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Multigrade teaching guide for Zambian teachers.

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Lesson preparation 1

Mathematics

Topic : Initiation in multiplication.

Material or teaching aids : rolls, plastic bags, sticks or bars.

Objectives: 1. The pupils realize that the multiplication is a abbreviate addition.

2. The pupils can group by 2 , 3 ... till 10 without remainder ( rest )

 Didactic methods Lesson activities A. Introduction    story. Bakers prepare a lot of rolls on Sunday. These rolls are put in bags. Bags with two rolls, 3 rolls, 4 rolls ... In the past bakers wrote their calculations like this:   2 rolls + 2 rolls + 2 rolls + 2 rolls ... 3 rolls + 3 rolls + 3 rolls + 3 rolls ... 4 rolls + 4 rolls + 4 rolls + 4 rolls ...   Bakers who sold a lot of rolls must make yards long accounts. One day, while all the other bakers of a village were doing their accounts, baker Phiri made a walk in the city centre with his wife. All the other bakers were looking very surprised through the window. Why baker Phiri was not doing his counts like they were doing ? Curious to know what is happening they asked some explanations. Look, told baker Phiri, I was tired of making every day these long bills. During the baking I thought about the problem and one day I had an idea: in stead of note down separate every bag with f.e. 3 rolls , I wrote: 20 bags of 3 ... 10 bags of 2... 30 bags of 4...   The other bakers followed the example of baker Phiri resulting in that all the bakers could now make a walk with their wive every Sunday of the year.   B. Development   Task:   - in bags of two rolls...   - we count  : 10 bags of  2 rolls andt the teachers write on the blackboard    10 bags of two or 2 + 2+2+2+2+2+2+2+2+2 =   See the difference   - In bags of three...    We count 6 bags of 3 and note on the blackboard   6 bags of 3 or 3+3+3+3+3+3 =   Work on the  demonstrationtable and the blackboard     How much does that make together ? The 5 bags are on the demonstrationtable , in each bag 2 rolls. Put a rope around it like a set. We are grouping. 5 bags of two is ten 2+2+2+2+2 = 10 Draw in a set 5 bags with 2 rolls on the BB. Let explain the children and note. Groupe also with 3,1,4... Let explain the children and note. Let realize the children that 5 bags of two rolls is the same as 2+2+2+2+2.   C. Evaluation   Working with the arithmeticbox and the arithmetic bars.   Lay 5 bars with number 2 What do this make ? We note and the children explain, repeat :           2+2+2+2+2= 10       or 5 bars of  2  equals 10       or 5 time 2 equals 10   Make more of these exercices with the arithmetic bars.    - Lay 3 bars of 3      Lay 8 bars of 1      Lay 1 bar of 6 The children must always explain and note.   D. Worksheet a. The teachers tells the story.                                                                           b The teacher put the rolls of baker Phiri in the bags.     Some rolls are lying on the demonstration table and sticks or bars.     counting   writing on the blackboard.     counting   writing on the blackboard.             Demonstrate with a rope = set     Drawing on the blackboard     Note     Realize                         Exercises with the AB

Lesson preparation 1

Mathematics

Topic Multiplication

Material or Teaching aids: rolls, plastic bags, sticks or bars.

Objectives: 1. The children can group in a concrete and a schematic way per 2,3,4...

