STRAND 1 NUMBERS.pptx CBC GRADE 6 FOR LEARNERS

By the end of the Sub Strand, the learner
should be able to:
• Use place value and total value of digits up to millions in real life,
• Use numbers up to millions in symbols in real life,
• Read and write numbers up to 100,000 in words in real life,
• Order numbers up to100,000 in real life situations,
• Round off numbers up to 100,000 to the nearest thousand in different
situations,
• Apply squares of whole numbers up to 100 in different situations,
• Apply square roots of perfect squares up to 10,000 in different situations
• Appreciate use of whole numbers in real life situations

Place value and total value of digits up to
million
millions
Group activities
In pairs copy and complete the following
9+1=10 ten
• 99+1=100 hundred
• 999+1=………. …………
• ……+1=10000
• …….+……..=…..hundred thousand
• 2 discuss the result and share with others

Example
• 999999+1 cann be written vertically and added as
• 999999
• + 1
1000000 the number 1000000,is called million

ASSESSMENT
1. If a city has a population of 7,654,321 people, how many individuals
live in the city?
2. In a bank account balance of Ksh 9,876,543.21, how many shillings
are in the account?
3. If a road trip spans 5,432,109 miles, how many miles were traveled?
4. What is the total value of the digits in the number 6,789,012?
5. If a company's annual revenue is Ksh15,678,901.23, what is the
value of the digit in the ten millions place?

NUMBERS UP TO MILLIONS IN SYMBOLS IN
REAL LIFE
1. An address like "123 Main Street" uses symbols to represent the house
number. Here, "123" is represented by the symbols for 1, 2, and 3.
2. A phone number such as "555-123-4567" uses symbols for dialing. Each digit,
from 0 to 9, is represented by a corresponding symbol on the phone keypad.
3. A price tag showing "Ksh 999.99" uses symbols to represent the cost of an
item. Here, each digit is represented by its respective symbol for numbers.
4. In a basketball game, a score of "76-54" represents the points scored by each
team. These numbers are represented by symbols on the scoreboard.
5. The population of a city, like "5,678,901," is often represented by symbols in
census reports or statistical data. Each digit is symbolized by its corresponding
numerical symbol.

Place value up to millions
The place value of a digit in a number is its position in the number
Group Activity
1 In pairs, write any seven digit number.
2. Represent the number using abacus.
3. Write the place value of each digit in the number.
4. Discuss the place value of each digit in the number and share the
results with other groups.

Example
Use a place value chart to show the number 2139408.
Write down the place value of each digit in the number
Solution
.

ASSESSMENT
1. In a car dealership, if a vehicle is priced at ksh45,678, how would you explain
the place value of each digit up to one million to understand its total value?
2. When reading a large phone number, such as a customer service hotline, how
does understanding the place value up to one million help in accurately dialing
the number?
3. In a census report, if a city has a population of 327,591, how would you explain
the significance of each digit's place value up to one million when analyzing the
city's population?
4. When dealing with large quantities of products in a warehouse, such as having
789,432 items in stock, how does understanding the place value up to one
million assist in managing inventory efficiently?
5. In a bank statement, if a person's account balance is ksh1,234,567, how would
you illustrate the importance of each digit's place value up to one million when
interpreting the total amount of money in the account?

READ AND WRITE NUMBERS UP TO 100,000
IN WORDS IN REAL LIFE
Group activity
In groups of two
Reading and Writing Numbers in Words:
10,000: Ten thousand
25,678: Twenty-five thousand six hundred seventy-eight
50,000: Fifty thousand
73,912: Seventy-three thousand nine hundred twelve
100,000: One hundred thousand
Examples:
The address "15,000 Maple Avenue" is read as "Fifteen thousand Maple Avenue."
A city with a population of 80,000 is written as "Eighty thousand people."
If a marathon is 26.2 miles long, it is read as "Twenty-six point two miles."

ASSESSMENT
1. How would you write the number 42,567 in words?
2. Read the number 85,432 aloud.
3. Write the word for the number 60,000.
4. What is the word form of the number 99,999?
5. If a school has 30,000 students, how is this number written in
words?

ORDERING NUMBERS UP TO100,000 IN REAL LIFE
SITUATIONS
• example
• Teachers often rank students based on their test scores. For example, if students scored
14648523, 23454192,21344678, , and 82134356,
they can be ordered from lowest to highest score.
solution
14648523, 21344678, 23454192, 82134356

ASSESSMENT
1. Arrange the following numbers in ascending order: 9 725 467; 6 132
890,4 218 532; 7 840 12 329 876.
2. Sort the following test scores in descending order: 1 788 985, 2 335
372, 5 678 894, 6 734 345, 8 986 578.
3. Order the publication years of the following books: 9 072 010, 4 432
008, 2 015 879, 8 672 005, 2 018 234
4. Arrange the following sports teams' points in ascending order: 56, 9
860 842, 8 797 863, 6 576 538, 4 976 454

ROUNDING OFF NUMBERS UP TO 100,000 TO THE
NEAREST THOUSAND IN DIFFERENT SITUATIONS
Example
Work in groups
1.Estimating populations of cities was 27548 people rounding number off to the
nearest thousand
For instance, a population of 72,548 can be rounded to 73,000.
• To round off a number to the nearest thousand, check the digit in the hundreds
place value.
• If the digit is less 5, the digit in the thousands place value remains the same; Write
zero in the hundreds, tens and ones place values.
• If the digit is 5 or greater than 5, increase the digit in the thousands place value by
1. Write zero in the hundreds, tens and ones place values.

Assessment
1. In a construction project, if you need to estimate the number of bricks required for a
wall and the calculation yields 87,482 bricks, how would you round this number to the
nearest thousand to get a more manageable estimate?
2. When planning a budget for a renovation, if the estimated cost of materials and labor
is ksh64,753, how would you round this amount to the nearest thousand to simplify
the budgeting process?
3. In a population census, if a city's population is reported as 385,269 residents, how
would you round this number to the nearest thousand to present a more concise
figure in reports and presentations?
4. When analyzing sales data for a retail store, if the monthly sales revenue is ksh98,746,
how would you round this amount to the nearest thousand to provide a clearer
snapshot of the store's performance?
5. In academic grading, if a student's cumulative grade point average (GPA) is calculated
as 3.874, how would you round this GPA to the nearest thousandth to accurately
represent the student's academic achievement?

APPLICATION OF SQUARES NUMBERS
In groups of three:
1. Obtain a square piece of paper measuring 6 cm by 6 cm.
2. 2. Divide the square paper into one centimetre squares.
3. 3. Count the number of one centimetre squares.
4. 4. Multiply 6 by 6.
5. 5. Compare the number of squares counted and the product of 6 by 6.
6. 6. Discuss and share the results with other groups.

EXAMPLE
The length of a garden 1s 32 meters on length. What is the are pf the
garden
Solution
32
x 32
64
+ 96
1024

ASSESSMENT
1. What is 5 squared?
2. Calculate the square of 10.
3. If a room has a side length of 8 meters, what is the area of the
room?
4. How many square units are there in a square with a side length of
12 units?
5. If a company plans to produce 5 units and each unit costs Ksh15,
what is the total budget?

Assessment
1. A square piece of cloth is of length 36 cm. What is the area of the
cloth?
2. A square piece of a card is of side 18 cm. What is the area of the
card?
3. A square parking area is of side 13 m. Find its area.
4. A square vegetable garden measures 26 m by 26 m. Find the area of
the garden.
5. A part of a square wall is covered by 400 tiles. Each tile measures 8
cm by 8 cm. Find the area of the part of the wall covered by the
tiles.

USE OF WHOLE NUMBERS IN REAL LIFE
SITUATIONS
• Counting: Whole numbers are used for counting objects, such as books,
fruits, or people. For example, counting the number of apples in a basket
or the number of students in a classroom.
• Measurement: Whole numbers are used for measuring quantities, such as
length, weight, or volume. For instance, measuring the length of a table in
meters or the weight of a bag of rice in kilograms.
• Money: Whole numbers are used for representing currency amounts, such
as shillings or cents. For example, calculating the total cost of groceries or
the amount of money saved in a piggy bank.
• Time: Whole numbers are used for representing time, such as hours,
minutes, or seconds. For instance, telling the time on a clock or calculating
the duration of a movie in hours.

ASSESSMENT
1. How are whole numbers used in counting objects? Provide an
example.
2. Explain how whole numbers are used in measuring quantities. Give
a real-life example.
3. Describe a situation where whole numbers are used for
representing money. Provide an example.
4. How are whole numbers applied in representing time? Give a
practical example.

BY THE END OF THE SUB STRAND, THE
LEARNER SHOULD BE ABLE TO;
1. Multiply up to a 4-digit number by a 2-digit number in real life
situations,
2. Estimate products by rounding off numbers being multiplied to the
nearest ten in real life situations,
3. Make patterns involving multiplication of numbers not exceeding
1,000 in different situations,
4. Appreciate use of multiplication in real life.

MULTIPLICATION OF UP TO A 4-DIGIT NUMBER BY
A 2-DIGIT NUMBER IN REAL LIFE SITUATIONS
• Total Cost: In shopping, when you need to buy multiple items at
different prices, you can use multiplication to calculate the total cost. For
example, if you want to buy 25 notebooks priced at Ksh2.50 each, you
can multiply Ksh2.50 by 25 to find the total cost.
• Determining Area: In construction or landscaping, multiplication is used
to find the area of rectangular or square areas. For instance, if you have
a rectangular garden measuring 35 meters by 18 meters, you can
multiply 35 by 18 to find the total area.

• Calculating Distance: In travel or transportation, multiplication helps
calculate the total distance covered. For example, if a car travels at a
speed of 60 miles per hour for 3.5 hours, you can multiply 60 by 3.5 to
find the total distance traveled.
• Determining Total Earnings: In employment or business, multiplication is
used to calculate total earnings. For instance, if an employee earns
Ksh15 per hour and works for 40 hours in a week, you can multiply
Ksh15 by 40 to find the total weekly earnings.

• Examples:
• Calculate the total cost of 30 shirts priced at Ksh12 each.
• Find the area of a rectangular field measuring 25 meters by 40 meters.
• Determine the total distance traveled by a train moving at 80 km/h for
6.5 hours.
• Calculate the total earnings of a worker who earns Ksh18 per hour and
works for 48 hours in a month.

ASSESSMENT
1. If a store sells 120 packets of pencils priced at Ksh1.50 each, what is the
total revenue?
2. A rectangular swimming pool measures 20 meters by 10 meters. What is
the total area of the pool?
3. A delivery truck travels at a speed of 50 miles per hour for 4 hours. How
far does it travel?
4. If a worker earns Ksh22 per hour and works for 35 hours in a week, what
is the total weekly earnings?
5. A garden is 60 feet long and 40 feet wide. What is the total area of the
garden?
6. A classroom has 25 students, and each student has 6 books. How many
books are there in total?

ESTIMATING PRODUCTS BY ROUNDING OFF
NUMBERS BEING MULTIPLIED TO THE NEAREST
TEN IN REAL LIFE SITUATIONS
Estimating products by rounding off numbers being multiplied to the
nearest ten is a practical skill used in everyday situations where precise
calculations are not necessary but a quick approximation suffices.
Here's an explanation with an example and five questions suitable for
Grade 6 students:
• Explanation:
• Estimating products by rounding off to the nearest ten simplifies
multiplication calculations while still providing a reasonable
approximation of the actual result. This technique is helpful when you
need to quickly estimate quantities or costs without the need for
exact values.

