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MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
The aim of the curriculum is the development of mathematically powerful individuals
“who understand and confidently us mathematical concepts principles across disciplines
and in everyday life” (OECS Education reform Unit (OERU), 1993, p33) additionally,
the curriculum should enable these individuals to be critical thinkers and problem
solvers who enjoy the challenges of mathematics and readily pursue solution to
problems.
If the mathematic curriculum is to achieve this aim, it should of necessity include from
the outset the attributes and behaviours that describe individuals. These learning
outcomes embody this range of appropriate attributes.
Analysis of the characteristics of the mathematically powerful individual as well
descriptions of an appropriate learning environment provides an indication of these
attributes. The description suggest that students should have developed and be able to
use:
- knowledge of mathematical concepts and procedures
- knowledge of mathematical relationships
- reasoning skills
- language and communication skills and
- problem solving skills
Mathematics consists of several facts, skills, concepts and general procedures or
strategies (Department of Education and Science (DES), 1987; National Council of
teacher of Mathematics (NCTM, 1989, 2000) Therefore, students should be provided
with opportunities to learn, not just concepts and facts, but also skills and procedures
thus are appropriate for their level of development. In developing these work habit,
attention should also be also be given to nurturing positive attitudes. The development
of a positive attitude towards mathematical should focus on ensuring that students
acquire:
 A fascination with the subject
 An interest in doing the subject
 An appreciation for the purpose and relevance of the mathematics that is studies
 Students’ confidence in their ability to do the subject (NTCM, 2000, OERU
1998)
These general elements are the foundation of the learning outcomes. Consistent with the
recommendations coming out of the 1998 sub-regional workshop, the learning
outcomes have been organized into five strands or content areas of mathematics
 Statistics
 Geometry
 Measurement
 Number Concepts
 Computation
The facts, skills, procedures and dispositive that student need to develop in each of
these areas have therefore been identified
The development of these elements of mathematics can be facilitated by appropriate
experiences, In this regard it is important to note that develop mathematical competence
and positive personal qualities through activities that allow them to examine and
restructure their knowledge (James, 1995, Hartfield, Edwards, S Bitter, 1999, Reyes,
Suydam, S Lindquis, 1984).
Based on the better statement, commencing from the June 2005 Primary Mathematics
Examinations, there will be a school based component for grade 6 students. 10% of the
Primary National Mathematics Examination score will be general towards this section.
Students are required to submit Mathematics Project based on one of the content area
from the 5 strands of:
 Measurement
7In everything set them an example by doing what is good. In your teaching show integrity,
1
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX




Geometry
Number Concept
Computation and
Statistics
The aim of the project is for students to demonstrate how Mathematics is used in their
daily lives
STRANDS:
1.
2.
3.
4.
5.
6.
NUMBER: THEORY, CONCEPTS AND OPERATIONS
MEASUREMENT
GEOMETRY
STATISTICS AND DATA HANDLING
ALGEBRA, PATTERNS AND FUNCTIONS
CONSUMER ARITHMETIC
Standards:
The learner will be able to:
1. Develop number sense, ways of representing numbers, relationships
among numbers and number systems and perform mathematical
computations
2. Construct an understanding of measurable attributes of objects and the
units, systems, and the processes of measurement.
3. Investigate properties of geometric shapes.
4. Use appropriate data gathering procedures, techniques for representing
data and interpreting data.
5. Discover algebraic properties and expressions and apply the operations
to the solution of algebraic equations and inequalities; read and interpret
graphs and use them to represent algebraic relationships.
6. Appreciate the role of the consumer in performing day-to-day
transactions involving money.
7. Solve problems using a variety of problem solving strategies (See
Polya.)
Attainment Targets:
The learner will be able to:
1. Apply number operations and relationships with speed and accuracy to
solve problems using mental strategies, paper/pencil or technology.
2. Make and use estimation and accurate measurement by applying
appropriate instruments, formulas and units to solve problems in a
variety of ways.
3. Identify and describe attributes of geometric shapes and apply this
knowledge to reason or solve problems about shape, size, position or
motion of objects.
4. Use a variety of strategies to collect, organize, analyze, and interpret
data to make decisions and solve problems.
5. Identify, describe and represent patterns and functional relationships to
solve mathematical and real-life problems with speed and accuracy.
6. Apply knowledge of money to solve problems related to day-to-day
transactions.