2. The can put into words the number of  equal groups.

They make use of  time

3. They realize that the multiplication is a abbreviate addition.

4. They can recognize the symbol x , use it at the note down and put it into words      as  time .

 Didactic methods Lesson activities Lesson 1   Teach the same lesson as in Grade 1 to refresh the childrens mind.   Lesson 2   A. Introduction   We operate with the arithmetic box. *Lay 6 bars of three.       Howmuch is this together ? Put into words : 3+3+3+3+3+3 = 18                       6 times 3  = 18                       *Lay 3 bars of six   How much is this together? Put into words:  6+6+6= 18                           3 times 6 = 18   We make as much as possible of these escercices till the whole class understands the principle.   Note:   0 times... 1 times...   B. Development   1. We train  the signs.   The teacher writes on the board the word plus Let it read by some children. Teacher asks: wich short sign do we use for plus ?    +  And for minus ?  - And for times, groups, bags ?    x  We all say times.   a. We train effortlessly   - The teacher has cards with + , - , x , = , >, < - The children have to put in words every card like:   +  plus, more, the sum, add, enumerate...           - minus, less, the difference, reduce,...           x times, groups, bags,bars...   b. We use and put into words   x   - 3 x 6  ( on the BB) The task must be execute with bars, draw in a set,... - The children are looking for the operation and put it into words.   2. We make carpets, walls and steps with the arithmeticbox or with paperslips.   An example:   *We let discover the children that the multiplications form a group, in wich the .............................. quality appears.   *Give the children the task to make a x wall with bar 8. Let them find out . After they did it we bring the solution on the BB. We do the same for 10,14,15,16,18,20. We make steps of 2,3,4... - The pupils make a step with bar 2. - The put into words and mention x or times   3. We work with the presentation of sets,arrows,...   We operate  first  with the magix box. two examples: A. - On the magix box is x  2 , that means: what you put in the magicbox will be two times bigger when it comes out of the MB. - The teacher put bar 3 in the MB - What is the MB doing ? she takes 2 times 3 or 3 times 2 ? - How much will come out of the box ?   2 bars of three, that makes 6. - We note 3  x  2  =  6  also 2  x  3  =  6 - Now you make several exercises like this. - In stead of taking bars you take cards with numbers.     B. The MB is doing x, but does not say how many times. .... times 3  = 12   - wich bar is going into the MB. 3 - How many bars are coming out ? 4 - What was the MB doing ?   4 x - How much is this together ?   Make more exertcises. Let participate as many children as possible.   C. Evaluation   Worksheets.

Lesson preparation 1

Mathematics

Topic: The table of multiplication and division by 1,2,5 and 10

Material or teaching aids:

Objectives: 1.The pupils discover and can put into words that the multiplication is a abbreviate addition and that  the division is a abbreviate subtraction.

2. They discover and can put into words that multiply and divide are inverted relations.

3. They have to build up ( and tell how they do it) the tables of 1,2,5,and 10.

4. They have to explain the product ( write) when 2 factors are given and reverse.

5. They have to explain the quotient (write) when dividend and divider are given and    reverse

Note  : information for the teacher

Multiply

The teacher will divide the class in equal groups. The pupils put into words times; they use the symbol x . The operator must be the first part of the multiplication.

Divide

ex. 3 groups with seven children each= 3 x 7 = 21

The division is the inverted relation of the multiplication.

We distinguish the partition and proportion division.

a. The partition division

Father  divides 60 kwacha  under three children.All of them get the same amount.We know the partition will be under three children, but we dont know how much each child will get.

The solution: 60 (kwacha) : 3 = 20 (kwacha).

Dividend and quotient can be named, the divider not.

b. The proportion division.

Father divides 60 kwacha under three children. They get each 20 kwacha.

We know how much each child get, but we dont under how many children the money was divided.

The solution: 60 (kwacha) : 20 (kwacha) = 3 (children)

Question: How many times goes twenty into sixty ?

A. The table of multiplication by 2

1.Some suggestions:

- Put a lot of alternation in your lesson.

- Make use of different methods.

- Make sure that all the children acquire insight.

- During the lesson the teacher has to repeat the next terminology, symbols and notions.

Product = Result of a multiplication ( = a shorter notation for the sum of different equal terms.

Quotient = Result of a division ( = a shorter notation for the deduction of different equal numbers)

Group = make groups of... ( = count in groups)

= times

= divide in...

2.Act and put into words:

a. The pupils group objects in groups of two, they can also work with bars.The operator must be first, in front.

Put into words:   1 times 2

a group of 2

The pupils lay the quantities ( de teacher note the products on the BB): bars, corralchain, hunderd field.

0 times 2    0                                            0 x 2 = 0           0 is a multiple of 2

1 times 2    2                                            1 x 2 = 2           2 is a multiple of 2

2 times 2    4                                            2 x 2 = 4           Also 4,6,8 are multiples.

3 times 2    6                                            3 x 2 = 6           Also f.e. 6 is the multiple of three of 2.

b. Then we handle the division table ( only as a proportion division)

How many times bar 2 goes into 2 ?  2  :  2  =  1

How many times bar 2 goes into 4 ?  4  :  2  =  2

How many times bar 2 goes into 6 ?  6  :  2  =  3

Put into words:  4 divided by 2

4 in groups of 2

c. You can also put in groups on the counting-frame.

d. On the number axis the multiplier can be fixed on the products.

1           2                       3                           4                             5                    6                   7

 1 2 3 4 5 6 7 8 9 10 11 12 13 14

The children will count on the number axis by 2 from 0 till 20 and back.

How many times 2 goes into 10, into 12 ...

e. The teacher has 4 plastic bags and in each bag he has 3 objects.

We count 3+3+3+3 = 12 of 4 x 3 = 12

How many plastic bags with stones are there when we have in all 12 stones.

f. Also playing cards and dies can be used.

