MATHEMATICS

Bonny and Tommy’s birthday party

EDUCATOR SECTION

Memorandum

Integrate the design of the hat and the gift wrap with Technology. This can be done classically.

All the calculations involving money and other quantities which the learners work with will enable them to realise that Mathematics is part of our daily activities.

From Module 3 onwards the learners will gradually progress to the more advanced work of Grade 3. It may be necessary sometimes to go back to previous work to expedite the transition to the advanced work.

It is important that the learners should realise that addition and subtraction combinations as well as the tables, multiplication and division, simply have to be repeated regularly and must be learnt until they know it! It is basic work that cannot be neglected.

Attached you will find a sheet with tables presented in a specific order. You can copy it and give it to the learners so that they can keep it with them.

These worksheets can be presented to the whole class at the same time. Learners must write the dates on the calendar on their own, therefore it is of the utmost importance that you will make quite sure that all the learners begin on the correct day in January. I suggest that you fill in 1 January yourself before copying the worksheet. If you like, you could even fill it in further, depending on the competence of the learners.

It is important for the learners to understand the difference between days of the week (7) and workdays, school days or week days (5), otherwise they may make numerous errors in their calculations.

The learners must be aware of the patterns that are used in completing tables, therefore they must identify the pattern initially before they try to complete the table.

This is a vertical numbers line. The negative numbers have been filled in so that the learner will realise that numbers smaller than 0 do exist. It is not necessary to give this aspect much attention at this stage. It can just be mentioned in passing, to satisfy the learners who are keen to know more.

Explain to the learners that they are seeing diagrams, and that each symbol represents the value of the place where it stands.

Regrouping the 10 is being done now. The learners must first lay it out on the mat, so that it is experienced as something concrete, and so that they can see that there are 12 units and that they can therefore make another ten. This ten is then grouped with the other tens.

It depends on the educator and the abilities of the learners whether they are going to use carried numbers when doing the vertical calculations

The breaking up of the ten is also learnt now. Learners must work with this on the mat in order to experience in concrete terms that there are not enough units and that a ten must be regrouped in order to get enough units. They must understand the breaking up (regrouping) of the ten very well before they can do it in writing.

Again it depends on the educator and the abilities of the learners whether they are going to make use of carried numbers in vertical calculations.

The important fact here is the equivalence of different coins. There are learners who will indicate 7c as 4c and 3c in coins, and who will not realise that such coins do not exist in our currency.

It is also the ideal opportunity for learners to learn 5x and ÷ if they have not yet done so.

Point out to the learners that in calculations the R and c are left out, but that they must be inserted in the completed number sentence (answers).

Encourage the learners to keep on drawing what they read and then to write the number sentence in order to solve the problem.

Make very sure that all the learners know that there will be 10 children at the party. (8 + Bonny + Tommy) If this information is incorrect, all the following calculations will be extremely difficult.

Designing and making the party hat can be done as part of Technology.

Demonstrate and discuss the 3 ways in which to draw a circle.

Do a great deal of practical work.

Make sure that they understand and know what the centre, diameter and radius of a circle is, and that 2x radius = diameter. Explain to the learners what the circumference of the circle is.

The learners must indicate all points with letters right from the beginning. Show them that it makes it much easier to discuss and explain various aspects of the construction. They must understand that they may use any letter, as long as the same letter is not used twice in the same construction.

Once more discuss the different ways in which to divide squares and rectangles into halves and quarters.

Much concrete and semi-concrete work must be done when the learners have to divide numbers into quarters, especially when the number is not a multiple of 4. Use objects such as fruit and soft sweets that can actually be broken up quite easily, and not hard objects such as marbles, stones or bottle caps.

Explain to the learners that it will depend on the problem whether you can break it up into fractions or not.

Look at this: Daddy has 25 sheep that have to be herded into 4 pens. How many sheep will there be in each pen? (The remaining sheep cannot be cut up.)

Daddy has slaughtered 25 sheep and takes them to 4 butcheries. How many does each butchery get? (It will certainly be possible to divide the remaining sheep into 4.) Discuss more similar examples.