7In
everything set them an example by doing what
is good. In your teaching show integrity,
2
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
GRADE 5 & 6:
STRAND: NUMBER: THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: WHOLE NUMBERS
UNIT: ONE
Focus Questions:
1. What is the relationship between numbers and the number systems
Learning Outcomes
Create and solve
problems involving
simple properties of
numbers
Create and solve
problems involving
factors and multiples of
whole numbers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Key Concepts
Place value
Types of numbers
Expanded notation
Prime
Odd
Even
Odd
Composite
Multiples
Factors
Rounding off
H.C.F
L.C.M
Ordering numbers
7In
Specific Objectives
Read numerals up to 99 999
Write numerals up to 99 999 in words and numerals
Identify the place and total value of any digit in a number with five digits
Write numbers with up to five digits in expanded notation
Classify numbers using several number concepts: prime, odd, prime and
even, prime and odd, composite and odd
List multiples of a given number
List factors of a given number
Explain the concept of prime number
Write a number as a product of its prime factors
Calculate the least Common Multiple of two or three numbers
Explain the concept of “Highest Common Factor”
Find Highest Common Factor of two or three numbers by listing factors
Round off numbers with up to five digits to the nearest ten, hundred, or
thousand
Arrange a set of whole numbers in order of magnitude
Strategies
 Draw place value charts, write the numerals in the correct column then write
the numbers in words
 Use the place value chart to help to find the place and total value of any digit
in a number with five digit
 Add the total value of all the digit in a number (expanded form)
 Express numbers as power of 10
 Given numbers 1-100 pupils will use the Eratosthenes sieve to classify them
as Prime or composite
 Given any number pupils will classify it as odd or even by the last digit
 Engage pupils in a bingo game involving odd, even, prime and composite
numbers
 Prepare factors trees to write numbers as product of prime factors. List the
multiples of sets of two or three numbers then idnetify the lowest common
multiple.
 List the factors of sets of two or three numbers then identify the highest
common factor/use prime factorizing
everything set them an example by doing what
is good. In your teaching show integrity,
3
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: NUMBER; THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: COMPUTATIONS
UNIT: TWO
Focus Question:
1. What are the basic facts of addition, subtraction, multiplication and division of whole numbers?
Learning Outcomes
Create and solve reallife problems involving
addition and subtraction
with numbers up to
100000
Specific Objectives
1. Recall the basic facts for addition, subtraction, multiplication and
division of whole numbers
2. Add sets of numbers with totals up to 99 999, without and with
regrouping
3. Carry out subtraction involving whole numbers with up to five
digits, without and with regrouping
4. Multiply two and three-digit numbers by one- and two-digit numbers
5. Divide whole numbers with up to five digits by one- and two-digit
numbers, without and with remainder
Create and solve reallife problems involving
multiplication and
division of numbers up
to 3 digit numbers
6. Identify real life situations that involve the use of Roman
numerals
Create and solve
problems involving
simple properties of
numbers
Key Concepts
Computation
vocabulary: sum,
product, total
quotient
divisor
7. State the Roman numerals for I, 5 and 10
8. Explain how the Roman numerals for 1, 5 and 10 should be
used to form other Roman numerals between 2 and 12
inclusive
9. Identify and write Roman numerals for numbers from 1 to 12







7In
Suggested activities
Engage pupils in a bingo game involving addition subtraction,
multiplication or division of whole numbers
Use arrow graphs to draw from pupils their knowledge of addition,
subtraction, multiplication or division
Use calculators, mental, strategies, pen and paper to investigate number
patterns and relationships
Use the lattice methods to multiply
Use rules for divisibility
Introduce to pupils, objects that are marked with roman numerals
e.g. clock, books (chapter)
Matching Roman numerals with corresponding Hindu-Arabic
numbers
everything set them an example by doing what
is good. In your teaching show integrity,
4
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: NUMBER; THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: IDENTIFICATION/EQUIVALENT FRACTIONS
UNIT: THREE
Focus Questions:
1. What is the relationship between different kinds of fractions?
2. Which fraction is smaller or bigger?
Learning Outcomes
Use and write basic
fractions and
decimals in a variety
of ways in real life
situations
1.
2.
3.
4.
5.
6.
7.
