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    This module is included inLens: Siyavula: Mathematics (Gr. R-3)
    By: SiyavulaAs a part of collection: "Mathematics Grade 3"

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Halving and Doubling

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Bonny and Tommy take a look at the seasons

EDUCATOR SECTION

Memorandum

This module still consists mostly of activities for consolidation, reinforcement and assessment of the work taught in the previous grades focusing on the number 100.

  • Number concept to 200.
  • Operations: - Consolidates all work covered in Grade 1 en 2.

The names of the months and the correct spelling thereof need to be attended to. Discussions about the seasons and a healthy environment (nature conservation) will provide opportunities for the integration with other learning areas.

Weather charts for the different seasons can be recorded e.g. February – summer; May – autumn; August – winter; November – spring. These are not the best months for the seasons but they are the months in which the learners attend school for the whole month. Complete a bar graph for every weather chart so that weather conditions can be compared and discussed. Having completed all the bar graphs these can be compared to one another and the learners can discover weather conditions relevant to their own regions as well as those relevant to each season. The educator can keep the graphs to compare the statistics with the next year’s graphs.

The tasks and activities in Learning Unit 2 are still mainly intended for consolidation of work covered in previous grades. It is essential, however, that educators continue to make use of concrete apparatus to repeat, explain and consolidate all concepts that were not fully mastered before.

It is of the utmost importance that learners must be totally familiar with the tens grouping of our numbers system:

10 ones are grouped as 1 group of ten

10 tens are grouped as 1 group of a hundred

10 groups of a hundred are grouped as 1 group of a thousand, etc.

Learners must work with counters that have been grouped in hundreds, tens and units. Should counters not be available, the following semi-concrete apparatus can be used.

Learners must work with counters that have been grouped in hundreds, tens and units. Should counters not be available, the following semi-concrete apparatus can be used.

Figure 1
Figure 1 (graphics1.png)

The expansion cards (flared cards) are very useful in explaining place values, renaming, unifying of numbers and the 0 as place-keeper.

Attached you will find an example of expansion cards (flared cards) and a key to writing all number names. Flared cards enable learners to build any number, and if learners know the basic number names, they can construct and write any number name from the given parts. Give each learner a copy to use, for example

Example:

Number name: one thousand one hundred and thirty seven

Figure 2
Figure 2 (graphics2.png)

If you wish to use this example, enlarge it and copy it on manilla.

Table 1
0 nought 1 one 2 two 3 three 4 four 5 five 6 six 7 seven 8 eight 9 nine 10 ten 1 1 eleven 12 twelve 13 thirteen 14 fourteen 15 fifteen 16 sixteen 17 seventeen 18 eighteen 19 nineteen 20 twenty21 twenty one22 twenty two23 twenty three24 twenty four25 twenty five26 twenty six27 twenty seven28 twenty eight29 twenty nine
10 ten20 twenty30 thirty40 forty50 fifty60 sixty70 seventy80 eighty90 ninety
100 one hundred 200 two hundred 300 three hundred 400 four hundred 500 five hundred 600 six hundred 700 seven hundred 800 eight hundred 900 nine hundred 101 one hundred and one102 one hundred and two103 one hundred and three104 one hundred and four105 one hundred and five106 one hundred and six107 one hundred and seven108 one hundred and eight109 one hundred and nine
1 000 one thousand 3 000 three thousand 5 000 five thousand 7 000 seven thousand 9 000 nine thousand 2 000 two thousand4 000 four thousand6 000 six thousand8 000 eight thousand10 000 ten thousand
  111 one hundred and eleven112 one hundred and twelve113 one hundred and thirteen114 one hundred and fourteen115 one hundred and fifteen116 one hundred and sixteen117 one hundred and seventeen118 one hundred and eighteen119 one hundred and nineteen120 one hundred and twenty121 one hundred and twenty one122 one hundred and twenty two123 one hundred and twenty three124 one hundred and twenty four125 one hundred and twenty five126 one hundred and twenty six127 one hundred and twenty seven128 one hundred and twenty eight129 one hundred and twenty nine  
  110 one hundred and ten120 one hundred and twenty130 one hundred and thirty140 one hundred and forty150 one hundred and fifty160 one hundred and sixty170 one hundred and seventy180 one hundred and eighty190 one hundred and ninety  

Frontpage.

It is essential to have an initial discussion on the changing of the seasons. Some learners may find it very stimulating to discover what causes seasons and why there are different seasons in the year.

Learners must complete the pictures by adding their own drawings to illustrate the typical seasonal qualities, e.g.:

Spring: flowers and blossoms; 2. Summer: anything to do with the seaside or the swimming pool; 3. Autumn: leaves in autumn colours on trees and the ground; 4. Winter: snow on the mountains or rain (where applicable), and leafless trees. Discuss it with the learners.

Learners are now expected to know the names of the seasons in the correct order, and to write them down. A “year and seasons clock” can be put up in the classroom, which can help the learners to master writing the names.

Explain the origin of the extra day every 4 years to the learners. Some of the learners may understand it at this stage, but it cannot be expected of them at all.

This work sheet may elicit a discussion on the Olympic games.

It is important that the learners must understand that if 1 is added to the 9 units of 99, there is another group of ten. There are now 10 groups of ten altogether, which are grouped together to make 1 group of a hundred.