ESTIMATING PRODUCTS BY ROUNDING OFF
NUMBERS BEING MULTIPLIED TO THE NEAREST
TEN IN REAL LIFE SITUATIONS
Example:
Suppose you want to buy 13 packs of pencils, and each pack costs
Ksh4.50. Instead of calculating the exact total cost, you can estimate by
rounding off the numbers:
Round 13 to the nearest ten, which is 10.
Round Ksh4.50 to the nearest ten cents, which is Ksh5.00.
Now, multiply the rounded numbers: 10 packs * Ksh5.00 = Ksh50.00.
So, the estimated total cost of 13 packs of pencils is approximately
Ksh50.00.

ASSESSMENT
1. Estimate the product of 27 and 16 by rounding each number to the
nearest ten.
2. If a box contains 38 chocolates, and each chocolate costs Ksh1.20,
estimate the total cost by rounding to the nearest ten.
3. Estimate the area of a rectangle with dimensions 48 meters by 32
meters by rounding each side length to the nearest ten.
4. A group of 45 students is going on a field trip, and each ticket costs
Ksh9.50. Estimate the total cost by rounding to the nearest ten.
5. Estimate the product of 89 and 24 by rounding each number to the
nearest ten.

MAKING PATTERNS INVOLVING MULTIPLICATION
OF NUMBERS NOT EXCEEDING 1,000 IN
DIFFERENT SITUATIONS
Patterns involving multiplication can be created by systematically multiplying
numbers within a specific range. These patterns help students understand
the relationship between numbers and identify recurring sequences. They
can be used in various situations, such as exploring geometric shapes,
analyzing sequences in nature, or understanding growth patterns in
mathematics.
• Example:
• Let's create a pattern by multiplying numbers not exceeding 1,000:
• Start with the number 5 and multiply it by consecutive whole numbers: 5 *
1 = 5 5 * 2 = 10 5 * 3 = 15 5 * 4 = 20 ...
• Continuing this pattern, we observe: 5, 10, 15, 20, 25, 30, ...
• This pattern shows multiples of 5.

ASSESSMENT
1. Create a pattern by multiplying 3 by consecutive whole numbers up
to 10.
2. Develop a pattern by multiplying 7 by consecutive whole numbers
up to 8.
3. Explore a pattern by multiplying 12 by consecutive whole numbers
up to 5.
4. Investigate a pattern by multiplying 9 by consecutive whole
numbers up to 12.
5. Develop a pattern by multiplying 6 by consecutive whole numbers
up to 15.

USE OF MULTIPLICATION IN REAL LIFE
• Calculating Total Cost: Imagine you're buying items at the store. Let's say you
want to buy 4 packs of markers, and each pack costs Ksh3. To find out how much
it will cost in total, you multiply Ksh3 by 4 to get Ksh12.
• Determining Area and Volume: When you're helping with gardening or building
projects, you might need to find the area of a rectangle or the volume of a box.
For example, if a garden bed is 5 feet wide and 8 feet long, you multiply 5 by 8 to
find the area, which is 40 square feet.
• Time and Distance: Let's say you're going on a road trip with your family. If you're
traveling at 60 miles per hour and you'll be driving for 3 hours, you multiply 60 by
3 to find out that you'll travel 180 miles.

• Scaling: Imagine you're building a model of a house. If the model is 1/4 the size of
the real house, you multiply the measurements by 4 to find the actual size.
• Budgeting and Finance: When you're planning how to spend your money or save
for something you want, multiplication helps. For example, if you earn Ksh10 per
hour and you work for 5 hours, you multiply Ksh10 by 5 to find out you'll earn
Ksh50.
• Recipes and Cooking: Let's say you're baking cookies. If a recipe makes 12 cookies
and you want to make double the amount, you'd multiply the ingredients by 2 to
get the right measurements.
• Growth and Proportions: Imagine you're studying a population of animals. If the
population grows by 20% each year, you'd multiply the current population by 1.20
to find out how many there will be next year.

• Example 2: A classroom has 25 students, and each student needs 4 pencils for the
school year.
• Calculation: To find out how many pencils are needed in total: Number of students
* Pencils per student = Total pencils needed 25 students * 4 pencils/student = 100
pencils
• Example 3: A baker bakes 8 loaves of bread each day, and the bakery is open for 6
days a week.
• Calculation: To find out how many loaves of bread are baked in a week: Loaves
baked per day * Days open per week = Total loaves baked in a week 8 loaves/day * 6
days/week = 48 loaves
• Example 4: A farmer has 12 fields, and each field can accommodate 30 cows.
• Calculation: To find out how many cows can be accommodated in total: Number of
fields * Cows per field = Total cows accommodated 12 fields * 30 cows/field = 360
cows

• Example 5: A company sells 15 boxes of cookies each day, and it operates for 5 days
a week.
• Calculation: To find out how many boxes of cookies are sold in a week: Boxes sold
per day * Days open per week = Total boxes sold in a week 15 boxes/day * 5
days/week = 75 boxes
• Example 6: A garden has 6 rows of flowers, and each row contains 20 flowers.
• Calculation: To find out how many flowers are there in total: Number of rows *
Flowers per row = Total flowers 6 rows * 20 flowers/row = 120 flowers

ASSESSMENT
1. If each pack of pencils contains 10 pencils, and you buy 6 packs,
how many pencils do you have in total?
2. A farmer has 8 fields, and each field has 15 apple trees. How many
apple trees are there in total?
3. If a bookshelf has 5 shelves, and each shelf can hold 25 books, how
many books can the bookshelf hold in total?
4. A pizza has 6 slices, and there are 10 pizzas. How many slices of
pizza are there in total?
5. If a store sells 7 packs of markers, and each pack contains 20
markers, how many markers are sold in total?

By the end of the Sub Strand the learner
should be able to;
• Divide up to a 4-digitnumber by up to a 3-digit number where the
dividend is greater than the divisor in real life situations,
• Estimate quotients by rounding off the dividend and divisor to the
nearest ten in real life situations,
• Perform combined operations involving addition, subtraction,
multiplication and division up to 3-digit number
• appreciate use of division of whole numbers in real life.

DIVISION OF UP TO A 4-DIGITNUMBER BY UP TO A 3-
DIGIT NUMBER WHERE THE DIVIDEND IS GREATER
THAN THE DIVISOR IN REAL LIFE SITUATIONS
Group Activity
• In groups of four:
• Discuss the relationship between multiplication and division, highlighting
division as the inverse operation of multiplication.
• Provide division problems where the dividend is greater than the divisor (e.g.,
4532 ÷ 32).
• Instruct students to use the long division method to solve each problem.
• Encourage students to check their division results using multiplication,
reinforcing the connection between the two operations.

DIVISION OF UP TO A 4-DIGITNUMBER BY UP TO A 3-
DIGIT NUMBER WHERE THE DIVIDEND IS GREATER
THAN THE DIVISOR IN REAL LIFE SITUATIONS
• Example
• Estimate how many times 342 can divide 548,1x342=342
• Write 1 above 8.
• Write 342 below 548 and subtract.
• Drop 6.
• Estimate how many times 342 can divide
2066,6x342=2052
.write 6 above 6
.write 2052 below 2066 and subtract
.therefore,5486÷ 342 =16rem14

solution
16
342 5486
-342
2066
2052
14

ASSESSMENT
1. How can division be applied in real-life situations like distributing electronic
components in a manufacturing plant?
2. Why is it important to divide the components equally among the production units?
3. What challenges might arise when dividing a large quantity like 4,782 components
among 129 units?
4. Explain the significance of ensuring each production unit receives an equal number of
components.
5. How does solving division problems in real-life scenarios contribute to understanding
the practical application of mathematical concepts?

ESTIMATION OF QUOTIENTS BY ROUNDING OFF
THE DIVIDEND AND DIVISOR TO THE NEAREST TEN
IN REAL LIFE SITUATIONS
• ACTIVITY
1. To work out quotients by rounding off the dividend and divisor to the nearest
ten, follow these steps:
2. Round the dividend and divisor to the nearest ten.
3. Divide the rounded dividend by the rounded divisor to find the quotient.
4. Optionally, adjust the quotient if necessary to account for the rounding.

ESTIMATION OF QUOTIENTS BY ROUNDING OFF
THE DIVIDEND AND DIVISOR TO THE NEAREST TEN
IN REAL LIFE SITUATIONS
• Example: Let's work out the quotient of 73 ÷ 17 by rounding off to
the nearest ten.
• Round the dividend (73) and divisor (17) to the nearest ten:
• Rounded dividend: 70
• Rounded divisor: 20
• Divide the rounded dividend by the rounded divisor: 70÷20=3.5
• Adjust the quotient if necessary: Since the original numbers were
rounded, we don't need to adjust the quotient.
• Therefore, the quotient of 73 ÷ 17, rounded to the nearest ten, is 3.5.

ASSESSMENT
1. In a charity event, 86 bags of groceries are to be distributed equally among 9
families. Estimate the number of bags each family will receive by rounding
off the total bags and the number of families to the nearest ten.
2. A garden has 154 flowers to be planted in rows, with each row
accommodating 16 flowers. Estimate the number of rows needed by
rounding off the total number of flowers and the capacity of each row to the
nearest ten.
3. A delivery truck has 248 boxes of goods to be unloaded into 20 storage
shelves. Estimate the number of boxes that can be placed on each shelf by
rounding off the total boxes and the number of shelves to the nearest ten.

ASSESSMENT
4. A book fair received 312 books to be sorted into boxes, with each box holding
28 books. Estimate the number of boxes needed by rounding off the total
number of books and the capacity of each box to the nearest ten.
5. A school cafeteria has 142 apples to be distributed among 12 baskets.
Estimate the number of apples in each basket by rounding off the total apples
and the number of baskets to the nearest ten.

COMBINED OPERATIONS INVOLVING ADDITION,
SUBTRACTION, MULTIPLICATION AND DIVISION UP
TO 3-DIGIT NUMBER
• ACTIVITY
• Provide students with a worksheet containing multi-operation
questions involving up to 3-digit numbers.
• Instruct students to independently solve each question using
appropriate methods for addition, subtraction, multiplication, and
division.
• Review answers as a class, discussing any challenging questions and
reinforcing key strategies.
• Emphasize the importance of showing work clearly and checking
answers for accuracy

COMBINED OPERATIONS INVOLVING ADDITION,
SUBTRACTION, MULTIPLICATION AND DIVISION UP
TO 3-DIGIT NUMBER
• Example: Calculate (145+32)×4−78÷2.
Solution:
Perform the addition inside the parentheses: 145+32=177.
Next, perform the multiplication: 177×4=708.
Then, perform the division: 78÷2=39.
Finally, perform the subtraction: 708−39=669.
So, (145+32)×4−78÷2=669.

ASSESSMENT
1. Calculate (156+24)×3−85÷5.
2. Find the value of 250−(32×4)+78÷2.
3. Evaluate 120×2−85+36÷4.
4. Determine (187+25)÷5−48×2.
5. Solve 360÷(18×2)−45+24.

USE OF DIVISION OF WHOLE NUMBERS IN
REAL LIFE.
• Activity: Division Practice with Digital Devices
• Objective:
• To practice dividing whole numbers using digital devices or other
resources.
• Instructions:
• 1. Divide the class into pairs or small groups.
• 2. Provide each group with access to digital devices such as tablets,
laptops, or smartphones with a division calculator app or website.
• 3. Present a series of division problems involving whole numbers to the
class.
• 4. Instruct students to work together to solve each division problem using
the digital devices.

