MATHEMATICS

Bonny and Tommy visit the farm

EDUCATOR SECTION

Memorandum

The learners each need a clock to handle and can construct one out of cardboard before the lesson.

In module 4 the number concept is extended to 600. Addition and subtraction calculations include two and three digit numbers. Multiplication and division calculations are done without regrouping of tens, and only up to 99.

In learning 3x and ÷ up to the 10th multiple, the tables that have to be mastered in Grade 3 are completed. Regular repetition and testing are vitally important from this stage on.

It is recommended that the reading of time be done with all the learners at the same time. Each learner must have a cardboard clock to use when the work is being done.

Such a clock can be made from a paper plate, or the learners can be allowed to design their own clock for Technology. However, it must be ready before the reading of time is started in class. A great deal of practical exercise is necessary before the learners can complete the worksheets.

Number concept is now extended from 400 to 600 and the number blocks of hundreds, tens and units, as well as the flared cards, (attached to Module 2), must still be used to promote the number concept. Give special attention once again to the 100 that must be regrouped when 300 and 500 are halved: 300 = 200 + 100 500 = 400 + 100

Counting in sixes must be done incidentally and can also be repeated on the multiples chart (Module 2). Learners must know: 1 dozen = 12.

Learners must have the opportunity, and be encouraged, to say what they can deduce from the graph, what can change and what will not change, before they have to write about it. Such a discussion will give you a good indication of what the learners understand and which aspects need more attention.

Learning 3x and ÷ must be done on the mat and with the use of concrete apparatus. The worksheets are only there to apply what has already been taught.

Learners must get the opportunity in class, on a daily basis if possible, to take measurements with the ruler, the metre stick and the trundle wheel. The more practice they get, the more accurately they will measure. However, always encourage them to estimate first.

This is enrichment work and if you find that it is too advanced, it can be done at a later stage. There may be learners who would like to accept the challenge.

Seeing that 3x and ÷ have just been done, it is easy to introduce thirds now. Give the learners loose paper shapes and allow them to fold and measure on their own, so that they can discover how it can be done. Some of the learners will know how to find sixths without any help. (Only enrichment)

The idea with the recipe is to make the learners understand that certain standard units and containers must be used, otherwise there is no chance of success with a recipe.

Let the learners mention more examples of the use of standard units in practice, e.g. petrol, milk, mixing medicines, prescriptions for administering medication, etc.

It is essential that all the different standard measuring containers and scales, as well as sand, water and objects used in measuring volume and mass, should be available in the classroom. Learners should be able to experiment every day with measuring and weighing, using standard units: litres and millilitres and grams and milligrams.

A bathroom scale is required to determine the mass of the learners.

Different methods are used for the multiplication and division calculations, but should you prefer another method and you find that the learners understand it better, it is their right to use the preferred method.

It is essential that many similar examples of the relevant number sentences be done orally before the learners are expected to complete this worksheet.

The regrouping of a hundred when adding or subtracting is now formally taught. Sufficient concrete work must be done beforehand. More advanced work where a ten and a hundred are regrouped simultaneously, should not be done at the same time. It will depend on the abilities of the group whether it should be done immediately hereafter or at a much later stage.

Whether the learners will be allowed to make use of carried numbers, remains the decision of the educator. e.g.

Learners will need a blank sheet of paper in order to calculate the shortest route. Some learners may find it difficult and may want to give up, but with a little help they should be able to do it.

A discussion on what they will see as they approach the farmstead by road is necessary before the learners will be able to draw it.

LEANER SECTION

Content

ACTIVITY: Mass [LO 1.8, LO 1.9, LO 2.2, LO 4.5]

• Bonny and Granny want to make some pancakes. If they want the pancakes to be a success, they have to measure the ingredients accurately.

Dry ingredients such as flour and sugar are measured in grams and kilograms. A standard measuring cup and standard measuring spoons are used. You may use a kitchen scale to weigh the ingredients. Remember: 1 000 g = 1 kg

Liquids such as oil, milk and water are measured in millilitres and litres, and a standard measuring jug and measuring spoons are used. Remember: 1 000 mℓ = 1ℓ

• Here is their recipe. Why don’t you try it out at school or at home

Ingredients:

4 cups (544g) cake flour

4 eggs

1 cup (250mℓ) oil

1 t (5mℓ) salt

¼ cup (63mℓ) vinegar

1ℓ water

4 t. (20mℓ) baking powder

Method:

1. Beat the eggs, oil, vinegar and a little of the water very well.

2. Sift the flour and the salt together.

3. Add the flour and the rest of the water little by little to the egg mixture and whisk it thoroughly.

4. Lastly, add the baking powder.

5. Heat a lightly oiled pan. Pour a small quantity of the batter into the pan. Turn it over to brown the pancake on both sides.

6. Turn it out onto a plate, sprinkle with cinnamon sugar, and roll it. This recipe makes 60 pancakes.

How many pancakes are there for each learner if there are 30 learners in the class? There are ___________________________________________________________

Calculate the ingredients you will need if you want to double the recipe:

_______________ cake flour

_______________ eggs

_______________ water

_______________ oil

_______________ baking powder

_______________ salt

Estimate which 5 learners in your class have the smallest mass, write their names in the table and ask your educator to weigh them.

