## Introduction to Lesson Note – Primary 3 Third Term Mathematics Week 6

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### Complete Lesson Objectives

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## Guidelines to Adapting Lesson Note – Primary 3 Third Term Mathematics Week 6 into you Lesson Plan

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## Lesson Note – Primary 3 Third Term Mathematics Week 6

Topic: Length, making estimates of lengths and distances

## OBJECTIVES

At the end the lesson, the pupils should have attained the following:

### A. Cognitive:

- Define length
- Differentiate between length and distance

### B. Affective

- Demonstrate the ability to make accurate estimates non-standard units of length
- Value other people’s opinion

### C. Psychomotor

- Measure the lengths of an object using non-standard methods

## PREVIOUS KNOWLEDGE

The pupils know what a ruler is. The boys might have measured the length of goalposts & line of defence in domestic football. While the girls have measured the length of plaiting thread.

# REFERNCE MATERIALS

Johnson, J. (2013). Early measurement history. S. Retrieved from https://www.slideshare.net/jackjackson6922/early-measurement-history

Mathematical Association of Nigeria (MAN). (2008). *MAN Primary Mathematics UBE Edition Book 3.* Ibadan: University Press Plc.

## ENTRY REQUIREMENT

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

## PRESENTATION

The teacher presents this Lesson Note – Primary 3 Third Term Mathematics Week 6 – in order of steps as follows:

### Step 1: Introduction

To introduce the lesson, the teacher begins from the previous knowledge. S/he does this by presenting the following scenarios – each for boys and girls.

#### Boys Scenario:

Once, some ten boys went to play football. They decided to have two teams of five members each. For each team, one member will be the goalkeeper. Four people will play from each side. The goalkeeper of the first team is called Alechenu. And the goalkeeper of the second side is called Ocheme.

They went to the field. But there were no goalposts. So, each goalkeeper made the goalpost of 12 feet for their team.

When it was half-time, the other team scored Alechenu 5 goals. But Ocheme did not concede even a goal. Immediately the game began after half-time, they scored Ocheme 2 goals. So, Ocheme wondered why they were now scoring him easily. He later found out that the goalposts in their new side are wider than those of their previous side. Hence, Ocheme raised alarm. The two teams game together. They checked the goalposts at both sides. And they confirmed that it was true. The goalposts were not equal. There was disagreement.

Alechenu’s team said the earlier 5 goals against them must be cancelled. But Ocheme’s side refused.

##### Questions:

- The goalposts at both sides are 2 feet each. Why was one wider than the other?
- After Ocheme raised alarm, the players confirmed that the goalposts were not equal. How do you think the players did this?
- How can they players have made goalposts that are exactly equal?

#### Girls Scenario:

Once, Ogwa went to plait her hair. The hairdresser gave her the thread to hold and cut for her. Ogwa cut the first set of thread and gave them to the hairdresser. But the hairdresser said it was too short. Then, Ogwa cut the second set of thread longer than the first set. She gave the second set to the hairdresser. Yet, the hairdresser said the second set of thread were too long.

So, the hairdresser showed Ogwa how she wants the thread to be using her armlength. Once Ogwa cut the thread at her armlength, there were still not up to the ones the hairdresser cut.

##### Questions:

- Both Ogwa and the hairdresser cut the thread at an armlength. Why were the threads not equal?
- How can Ogwa cut thread that is exactly equal to the hairdresser’s?

After the discussion that will ensue from the pupils’ attempts to answer the questions, the teacher informs the pupils that they shall in the week’s lessons; learn how to accurately measure the length of an object. Thereafter, the teacher writes/projects the topic on the board and explains the lesson objectives to the pupils

### Step 2: Meaning of Length and Distance

To continue the lesson, the teacher tells the pupils that they shall begin with the meaning of length & distance. Hence, the teacher asks the pupils’ opinion of the meaning and differences between both.

After receiving several attempts, the teacher thoroughly explains the meaning and differences between length and distance is as simple terms as possible as below:

Length is the amount of gap between the beginning and the end of an object or the amount of gap between two points along the longest side of an object.

#### Examples of Length

Teacher illustrates the meaning of length with examples such as the following:

- The length of a pencil is the gap between the beginning and the end of the pencil.
- The length of the board is the amount of gap from the beginning to the end of the board.
- We can measure the length (amount of gap) from the beginning to the end of middle of a desk.
- There is the length of one’s trousers from waist to the feet.

#### Activity 1

After the teacher had thoroughly explained the meaning of length with many examples, s/he gives the pupils this activity:

##### Stage Evaluation Questions

- Invite pupils to step forward to place their hands to show the length of a given object – duster, desk, piece of chalk, stick, shoes, piece of cloth, door, window, etc. – note that length is along the longest side of the object.
- Exercise: Following the physical activity in (1) above, the teacher gives the pupils these simple exercises in their workbook.