USE OF DIVISION OF WHOLE NUMBERS IN
REAL LIFE.
• Grocery Shopping: Dividing 240 apples into bags of 12 for sale in a
market.
• Classroom Supplies: Distributing 360 pencils equally among 30
students in a class.
• Baking Recipes: Dividing a cake recipe by 2 to make a smaller batch,
such as halving a recipe that originally made 24 cupcakes.
• Budgeting Finances: Splitting a total budget of Ksh600 evenly
between 4 categories, allocating Ksh150 to each.
• Sports Teams: Dividing 160 players into 8 teams for a soccer
tournament, with 20 players on each team.

ASSESSMENT
1. A farmer has 420 apples and wants to pack them into crates, with
each crate holding 35 apples. How many crates can the farmer fill?
2. A construction company needs to lay 960 tiles evenly across 6 floors
of a building. How many tiles should be laid on each floor?
3. A teacher has 180 books and wants to distribute them equally
among 9 students. How many books will each student receive?
4. A bakery sells 300 cupcakes each day. If they want to pack them
into boxes containing 25 cupcakes each, how many boxes will they
need?
5. A delivery truck has 640 boxes to be unloaded into storage shelves,
with each shelf holding 80 boxes. How many shelves will be needed
to accommodate all the boxes?

Fraction
 By the end of the sub-strand the learner should be able to;
 add fractions using LCM in different situations,
 subtract fractions using LCM in different situations,
 add mixed numbers in different situations,
 subtract mixed numbers in different situations,
 identify reciprocal of proper fractions up to a 2- digit number in different
situations,
 work out squares of fractions with a numerator of one digit and
denominator of a 2- digit number different situations,
 express a fraction as a percentage in different

Adding and Subtracting Fractions Using LCM and Listing
Multiples
ACTIVITY 1 : Fraction Addition Race
• Write down the prime factorization of each number.
• Identify the highest power of each prime factor that appears in any of the
factorizations.
• Multiply these highest powers together to find the LCM.
• Example: Let's find the LCM of 12 and 18 using number cards.
• Prime factorization of 12: 12=22×31.
• Prime factorization of 18: 18=21×32.
• The highest power of 2 is 22, and the highest power of 3 is 32.
• Multiply these highest powers together: 22×32=36.
• So, the LCM of 12 and 18 is 36.

ASSESSMENT
1. Sam has
2
3
of a cake, and Anna has
5
6
of the same cake. What fraction of the cake
do they have together?
2. A recipe calls for
3
4
cup of flour and
2
5
cup of sugar. What is the total amount of
flour and sugar needed?
3. John completed
4
5
of his homework, and Emily completed
3
8
of the same
homework. What fraction of the homework have they completed together?
4. A tank is filled with
7
8
gallon of water on Monday and
3
5
gallon of water on
Tuesday. How much water is in the tank altogether?
5.In a basketball game, Mark scored
2
3
of the total points, and Sarah scored
3
5
of the
total points. What fraction of the total points did they score together?

Adding and Subtracting Fractions Using LCM
and Listing Multiples
• Activity 2 : Fraction Subtraction Race
• Objective: To practice subtracting fractions using the Least Common
Multiple (LCM) in an engaging and competitive activity.
• Materials Needed:
• Fraction cards (prepared in advance with fractions to subtract)
• Timer or stopwatch
• Whiteboard or chart paper
• Markers or chalk

Subtracting Fractions Using the Least
Common Multiple (LCM)
• Activity
1. Divide the class into small groups and distribute fraction cards
containing subtraction problems.
2. Each group takes turns drawing a card, solving the subtraction
problem using the LCM method.
3. Groups write their answers on a whiteboard or chart paper and earn
points for correct answers.
4. The group with the most points at the end of the activity wins the
Fraction Subtraction Race.

ASSESSMENT
• Sarah has
5
6
of a pizza, and she eats
1
3
of it. How much pizza is left?
• John has
4
5
of a cake, and he shares
2
3
of it with his friend. How much
cake does John have left?
• A recipe calls for
3
4
cup of flour, but only
1
2
cup is left in the pantry.
How much flour is needed to complete the recipe?
• Mark has
7
8
gallon of water in his tank, but he spills
1
4
gallon by
accident. How much water is left in the tank?
• Emily has
5
6
of a pie, and she gives
1
2
of it to her neighbor. How much
pie does Emily have left?

Adding and Subtracting Mixed Fractions by
Converting to Improper Fractions
Addition of mixed fractions by adding whole numbers and fraction part
separately
Group activity
Find 2
1
2
+ 3
2
3
ln groups of three:
I. Write each mixed fraction as a whole number and a fraction.
2. Add whole numbers.
3. Add the fractions.
4.Add the whole number in (2) above and the fraction in (3)above.
5. Discuss your results and share with other groups.

Note
To add mixed fractions:
(i) Add the whole numbers.
(ii) Add the fractions.
(iii) Add the two results in (i) and (ii).

Example
3
1
3
+2
2
5
3
1
3
+2
2
5
= 3 +
1
2
+ 2 +
2
5
……… write each fraction as a whole number and a
fraction
3 + 2 +
1
2
+
2
5
………….. add whole numbers
5+ 5+4 ……………………. add fraction part
10
5+9
10
5
9
10
…add whole number and fraction part

Assessment
1. If a recipe requires 1 1/2 cups of flour and you already have 2 1/4 cups,
how much more flour do you need in improper fraction form?
2. A construction project needs 5 3/4 meters of lumber, and 3 1/2 meters
have already been used. How much lumber is left in improper fraction
form?
3. If a recipe needs to bake for 2 1/2 hours and it has been in the oven for 1
3/4 hours, how much longer does it need to bake in improper fraction
form?
4. A family travels 8 1/3 kilometers on a road trip, and they've already
driven 4 2/3 kilometers. How much farther do they need to travel in
improper If you budget ksh100 for groceries and have already spent
ksh75 1/4, how much money do you have left in improper fraction form?

