ENTRY REQUIREMENT

This lesson assumes that the pupils are able to perform vertical addition and subtraction of ordinary numbers.

PRESENTATION

INTRODUCTION

In continuation of the Week 6 lesson, the teacher teaches the pupils the need for, and how to carry out standard measurement (units) of lengths.

S/he begins this by telling them that there are some problems with non-standard measurements of length. Therefore, the teacher asks the pupils’ opinion of possible problems of non-standard measurement of length.

After receiving as many as possible, the teacher lists and explains the following as the problems of non-standard measurement of length and the need for standard measurements – units.

1. Uniformity or Inequality

Because non-standard measurements of length are different from person to person; it makes it difficult to replicate equal measure of length by different people.

The teacher explains this further by referring to the introductory scenarios in week 6 lesson. Ocheme could not replicate goalposts of equal width as Alechenu; just as Nafisat could not replicate exactly the length of rope as the hairdresser.

2. Verifiability

Another problem of non-standard measurement of length is that it is difficult to verify. To verify means to check and see if it is as someone said it is.

For example, if a tailor in Sokoto measures and cut 20 armlength of a piece of cloth and sends it to someone in Port Harcourt; the person in Port-Harcourt may not be able to verify that the piece of cloth is truly 20 armlength since his armlength may not be the same as that of the tailor in Sokoto.

3. Inaccuracy

Non-standard measures of length are not accurate. Accurate means to be exactly equal or the same as one said it is.

If you measure the length of your desk for the first time and opened your fingers very wide; you may get 10 handspans. But if you try measuring the length of the same desk again, you may get 9 ½, 9 ¼, 10 ½ or 10 ¼. This makes non-standard measures of length not to be very accurate.

4. Not Scientific

Something that is not verifiable and not accurate is not scientific. Scientific means something that scientists can use and make. Scientists want something that is very accurate and verifiable.

Because non-standard measurements of length are not scientific, we cannot use them to make things like chairs, fans, windows, desks, duster, board, cars, computer, etc.

But we need to use length to make all these things and even many more things. That is why we need standard measurements of length.

After the forgoing explanations, and any ensuing discussion; the teacher may ask the pupils the following questions as revision:

Stage Evaluation Questions

1. What is length?
2. Mention 3 non-standard ways of measuring length
3. John is 3 years old. And James is 7 years old. John measured the length of their dining table and it is 20 cubits. But James measured the same dining table and got 17. Both of them have been arguing that they are correct
4. a) Who do you think is correct?
5. b) How will you settle the argument?
6. Mention 4 problems of non-standard measurements of length
7. Mention 3 reasons why we need standard measurement of length

Step 2: Standard (Units) Measures of Length

Succeeding the revision as in the stage evaluation questions above, the teacher informs the pupils that they shall from then learn how to measure length in the standard way.

Meaning of Standard (Units) Measures of Length

First, the teacher explains that standard measurement of length is the measurement of length that is accepted and the same all over the world.

The teacher continues that in standard measurement, there are sta2ndard sizes of length and instruments for measuring these sizes. To conclude the preliminary explanation, the teacher reveals that the standard sizes have names to make it very easy for people to know the size whenever it is mentioned. Each of the named sizes of length is called the unit of length.

Standard (S.I) Unit of Length

Thereafter, showing the meter rule, the teacher tells the pupils that that is the size (measure or unit) of length that is accepted all over the world – this is known as the S.I (Système International) unit of length.  S/he also explains that that size (unit) of length is called a meter (one meter). The short form of meter is m. Hence, 1m = 1 meter.

Therefore, whenever anyone in the world say 1 meter of wood, glass or clothe, people that understands SI units will also know how long the material they talking about is.

The teacher may concretize this concept by asking the pupils if they have ever seen a real one-meter-long candy/biscuit before. Repeat this for as many common objects as possible: a meter-long phone, key, desk, TV, Radio, Speaker, bread, book, pencil, pen, etc.

Other Units of Length

To conclude the discussion on the units of length, the teacher explains that some things are several thousand meters and other things are far less than a meter.

For example, it is difficult to say the length of one’s fingers in meters because fingers are far less than a meter.

Consequently, there are divisions of meter to use in standard measurement of length. These include:

1. Millimetre –

Millimetre is the length you get when you divide 1 meter into 1000 equal places. The teacher shows the pupils the equivalent of a millimetre on a ruler. S/he tells the pupils to bring out their ruler. Then, the teacher shows them the millimetre graduation scale and the amount of gap equivalent to 1 millimetre.

The teacher may help the pupils in further conceptualizing the size of millimetre by asking them to guess how many millimetres make up objects. The teacher applauds probable guesses and allows for retry for non-probable guesses.

S/he finalizes on millimetre by revealing that the short form of millimetre is mm.

2. Centimetre

Centimetre is the length that you get when you divide 1 metre into 100 equal parts. The teacher shows the pupils the equivalent of 1 centimetre on a ruler. S/he tells the pupils to bring out their ruler. Then, the teacher shows them the centimetre graduation scale and the amount of gap equivalent to 1 centimetre.

The teacher may help the pupils in further conceptualizing the size of centimetre by asking them to guess how many centimetres make up objects. The teacher applauds probable guesses and allows for retry for non-probable guesses.

S/he finalizes on centimetre by revealing that the short form of centimetre is cm.

3. Kilometre

Kilometre is the length that you get when you put 1000 metres together – i.e. when you multiply 1m by 1000.

The teacher helps the pupils to conceptualize the size of kilometre by giving them instances of the distance between two places that the teacher knows will be within 1 kilometre.

