MATHEMATICS

Bonny and Tommy at the sea

EDUCATOR SECTION

Memorandum

It will probably only be learners in the first group who will progress as far as this module. Do not discourage learners who want to do this module. Even if they can only do a few of the activities they must be given the opportunity to do so. This must be handled carefully so that learners are not discouraged or feel inferior towards other learners. Neither must they develop negative attitudes towards Mathematics.

A considerable amount of advanced and enrichment work is included and the educator must be familiar with each activity before the learners are expected to complete them.

In Module 8 number concept is extended to 2 000. All operations are revised and consolidated. Several enrichment and challenging activities are included in this module and should only be given to learners who can manage them and who enjoy challenges. This selection process must be handled carefully and the other learners must not be discouraged or feel inferior towards other learners or the subject Mathematics.

A thorough discussion and explanation of the map on p. 3 as well as the table of distances on p. 4 should help learners complete these worksheets.

Number concept is extended to 2 000.

This is consolidation of the operations as in the previous modules. It offers an opportunity to identify problem areas.

These are to determine to what extent the learners’ logical thought processes have developed and to test and consolidate the basic work.

Telling the time on digital clocks/watches should only be done with learners who have mastered the telling of time on ordinary (analogue) clocks/watches. They need much practice in telling the time on ordinary clocks/watches and the corresponding time on digital clocks/watches before completing the worksheets.

Give the learners the opportunity to do these problems without help so that their progress can be determined.

Show examples and discuss ethnic patterns with the learners. Encourage them to bring examples to school and to share these with the class.

Use this for assessment purposes.

This is enrichment work and the educator should study this work first and then decide which of these worksheets should be used for which learners.

All learners who have progressed to Module 8 should be able to complete these worksheets with ease.

Do this activity practically in the classroom and let several learners explain what they see in front of them when walking behind someone. Let three learners stand next to one another and let the other learners stand in front of them. They must walk around the three standing in a line and observe them from behind so that they can discover that the order from left to right has changed.

Not much explanation is needed here as this activity is similar to the one where they used the table of distances.

LEANER SECTION

Content

ACTIVITY: Area [LO 1.4, LO 1.8, LO 1.9, LO 1.10, LO 1.12, LO 2.2, LO 2.4, LO 3.1, LO 3.5, LO 4.6]

This is a floor covered with tiles.

Figure 1

• How many tiles are needed to cover the whole floor?
• Write a number sentence to show how you did the calculation.

Number sentence: _____________________________________________________

You multiplied the length and the breath.

If I want to find out how big the space inside a rectangle is, I can say: length x breadth = space inside (area), therefore:

Area = l x b

Figure 2

• Calculate the area of the square.

Figure 3

The length is 5 cm and the breadth is 5cm, therefore it is 5 cm x 5 cm = 25 cm².

Take 25 counters and make a square with them. Draw them. There are five rows of 5.

• Take nine counters and make a square with them. Draw them. There are _________.

Because the length and the breadth are equal it is unnecessary to ask what the length and what the breadth is. Ask: What is the square root of 9? The square root of 9 is 3.

• Take 16 counters and make a square with them. Draw them. There are ________.
• What is the square root of 16? _____ Write:
• Take four counters and make a square with them. Draw them. There are ________.
• What is the square root of 4? _____ Write:
• Draw the squares on the squared paper. Write how many blocks in each square.
• Colour them in.

Figure 4

• Complete each row:

Figure 5

• How many groups of ten can I make?

520 = _____ tens 790 = _____ tens

900 = _____ tens 1 000 = _____ tens

• How many groups of hundred can I make?

1 200 = _____ hundreds 1 500 = _____ honderde

1 900 = _____ hundreds 2 000 = _____ honderde

• Rename:

1 652 = _____ + _____ + _____ + _____

1 508 = _____ + _____ + _____ + _____

1 870 = _____ + _____ + _____ + _____

• Join:

1 000 + 700 + 80 + 4 = ________

1 000 + 500 + 260 + 9 = ________

1 000 + 600 + 130 + 25 = ________

1 000 + 800 + 1 10 + 91 = ________

• Fill in >, < of = :

2 000 - 200 ...... 1 000 - 100 1504 + 20 ...... 1 304 + 200

1 450 + 130 ...... 1 680 - 100 1 280 + 40 ...... 1 280 + 400

• Make each number 1 1 1 more:

1 446 : _______ 1 095 : _______ 1 901 : _______

• Complete:

Figure 6

• Follow the fish to discover the chest of diamonds!

Figure 7

It has been a long year and your teacher is tired. Help her to mark the work.

• Write the correct answer where you find mistakes.

1 332 is an even number.

2 195 is an even number.

1 998 > 1 989

1 824 < 1 842

1 000 + 300 + 63 = 1 336

1 643 = 1 000 + 500 + 143

1 505 comes just before 1 506

1 999 comes just before 1 998

566 doubled is 1 012

The halve of 1 840 is 920

2 x 349 = 698

624 ÷ 3 = 206

1 637 is 3 more than 1 640.

1 785 is 5 less than 1 790.

1 675 is halfway between 1 670 and 1 680.

Table 1

Mark the correct word with a  :	True	False
A rectangle can have 3 right angles.
A sphere has the shape of a ball.
An isosceles triangle’s sides are all the same length.
A cool drink tin is cylindrical.
An egg is spherical.
A rectangle has 4 right angles.

• Underline the correct word:

A (right angle / obtuse angle / acute angle) is 90° .

A cube has (4 / 6 / 8 ) faces.

An equilateral triangle has ( 1 / 2 / 3 ) sides that are equal.

• Write holiday stories for these number sentences and do the calculations.

167 + 205 + 99 =

750 - 145 - 260 =

34 x 3 - 57 =

255 - 191 ÷ 4 =

• Mom, Dad, Bonny and Tommy are walking along the sea. Colour in the picture.

Figure 8

• You are walking directly behind them. Draw what you see in front of you.

It is the last school day of the year.

Bonny and Tommy want to say good-bye because at 6:00 tomorrow morning they are leaving for Cape Town.

• Decipher their greeting:

Figure 9

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

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;

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.

Assessment Standard 1.12: We know this when the learner checks the solution given to problems by peers.

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;

Assessment Standard 2.4: We know this when the learner describes observed patterns;

Learning Outcome 3:The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.

Assessment Standard 3.1: We know this when the learner recognises, identifies and names two-dimensional shapes and three-dimensional objects in the environment and in pictures,

Assessment Standard 3.5: We know this when the learner recognises and describes three-dimensional objects from different positions;

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

Assessment Standard 4.6: We know this when the learner investigates (alone and/or as a member of a group or team) and approximates.