes? .
3. c) Which is heavier: a box of tea bags or a box of cornflakes? .
4. d) Yes, it depends on the size of the box of cornflakes. One can get a box of cornflakes that has the same mass as 100 tea bags.

What would that mass be? .

1.3 Carefully take out one tea bag. Handle it carefully, as it can break easily. Pass it around the group.

a) Estimate the mass of one tea bag. What do you think is its mass, when you

hold it in your hand? .

b) Now discuss in your group: How can you calculate the mass of one tea bag, using the information that you have at present? An adult is not to tell you, please!

Hint: Look at the writing on the box. There’s something there that can help you.

c) Now use the weight watcher’s scale to measure the mass of one tea bag. What is it? (It’s a small mass, and not so easy to read. Maybe your educator

d) Use the kitchen scale to measure the mass of the box of tea bags and the box of cornflakes. Is the writing on the outside of the boxes accurate?

1.4 Now, carefully, pass the brick around. Estimate the mass of the brick. Complete the table, USING “GRAMS” OR “KILOGRAMS” as necessary. Write in “g” or “kg”:

 Object My estimation Actual measured mass 1 Tea bag Margarine Brick ME!

2. Measuring Length and Distance.

Hands on: practical work

You will need a tape measure, a ruler and any other measuring instruments that you can bring (e.g. tape for measuring “Long Jump”. You may work in groups. In each of the following tasks, ESTIMATE the length and write down your estimation BEFORE you actually measure. You may ask a friend to help with the accurate measurement. Write your findings in the table on the next page.

Recordings:

 Item ESTIMATION Actual Measurement Round my head Round my friend’s head My foot (length) My height (height) A very tall person: My eye-lash (length) My thumb-nail (width) My longest finger (length)

You probably used millimetres(mm) and centimetres (cm) quite often.

Know this!

10 mm = 1 cm

100 cm = 1 metre

1 000 mm = 1 m

1 000 m = 1 km

2.8 Estimate and then measure each thing listed below, and complete the table below:

 Item ESTIMATION Actual Measurement Height of door Width of window Length of corridor/passage Distance to headmaster’s office Length of rugby field Width of soccer field

3. Measuring Capacity (best done outside on the sports field).

Hands on: practical work

You will need: a measuring jug (ask Mum); a syringe, but NO needle (ask the vet!); water and red colouring matter that you put in food (ask Mum); an empty cooldrink tin; an empty milk packet; an empty bucket; a teaspoon; your mug/cup; a baby’s bath and other empty containers of liquid that you find interesting. You may work in groups. Use the above containers to find out how much liquid each item can hold. ESTIMATE first, write down your estimation and then measure the actual amount.

 Item ESTIMATION(How much liquid) Measurement(How much liquid) The bucket (measure with a litre milk packet) The cooldrink tin Cooldrink tins in a litre packet Liquid in a teaspoon (measure with the syringe) Teaspoons in a litre packet A baby’s bath I need, in my bath A school swimming pool needs

You probably worked with millilitres and litres here.

Know this!

1 000 ml = 1 litre

3.2 Now put two and a half mℓ of (edible) red colouring matter into a glass of water. (Use the teaspoon or syringe). Stir, and admire the result. Taste it. Does it taste like cooldrink? Discuss. (Some Foundation Phase learners cannot understand this!)

4. Big pieces, small pieces.

Think carefully and put in the correct sign from >; <; =.

4.1 500 g ___________ half a kg.

4.2 62 mm ___________62 cm.

4.3 1 850 mm _____________ 2 m.

4.4 1 kℓ ____________ 900 litres.

4.5 125 mℓ_____________________ 125 litres.

Discuss your answers with a friend or other members of your group. Then try to make up some similar questions to put to the class.

5. Converting units of measurement.

(Think back to Module 2: fractions and decimal fractions).

• Length.

Remember: 100 cm = 1 m

1 000 mm = 1 m

1 000 m = 1 km

Look at the tape measure. Find 25 cm. It looks like quite a long piece (nearly as long as a ruler). But it’s only a part of a metre. We need 100 cm to make 1 metre.

So 25 cm = 2510025100 size 12{ { { size 11{"25"}} over { size 11{"100"}} } } {} m or (25 ÷ 100) m. Now use a calculator:

25 ÷ 100 =

25 cm =

25 cm are a part (fraction) of a metre.

