MATHEMATICS

Bonny and Tommy visit the zoo

EDUCATOR SECTION

Memorandum

(In the following module remainders with regrouping of the tens are practised again).

In Module 6 the number concept is extended to 1000. Addition and subtraction is done with two- and three-digit numbers, with and without regrouping of tens and hundreds. Multiplication is done with two- and three-digit numbers with and without regrouping of tens. Division is done with two-digit numbers and regrouping of tens only, without a remainder in Module 6,

e.g. 75 ÷ 5 = £ (In the following module, the remainder will be included in regrouping.)

Learners need to know what the actual paper money looks like: R10-, R20-, R50-, R100- and R200-notes.

They must understand the values and be able to do simple calculations.

Explain what drawing to scale signifies. They will have to be able to grasp this concept very well before they will be able to calculate the lengths of the elephants’ trunks. Provide similar examples to ensure that they are able to do the exercise.

The learners need to develop a concrete image of the numerical value of 1000.

999 + 1 completes a ten that is taken to the tens to complete 10 tens which make a hundred. The hundred is taken to the hundreds to complete 10 hundreds. These make a group of a thousand which has to be taken to the thousands.

1000: the 1 represents 1 group of a thousand and the 3 noughts are the placeholders for the hundreds, tens and units.

Once the learners have completed the number block, it must be used for many counting exercises in tens and hundreds, counting forwards and backwards.

If learners are still struggling to master doubling and halving, they should be encouraged to use the "cloud" to assist the thinking process.

First work orally with similar examples using letter values, before allowing the learners to do the worksheet.

Multiplication with three-digit numbers, with regrouping of the tens, must first be practised orally and in the concrete.

Let the learners count in 9’s before asking them to write it.

Help them to realise that it is easier to start by adding 10 and subtracting 1 than it is to add 9. The opposite is done when 9 is subtracted: take away 10 and add 1. Let them use counters.

If 10c and 1c pieces are used to explain the idea of regrouping tens during division, the learners will be helped to grasp that the tens have to be broken up and regrouped with the ones before it can be shared out. (Play money could be used.)

The learners may need much practice before they will have enough skill to complete the worksheet.

It might help them to draw the diagrams.

The decision to make use of carried numbers is left to the educator.

First supply paper shapes for dividing into tens, so that the learners may discover for themselves that tenths, like thirds and fifths, have to be calculated and measured. It is not simply a matter of folding and folding again as in the case of a ½ and a ¼ .

Guide them to discover that they, by first obtaining fifths, can divide each fifth down the middle to obtain tenths.

Discuss symmetrical shapes with the learners. Let them identify symmetrical objects in the classroom. They should complete the drawing after this exercise.

LEANER SECTION

Content

ACTIVITY: Number block [LO 1.1, LO 1.3, LO 1.4, LO 1.5, LO 1.8, LO 1.9, LO 1.10]

• Which numbers do these diagrams represent?

Figure 1

• Here we have 9 hundreds, 9 tens and 9 units. Add 1 more unit to the last ten.
• Group the ten and then the hundred.

Now there are hundreds. It is equal to ________________________

• Complete the diagrams:

Figure 2

• Complete the number block:

Table 1

10	20	30	40	50	60	70	80	90	100
1 10					160				200
210
									400
			440
510									600
						670
710									800
910

• When you move horizontally across the number block, you count in tens.

780 790 ________ ________ ________ _______ _______ _______ 860

920 930 ________ ________ ________ _______ _______ _______ 1000

950 940 ________ ________ ________ _______ _______ _______ 870

860 850 ________ ________ ________ _______ _______ _______ 780

• When you move vertically down the number block, you count in hundreds.

200 300 ________ ________ ________ _______ _______ _______ 1000

120 220 ________ ________ ________ _______ _______ _______ 920

9650 860 ________ ________ ________ _______ _______ _______ 160

• Complete:

Figure 3

• Write down all the 3-digit numbers that you can make with the numbers 3, 8 and 9:
• In which number does the 3 have the highest place value?_________________
• In which of these numbers does the 9 have the lowest place value? _______________________________________________________________
• Arrange the numbers from the most to the least:

_______________________________________________________________

• Fill in <, > of = :

650 + 30 ...... 630 + 50

500 + 1 62 ...... 500 + 1 26

348 + 1 00 ...... 200 + 250

730 - 1 1 0 ...... 720 - 1 00

852 - 400 ...... 852 - 452

900 - 500 ...... 900 - 400

• Give the even numbers to the elephant and the uneven numbers to the lion:

1 1 7 426 853 555 851 504 912 963

404 765 299 510 400 889 668 1000

Figure 4

• What is the difference in mass between the lion and the bear?_____________
• What is the sum of the mass of the lion and the bear? ____________________
• Which animal has a greater mass than the bear? __________________
• Which mammal has a smaller mass than the lion? ______________________

• Double all the numbers on the tortoise’s shell.

Figure 5

• Halve all these numbers.

Figure 6

• Write the number that comes 4 places before:

837:_____ 964:_____ 850:_____ 900:_____

802:_____ 903:_____ 892:_____ 1000:_____

• Write the number that comes 6 places after:

833:_____ 952:_____ 830:_____ 990:_____

824:_____ 974:_____ 899:_____ 993:_____

• Write the number names:

319: _________________________________________________________________

490: _________________________________________________________________

682: _________________________________________________________________

807: _________________________________________________________________

973: _________________________________________________________________

• Write the numbers:

four hundred and thirty seven: ____________________________________________

two hundred and six: ___________________________________________________

seven hundred and sixty five: _____________________________________________

eight hundred and fourteen: ______________________________________________

nine hundred and ninety three: ___________________________________________

• Fill in x or ÷ signs:

Figure 7

• Complete the pyramid:

Figure 8

• Fill in the missing numbers:

Figure 9

• Complete:

615 = 600 + ____ + 5

937 = 800 + ____ + 7

550 = ____ + 140 + ____

453 = 400 + ____ + 13

749 = ____ + 1 40 + ____

824 = 600 + ____ + ____

• Use the values of the letters to do the calculations:

a = 800 m = 50 p = 70 t = 5 w = 9

m + p + w = _____ + _____ + _____ = _____

a + m + t = _____ + _____ + _____ = _____

a - p - w = _____ + _____ + _____ = _____

• Complete:

888 890 ________ ________ ________ _______ _______ _______ 904

97 1 973 ________ ________ ________ _______ _______ _______ 987

800 803 ________ ________ ________ _______ _______ _______ 824

880 884 ________ ________ ________ _______ _______ _______ 912

915 920 ________ ________ ________ _______ _______ _______ 955

• Complete:

860 858 ________ ________ ________ _______ _______ _______ 844

913 911 ________ ________ ________ _______ _______ _______ 897

999 996 ________ ________ ________ _______ _______ _______ 875

812 808 ________ ________ ________ _______ _______ _______ 780

830 825 ________ ________ ________ _______ _______ _______ 790

• Add the numbers horizontally and vertically:

Figure 10

• Write an animal story to match the number sentence and do the calculation.

136 + 160 - 82 = ____________________________________________________

• Complete:

Figure 11

• Use your own method to do the calculations:

164 + 103 + 131 = __________________________________________________

150 + 247 - 153 = ___________________________________________________

374 - 150 - 1 1 7 = ___________________________________________________

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 1.9: 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.