Key Concepts
Fractions
Mixed numbers
Fractions:
Improper
Equivalent
Least Common
Denominator
Greatest Common
Factor
Ordering fractions
7In
Specific Objectives
Use diagrams/pictures to represent unit, proper and improper fractions
and mixed numbers
Convert an improper fraction to a mixed number and vice versa
Explain the concept of ‘lowest terms’ and its relationship to equivalent
fractions
Express fractions in their lowest terms
Generate fractions that are equivalent to a given fraction
Calculate the lowest common denominator for fractions with unlike but
related denominators
Arrange a set of fractions in order of magnitude
Strategies
 Students will draw pictorial representations of various types of fractions e.g.
unit, proper, improper fractions and mixed numbers.
 Make equivalent fractions by multiplying both terms by the same number.
E.g. 3/6 x 2/2 = 6/12
 Reduce fractions to lowest term by dividing both terms by the greatest
common factor. E.g. 5/10 ÷5/5 =1/2
everything set them an example by doing what
is good. In your teaching show integrity,
5
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: NUMBER; THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: FRACTIONS/OPERATIONS
UNIT: FOUR
Focus Question:
1. What are the various types of fractions?
2. How do we carry out operations involving whole numbers and fractions
Learning Outcomes
Use and write basic
fractions and decimals
in a variety of ways in
real life situations
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Key Concepts
Fraction
Proper
Fractions
Denominator
Numerator
Improper
Fractions
Mixed numbers
7In



Specific Objectives
Add proper fractions with like or unlike but related denominators
Add a whole number to a proper fraction
Add a proper fraction and a mixed number with like denominators
Add a proper fraction and a mixed number with unlike but related
denominators
Carry out subtraction involving proper fractions with like denominators
Carry out subtraction involving proper fractions with unlike but related
denominators
Subtract a proper fraction from a mixed number with like denominator,
without regrouping
Subtract a proper fraction from a mixed number with unlike but related
denominator without regrouping
Subtract a proper fraction from a whole number
Multiply a proper fraction by a whole number
Multiply a whole number by a proper fraction
Multiply two proper fractions
Divide a proper fraction by a whole number
Suggested activities
Use fractions charts to add and subtract proper fractions of the same
family
Shade fractional parts of a whole
Divide wholes into fractional parts to show improper fractions
everything set them an example by doing what
is good. In your teaching show integrity,
6
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: NUMBER; THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: DECIMALS/IDENTIFICATION
UNIT: FIVE
Focus questions:
1. What is the relationship between decimal numbers and whole numbers?
2. Which decimal is larger or smaller?
Learning
Outcomes
Use and write
basic fractions and
decimals in a
variety of ways in
real life situations
Specific Objectives
1.
2.
3.
4.
5.
6.
7.
8.
9.
Key Concepts
Relationship
between decimals
and whole numbers
Place value & total
value
Relationship
between fractions
and decimals
Explain how decimal numbers and whole numbers are related
Identify the place and total value of the digits in a decimal number with up
to two decimal places
Represent simple decimal numbers with up to two decimal places using
diagrams
Read decimal numbers with up to two decimal places
Write decimal numbers with up to two decimal places
Arrange a set of decimal numbers with up to two decimal places in order of
magnitude
Explain how fractions and decimals are related
Write a decimal number as a fraction
Write a fraction as a decimal number
Strategies
 Pupils will complete the place value charts which include both whole numbers
and decimal numbers.
 Use place value chart to find the total value and place value of decimal
numbered up to two decimal places.
 Given a hundred squared grid, pupils will colour code various number of
squares to represent decimal places up to hundredths
 Match decimal number with its corresponding fraction e.g. 0.3 = 3/10
Conversions
7In
everything set them an example by doing what
is good. In your teaching show integrity,
7
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: NUMBER; THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: DECIMALS/OPERATIONS
UNIT: SIX
Focus Question:
1. What is the relationship between decimals and whole numbers?
Learning Outcomes
Use and write basic
fractions and decimals in
a variety of ways in real
life situations
Specific Objectives
Explain how computation procedures for whole numbers can be applied
to decimal numbers
Add decimal numbers with up to two decimal places, without and with
regrouping
Carry out subtraction involving decimal numbers with up to two decimal
places, without and with regrouping
Multiply a decimal number with up to two decimal places by a one-digit
number
1.
2.
3.
4.
Key Concepts
Whole number
Tenths
Hundredths
Decimal point
Suggested activities
 Teacher demonstrate how to compute decimals with the use of place value
chart and number line
 Engage pupils in a decimal cross number puzzle
STRAND: NUMBER; THEORY, CONCEPTS AND OPERATION
UNIT TITLE: PERCENTAGES
UNIT: SEVEN
Focus question:
1. What does percentage mean?
2. How are percentages relevant to everyday life?
Learning Outcomes
Use and write basic
fractions and decimals in a
variety of ways in real life
situations
Solve problems
involving fractions,
decimals and percent
1.