Instruction: Draw a straight line to show the length of each of these items:

- Fish
- Earthworm
- Belt
- Bottle
- Block
- Extension box
- Eraser
- Pineapple
- Boy
- Height

#### Differences between Length and Distance

Soon as the teacher ascertains that the pupils have understood the meaning of length, s/he differentiates between length and distance thus:

Length and distance are similar but slightly different. Length is the amount of gap between two points along the longest part of **an object**. Whereas, distance is mostly the amount of gap from one **place** to another. In a nutshell, distance is a longer length (amount of gap) between two points while length is a short amount of gap between two points.

##### Exercise

Succeeding the explanation above, the teacher carries out the following activities with the pupils:

Instruction: state whether each of the following amount of gap is a length or distance

- The gap from one end of a piece of cloth to the other end.
- Amount of gap from Lagos to Enugu.
- Amount of gap between ends of a biscuit
- The amount of gap from one block of classroom to another block in the school.
- Amount of gap around or between the ends of the school football field. Etc.

#### Breadth, width, height

In addition to the forgoing explanation, the teacher teaches the pupils the meaning of the following associated terms:

Width – is the amount of gap across and object from one side to the other. Width may mean the same thing as breadth.

Height – is the amount of gap from the top to the bottom of an object.

##### Exercise

The teacher follows the preceding with exercises for pupils to identify the length, width and height of different real objects. I recommend that the teacher uses cubes and cuboids.

### Step 3: How to measure Length

After the exercise on the meaning of length, the teacher applauds the progress of the pupils. Thereafter, the teacher asks how we may measure the length of an object. S/he receives as many attempts as possible. Subsequently, the teacher explains that there are many ways of measuring length. These many ways of measuring length are grouped int two categories:

- Non-standard means of measuring length; and
- Standard means of measuring length.

#### Non-Standard Measurement of Length

S/he explains further that non-standard ways of measuring length are the ways whose result may not be the same for everybody but may be different from one person (that measured the length) to another. This is because it involves the use of body parts that may be longer or shorter from person to person.

Non-standard Measures of Length includes:

Handspan |
| |

Cubit |
| |

Armlength, arm span or fathom |
| |

Foot length | ||

Pace |

The teacher explains what each of the above means. Then, s/he demonstrates and guides the pupils to measure given items by each of the methods.

Board – handspan

Rope – armlength

Length of classroom – foot

Distance from one classroom block to another – pace

Desk – cubit

#### Activity 1

The teacher groups the pupils. Then, s/he shows the class how to measure the objects I have mentioned above using the stated non-standard ways. S/he also teaches the pupils to tabulate his measurements. Then makes each group leader to do the same after the teacher. Each group leader should also record their measurements.

So, at the end; the tabulated measurements should be as follows:

## NAME | ## Board | ## Rope | ## Length of classroom | ## Length between blocks | ## Desk |

Teacher | 15 hs | 5ams | 25fts | 10pcs | 3cubits |

Group A Leader | |||||

Group A Leader | |||||

… | |||||

Group n Leader |

#### Activity 2: Group

Succeeding activity 1 above, the pupils separates into their various groups with the group leader. Then, for each group; the leader leads the group members to do their own measurements. The leader tabulates the measurements as follows. Thereafter, the group members copy the record into their notes.

## NAME | ## Item 1 (handspan) | ## Item 2 (cubit) | ## Item 3 (armlength) | ## Item 4 (feet) | ## Item 5 (pace) |

Leader | |||||

Group member 1 | |||||

Group member 2 | |||||

… | |||||

Group member n |

### Step 4: Analysis of Reports and Valuing Individual Differences

In continuation of the lesson, after the teacher had marked the pupils reports from the previous activity; s/he once again draw the pupils’ attention to the differences in the reading. The teacher enquires why the readings are different despite that all the members of the same group measured the same item.

After receiving attempts/answers; s/he reiterates that the readings are different because the means the pupils used to measure the length of the objects depends on the size of the individual’s legs and hands – which are different. And because these means yield different results; we say handspan, cubit, armlength, foot and pace are **non-standard** means of measuring length.

In addition, the teacher hinges on the difference in measurement to teach the pupils the value of individual differences as follows.

#### Valuing Individual Differences

The teacher displays the tabulated non-standard measurements of length with the group leaders. Then s/he explains the uniqueness in the differences of every individual.