Look at when you put it into words.

f.e.

6 are 3 groups of 2

6 is a multiple of 2

6 is the multiple of three of 2

the product of 3 and 2 is 6

2 is a divider of 6µ

2 goes 3 times into 6

0,2,4,6,...are multiples of 2.

3.Shematise and put into words:

How much is 4  x  2  ?

The children put into words:

2+2+2+2

4 x 2

4 times 2

4 groups of 2 elements

4 subsets of 2 elements

8 is the quadruple of 2

2 is a divider of 8

How many groups ( subsets) of 2 in 8 ?

Use of the magic box.

 Task  draw the arrows                                          Is a multiple of 2 Solution                                        Is a multiple of 2 is a divider of... Is a divider of

4. Applications:

Exercises on the BB

Make groups ( subsets)

Draw the subsets and  fill in the label.

12 in groups of 2 = .... groups

12  :  2  =

B. The table of multiplication by 10 , 5

1. Act and put into words.

a. We work analogous  ( ref. table of 2) but we can start our lesson with the hunderd field.

We put into words:

0                    0  x  10  =  0

10                  1  x  10  =  10

10  +  10        2  x  10  =  20

and so on...

How many times 10 goes into 0 ?  0  :  10  =  0     0,10,20 ... are multiples of 10

How many times 10 goes into 10 ? 10  :  10  = 1   0,10,20 ...  are multiples of 10

How many times 10 goes into 20 ? 20  :  10  = 2   10 is a divider of ... ( f.e. 30)

How many times 10 goes into 30 ? 30 : 10 = 3      30 is the multiple of three of 10.

Also how many groups ( subsets) of 10 in ...

b. Use of the bars.

c.idem for the table of 5

2. Schematise and put into words:

a.

Draw the arrows

 is a multiple of ... is a multiple of

Is a divider of  ...                                                        Is a divider of ...

b. Other applications ( write the exercises on  the BB )

1. Make groups ( subsets ) of 10                                  Draw yourself and fill in the label.

40 in groups of 10                                                     4  x  5  =  ...

40  :  10  =  ...

PREPARATION OF A SERIES OF LESSONS ON

THE KITE

WEEKLY PLANNING

Monday

First lesson:

Subject: Language

Topic: The Kite, vocabulary

Teaching aids: the material to make a kite.

-Long string, sticks nails, hammers, and piece of wood, plastic, scissors, and knife.

Objectives:

I. Introduction

The teacher asks the children to name some objects that can fly. When one of the children is saying a butterfly, you ask what this butterfly might look like.

You have a child draw on the blackboard, if you have colour chalk, let him colour.

Then you tell the children that you know a song of a butterfly named "Butterfly fly away".

The song

-------------

Butterfly fly away

------------------------

II. Development

Now the teacher puts a basket with objects on the table in front of the class. The basket contains the materials to make a kite. The teacher calls some pupils in front of the class and asks them to take out all the objects one by one. Each child tries to name each object. The word kite is not mentioned already.

When all the objects are on the table, the teacher will ask the children what we can do or what we can make with all these objects. The children will give a right answer.

Now the teacher asks the children if all the objects are in the right order. While putting now all the objects in the right order the objects are to be denominated again.

So:

-          Make the children put all the objects in the right order.

-          Let the children name each object.

-          You put a picture under each object.

-          You put a card with the name under each picture.

-          Each word can be linked to a sentence. These sentences explain what to do with the objects.

-           The words                             The sentences

The stick                              You have to  cut two long thin sticks to make the frame.

The nail                               Zama uses a nail to make a cross.

The hammer                        Please could you pass me the hammer and a  nail ?

The plastic                          Chanda cuts plastic into small pieces to make the tail of the kite.

# The tail

The scissors                        I need the scissors to cut the plastic into the right shape.

The needle                          Zama, you have to sew the plastic to the frame with the needle and the

Cotton                               Could you give me some cotton?

The string                          This piece of string isn`t long enough to fly the kite.

Thick piece of wood          You must use that piece of wood to make the handle.

The kite                             You tie the end of the string to the kite.

The verbs

To make

To attach

To wrap

To join

To cut

Two key-questions

1.       What do we need ?

2.       What do you do with it ?

III. Evaluation

You can divide the class into five teams to make pupils work together and to stimulate the competition between the teams.

1.      Put the materials in the right order to make a kite.

2.      Combine each object with the right picture and name the picture.

3.      Associate each picture with the right card at the back of which is written the name of the object.

4.      Join the right sentence to each picture.

5.      Explain every word.

Tuesday

Second lesson

Topic:  The kite

Teaching aids : idem

Objectives:

I.                 Introduction

Read the words or the sentences or the text of the previous lesson.