2.
3.
4.
5.
6.
7.
8.
9.
Specific Objectives
Explain the concept of percent
Represent a given percent using pictures/diagrams and symbols
Explain the meaning of a given percent
Describe and Analyze situations in real life that involve percents
Explain the relationship between fractions, decimals and percents
Express a percent as a decimal or fraction
Express simple proper fractions and decimals as percents
Solve problems involving fractions, decimals and percent
Analyze problems involving fractions, decimals and percent
Analyze problems
involving fractions,
decimals and percent
Key Concepts
Percent
Decimals
Relationship between
fractions, decimals and
percents
Real life situations
7In
Strategies
 Use the hundred square grids to explain the concept that percent means out
of a hundred. E.g. five percent means five out of a hundred 5% = 5/100
 Solve problems involving percent. E.g. find 5% of $20.00
 Given a percentage, pupils will represent it as a fraction and a decimal e.g.
37% = 37/100 = 0.37
everything set them an example by doing what
is good. In your teaching show integrity,
8
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: NUMBER; THEORY, CONCEPTS AND OPERATIONS
Unit Title: PERCENTS
UNIT: EIGHT
Focus Question:
1. What does percentage mean?
2. How relevant is percentage in everyday life?
Learning Outcomes
Use and write basic
fractions and decimals
in a variety of ways in
real life situations
1.
2.
3.
4.
Key Concepts
Percentage
Profit
Loss
Cost price
Selling price
Specific Objectives
Calculate a percent of a number
Express one number as a percent of another
Calculate profit or loss, given the cost price and selling price of an
article
Calculate profit or loss as a percent of the cost price of an article
Suggested activities
 Present picture representing priced items and allow pupils to calculate
percentages of each items
 Put pupils in groups and give them worksheet with problems involving
percentages
 Question pupils on whether there is a loss or profit
 Students work together and individually to calculate profit & loss.
STRAND: MEASUREMENT
Unit Title: LENGTH, CAPACITY, MASS
UNIT: NINE
Focus Question:
1. What is the metric unit used to measure length, capacity, mass
Learning Outcomes
Create and solve problems
using different units of
length
Create and solve real life
problems involving basic
standard units of mass
Create and solve real life
problems involving basic
standard units of capacity
1.
2.
3.
4.
5.
6.
7.
8.
Key Concepts
Metre
Centimeter
Kilometer
Kilogram
Gram
Milligram
Celsius
Scale
7In
Specific Objectives
Estimate and measure lengths and heights using the metre,
centimetre and / or millimeter as the units of measure
Estimate and measure distances using the metre / and / or centimeter
as the units of measure
Identify and interpret the scale that was used in a scale drawing
Use scale drawings to determine actual measurements in metres or
kilometers
Make simple scale drawings
Estimate and measure the mass of objects using kilograms, grams,
and / or milligrams as the units of measure
Estimate and measure the capacity of containers using litres,
centiliters, and / or milliliters as the units of measure
estimate and measure temperatures using the Celsius scale
Suggested activities
 Estimate and measure the lengths and heights of various objects in
the classroom in centimeters, millimeters and meters
 Given a map drawn to scale, pupils will find actual distances
between places by using the scale
 Pupils draw their floor plan of a dream home
 Pupils use the beam balance to find the mss of given objects
 Pupils will use graduated measuring cylinders to find capacity of
given liquids
 Pupils will use thermometer to find the temperature of the room,
body, liquids.
everything set them an example by doing what
is good. In your teaching show integrity,
9
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: GEOMETRY
UNIT TITLE: GEOMETRY/LINES/ANGLES
UNIT: TEN
Focus Question:
1. What types of angles are present in 3D shapes?
Learning
Outcomes
Investigate the nets of
regular 3-D shapes
Key Concepts
3Dimensional shapes
Edges
Vertices
Comparing size of angles
Acute angles
Obtuse angles
Right angles
Horizontal,
Vertical,
Parallel,
Perpendicular lines
7In
Specific Objectives
1.
2.
3.
4.