The teacher teaches that we are all different from all other people in many ways such as shown in the table. These individual differences are what make every human being unique (special). We are all special in our sizes – sizes of our body parts; in how we do things; in what we like and what we do not like; in what we think; in how we speak; in our environment, languages, culture and religions.

##### No superiority in difference

Nobody is bad or backward because of these differences that make us special. When people ask or interact with other people; they do so with their differences. Therefore, do not expect everybody to answer or relate with you in the same way. Instead, expect different answers and different way of interaction with different people. This is because we are different and special.

Do not laugh at anybody because of how they answer questions or interact. Son not easily get offended by other people’s differences. Instead, always remember your own differences – your culture; your religion; and the good behaviours you have learned from your home, churches, mosques and school. So that when you see someone behaving in a way that you know is bad, you can help the person.

Every society put laws and norms to help us know when someone’s behaviour is bad – that is, bad differences. You can help people to solve the problem of their differences that are not good in two ways:

- Talking to them if they are not dangerous or can overpower us
- Telling a trusted adult like teachers and parents to help them

When you want to talk to them, tell that them that you had learned that what they are doing is not good. Then tell them why it is not good. And if they continue to do the bad thing, you should tell an adult. If they will not stop their bad behaviour; you may stop interacting with them so that they won’t teach you the bad behaviour as well.

#### Affirmation

After the talk, the teacher makes the pupils to copy and affirm the following sentences, several times:

I am different. I am special

Everybody is different. Everybody is special.

I will always contribute my answer even if it is different.

I will also allow everybody to contribute their answer even if it is different.

Because we are all different. And we are all special

The teacher evaluates the pupils’ assimilation of this by constantly observing how the pupils adjust in allowing their mates’ opinion during subsequent class discussion.

### Step 4: Estimating Non-Standard Measurement of Length

Following step 3 above, the teacher teaches the pupils how to estimate non-standard measurement of length.

First, s/he explains that to estimate means to make calculated guess of the measure of an item. For example, we can estimate the number of people in a room after we hear their voices. Also, after we count how many times a pupil drank water on Monday, Tuesday & Wednesday; we can estimate how many times such pupil will drink water on Thursday.

Same also is estimating non-standard measurement of length. If we know the size of our handspan, cubit, armlength, foot and pace; we can estimate/calculate/guess the non-standard length of an object.

Succeeding this, the teacher displays some objects and demonstrate how to estimate to the pupils:

- Pick or observe the object
- Look at the non-standard measure
- Imaginatively mark the non-standard measure along the object
- Count the imaginary markings

After this, the teacher leads the pupils in estimating his/her length measurement of the objects at hand. Thereafter, the teacher performs the actual measurement and compares the accuracy of the estimation.

#### Group Activity

The teacher guides the pupils to carryout the non-standard estimation of length in groups:

- Group the pupils into 5 – 10
- Pick group leaders
- Demonstrate how to estimate to the pupils
- Tabulate your reading

NAME | Item 1 | Item 2 | Item 3 | |||

Estimate | Actual | Estimate | Actual | Estimate | Actual | |

## SUMMARY of Lesson Note – Primary 3 Third Term Mathematics Week 6

Prior to ending the lesson on Lesson Note – Primary 3 Third Term Mathematics Week 6; the teacher summarizes the entire class which s/he reviews with the pupils.

- Length is the amount of gap between the beginning and the end of an object or the amount of gap between two points along the longest side of an object.
- Length and distance are similar but slightly different. Length is the amount of gap between two points along the longest part of an object. Whereas, distance is mostly the amount of gap from one place to another. In a nutshell, distance is a longer length (amount of gap) between two points while length is a short amount of gap between two points.
- Width – is the amount of gap across and object from one side to the other. Width may mean the same thing as breadth.
- Height – is the amount of gap from the top to the bottom of an object.
- There are many ways of measuring length. All the ways are grouped into two categories. These are the standard and the non-standard categories of measuring length.
- Non-standard ways of measuring length are the ways whose result may not be the same for everybody but may be different from one person (that measured the length) to another.
- The non-standard ways of measuring length include handspan, cubit, armlength, foot, and pace.
- Measurement of length using non-standard ways give different result because we are different. And our individual differences make us special.
- Estimation means the calculated guess of the measure of an item.

## EVALUATION

The teacher assesses the pupils’ understanding of the lesson by asking them questions based on the lesson; giving them practical exercises as well as exercises from their recommended textbooks.

## CONCLUSION

The teacher concludes the lesson by marking the pupils’ note, recording their scores and providing adequate feedback. Thereafter, s/he links the current topic to the following week’s topic. To do this, the teacher tells the pupils that they shall in the following week discuss standard measurement of length.

[qsm quiz=3]