Make sure all the children are given a chance to read some words or sentences or paragraphs.

## II.             Development

The children  answer orally in their groups.(oral)

The teacher writes the right answer under the question on the blackboard.

1.What are Mubita and Zama making ?

They are making a kite.

2.Why Mutinta must cut two long sticks ?

To make the frame.

3.What does Zama need  to make a cross ?

He needs a hammer and nails.

4.What do you need plastic for?

To make the body of the kite.

5.With what do you sew the plastic to the frame?

With the needle and  the thread.

6.Where do you have to tie the string?

At the end of the kite.

7.What do you need the wood for ?

To make the handle.

8. Where do you tie the end of the string?

To the kite.

9. Where do you tie the other end of the string?

To the handle.

10. What can you do now?

Now we can fly our kite.

First the teacher asks one team to read some of the sentences.

Then the teacher asks a question to one of the teams.

The groups give an answer without looking the text.

The right answer is written on the blackboard.

III.         Evaluation

The children write the questions and the answers in their exercise-books.

Afterwards there will be an individual test based on the ten questions.

Wednesday

Third lesson

Subject: Language,Spelling

Topic: the Kite

Objectives:

I.                 Introduction

Depending on the grade in which you are teaching, you can start by reading the words or the sentences.

First you give the opportunity to the children to read the words or sentences. If a child doesnt read very well, the teacher will repeat or ask one of the good pupils to repeat. All the words or the sentences will be on the blackboard. Use also the objects and  the cards with the words and the sentences.

### II.Development

The teacher writes word per word on the blackboard, the children will do the same  in their exercise-books and control if the word is written correctly.

The children are helping each other and the control will be done within the team. Make sure that each group has a good element, a good pupil.

Do the same with the sentences.

You write one sentence on the blackboard and you analyse the difficulties.

Example:

I need the scissors to cut the plastic into the right shape.

-          in this example you explain the orthography of the words scissors, plastic ,right and shape.

-          You ask some of the pupils  to write  the words on the blackboard.

-          Dont leave words wrongly spelled on the board.

-          Make them write the sentence in the exercise-books.

Repeat the same method for the other sentences.

II.Evaluation

Dictation of the words or the sentences.

Dictate word by word.

Speak slowly.

Repeat every word.

Dictate every sentence word by word.

Speak slowly.

Repeat every sentence.

Correction to be done classically.

Thursday

Fourth lesson

Subject: mathematics, geometry,cm

Topic: The Kite

Teaching aids: a ruler,paper,a pencil,concrete shapes,pictures of shapes,chart of shapes,chart of a house,a kite on a chart.

Objectives:

I.Introduction

This lesson of the kite can be part of the annual planning of geometry. It will be one of the first lessons of geometry.

We make a walk in the schoolyard  and the children collect concrete material from the environment, and bring it in the class. Ask the children  which shapes they can distinguish.

Then let them look carefully around and ask them to distinguish different shapes in the classroom.

Ask the pupils to have a close look at a house or a building on the schoolyard and ask again to distinguish different shapes.

II.             Development

The teacher prepared a drawing of a house and asks  the pupils  if they recognise the different shapes. Make sure the shape of the kite figures on the drawing of the house. Let the children discover the shape of the kite.

Now we are going to establish sets of shapes.

a.      First we put all the shapes of the house  in the set of the FLAT SHAPES :

the circlse, the polygons, the quadrilaterals ,the triangles,the kites.

b.      Now we distinguish  the set of the polygons.

c.       Then we distinguish the quadrilaterals.

d.      Finally we distinguish the kite.

The teacher will draw the kite on the blackboard, again step by step.

a.       the short stick

b.       the long stick

c.        make a cross

d.       denominate the angles by the letters a,b,c,d.

e.        connect the angles.

f.         You ask the pupils how we call this shapes  =  the kite a,b,c,d.

g.       Measure the sides in cm

ab = cm

bc = cm

cd =cm

da=cm

What do we discover when we compare  the length of the sides? they are alike two by two.

h.       Calculate the total perimeter of the kite in cm.

i.         The teacher now shows a chart of the kite with the name of the shapes, the measures, and the name of the angles.

j.         The teacher also shows a chart with the set of shapes.

III. Exercises

All the children are going to make the picture of the kite as they saw the teacher doing  in the development of the lesson.

One pupil will do it on the blackboard while the teacher is guiding him.

 The polygons
 Flat shapes

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