Identifying reciprocal of fraction
Group activity
In groups
Use repeated addition to
1.Multiply
1
2
x 2
2 multiply
1
3
x 3
3 multiply
1
5
x 4
4 multiply
1
6
x5
Discuss the result and share with other groups

Note
The product in each case is 1
Each number is a reciprocal of the other
For example
1
4
x 4 =1,
1
4
is the recipricol of 4
4 is the recipricol of
1
4
To find the reciprocal of a fraction, interchange the numerator andthe
denominator (the top and bottom numbers of the fraction).

Assessment
1. If a recipe calls for 1/2 cup of milk, what is the reciprocal of this fraction, and
how could it be used to scale the recipe?
2. If you cover 3/4 of a mile on a bicycle, what is the reciprocal of this fraction,
and how could it be used to find out how many times you would need to bike
to complete a 5-mile route?
3. If you spend 2/3 of an hour studying, what is the reciprocal of this fraction, and
how could it be used to calculate how many hours it takes to complete a full
study session?
4. If you save 1/4 of your monthly income, what is the reciprocal of this fraction,
and how could it be used to determine how many times your income you need
to save to reach a specific savings goal?
5. If a recipe calls for 3/5 cup of sugar for every 2 cups of flour, what is the
reciprocal of the fraction representing the sugar-to-flour ratio, and how could it
be used to adjust the recipe if you only have 1 cup of flour available?

Square of fraction
The fraction shaded twice is the square of
3
4
32
4
m means
3
4
x 3
4
= 3x3 =9
4x4 16
To find the square of fraction. square the numerator and the
denominator

Assessment
1. If a rectangular garden measures 3/4 of a meter by 2/3 of a meter, what
is the area of the garden in square meters?
2. If a container has a base measuring 1/2 of a meter by 1/2 of a meter and
a height of 1/3 of a meter, what is the volume of the container in cubic
meters?
3. If a car travels at 2/3 of its maximum speed, what fraction of its
maximum speed is the car traveling at? What is the square of this
fraction?
4. If there is a 1/5 chance of winning a prize in a lottery, what is the
probability of winning the prize twice in a row?
5. If an investment grows by 3/4 of its initial value each year, what is the
growth factor for the investment over two years?

Converting fractions to equivalent fractions
with denominator l00
• Group Activity
• Write the equivalent fraction of 3/20 with a denominator l00.
• In pairs:
• Find the number that multiplies 5 20 to get I00.
2. Multiply the numerator and the denominator by the same number.
3. Write the fraction obtained in step 2 above.
4. Discuss the results and share with other groups.
Note
To get equivalent fraction with a denominator l00, multiplųboth numerator
and denominator by the number that makesthe denominator |00.

Example
• Write the equivalent fraction with denominator 100
•
3
4
=
3
4
x 25
25
=
75
100

Assessment
1. write the equivalent fraction with a denominator 100 of each of
the fraction
2.
3
4
3.
2
10
4.
22
25
5.
13
40

Percentage
Identifying a percentage as a fraction with denominator 100
Group Activity
In groups of four:
1. Draw a square of side 10 cm.
2. Divide the square into I cm squares.
3. Count the number of I cm squares formed.
4. Shade 12 of the l cm squares.
5. Write the shaded part as a fraction of the total number ofI cm squares.
6. Discuss your results and share with other groups

Note
(i) The 10 cm square is divided into 100 cm squares.
(ii) The number of squares shaded as a fraction of total number of
squares is 12/100
(iii) The fraction with a denominator l00 is called a percentage.
(iv) Per cent means out of a hundred.
(V) In short, per cent is written as %.
Therefore,12/100
12/100 is 12%.

Assessment
1. If a store offers a 25% discount on a ksh80 item, what fraction of the
original price is the discount, expressed with a denominator of 100?
2. If a student scores 85% on a test, what fraction of the total marks did
they achieve, with a denominator of 100?
3. If a bank offers a 4.5% annual interest rate on a savings account, what
fraction of the initial deposit is earned as interest each year, with a
denominator of 100?
4. If the sales tax rate in a region is 8.25%, what fraction of the purchase
price is paid as tax, with a denominator of 100?
5. If a town's population increases by 3.5% per year, what fraction of the
current population is the annual growth, with a denominator of 100?

Converting fractions to percentages and
percentages to fractions
Group Activity
Convert 15/20 to a percentage
In pairs:
Multiply the denominator by a number to make it 100.
2. Multiply the numerator by the same number.
3. Write the fraction formed.
4. Write the fraction in (3) above using the percentage symbol.

Note
(i) The fraction formed is equivalent toI520
(i) The fraction formed has I00 as denominator.
(iii) The fraction with 100 as denominator is a percentage

Assessment
1. If you buy a dress that was originally priced at 3/5 of its original cost
during a sale, what percentage discount did you get?
2. If a cereal box states that it contains 25% of your daily fiber intake per
serving, what fraction of your daily fiber intake does one serving
provide?
3.
If a hybrid car can travel 60 miles on 3/4 of a gallon of fuel, what is its
mileage in miles per gallon (MPG)?
4. If you score 80% on a math test, what fraction of the total marks did you
achieve?
5. If a recipe calls for 2/3 cup of flour and you only want to use half of that
amount, what percentage of the original amount are you using?