Table 1

Name	Estimated mass	Weighed mass	Too much or too little

• Who of the 5 learners have the greatest mass?_________________________
• Who of the 5 learners have the smallest mass?_________________________
• What is the difference between the two masses?________________________
• What is the total mass of the 5 learners?______________________________

• Find the mass of the following objects, but first estimate whether it is more or less than 1 kg:

Table 2

Object(s)	More/less than 1 kg	Weighed	Right/wrong
Your shoes
School bag
Lunch box
A brick
10 books

• Calculate the total mass of each of the following. Mother buys:

3 x 2 kg rice _________________________________________

5 x 10 kg potatoes____________________________________

6 x 100 g jelly________________________________________

4 x 150 g sweets_______________________________________

2 x 500 g margarine____________________________________

1. Think!

2 x 7 = _____ 9 x 2 = _____ 16 ÷ 2 = _____

5 x 5 = _____ 10 x 3 = _____ 9 ÷ 3 = _____

3 x 9 = _____ 8 x 4 = _____ 20 ÷ 5 = _____

10 x 7 = _____ 6 x 10 = _____ 12 ÷ 4 = _____

4 x 6 = _____ 5 x 2 = _____ 24 ÷ 3 = _____

2 x 8 = _____ 7 x 4 = _____ 10 ÷ 2 = _____

5 x 6 = _____ 6 x 2 = _____ 40 ÷ 10 = _____

10 x 8 = _____ 9 x 4 = _____ 5 ÷ 5 = _____

3 x 0 = _____ 4 x 5 = _____ 16 ÷ 4 = _____

4 x 7 = _____ 6 x 3 = _____ 21 ÷ 3 = _____

2 x 9 = _____ 7 x 5 = _____ 14 ÷ 2 = _____

10 x 10 = _____ 4 x 4 = _____ 36 ÷ 4 = _____

5 x 3 = _____ 5 x 10 = _____ 27 ÷ 3 = _____

3 x 8 = _____ 6 x 5 = _____ 4 ÷ 2 = _____

4 x 9 = _____ 3 x 2 = _____ 45 ÷ 5 = _____

10 x 1 = _____ 8 x 5 = _____ 90 ÷ 10 = _____

2 x 5 = _____ 3 x 3 = _____ 30 ÷ 5 = _____

2. Look at the pattern that Bonny and Tommy have discovered. Complete it:

1 x 2 = 2 10 x 2 = 20 100 x 2 = 200

1 x 3 = _____ 10 x 3 = _____ 100 x 3 = _____

1 x 4 = _____ 10 x 4 = _____ 100 x 4 = _____

1 x 5 = _____ 10 x 5 = _____ 100 x 5 = _____

1 x 6 = _____ 10 x 6 = _____ 100 x 6 = _____

2 x 1 = _____ 20 x 1 = _____ 200 x 1 = _____

2 x 2 = _____ 20 x 2 = _____ 200 x 2 = _____

2 x 3 = _____ 20 x 3 = _____ 200 x 3 = _____

2 x 4 = _____ 20 x 4 = _____ 200 x 4 = _____

2 x 5 = _____ 20 x 5 = _____ 200 x 5 = _____

3 x 1 = _____ 30 x 1 = _____ 300 x 1 = _____

3 x 2 = _____ 30 x 2 = _____ 300 x 2 = _____

3 x 3 = _____ 30 x 3 = _____ 300 x 3 = _____

4 x 1 = _____ 40 x 1 = _____ 400 x 1 = _____

4 x 2 = _____ 40 x 2 = _____ 400 x 2 = _____

5 x 1 = _____ 50 x 1 = _____ 500 x 1 = _____

5 x 2 = _____ 50 x 2 = _____ 500 x 2 = _____

• Let us see how Bonny and Tommy have solved this problem.

Granny baked some cookies and packed them into 3 tins. There are 23 cookies in each tin. How many cookies did she bake altogether?

Figure 1

• Try to solve this problem in the same way.

Grandpa planted 4 rows of trees. There are 12 trees in each row. How many trees did he plant altogether?

Figure 2

• Do the calculations and use the method you like best:44 x 2 =

32 x 3 =

2 1 x 4 =

1 1 x 5 =

• Use your own method to solve the problems. Show how you do it:

The past 4 days Granny collected 22 eggs from the nests every day. How many eggs did she collect altogether?

• She collected ___________________________________________________

On Monday Granny and Bonny baked 120 cookies. On Tuesday they baked 48 and on Wednesday another 100. How many cookies did they bake altogether?

• They baked _____________________________________________________

Assessment

Learning Outcome 1:The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.8: We know this when the learner can perform calculations, using appropriate symbols, to solve problems;

Assessment Standard 1.9: We know this when the learner performs mental calculations;

Learning Outcome 2:The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.2: We know this when the learner copies and extends simple number sequences to at least 1 000;

Learning Outcome 4:The learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.

Assesseringstandaard 4.5: We know this when the learner estimates, measures, compares and orders three-dimensional objects using non-standard and standard measures.