Alternatively, if there are marked measurements of up to 1km within the school, the teacher may refer to it.

Succeeding, teacher may help the pupils in further conceptualizing the size of kilometre by asking them to guess how many kilometres will the distance between given places will be. The teacher applauds probable guesses and allows for retry for non-probable guesses.

Metric Charts of Length

Following the identification of the standard units of length, the teacher leads the pupils to memorize the metric units.

First, s/he engages the pupils in a brainteasing exercise with the following questions:

1. If 1mm is 1m divided into 1000; and 1cm is 1m divided into 100; how many mm makes 1cm?
2. How many cm makes 1 metre?
3. If 1km is 1m times 1000; and 1cm is 1m divided into 100; how many cm makes 1km?

Eventually, the teacher displays the metric chart of length. Then, s/he makes the pupils to read/recite the charts any times:

The unit of length is centimetre (cm):

1000m = 1km

1m  100 = 1cm

1m  1000 = 1mm

10mm = 1cm

100cm = 1m

1000m = 1km

Stage Evaluation Questions

Before the teacher continues to the remaining part of the lesson, s/he assesses the pupils’ understanding of the concepts in this stage. S/he does this by asking them the following questions:

1. What is the full meaning of S.I?
2. The measurements of length that is accepted and the same all over the world are called ______
3. What is the S.I unit of length?
4. Which unit of length is abbreviated as cm?
5. In units of length, m­m means ___________ while km means ___________
6. A metre in a 1000 place is called _______________________
7. One part of a metre shared into 1000 parts is called ______________
8. How many centimetres make a metre?
9. How many millimetres make a metre?
10. _____________ metres make a kilometre

Step 3: Instruments for Standard Measurement of Length

To continue the lesson, the teacher teaches the instruments for standard measurement of length. S/he begins by initiating discussion – in non-standard measurement of length, we use arm to know the length in cubit or armlength; legs for foot/feet & pace; and fingers to know the length in handspan. But how do we know how many millimetres, centimetres, metres or kilometres are there in a given (measurement of) length?

Succeeding the resulting discussion, the teacher explains that there are different instruments for measuring lengths in standard way. These include:

1. Ruler
2. Tape

Thereafter, the teacher shows and explains the graduation of each to the pupils. Afterwards, /she teaches the pupils how to use ruler to measure length:

1. Pick the object that you want to measure. Or mark off the points that you want to measure.

2. Pick the ruler and identify the side with the graduated unit of measurement that you intend to use. Then note the origin of the unit.

3. Accurately place the mark of origin on one point of the object that you want to measure. Do this such that the other side of the ruler lies on the remaining part of the object.

4. Count the units of measurement and record your reading.

Avoid reading error by looking directly on the measurement instead of from an angle.

The teacher practically demonstrates this by using ruler to measure the length of different objects for the pupils to see.

Group Activity

Once the teacher has demonstrated how to use ruler for the class to see, s/he groups the pupils. Then calling the attention of the group leaders, s/he repeats the demonstration once again.

Finally, s/he gives an item to each pupil and directs the group leaders to lead the members in measuring and recording the length of their items. The group leader and/or other members are to verify each member’s reading before such a member records the reading.

Stage evaluation exercise

After the group activity, the teacher gives the pupils individual activities:

1. Use your ruler to measure and label the length of the following lines in centimetres (cm):

2) Use your ruler to measure and label the length of the following lines in millimetres (mm):

3) Write all your answers from 1 and 2 above in the table below. Compare the measurements then complete the table:

4) Use the diagram below with your ruler to measure and record/answer the questions that follows:

The length from:

1. M to N = ______________________________
2. L to M = ______________________________

• L to N = _______________________________

1. W to X = ______________________________
2. X to Y = ______________________________
3. Y to Z = _______________________________

• P to Q = ______________________________
• P to R = ______________________________

SELECT THE CORRECT OPTION IN THE FOLLOWING

Which of the following is correctly the height of the building?

1. W to Z
2. W to X
3. X to Y
4. Y to Z

The width of the door is ______________

1. RS
2. PR
3. QS
4. QR

Step 4: Estimating Standard Measurement of Length

Following step 3, the teacher guides the pupils to estimate standard measurement of length as in the following steps:

1. Revise the meaning of estimation from the previous week
2. Pick the object to estimate

• Look at the size of the standard unit

1. Imaginatively mark the size standard unit along the object
2. Count the imaginary markings and write down the result
3. Carryout the actual measurement of the object and tabulate your readings as in the table below

The teacher does this estimation on different objects for the pupils to see. Thereafter, s/he groups the pupils and make them estimate standard measurement of length in group as they did for non-standard measurement of length.

Stage Evaluation

Before proceeding to the remaining part of the lesson, the gives the pupils the following exercises either as individual homework or classwork to assess their understanding:

1. Page 145 of MAN Mathematics Book 3
2. Using a pair of dividers, your fountain pen, a ruler, a plywood, sand paper, hand saw and the instruction below; create and graduate a ruler in cm.

Instruction

1. Use the hand saw to cut the plywood to the size of a ruler – 15cm or 30cm
2. Choose the smooth side of the plywood and use the sand paper to smoothen it further

• Pick the pair of dividers and extend it against 1cm gap on the ruler

1. Keep the extension the same and mark off the same gaps on the plywood to create the graduation
2. Use the fountain pen to trace the markings/graduation
3. Write your name at the opposite side of your new ruler.

The teacher may demonstrate this with the pupils prior to the individual project

….TO BE UPDATED….