1.5 DECIMAL
Identifying ten thousands
Group activity
In pairs
Copy and complete the following
One tenth is
1
10
=0.1
One hundredth
1
100
=
One thousandth is
1
1000
=
Discuss and share your result with other groups

Example
• Write each of the following in decimal form
• 174 ten thousandth is
174
10000
=0.0174
b)2145 ten thousandth is
2145
10000
=0.2145

Assessment
1.In pairs write each of the following in decimal form
a) 5 ten thousandths b) 10 ten thousandths c) 58 ten thousandths
c) 68ten thousandths
2.Write each of the following in decimal form
a
2145
10000
b
145
10000
e
215
10000

Place value of decimals up to ten thousandths
In the decimal number 0.0001, the place value of digit I is ten thousandths.
Group Activity
Represent the following numbers in a place value chart
(b) 5.0021 (c) 12.4275 (a) 3.6447
In groups of three:
2. Draw a place value chart with columns tens, ones, tenths, hundredths,
thousandths and ten thousandths.
2. Represent each of the given decimal numbers.
3. Discuss in your group and share with others.
4. Display your work.

Example
Write the place value of the underlined digits in the decimal number 5.6837.
solution
ones tenth hundedth Thousandth Ten thousandths

• Place value of digit 5 is ones.
• Place value of digit 8 is hundredths.
• Place value of digit 7 is ten thousandths.

Assessment
In pairs copy and complete the following
a) 3.45 is ….ones…..tenths…..hundredth
b)47.358is….tens …….ones…..tenths….hundredth…thousandth…..

Number of decimal places
• Group activity
• In groups of three copy and complete the table below
Decimal number Number of decimal places Number of place value
after decimal point
3.6
5.73
49.863
12.3056

• 2. Compare the number of digits and that of place values after the decimal
point
• .3. Discuss your results with other groups.
• Note
• The number of digits and place values to the right of the decimal point are
equal.
• (i) The number of place values to the right of the decimal point is also
called the number of decimal places.

Example
Write the number of decimal places in each of following:
Solution
(a) 2.4 (b) 36.465 .(b) 36.465 .(c) 43.3057
(a) 2.4 has one decimal places
(d) 0.270 has three decimal places.
(c) 43.3057 has four decimal places
(d) 0.270 has three decimal places

Assessment
2. Write the number of decimal places in each of the following:
(a) 5.79 (b) 0.2 (c) 29.0005 (d) 20.0060
3. Write a decimal number with:
(a) 2 decimal places
(b) I decimal place
(c) 3 decimal places
(d) 4 decimal places

Round off decimal
Group activity
Round off each of the following correct to 1 decimal place
a)5.43 b)5.49
In groups of three:
2.Copy and label the number line
5.4 5.41 5.5
.
Circle 5.43 and 5.49
Is 5.43 nearer r to 5.4 or 5.5?
Is 5.49 nearer to 5.4 or 5.5.
Compare the digits in the hundredths place value with digit 5.
Discuss your results and share with other groups

Note
• A decimal may be written or rounded off correct to a given number
of decimal places.
• (ii) To round off a decimal correct to a given number of decimal
places, consider the digit in the next lower place value. If the digit is
(a) less than 5, take the number up to the required decimal places (b)
5 or greater than 5, then increase the digit in the required place value
by I and ignore the digits in the other lower place values.

Example
Round off 5.7819 correct to:
(a) 1 decimal place b) 2 decimal place (c) 3 decimal places
Solution
(b) 2 decimal places(a) The digits in the hundredths place value is
greater than 5.Therefore, 5.7819 is 5.8 correct to 1 decimal place.
(b) The digit I in the thousandths place value is less than 5.Therefore,
5.7819 is 5.78 correct to 2 decimal places.
(c) The digit 9 in the thousandths place value is greater than
5.Therefore, 5.7819 is 5.782 correct to 3 decimal places.

Assessment
1.Write 8.3547 to the nearest:
(a) tenth (b) hundredth (c) thousandth
2.The length of a building was given as 15.39 metres. What is the
length correct to 1 decimal place?
3.The mass of a bull was given as 450.703 kg. What was this mass
correct to 2 decimal places?

Converting decimals to fractions
• Group Activity
• In groups of three:
• Draw a rectangular grid with 10 equal parts as shown.
• 2. Shade four parts.
• 3. Write the decimal representing the shaded part.
• 4. Write the fraction representing the shaded part.
• 5. Write the unshaded part as a decimal and as a fraction.
• 6. Discuss your result with other group

Note
• A decimal can be expressed as a fraction for example 0.9=
9
10
• Example
• Convert each of the following decimal to fraction
• a)0.56 b)0.225 c)0.4572
• Solution
a) 0.56= b)0.225=
225
1000
c)0.4572=
4572
10000

Assessment
1. If a recipe calls for 0.75 cups of sugar, what fraction of a cup is this?
2. A contractor needs to cut a piece of wood into sections, each
measuring 0.6 meters. What fraction of a meter is each section?
3. A car traveled 0.4 miles on a single lap around the track. What
fraction of a mile did it travel?
4. If a student scored 0.85 on a test, what fraction of the total possible
points did they score?
5. A farmer used 0.625 acres of land for planting crops. What fraction
of an acre did the farmer use?

Converting fraction to decimal
Note
One square in the grid represent
1
100
or 0.01
Convert the following fraction to decimals
a)
56
100
=0.56
3958
10000
=0.3958

Assessment
1. A recipe calls for
5
7
cup of milk. What is this quantity in decimal
form?
2. Gasoline costs ksh1.75 per gallon. Express this price per gallon as a
decimal.
3. A piece of rope is 5
1
2
feet long. Convert this length to decimal form
in feet.
4. A baker needs 8
1
2
kilograms of flour for a recipe. Convert this
quantity to decimal form in kilograms.
5. A student's point is 3
1
2
. Convert this points to decimal form.