Identify angles in three-dimensional and plane shapes
Draw and label angles
Explain what is a right angle
Classify angles according to size, as equal to, larger than, or smaller than a
right angle
5. Identify acute and obtuse angles
6. Describe acute and obtuse angles
7. Draw and label line segments
8. Explain the concepts of horizontal, vertical, parallel and perpendicular lines
9. Identify horizontal and vertical line segments
10. Draw horizontal and vertical line segments
11. Identify parallel and perpendicular lines
12. Draw parallel and perpendicular lines
Suggested activities
 Name objects in classroom that have right angles make right angles with
pieces of paper
 Trace out angles on a piece of paper and compare them with right angle
to see which are smaller, larger or the same size
 For a project, compile a scrapbook of angles and lines
everything set them an example by doing 10
what is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: GEOMETRY
UNIT TITLE: ANGLES
UNIT: ELEVEN
Focus Question:
1. What types of angles are present in 2D shapes?
2. How are angles useful in everyday life?
Learning Outcomes
Investigate properties of 2D shapes in terms of lines
and angles
1.
2.
3.
4.
5.
6.
7.
8.
Key Concepts
2Dimensional shapes
Edges
Vertices
Specific Objectives
Describe two-dimensional shapes in terms of the number and type
the type of angles
Explain the concept of ‘circumference of a circle’
State the relationship between radii and diameters of circles
Draw circles
Identify the following parts: circumference, radius, diameter, centre
Identify 2Dimensional shapes that have the same size and shape
Explain the concept of ‘congruent figures’
Classify two-dimensional shapes using a variety of attributes
Suggested activities
 Using information given in charts, pupils will complete sentences to
tell the proprieties of 2 D
 Use string to measure the length of curriculum conference
 Calculate the radii when given the diameter or the diameter when
given of circles
 Given pupils charts with the parts of circle, pupils will copy diagrams
in their note book
 Colour shapes then are congruent to given shapes.
Parts of a circle:
Circumference
Radius
Diameter
Centre
Attributes: open, closed,
symmetrical, congruent,
number of sides and angles,
types of angles and sizes
Congruent figures
STRAND: MEASUREMENT
Unit Title: MONEY
UNIT: TWELVE
Focus Question:
1. What does money play in trade/everyday situations
Learning
Outcomes
Create and solve real
life problems
involving the
calculation of bills and
change
Specific Objectives
1.
2.
3.
4.
5.
6.
7.
8.
9.
Key Concepts
7In
Read and write amounts of money up to $99 999
Describe situations that involve the use of large amounts (thousands)
Describe the role of cheques in transactions involving money
Represent amounts of money in a variety of ways
Calculate the total cost of a set of items, given the cost of one item and / or
the cost of multiple of items
Make up bills
Calculate change
Explain the concepts of cost price, selling price, profit, and discount
Use the concepts of cost price, selling price, profit, loss and discount in
descriptions of situations involving buying and selling
Suggested activities
everything set them an example by doing 11
what is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
 Role play a shopkeeper dealing with his/her customers to bring out the
concepts of selling price
 Role play a shopkeeper buying from a wholesale to bring out the concept of
cost price
 Put pupils into and give each group a set of invoices or bills to calculate the
profit and loss based on the cost price and selling price
 Use labels form stores to calculate actual discount on items
Cost price
Selling price
Profit
Loss
Discount
Buying and selling
STRAND: GEOMETRY
UNIT TITLE: PERIMETER & AREA
UNIT: THIRTEEN
Focus Question:
1. How do we find the perimeter and area of a space?
2. How do perimeters and areas help to relate everyday situations?
Learning
Outcomes
Investigate
properties of
triangles in terms of
angles and sides
Specific Objectives
1.
2.
3.
4.
5.
Key Concepts
2 Dimensional
Perimeter
Area
Irregular figures
Squares
Rectangles
Calculate the perimeter of a two-dimensional shape
Identify appropriate units for the measurement of small and large areas
Calculate the area of a rectangle or square by using the formula, Area =
length X width
Calculate the area of irregular figures that are comprised of squares, and / or
rectangles
Sketch squares, rectangles, or irregular figures with a given area and / or
perimeter
Suggested activities
 Given two dimensional shapes, pupils will calculate the perimeter by
counting on the grid and by using the formulae where applicable
 Given irregular shapes, pupils will dissect them into squares and rectangles then
find their areas by using the grid and appropriate formulae
STRAND: GEOMETRY
UNIT TITLE: 3D SHAPES
UNIT: FOURTEEN
Focus Question:
1. What is the relationship between faces, edges and vertices of 3D shapes?
2. How are 3D shapes useful in everyday life?
3. Where can we find 3D shapes in our surroundings?
Learning Outcomes
Investigate the nets of 3D shapes
1.
2.
3.