• Capacity.

Remember: 1 000 mℓ = 1 litre

1 000 litres = 1 kℓ

Look at 750 mℓ of water in a measuring jug. It looks quite a lot, yet it’s only a fraction of a litre. We need 100 mℓ to make a litre.

750 mℓ = 75010007501000 size 12{ { {"750"} over { size 11{"1000"}} } } {} litres. Use a calculator if necessary:

750 ÷ 1 000 =

750 mℓ = 0, litres.

• Mass.

Remember: 1 000 mg = 1 g

1 000 g = 1 kg

Hold a kg packet of sugar in your hand.

500 g = 0,____________kg. Use a calculator if necessary.

• Now write down the missing quantities. Then compare your answers with a friend and if necessary, check on a calculator (using division).

a) 125 mm = 0, _________mm

b) 843 m = 0, _________km

c) 65 litres = 0, __________kℓ

d) 650 litres = 0, __________kℓ

e) 450 mg = _____________g

f) 3 845 g = _________kg

5.5 Make up similar questions to put to the class.

Activity 2:

To solve problems using S.I. units [LO 4.6]

1. The following table shows the rainfall at the Helderberg Nature Reserve in 2003. The records in this table are genuine records that are to be found at a real place.

• Study the table and calculate and fill in the total amounts of rain for each month.
 Month Amounts of rain in ml in that month Total amount of rain in that month January 17,4 February March 9,2; 9,2; 40,2 April 6,7; 2,0; 21,0; 0,8 May June 8,0; 4,0; 2,5; 2,5 July 17,4; 10,5; 16,0; 14,0; 2,5
• Check your totals with a friend. Do you agree?

• Can 2,5 ml be fitted into a teaspoon?

• How much liquid does a full teaspoon hold?

• How full is a teaspoon with 2,5 ml of rain in it?

• During which months was there no rain?

• In which rainfall area is this nature reserve: summer rainfall; winter rainfall; all year rainfall? Explain.

• How much rain fell in the Helderberg Nature Reserve during the first six months of 2003?

Write down calculations and answers for the following:

2. At the school Athletics Meeting, in the U/11 Boys Long Jump event, the longest jump of each competitor was recorded as follows:

John 4,4 m

Paul 4,1 m

Garry 4,6 m

Peter 4,0 m

Steve 4,5 m

Tom 3,9 m

David 3,8 m

Colin 3,7 m

Simon 3,5 m

• Who won this event?

• Explain why?

3. A travelling salesman went from Johannesburg to Cape Town, which is approximately 1 442 km; from Cape Town to Windhoek, which is 1 508 km and from Windhoek to Maputo, which is 2409 km and then back to Johannesburg, another 599 km. What was the total distance that he travelled altogether?

4. At the end of a trip the odometer of a car of Easy Hire Car Hire Company shows 3068,4. When the car was hired, it showed 2687,5. What distance did the tourist who hired it travel?

5. In Mother’s shopping bag were:

500 g margarine; 1,2 kg mince; one 450 g tin of jam; 10 g yeast and 5 kg flour. What was the total mass of all the shopping that she had to carry home?

Activity 3:

To investigate and approximate perimeter [LO 4.8.1]

A ssignment:

You may do this in a group under the guidance of your educator. You will need a ball of string, four sticks, measuring tapes and a trundle wheel.

1. Go outside onto a playing field if possible, and peg out a suitable hen-run for your five chickens which your grandfather is going to give you. Discuss the size of the run, its shape and position. Write down the measurements that you decide upon.

Length of run: ________ Width of run: ________________ .

2. Then put a stick in the ground at each corner. Tie the end of the string round one stick and unwind the string along the edge of your hen-run, going round each stick until you get back to where you started. Cut the string and tie it to the stick. Your string marks where you want to put a fence.

3. Measure how much string you used and write it down.

5. Calculate how much wire-netting you will need to go right round the hen-run. (You do not need a gate; you can step over.)

6. Challenge: Make a model of your hen-run. You may even make it to scale. Ask your educator to help you. (Use a simple scale, e.g. 1 cm =1 m).