As soon as the learners understand that 4x is 2 times doubled, and 4÷ is two times halved, this can be drilled, because they must know the tables.

This is a wonderful way of familiarising learners with posing problems, but it demands much and regular practice. As soon as they understand it and can do it with confidence, they put forward wonderful ideas.

Begin with a very simple number sentence, e.g. 3 + 4 = □. Initially, let the learners name objects with which they can possibly work, and write these suggestions on the blackboard: trees, flowers, sweets, sheep, dogs, etc.

Everyone must be involved and try to give suggestions. Make the rows compete and then let them pose the problems as a kind of competition.

The vertical addition and subtraction calculations have been graded from simple to difficult so that it will be easy for you to determine a learner’s problem(s). This will enable you to concentrate on the problem areas only and to give appropriate similar exercises to help them.

With the last row of addition calculations, completing the hundred (carrying over the tens) is done incidentally to determine which of the learners understand this already. However, you are free to facilitate this formally now.

It must be a pattern that is repeated every 2 blocks and therefore it must be exactly the same throughout. It can also be offered with Technology, and the learners can then draw their own blocks on a larger sheet of paper.

Explain rounding off to the nearest R to the learners. Let them bring old catalogues and practise rounding off until they understand it.

This worksheet will give you a good idea of which learners are able to follow and carry out instructions.

Any learner who has a good grasp of hundreds, tens and units at this stage, should be capable of completing this worksheet quite easily. Point out to the learners that if they do not get the same answer in the balloon vertically and horizontally, there is a mistake somewhere and they will have to check the answers vertically and horizontally again.

More examples with smaller numbers can also be given.

LEANER SECTION

Content

ACTIVITY: Numbers [LO 1.1, LO 1.3, LO 1.4, LO 1.5, LO 1.8, LO 1.10, LO 4.2, LO 4.3, LO 5.1]

• It is Bonny and Tommy’s birthday on 13 May. They want to know how many days are still left before their birthday.
• Complete the calendar. Use the calendar in the classroom or at home and make very sure that you start on the correct day in January.

Figure 1

• Encircle the date of Bonny and Tommy’s birthday on the calendar.
• Encircle today’s date as well. Now count how many days are left. (Remember that you can’t add 13 May as well.)

Write: There are __________________________________________left.

• Encircle the date on which you have your birthday. Is your birthday before or after theirs?

Write: My ___________________________________________________________

• Encircle your teacher’s birthday. Has she had her birthday already?
• Bonny and Tommy have also made a “week clock” for themselves, because the days of the week also go around and around, just like the months of the year.

Figure 2

• Do you know the names of the days of the week in the proper order, and can you write them correctly?

Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday

• Complete:

1. There are __________________________________________ days in a week.

2. There are _______________ school days (week days or work days) in a week.

3. The first day of the week is ______________________________________

4. The last day of the week is ______________________________________

5. Together these two days are called a _______________________________

• Make a * next to the day/days on which you do it:

Table 3

	Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
Sport	______	______	______	______	______	______	______
Homework	______	______	______	______	______	______	______
Play	______	______	______	______	______	______	______
Watch T.V.	______	______	______	______	______	______	______
Go to church	______	______	______	______	______	______	______

• What do you do most in a week?__________________________________
• Which day is your busiest day?__________________________________
• Use your calendar again to fill in the day and the date:

Today it is ________________ _____ _________________.

Yesterday it was ________________ _____ _________________.

This term the school will close on _______________ ____ __________.

This year Christmas will be on _______________ _____ _______________.

• Count on the calendar:

In January this year there are ________________________________ Fridays.

In the whole year there are ____________________________________ Sundays.

Die jaar het _____________________________________________ dae.

Is it a leap year this year?_______________________________

How do you know?_________________________________________

• Solve the problems, using your own method, but show how you did it.

1. We visited our grandmother and grandfather on the farm for 3 weeks. How many days did we spend there altogether?

We were there for _________________________________________________

2. Mary was in bed with chicken pox for 2 weeks. How many school days did she miss?

She missed _________________________________________________.

3. My father drives 6 km to work every day. How many km does he drive in 1 week if he goes to work every workday?

He drives _________________________________________________

4. Bonny and Tommy play with their puppy every day of the weekend for 1 hour. How many hours have they played with him after 5 weeks?

They played _________________________________________________

Table 4

Complete:

weeks 1 2 3 4 5 6 7 8 9 10 school days 5

• Bonny and Tommy can climb up the number ladder as far as 1 000 or down as far as –100.

Figure 3

• Count forwards in hundreds, and then back again:

100 200 _____ _____ _____ _____ _____ _____ _____ 1 000

1 000 900 _____ _____ _____ _____ _____ _____ _____ 100

• Sometimes Bonny and Tommy use diagrams to represent numbers.

Figure 4

• What will happen if you add another hundred to each one of these numbers?

_____ + 100 = _____ _____ + 100 = _____ _____ + 100 = _____

• Bonny and Tommy have hidden a number sentence among the numbers in this block.
• Find all the numbers between 300 and 400 and colour the squares with an ordinary pencil.

Table 5

200	315	178	612	144	447	162	333	554	128	419	304	109
155	301	290	422	515	167	298	303	818	422	191	320	715
524	321	188	661	176	325	327	329	336	340	222	348	199
432	350	569	351	208	184	529	357	177	282	555	363	999
191	362	365	369	370	171	284	375	286	612	444	377	813
946	914	755	384	123	456	678	789	800	876	753	531	179

1. Have you found it? Write it down and complete it: _____________________

_____________________________________________________________________

2. Now add two noughts to each number and write the new number sentence.

_____________________________________________________________________

3. Find all the numbers in the block with 2 hundreds and write them down here:

_______ _______ _______ ______ ______ ______ ______ ______

4. Arrange them from the most to the least:

_______ _______ _______ ______ ______ ______ ______ ______

5. Fill in the missing numbers:

205 206 207 _____ _____ _____ _____ _____ _____ 214

221 223 225 _____ _____ _____ _____ _____ _____ 239

230 235 240 _____ _____ _____ _____ _____ _____ 275

203 213 223 _____ _____ _____ _____ _____ _____ 293

275 274 273 _____ _____ _____ _____ _____ _____ 266

258 256 254 _____ _____ _____ _____ _____ _____ 240

265 260 255 _____ _____ _____ _____ _____ _____ 220

297 287 277 _____ _____ _____ _____ _____ _____ 207

• See how Bonny and Tommy have solved their problem.
• Bonny has 25 sweets and Tommy has 17. How many sweets do they have altogether?

• See how Bonny and Tommy have solved their problem.
• Bonny has 25 sweets and Tommy has 17. How many sweets do they have altogether?

Figure 5

• Here is a calculation that could cause problems.
• See what Bonny and Tommy have done:

Mother bakes 52 cookies and they eat 16 of them. How many cookies are left?

Figure 6

There are not enough units to take away the 6. Regroup a ten.

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 1.1: We know this when the learner counts forwards and backwards in:

1.1.1 the intervals specified in grade 2 with increased number ranges;

Assessment Standard 1.3: We know this when the learner knows, reads and writes number symbols and names from 1 to at least 1 000;

Assessment Standard 1.4: We know this when the learner orders, describes and compares numbers;

Assessment Standard 1.5: We know this when the learner recognises the place value of digits in whole numbers to at least 3-digit numbers;

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

Assessment Standard 1.10: We know this when the learner uses the following techniques:

1.10.1 building up and breaking down numbers;

1.10.2 doubling and halving;

1.10.3 number-lines;

1.10.4 rounding off in tens.

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

Assessment Standard 4.2: We know this when the learner solves problems involving calculations with and conversions;

Assessment Standard 4.3: We know this when the learner identifies important dates on calendars;

Learning Outcome 5: The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.

Assessment Standard 5.1: We know this when the learner collects data (alone and/or as a member of a group or team) in the classroom and school environment to answer questions posed by the teacher and class (e.g. ‘how many learners walk to school?’).