4.
5.
6.
Key Concepts
3D shapes
faces, edges
vertices
cubes
cuboids
cylinder
nets
cones
7In
Specific Objectives
Describe three-dimensional shapes in terms of the number and type of
faces and the number of edges and vertices
Use the attributes of a 3Dimensional shape to formulate reasons for its
uses in every day life
Identify and describe cubes, cuboids, cylinders, cones and spheres
Make nets of cubes, cuboids and cylinders
Identify nets that will form a cube, cuboid or cylinder
Construct cubes, cuboids and cylinder
Suggested Activities
 Given concrete objects pupils will describe them in terms of type of faces and
the numbers of edges and vertices.
 Students bring in examples of cube, cuboid and cylinders (match box, shoe box,
gift box, Pringles containers)
 The open out/cut containers apart and observe how they were made up (put
together).
 Student the make their own nets using Manila paper.
 Engage pupils in making models of cubes, cuboids and cylinders.
everything set them an example by doing 12
what is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: GEOMETRY
UNIT TITLE: COORDINATES
UNIT: FIFTEEN
Focus Question:
1. What are coordinates?
Learning Outcomes
Create and solve
problems involving
plane shapes
Key Concepts
Concepts: angles,
symmetry,
congruency
Specific Objectives
1. Describe a simple co-ordinate system with only positive numbers
2. Plot points on a simple co-ordinate system
3. Identify points on a simple co-ordinate system
4. Create and solve problems involving simple co-ordinate systems
Suggested activities
 Organize and display data in line graphs. Using y axis with intervals of
1,2,4,5, or 10 and x axis with no more that 10 time intervals and whole
numbers
 Use information on line graph to answer comprehension questions.
Co-ordinates
STRAND: STATISTICS AND DATA HANDLING
UNIT TITLE: STATISTICS
UNIT: SIXTEEN
Focus Questions:
1. When do I collect data?
2. Where do I collect data?
3. How do I collect data?
Learning Outcomes
Collect data to solve
simple problems using a
variety of methods
1.
2.
Use, construct and
interpret simple graphs
using simple scales
3.
4.
5.
6.
7.
Key Concepts
Observation
Interview
Data collection
Suggested activities
 Identify and describe situations where data collection, representation, and
interpretation could be used to solve problems

7In
Specific Objectives
Describe procedures for collecting data using observation, interview, or
simple questionnaire
Identify similarities and differences between interviews and
questionnaire
Explain when it is appropriate to use interviews and questionnaire to
collect data
Select the data collection method that is appropriate for a particular
problem situation, and
Give reasons for their selection
Plan data collection activities
Create problems whose solutions require data
Collect date by conducting surveys observations and interviews and
organizing and displaying data collected using bar graphs, tally charts, line
graphs, pictograph
everything set them an example by doing 13
what is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
STRAND: STATISTICS AND DATA HANDLING
UNIT TITLE: REPRESENTATION OF DATA
UNIT: SEVENTEEN
Focus Question:
1. What are the different methods to represent data?
2. What is the best method to represent data?
Learning
Outcomes
simple problems
using a variety of
methods
Use, construct and
interpret simple
graphs using simple
scales
Key Concepts
Data
Scales
Tables
Bar graphs
Line graphs
Pictographs
Charts
Specific Objectives
1.
2.
3.
4.
5.
6.
Select appropriate methods to represent data
Select appropriate scales to represent data graphically
Explain why a selected data representation method or scale is appropriate
Represent data using pictographs or bar charts
Identify similarities and differences between bar graphs and line graphs
Explain when it is appropriate to use bar graphs and line graphs to represent
data
Suggested Activities
 Through pictorial representation, pupils are allowed to identify and select
appropriate methods to represent data.
 Elicit from pupils the similarities and differences between two graphs.
STRAND: STATISTICS AND DATA HANDLING
UNIT TITLE: INTERPRETING DATA
UNIT: EIGHTEEN
Focus Question:
1. What does the data mean?
Learning Outcomes
Collect data to solve simple
problems using a variety of
methods
1.
2.
3.
Specific Objectives
Read data presented in tables, pictographs, bar charts and line graphs
Interpret data presented in tables, pictographs, bar charts and line
graphs
Calculate the mean / average of a set of data
Use, construct and interpret
simple graphs using simple
scales
Key Concepts
Data
Scales
Tables
Bar graphs
Line graphs
Pictographs
Charts
7In
Suggested activities
 Read the data presented in tables to answer comprehension questions.
