THE KENYA NATIONAL EXAMINATIONS COUNCIL
Marking Scheme
Question Question Marking scheme
No
1 A teacher trainee plans to guide learners on how to find the area of rectangles, 1
squares and triangles practically.
1
Describe how the teacher trainee would use arbitrary units to lead learners on how to Take an arbitrary unit such as an exercise book
find the area of the top surface of a rectangular table. Cover the top of the table with the exercise books completely without overlapping or
leaving gaps.
1. 1
Count the number of exercise books used to cover the top surface of the table.
Relate the total number of books used to cover the surface to the area of the top of
the table.
1
4
2 The task shown was prepared as an assessment item for Grade 6 learners:
Calculate the expenditure as buying price + transport cost as
1
Mary bought 3 trays of eggs at sh 400 per tray. She paid sh 200 for transport. She sh 3×400+200=sh 1400
later sold all the eggs at sh 600 per tray. How much profit did Mary make? Calculate the income from sale of eggs as
1
2sh 600×3=sh 1800
Describe the steps the teacher would follow to guide the learners in calculating the Calculate the profit by subtracting the expenditure from the income to get sh 1800-
profit. 1
1400=sh 400
3
3 A teacher planned to guide learners on how to convert time from 12 hour to 24
hour system in a real life situation. She wrote the following question on the
chalkboard. Express the starting time in hours and minutes as 1
A meeting began at 10.20 a.m. The meeting took 3 hours 55 minutes. What time
in 24 hour system did the meeting end? 3 Add the starting time and time taken 1
Describe how the teacher will guide the learners to work out the question.
Write the time in 24 hour clock system as 1
3
4 A teacher plans to demonstrate the concept of Least Common Multiples (L.C.M) Express each number as a product of its prime factors
of whole numbers. 24=2×2×2×3
36=2×2×3×3
Describe how the teacher would guide learners to find the L.C.M of 24, 36 and 1
45=3×3×5
45 using prime factorisation.
1
Take each prime factor that occurs in the product with the highest power as
42 is 2×2×2=2^3 1
3 is 3×3=3^2 1
5 is 5=5^1
Find the product of the prime factors with the highest power as
〖2×2×2×3×3×5=2〗^3×3^2×5^1
=360
4
5 The following is an extract from a Mathematics Grade 5 curriculum design: 1
Arrange the numbers vertically and align digits according to the place values.
Sub Subtract the digits in ones place value - 3 kg take away 2 kg to get 1 kg. 1
Strand Specific Learning Outcome
strand Record 1 kg in the ones place value 1
By the end of the sub strand, the learner should be able to Regroup the one hundreds to tens to get 11 tens and subtract the 8 tens to get 3
1.0 1.3 5
subtract up to 4-digit numbers with regrouping in real life tens 1
Numbers Subtractionsituations.
Subtract the 6 hundreds from 6 hundreds to get 0.Bring down the 5. 1
A teacher guided learners to work out the following question:
Conclude that 5713 kg-682 kg=5031 kg
A trader bought 5713 kg of groundnuts. She sold 682 kg of the groundnuts. How
many kilograms of groundnuts remained? 5
Describe the steps the teacher would follow to lead the learners to work out the
question.
6 A Grade 3 teacher is carrying out a lesson on Multiplication of whole numbers as The teacher will guide the learner to:
repeated addition. The teacher used the following the question:
Take 6 bottle tops to represent sh 6, the cost of one pencil 1
Lewa bought 9 pencils. The cost of each pencil was sh 6. How much money did
Put the 6 bottle tops in one group. 1
he pay altogether?
6
Using bottle tops as a learning resource, describe the steps the teacher would use to Count 6 more bottle tops to represent the cost of another pencil and put the 1
guide the learners to work out the question. bottle tops in another group.
Continue counting in groups of 6 bottle tops in each case.
Add to get 54 which is the cost of 9 pencils.
3
7 The following is an extract from a Mathematics Grade 5 curriculum design: 1
Round off 378 to the nearest ten to get 380 and round off 23 to the nearest
Sub 7 ten to get 20 1
Strand Specific Learning Outcome
strand Divide 380 by 20 to get 19 and conclude that each group received 19 tanks.
By the end of the sub strand, the learner should be able to estimate
1.0 1.5
quotients by rounding off the dividend and divisor to the nearest ten in 2
Numbers Divisionreal life situations.