Likewise, they must understand that if they want to take away units from a hundred, they first have to dissolve the group of one hundred, and then dissolve 1 group of ten, before they will have units to take away.

The 0 as place-keeper might cause problems for some learners, Therefore it is essential that the learners must use counters that are grouped in hundreds, tens and units (or the copied blocks), as well as the flared cards, when this work is being done. If necessary, provide similar activities.

If the learners find it difficult to master place values, lay out the numbers with the flared cards.

On the next page there is an example of the multiples chart. It can be utilised very effectively, therefore it is suggested that each learner is given a copy.

This example has been done further than the one on the work sheet, but it can be used for the whole year. Besides, there are learners who are able and keen to count in 6,7,8 and 9.

Show the learners how to find the answers to the tables, x and + from the chart.

Example: 2 x 4 = 8 Go right from 2 and above from 4 downwards – meet at 8 (see arrows)

15 ÷ 3 = 5 Go left from 15 to 3 and up from 15 - 5th multiple

Multiples: Count up to the 10 th multiple and back.

Figure 3
Figure 3 (graphics3.png)

At this stage the learners must know that 100c = R1. The learners now have a good concept of 100 and will realise that 120c equal R1 plus 20c, thus they can now learn to write it correctly, namely 120c = R1,20. Master it up to 199c = R1,99.

Once they have mastered it, do the reverse: R1,20 = 120c up to R1,99 = 199c.

It is imperative that the learners understand the completion and solution of a ten completely. This is an investment for the future. The more concrete work that is done here, the better the learners’ understanding of these concepts. They must be able to relate what they are doing. If they cannot say how they arrived at an answer, it means that the concrete image has not been properly consolidated. Give them many and regular exercises of this kind.

Remember, if you prefer not to do solution directly after the completion, you are free to alter the sequence of the work sheets to suit yourself.

(i) Various triangles: the isosceles; equilateral and rectangular and any other types of triangle.

(ii) Various rectangles and squares.

(iii) Protractors and rulers, enough for everyone in the group.

First establish what the learners already know about the sides and angles of triangles, rectangles and squares.

Measuring angles:

Explain what a right angle is (angle equal to 90°) if they do not know it. Show the learners the protractor and how to measure an angle with it. Make sure that they know exactly how to measure angles.

Let them measure the angles of the various forms on the mat. They must say what they have discovered about the angles of the triangles, rectangles and squares.

All the angles of the rectangles and the squares are right angles. Give them the opportunity to discover other right angles in the classroom.

Have they discovered that a triangle never has more than one right angle? A triangle with a right angle is called a rectangular triangle.

Measuring sides:

Give the learners rulers to measure the sides. Make very sure that all the learners know how to measure using a ruler.

They must discover their own:

There are triangles of which the 3 sides are of the same length. That is an equilateral triangle.

There are triangles of which 2 sides are the same length. That is an isosceles triangle.

There are triangles of which the sides are all different.

The 4 sides of a square are of equal length.

The 2 opposite sides of a rectangle are the same length.

This work will probably not all be done in one mat session, and the time needed will vary depending on the group involved. It is advisable to complete measuring angles in one session and measuring sides in another.

If the learners have already mastered halving of unequal numbers, it is only necessary to explain how to write ½ That means 1 of the 2 parts into which it has been divided:

Table 2
1 is numerator
2 is denominator

This is about halving 3,5,7 or 9 groups of ten. There is always 1 ten that must be solved. Encourage the learners to regroup before they halve. They must first do it concretely on the mat.

Figure 4
Figure 4 (graphics4.png)
Figure 5
Figure 5 (graphics5.png)

Every time the numbers 6 to 9 are doubled, a ten is completed.

The learners must indicate it on the work sheet by drawing a circle around the ten.

Figure 6
Figure 6 (graphics6.png)

If there is no calculator available, the educator or one of the learners can write the answers on the blackboard after completing the work sheet. However, the learners who are able to do the calculations on their own, must be allowed to do it.

Encourage the learners to persevere until they find the right “path”. They may require an extra sheet of paper on which to write the numbers while trying to find the correct ones.7

LEANER SECTION

Content

ACTIVITY: Halving and Doubling [LO 1.8, LO 1.9, LO 1.10]

  • Here are 30 smarties. Show me how you are going to divide them between Bonny and Tommy. Make Bonny’s smarties red and Tommy’sgreen.

Figure 7
Figure 7 (graphics7.png)

Bonny and Tommy say they are going to try very hard to double their pocket money. That means that they will also have to do double the number of jobs.

  • You will remember that Bonnyearned R2 and Tommy R2,20. Calculate how much each will get if it is doubled.

Bonny will get R_____ and Tommy will get R_____.

Figure 8
Figure 8 (graphics8.png)

Bonny and Tommy know there is a treasure in the cottage across the river, but they do not know how to get there. Can you help them?

Here is a clue .

As you walk, add together the numbers on the stones. If you get 200 when you add the 8 on the stone directly in front of the cottage, you have found the right way. Be careful, because there are stones on which you must not step. Now draw the route that you have taken on the picture.

Figure 9
Figure 9 (graphics9.png)
  • Write down the value of all the stones that you have used to cross the river. Add them.

_____________________________________________________________________

_____________________________________________________________________

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;

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.

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