MATHEMATICS

Common and Decimal Fractions

Common Fractions

EDUCATOR SECTION

Memorandum

INTRODUCTION

The learning programme for grade six consists of five modules:

1. Number concept, Addition and Subtraction

2. Multiplication and Division

3. Fractions and Decimal fractions

4. Measurement and Time

5. Geometry; Data handling and Probability

COMMON AND DECIMAL FRACTIONS (LO 1; 2 AND 5)

LEARNING UNIT 1 FOCUSES ON COMMON FRACTIONS

1.1

a) 118118 size 12{ { { size 8{"11"} } over { size 8{8} } } } {} 1

b) 4848 size 12{ { { size 8{4} } over { size 8{8} } } } {}

c) 168168 size 12{ { { size 8{"16"} } over { size 8{8} } } } {}

d) 6464 size 12{ { { size 8{6} } over { size 8{4} } } } {}

e) 6868 size 12{ { { size 8{6} } over { size 8{8} } } } {}

1.2

a) 1414 size 12{ { { size 8{1} } over { size 8{4} } } } {}

b) 6868 size 12{ { { size 8{6} } over { size 8{8} } } } {}

c) 2424 size 12{ { { size 8{2} } over { size 8{4} } } } {}4848 size 12{ { { size 8{4} } over { size 8{8} } } } {}

d) 5454 size 12{ { { size 8{5} } over { size 8{4} } } } {}

e) 3232 size 12{ { { size 8{3} } over { size 8{2} } } } {}6464 size 12{ { { size 8{6} } over { size 8{4} } } } {}

f) 148148 size 12{ { { size 8{"14"} } over { size 8{8} } } } {}

g) 8484 size 12{ { { size 8{8} } over { size 8{4} } } } {}168168 size 12{ { { size 8{"16"} } over { size 8{8} } } } {}

2. BRAIN TEASER!

2.1 612612 size 12{ { { size 8{6} } over { size 8{"12"} } } } {}

2.2 12151215 size 12{ { { size 8{"12"} } over { size 8{"15"} } } } {}

2.3 6767 size 12{ { { size 8{6} } over { size 8{7} } } } {}

2.4 8989 size 12{ { { size 8{8} } over { size 8{9} } } } {}

2.5 510510 size 12{ { { size 8{5} } over { size 8{"10"} } } } {}

3.

3.2 <

3.4 <

3.5 First make denominators the same

Figure 1

5.

5.2 >

5.3 First find common denominator

6.

6.2 20

6.4 40

6.5 10

7.

7.1 2525 size 12{ { { size 8{2} } over { size 8{5} } } } {}

7.2 4949 size 12{ { { size 8{4} } over { size 8{9} } } } {}

7.3 4747 size 12{ { { size 8{4} } over { size 8{7} } } } {}

LEANER SECTION

Content

ACTIVITY: To recognise and classify numbers in order to describe and compare them [LO 1.3.3]

We have looked at fractions on a number line in earlier grades. When they are positioned as clearly as they are on the number line below, it is child’s play to compare them with each other and determine which are equivalent, which are larger or which are smaller than a given fraction. Here we have a few exercises to see if you are able to apply your knowledge of equivalent fractions correctly.

1. Examine the following diagram.

Figure 2

1.1 Write down the fractions that are missing:

a) ………………………………………………..

b) ………………………………………………..

c) ………………………………………………..

d) ………………………………………………..

e) ………………………………………………..

1.2 Write equivalent fractions for:

a) 2828 size 12{ { {2} over {8} } } {} ………………………………………………..

b) 3434 size 12{ { {3} over {4} } } {} ………………………………………………..

c) 1212 size 12{ { {1} over {2} } } {} ………………………………………………..

d) 108108 size 12{ { {"10"} over {8} } } {} ………………………………………………..

e) 128128 size 12{ { {"12"} over {8} } } {} ………………………………………………..

f) 7474 size 12{ { {7} over {4} } } {} ………………………………………………..

g) 4242 size 12{ { {4} over {2} } } {} ………………………………………………..

Figure 3

3. Fill in: < ; > or = :

3.1 5656 size 12{ { {5} over {6} } } {} ............... 2323 size 12{ { {2} over {3} } } {}

3.2 4545 size 12{ { {4} over {5} } } {} ............... 910910 size 12{ { {9} over {"10"} } } {}

3.3 7979 size 12{ { {7} over {9} } } {} ............... 21272127 size 12{ { {"21"} over {"27"} } } {}

3.4 5858 size 12{ { {5} over {8} } } {} ............... 21322132 size 12{ { {"21"} over {"32"} } } {}

3.5 Are you able to explain how you found the answers?

4. Help to “catch” all the fish that have a value above 1212 size 12{ { {1} over {2} } } {} by colouring them in neatly.

Figure 4

5. Work with a friend and fill in: < ; > or = :

5.1 3434 size 12{ { {3} over {4} } } {} ............... 5656 size 12{ { {5} over {6} } } {}

5.2 2323 size 12{ { {2} over {3} } } {} ............... 3535 size 12{ { {3} over {5} } } {}

5.3 Explain to the rest of the class how you arrived at the answer.

6. Complete the following table:

Table 1

	FRACTIONS	COMMON DENOMINATOR
E.g.	1212 size 12{ { {1} over {2} } } {}, 1313 size 12{ { {1} over {3} } } {}	6
6.1	1919 size 12{ { {1} over {9} } } {}, 1717 size 12{ { {1} over {7} } } {}
6.2	1414 size 12{ { {1} over {4} } } {}, 1515 size 12{ { {1} over {5} } } {}
6.3	1616 size 12{ { {1} over {6} } } {}, 1919 size 12{ { {1} over {9} } } {}
6.4	1515 size 12{ { {1} over {5} } } {}, 1818 size 12{ { {1} over {8} } } {}
6.5	1212 size 12{ { {1} over {2} } } {}, 1515 size 12{ { {1} over {5} } } {}

7. Draw a circle round the smallest fraction:

7.1 2525 size 12{ { {2} over {5} } } {} , 3636 size 12{ { {3} over {6} } } {}

7.2 3838 size 12{ { {3} over {8} } } {} , 4949 size 12{ { {4} over {9} } } {}

7.3 4747 size 12{ { {4} over {7} } } {} , 3434 size 12{ { {3} over {4} } } {}

TIME FOR SELF-ASSESSMENT

How have you managed up to now? Are you ready for the next section of the work? Assess yourself on a scale of 1 - 4 to show us how you are coping:

1. = needs attention

2 = fairly good3 = very good

4 = outstanding

Table 2

CRITERIA	CODE
I could match the words to the correct explanation on p. 3.	1	2	3	4
I could answer no. 1 of Activity 1.1 correctly.	1	2	3	4
I could find the proper fractions in no. 3. (LO 1.3)
I could find the improper fractions in no. 3. (LO 1.3)	1	2	3	4
I could find the mixed numbers in no. 3. (LO 1.3)	1	2	3	4
I could complete the table correctly in no. 4. (LO 1.3)	1	2	3	4
I could explain what equivalent fractions are. (LO 1.8)	1	2	3	4
I could correctly indicate my own equivalent fractions for 1414 size 12{ { {1} over {4} } } {} in no. 5.2. (LO 1.8)	1	2	3	4
I could also write down equivalent fractions for other fractions (no. 6).	1	2	3	4
I could fill in relationship signs correctly.	1	2	3	4

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 1.3: We know this when the learner recognises and represents the following numbers in order to describe and compare them:

1.3.3 common fractions, including specifically tenths, hundreds and percentages.