1. Complete the following:

• 6 578 g = ____________kg
• 5,703 km = ______________ m
• 6 712 ml = ______________litres
• 7 68 mm = _______________ m
• 34 mm = _______________________m (5)

Solve the following sums and write down all the steps of your calculations:

2. 87 mm + 4 568 mm + 1,250 m (answer in metres)

3. An ant runs round the edge of a book that is 15 cm wide and 21,5 cm long. How far does the ant run?

4. Peter drinks 250 ml of water after a tennis match and then the coach gives him 350 ml of orange juice. How much liquid does he drink altogether?

5. The mass of a van is 2 250 kg when it is empty. Sixteen bags of oranges each with a mass of 15 kg are loaded onto the van. What is the mass of the van and its load together? (4)

6. Mother has 5 kg of flour. She uses three and a half kg of it. How much flour is left? (2)

## Assessment

 LO 4 measurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts. We know this when the learner: 4.1 reads, tells and writes analogue, digital and 24-hour time to at least the nearest minute and second; 4.2 solves problems involving calculation and conversion between appropriate time units including seconds, minutes, hours, days, weeks, months and years; 4.3 uses time-measuring instruments to appropriate levels of precision, including watches and clocks; 4.4 describes and illustrates ways of measuring and representing time in different cultures throughout history; 4.5 estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for:mass using grams (g) and kilograms (kg); capacity using millilitres (ml) and litres (l); length using millimetres (mm), centimetres (cm), metres (m) and kilometres (km); 4.6 solves problems involving selecting, calculating with and converting between appropriate S.I. units listed above, integrating appropriate context for Technology and Natural Sciences; 4.7 uses appropriate measuring instruments (with understanding of their limitations) to appropriate levels of precision including:bathroom scales, kitchen scales and balances to measure mass; measuring jugs to measure capacity; rulers, metre sticks, tape measures and trundle wheels to measure length; 4.8 investigates and approximates (alone and/or as a member of a group or team):perimeter, using rulers or measuring tapes.

## Memorandum

ACTIVITY 1 measuring

1. Mass

1.1 500 g (or other sizes)

1.2 (a) 500 g; (b) cornflakes; (c) depends on size; (d) 250 g

1.3 (a) own; (b) own (2,5 g); (c) 2,5 g; (d) own

1.4

 Object My estimation Actual measured mass Tea-bag own 2,5 g Margarine own 500g (or other) Brick own About 3 kg Me own Own

2. Length and Distance

2.1 to 2.7 Recordings:

 Item Estimation Actual Measurement Head own Own Friend’s head “ “ Foot “ “ Height “ “ Tall person: height “ “ Eye-lash “ “ Thumb-nail: width “ “ Longest finger: length “ “

2.8

 Item Estimation Actual Measurement Height of door own 2m Width of window “ They vary Length of corridor “ “ Distance to Office “ “ Length of rugby-field “ “ Width of soccer-field “ “

(The size of school sports-fields are smaller than ones for adults.)

3. Measuring Capacity

 Item Estimation Actual Measurement Bucket own Usually 5 or 10 or 15 Cool drink tin “ Depends on size of tin Cool drink tins in a litre packet “ “ Tea-spoon “ 5 ml Tea-spoons in a titre packet “ 200 Baby’s bath “ Depends My bath “ “ School swimming-pool “ “

Pools differ in size

• Practical (colouring matter does not give flavour)

ACTIVITY 2 problems using S.I. units

1.1

 Month Rainfall in ml that month Total for that month January 17,4 February March 58,6 April 30,5 May June 17,0 July 60,4

1.2 oral

1.3 yes

1.4 5 ml

1.5 half

1.6 February and May

1.7 autumn according to these figures – 89,1ml then; 77,4ml in winter so far, but the rainfall for August has not been included. (It is actually a winter rainfall area.)

1.8 123,5 ml

2.1 Gary 2.2 4,6 m is the longest jump.

3. 5 958 km

4. 380,9 km

5. 7,17 kg

ACTIVITY 3 perimeter – practical investigation

1 to 6 Own practical measurement and recording

1.1 6,578 kg

1.2 5 703 m

1.3 6,712 liter

1.4 0,768 m

1.5 3,4 cm

1. 5,905 m

2. 73 cm

3. 600 ml

4. 2 490 kg

5. 1,5 kg

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