 Measure in cm the heights of boys and girls in class. Record the
information in a table. Use the information to draw bar graphs, line graphs,
and pictographs. Use information to find the average height.
everything set them an example by doing 14
what is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
1x Table
2x Table
1x1 =
1
1x2 =
2
2x1 =
2
1x3 =
3
2x2 =
4
1x4 =
4
2x3 =
6
1x5 =
5
2x4 =
8
2x5 =
10
1x6 =
6
2x6 =
12
1x7 =
7
2x7 =
14
1x8 =
8
2x8 =
16
1x9 =
9
2x9 =
18
1 x 10 =
10
2 x 10 =
20
1 x 11 =
11
2 x 11 =
22
1 x 12 =
12
2 x 12 =
24
3x Table
4x Table
3x1 =
3
3x2 =
6
3x3 =
9
3x4 =
12
3x5 =
15
3x6 =
18
3x7 =
21
3x8 =
24
3x9 =
27
3 x 10 =
30
3 x 11 =
33
3 x 12 =
36
5x Table
4x1 =
4
4x2 =
8
4x3 =
12
4x4 =
16
4x5 =
20
4x6 =
24
4x7 =
28
4x8 =
32
4x9 =
36
4 x 10 =
40
4 x 11 =
44
4 x 12 =
48
6x Table
5x1 =
5
6x1 =
6
5x2 =
10
6x2 =
12
5x3 =
15
6x3 =
18
5x4 =
20
6x4 =
24
5x5 =
25
6x5 =
30
5x6 =
30
6x6 =
36
5x7 =
35
6x7 =
42
5x8 =
40
6x8 =
48
5x9 =
45
5 x 10 =
50
6x9 =
54
5 x 11 =
55
6 x 10 =
60
5 x 12 =
60
6 x 11 =
66
6 x 12 =
72
7In
everything set them an example by doing 15
what is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
7x Table
8x Table
7x1 =
7
8x1 =
8
7x2 =
14
8x2 =
16
7x3 =
21
8x3 =
24
7x4 =
28
8x4 =
32
7x5 =
35
8x5 =
40
7x6 =
42
8x6 =
48
7x7 =
49
8x7 =
56
7x8 =
56
8x8 =
64
7x9 =
63
8x9 =
72
7 x 10 =
70
8 x 10 =
80
7 x 11 =
77
8 x 11 =
88
7 x 12 =
84
8 x 12 =
96
9x Table
10x Table
9x1 =
9
10 x 1 =
10
9x2 =
18
10 x 2 =
20
9x3 =
27
10 x 3 =
30
9x4 =
36
10 x 4 =
40
9x5 =
45
10 x 5 =
50
9x6 =
54
10 x 6 =
60
9x7 =
63
10 x 7 =
70
9x8 =
72
10 x 8 =
80
9x9 =
81
10 x 9 =
90
9 x 10 =
90
10 x 10 =
100
9 x 11 =
99
10 x 11 =
110
108
10 x 12 =
120
9 x 12 =
11x Table
7In
12x Table
11 x 1 =
11
12 x 1 =
12
11 x 2 =
22
12 x 2 =
24
11 x 3 =
33
12 x 3 =
36
11 x 4 =
44
12 x 4 =
48
11 x 5 =
55
12 x 5 =
60
11 x 6 =
66
12 x 6 =
72
11 x 7 =
77
12 x 7 =
84
11 x 8 =
88
12 x 8 =
96
108
11 x 9 =
99
12 x 9 =
11 x 10 =
110
12 x 10 =
120
11 x 11 =
121
12 x 11 =
132
11 x 12 =
132
12 x 12 =
144
everything set them an example by doing 16
what is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose
you may be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
2
107
3
109
5
113
7
127
11
131
13
137
17
139
19
149
23
151
29
157
31
163
37
167
41
173
43
179
47
181
53
191
59
193
61
197
67
199
71
211
73
223
79
227
83
229
89
233
97
239
101
241
103
251
Finding the square root of a number is the inverse operation of
squaring that number. Remember, the square of a number is that
number times itself.
7In
everything set them an example by doing what17
is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose you may
be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
The perfect squares are the squares of the whole numbers.
The square root of a number, n, written below is the number that
gives n when multiplied by itself.
Metric Customary
1 kilometer = 1000 meters 1 mile = 1760 yards 1 meter = 100 centimeters 1 mile = 5280
feet 1 centimeter = 10 millimeters 1 yard = 3 feet 1 foot = 12 inches
CAPACITY AND VOLUME
Metric Customary
1 liter = 1000 milliliters
1 gallon = 4 quarts
1 gallon = 128 fluid ounces
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 fluid ounces
MASS AND WEIGHT
Metric Customary
7In
everything set them an example by doing what18
is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose you may
be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
1 kilogram = 1000 grams
1 ton = 2000 pounds
1 gram = 1000 milligrams 1 pound
TIME
1 year = 365 days
1 year = 12 months
1 year = 52 weeks
1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Perimeter rectangle P = 2l + 2w or P = 2(l + w)
Circumference circle C = 2πr or C = πd
AREA
Rectangle A = lw or A = bh
Triangle A = bh or A
Trapezoid A = (b1 + b2)h or A
Regular polygon A = aP
Circle A = πr 2 1 2 bh 2 1 2 (b1 + b2)h 2 1 2
P represents the Perimeter of the Base of a three-dimensional
B represents the Area of the Base of a three-dimensional figure.
Surface Area
Cube (total) S = 6s 2
Prism (lateral) S = Ph
Prism (total) S = Ph +2B
Pyramid (lateral) S = Pl
Pyramid (total) S = Pl + B
Cylinder (lateral) S = 2πrh
Cylinder (total) S = 2πrh +2πr 2 or S =2πr(h + r)
Cone (lateral) S = πrl
Cone (total) S = πrl + πr 2 or S = πr(l + r)
Sphere S = 4πr 2
Volume
Prism or cylinder V = Bh
Pyramid or cone V = Bh
Sphere V = πr 3
Special Right Triangles
30°, 60°, 90° x, x√3, 2x 45°, 45°, 90° x, x, x√2
Special Right Triangles
30°, 60°, 90° 45°, 45°, 90°
x, x√3, 2x x, x, x√2 __
Pythagorean Theorem a 2 + b 2 = c 2
Distance Formula d = √ (x2 − x1) 2 + (y2 − y1) 2 Slope of a Line m = y2 − y1
x2 − x1
Midpoint Formula M =
(,
x1 + x2 , y1 + y2
2
7In
)
2
everything set them an example by doing what19
is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose you may
be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
Quadratic Formula x = − b ± √b 2 − 4ac 2a
Slope-Intercept Form of an Equation y = mx + b
Point-Slope Form of an Equation y − y1 = m(x − x1)
Standard Form of an Equation Ax + By = C
Simple Interest Formula I = prt
Shapes
Formula
Rectangle:
Area = Length X Width
A = lw
Perimeter = 2 X Lengths + 2 X
Widths
P = 2l + 2w
Parallelogram
Area = Base X Height
a = bh
Triangle
Area = 1/2 of the base X the height
a = 1/2 bh
Perimeter = a + b + c
(add the length of the three sides)
Trapezoid
Perimeter = area + b1 + b2 + c
P = a + b1 + b2 + c
Circle Try the Online tool.
The distance around the circle is a
circumference. The distance across the
circle is the diameter (d). The radius
(r) is the distance from the center to a
point on the circle. (Pi = 3.14) More
about circles.
d = 2r
c = d = 2 r
A = r2
=3.14)
Rectangular Solid
Volume = Length X Width X Height
V = lwh
Surface = 2lw + 2lh + 2wh
Prisms
Volume = Base X Height
v=bh
Surface = 2b + Ph (b is the area of
the base P is the perimeter of the
base)
7In
everything set them an example by doing what20
is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose you may
be ashamed because they have nothing bad to say about us. Titus 2:7,8
MINISTRY OF EDUCATION 2009 CURRICULUM GUIDES
MATHEMATICS,
GRADES FIVE & SIX
Cylinder
Volume = r2 x height
V = r2 h
Surface = 2 radius x height
S = 2rh + 2r2
Pyramid
V = 1/3 bh
b is the area of the base
Surface Area: Add the area of the
base to the sum of the areas of all of
the triangular faces. The areas of the
triangular faces will have different
formulas for different shaped bases.
Cones
Volume = 1/3 r2 x height
V= 1/3 r2h
Surface = r2 + rs
S = r2 + rs
=r2+r
Sphere
Volume = 4/3 r3
V = 4/3 r3
Surface = 4r2
S = 4r2
7In
everything set them an example by doing what21
is good. In your teaching show integrity,
seriousness 8and soundness of speech that cannot be condemned, so that those who oppose you may
be ashamed because they have nothing bad to say about us. Titus 2:7,8