Converting fractions to decimals using
equivalent fractions or by dividing
• Group Activity
• In groups of three:
• Convert
3
5
to a decimal.
• Write the equivalent fraction of
3
5
with 10 as the denominator.
• Write the new fraction as a decimal.
• Discuss your results and share with other groups.

Note
• (i) A fraction can be converted to a decimal by getting itsequivalent
fraction with the denominator 10, 100, 1000 or10000.
• ii
3
5
=
3
5
×
×
25
25
75
100
0.75

Assessment
1. A meeting lasts for 3/4 of an hour. Convert this fraction to a decimal
to express the duration of the meeting in hours.
2. A baker uses 5/8 of a kilogram of sugar in a cake. Convert this
fraction to a decimal to determine the amount of sugar in
kilograms.
3. A runner covers 2/3 of a mile during their morning jog. Convert this
fraction to a decimal to express the distance in mile
4. A car travels 1/5 of a mile on one gallon of gasoline. Convert this
fraction to a decimal to find out how many miles per gallon the car
can travel.

Conversion of decimals to percentages
Group Activity
Convert 0.7 to a percentage.
In groups of three:
1. Convert 0.7 to a fraction.
2. Write the equivalent fraction with 100 as a denominator.
3 . Discuss your results s with other groups.

Assessment
1. A student scored 0.85 on a test. Convert this decimal to a percentage
using equivalent fractions or by multiplying by 100.
2. An item is on sale at 0.25 times its original price. Convert this decimal to
a percentage to determine the discount percentage.
3. A bank offers an annual interest rate of 0.045 on a savings account.
Convert this decimal to a percentage to find out the annual interest rate.
4. The sales tax rate in a region is 0.07. Convert this decimal to a percentage
to determine the sales tax percentage.
5. A student's point is 3.75. Convert this decimal to a percentage to express
the point as a percentage.

Example
Convert each of the following decimal to a percentage
a)0.2=
2
10
=
20
100
=20%

Conversion of percentages to decimals
Group Activity
Convert the following percentages to decimals:
(a) 97.2%
1Convert each percentage into a fraction.
2. Express the fraction as a decimal.
3. Discuss your results with other groups.
Note
To convert a percentage to a decimal:
(i) Convert the percentage to a fraction.
(ii) Express the fraction as a decimal.

Example
• Convert each of the following percentage to decimal
36.5
36.5% 36.5=36.5 x 10
100 x 10
365
1000 =0.365

Assessment
1. If you receive a 20% discount on a purchase, how would you convert this
percentage to a decimal to calculate the discounted amount?
2. When calculating the interest rate on a loan or credit card, how do you
convert a percentage to a decimal to use it in financial calculations?
3. In tax calculations, if a tax rate is given as 15%, how would you convert
this percentage to a decimal to determine the amount of tax owed?
4. When figuring out the tip at a restaurant, if you want to leave a 18% tip
on your bill, how do you convert this percentage to a decimal to calculate
the tip amount?
5. In grading systems, if a student's performance is evaluated as 85%, how
would you convert this percentage to a decimal to determine their grade
point average (GPA) or cumulative score?

Addition of decimals up to ten thousandths
Group Activity
Add 2.356 to 7.4123
In pairs:
1.Represent the decimal 2.356 on an abacus.
2. On the same abacus represent 7.4123.
3. Count and record the number of rings in each place valuestarting
from ten thousandths.
4. Write the decimal represented on the abacus.

Example
a)4.25 +2.346
4.250
+ 2.346
6 .596
Note
When adding decimals, align the digits according to their decimal
places.

Assessment
• Addition of decimals up to ten thousandths
• If you buy apples weighing 2.3456 kilograms and oranges weighing 1.6789
kilograms, what is the total weight of fruits you purchased?
• If you deposit ksh2456.789 into your bank account and then withdraw
ksh1234.567, what is the total amount left in your account?
• You use 3.4567 liters of milk and 1.2345 liters of cream in a recipe. What is
the total volume of dairy products used?
• In a track event, the first runner finishes in 10.1234 seconds, and the
second runner finishes in 11.9876 seconds. What is the total time taken by
both runners?
• In a laboratory experiment, a chemical reaction takes 8.9012 seconds to
complete in one trial and 6.7890 seconds in another. What is the total time
taken for both trials?

Subtraction of decimals up to ten
thousandths
Group Activity
Work out 14.6875 -3.5324
In groups of four:
1.Represent 14.6875 on an abacus.
2. Remove;
(a) 4 rings from the ten thousandths.
(b) 2 rings from the thousandths.
(c) 3 rings from the hundredths.
(d) 5 rings from the tenths.
(e) 3 rings from the ones.
3. Count the number of rings remaining in each place value starting from the ten thousandths.

Assessment
• Subtraction
7.1324 from 8.4536
8.4536
- 7.1324
1.3212

Assessment
1. If you have ksh5000 in your bank account and you spend ksh432.58 on groceries,
how would you subtract the cost of groceries from your account balance,
considering both amounts involve decimals up to ten thousandths?
2. In construction, if a piece of lumber measures 15.738 meters and you need to cut
off 3.245 meters to fit it into a specific space, how would you subtract the length
you need to cut off from the original length to determine the remaining usable
length?
3. In scientific experiments, if you have a solution with a volume of 25.672 milliliters
and you use 12.345 milliliters during an experiment, how would you subtract the
volume used from the original volume to find out how much remains?
4. When managing inventory in a retail store, if you receive a shipment of 478.259
units of a product and 123.456 units are sold, how would you subtract the number
of units sold from the total received to determine the remaining inventory?
5. In cooking recipes, if a recipe calls for 2.543 kilograms of flour and you have already
used 0.789 kilograms, how would you subtract the amount used from the original
amount to know how much flour is left for future use?

STRAND 1 NUMBERS.pptx CBC GRADE 6 FOR LEARNERS

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