A teacher guided learners to work out the following question:
Marking Scheme
Question Question Marking scheme
No
1 A teacher trainee plans to guide learners on how to find the area of rectangles, 1
squares and triangles practically.
1
Describe how the teacher trainee would use arbitrary units to lead learners on how to Take an arbitrary unit such as an exercise book
find the area of the top surface of a rectangular table. Cover the top of the table with the exercise books completely without overlapping or
leaving gaps.
1. 1
Count the number of exercise books used to cover the top surface of the table.
Relate the total number of books used to cover the surface to the area of the top of
the table.
1
4
2 The task shown was prepared as an assessment item for Grade 6 learners:
Calculate the expenditure as buying price + transport cost as
1
Mary bought 3 trays of eggs at sh 400 per tray. She paid sh 200 for transport. She sh 3×400+200=sh 1400
later sold all the eggs at sh 600 per tray. How much profit did Mary make? Calculate the income from sale of eggs as
1
2sh 600×3=sh 1800
Describe the steps the teacher would follow to guide the learners in calculating the Calculate the profit by subtracting the expenditure from the income to get sh 1800-
profit. 1
1400=sh 400
3
3 A teacher planned to guide learners on how to convert time from 12 hour to 24
hour system in a real life situation. She wrote the following question on the
chalkboard. Express the starting time in hours and minutes as 1
A meeting began at 10.20 a.m. The meeting took 3 hours 55 minutes. What time
in 24 hour system did the meeting end? 3 Add the starting time and time taken 1
Describe how the teacher will guide the learners to work out the question.
Write the time in 24 hour clock system as 1
3
4 A teacher plans to demonstrate the concept of Least Common Multiples (L.C.M) Express each number as a product of its prime factors
of whole numbers. 24=2×2×2×3
36=2×2×3×3
Describe how the teacher would guide learners to find the L.C.M of 24, 36 and 1
45=3×3×5
45 using prime factorisation.
1
Take each prime factor that occurs in the product with the highest power as
42 is 2×2×2=2^3 1
3 is 3×3=3^2 1
5 is 5=5^1
Find the product of the prime factors with the highest power as
〖2×2×2×3×3×5=2〗^3×3^2×5^1
=360
4
5 The following is an extract from a Mathematics Grade 5 curriculum design: 1
Arrange the numbers vertically and align digits according to the place values.
Sub Subtract the digits in ones place value - 3 kg take away 2 kg to get 1 kg. 1
Strand Specific Learning Outcome
strand Record 1 kg in the ones place value 1
By the end of the sub strand, the learner should be able to Regroup the one hundreds to tens to get 11 tens and subtract the 8 tens to get 3
1.0 1.3 5
subtract up to 4-digit numbers with regrouping in real life tens 1
Numbers Subtractionsituations.
Subtract the 6 hundreds from 6 hundreds to get 0.Bring down the 5. 1
A teacher guided learners to work out the following question:
Conclude that 5713 kg-682 kg=5031 kg
A trader bought 5713 kg of groundnuts. She sold 682 kg of the groundnuts. How
many kilograms of groundnuts remained? 5
Describe the steps the teacher would follow to lead the learners to work out the
question.
6 A Grade 3 teacher is carrying out a lesson on Multiplication of whole numbers as The teacher will guide the learner to:
repeated addition. The teacher used the following the question:
Take 6 bottle tops to represent sh 6, the cost of one pencil 1
Lewa bought 9 pencils. The cost of each pencil was sh 6. How much money did
Put the 6 bottle tops in one group. 1
he pay altogether?
6
Using bottle tops as a learning resource, describe the steps the teacher would use to Count 6 more bottle tops to represent the cost of another pencil and put the 1
guide the learners to work out the question. bottle tops in another group.
Continue counting in groups of 6 bottle tops in each case.
Add to get 54 which is the cost of 9 pencils.
3
7 The following is an extract from a Mathematics Grade 5 curriculum design: 1
Round off 378 to the nearest ten to get 380 and round off 23 to the nearest
Sub 7 ten to get 20 1
Strand Specific Learning Outcome
strand Divide 380 by 20 to get 19 and conclude that each group received 19 tanks.
By the end of the sub strand, the learner should be able to estimate
1.0 1.5
quotients by rounding off the dividend and divisor to the nearest ten in 2
Numbers Divisionreal life situations.
A teacher guided learners to work out the following question:
