TOS

Topics: Fractions (1) & Fractions (2) Level: Primary 5 Purpose of test: To test pupils’ understanding and grasp of the concept – Fractions (1) and (2). The focus of the test is on pupils’ ability to understand word problems relating to fractions, and apply appropriate fractions concepts to solve the word problems.

Target pupils: Pupils are of middle to high ability. Pupils were identified to be weaker in solving word problems relating to fractions, and hence teacher has spent more time teaching and drilling pupils to answer word problems on fractions. Pupils are generally well-verse in the algorithms relating to fractions.

Duration of test: 1h 45min Table 1: Relative Weightings Subtopics & test objectives Like and Unlike Fractions 1. Differentiate a like fraction from an unlike fraction.

Adding Unlike Fractions 2. Find the sum of two unlike fractions.

Subtracting Unlike Fractions

No. of periods

Relative weighting (%)

2

3.8

4

7.7

3

5.8

4

7.7

3. Subtract two unlike fractions without regrouping.

Fractions and Division 4. Associate fractions with division.

5. Use ‘conversion of improper fraction to mixed number’ to express division as a mixed number.

QCM 502 TEST CONSTRUCTION 1

Converting Fractions to Decimals 6. Convert mixed number to decimal by changing the denominator to1000 7. Convert mixed number to decimal by using long division.

Adding Mixed Numbers 8. Add two mixed numbers with or without renaming.

Subtracting Mixed Numbers 9. Subtract a mixed number from another mixed number with regrouping.

Word Problems

3

5.8

3

5.8

3

5.8

4

7.7

4

7.7

4

7.7

4

7.7

3

5.8

4

7.7

3

5.8

10. Solve word problems by relating to concepts in addition and subtraction.

Product of Proper Fractions 11. Find the product of two proper fractions and express it in the simplest form.

12. Use cancellation (simplification) method to compute product of two proper fractions.

Word Problems (1) 13. Solve two-step word problems involving product of two proper fractions.

Product of an Improper Fraction and a Proper or Improper Fraction 14. Find the product of an improper fraction and a proper or improper fraction, and express the answer in the simplest form.

Product of a Mixed Number and a Whole Number 15. Use regrouping process to compute product of a mixed number and a whole number.

Word Problems (2) 16. Solve multiple-step word problems involving the product of a whole number and a mixed number.

Dividing a Fraction by a Whole 2 QCM 502 TEST CONSTRUCTION

17. Use 3 different methods to divide a fraction by a whole number.

Word Problems (3) 18. Solve two-step word problems by relating to concepts in subtraction and division.

19. Solve multiple-step word problem by relating to concepts in product.

4

7.7

QCM 502 TEST CONSTRUCTION 3

Table 2: Table of Specifications MCQ

Wt

Fraction 1

Topic

Subtopics & Test Objectives

(%)

# of QNS

K

Short-Answer C

A

# of QNS

Like and Unlike Fractions 1. Differentiate a like fraction from an unlike fraction.

C

# of QNS

K

C

Marks A

Sub Total

Wt (%)

1

2.0

1

2.0

0

0

2

4.0

1

2.0

X 3.8

1

Adding Unlike Fractions 2. Find the sum of two unlike fractions.

K

Long-Answer

(1 )

X 7.7

1

(1 )

Subtracting Unlike Fractions 3. Subtract two unlike fractions without regrouping.

Fractions and Division 4. Associate fractions with division.

5. Use ‘conversion of improper fraction to mixed number’ to express division as a mixed number.

Converting Fractions to Decimals 6. Convert mixed number to decimal by changing the denominator to1000 7. Convert mixed number to decimal by using long division.

4 QCM 502 TEST CONSTRUCTION

5.8

7.7

1

X (2 )

5.8

1 X (1 )

Topic

Subtopics & Test Objectives

MCQ

Wt (%)

# of QNS

Adding Mixed Numbers 8. Add two mixed numbers with or without renaming.

K

Short-Answer C

A

# of QNS

K

C

Long-Answer # of QNS

K

C

Marks A

Sub Total

Wt (%)

1

2.0

8

16

1

2.0

9

18

1

2.0

1 5.8

1

(1 )

Subtracting Mixed Numbers 9. Subtract a mixed number from another mixed number with regrouping.

Word Problems

Fraction 2

10. Solve word problems by relating to concepts in addition and subtraction.

5.8 12 7.7

1

(2 )

X,X 2

(3,3)

Product of Proper Fractions 11. Find the product of two proper fractions and express it in the simplest form.

12. Use cancellation (simplification) method to compute product of two proper fractions.

7.7

1

(1 )

Word Problems (1)

X

13. Solve two-step word problems involving product of two proper fractions.

7.7

Product of an Improper Fraction and a Proper or Improper Fraction

7.7

14. Find the product of an improper fraction and

X

1

2

(2 ) 1

X

15

X

(3)

(4)

(1 )

QCM 502 TEST CONSTRUCTION 5

Topic

Subtopics & Test Objectives

MCQ

Wt (%)

# of QNS

K

Short-Answer C

A

# of QNS

K

C

Long-Answer # of QNS

K

C

Marks A

Sub Total

Wt (%)

1

2.0

12

24

3

6.0

9

18

50

100

a proper or improper fraction, and express the answer in the simplest form.

Product of a Mixed Number and a Whole Number

8 5.8

1

15. Use regrouping process to compute product of a mixed number and a whole number.

Word Problems (2)

(1 )

5

16. Solve multiple-step word problems involving the product of a whole number and a mixed number.

Dividing a Fraction by a Whole

7.7

17. Use 3 different methods to divide a fraction by a whole number.

5.8

1

(2 )

13 1

4 1

(2 )

X,X 2

(4,4)

X 1

(1 )

(2 )

Word Problems (3) 18. Solve two-step word problems by relating to concepts in subtraction and division.

19. Solve multiple-step word problem by relating to concepts in product.

Total:

6 QCM 502 TEST CONSTRUCTION

7.7

100

2

7

(2 )

(4 )

(4 )

7

(6 )

(4 )

8

(0 )

21

22

(4)

(5)

(13)

(17)

QCM 502 TEST CONSTRUCTION 7

Table 3: Weighting for each cognitive level Cognitive Level

Weighting

Knowledge

16%

Comprehension

42%

Application & Analysis

42%

Total

100%

Explanation for higher weighting of comprehension questions: As the purpose of this test is to check whether pupils are able to correctly answer word problems on fractions, the test was designed to include more long-answer questions (LAQ). Since there is a higher percentage of LAQ, the percentage of marks allocated to Comprehension and Application & Analysis questions are higher as well.

8 QCM 502 TEST CONSTRUCTION