STRANDS: 1. NUMBER: THEORY, CONCEPTS AND OPERATIONS 2. MEASUREMENT / CONSUMER ARITHMETIC 3. GEOMETRY 4. STATISTICS AND DATA HANDLING 5. ALGEBRA, PATTERNS AND FUNCTIONS 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.
22
Embed
STRANDS: 4. STATISTICS AND DATA HANDLING · 4. STATISTICS AND DATA HANDLING 5. ... 1 + -1 = 0-2 = 0 n + -n = 0 for any positive integer n ... subsets of real numbers 4.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
STRANDS:
1. NUMBER: THEORY, CONCEPTS AND OPERATIONS 2. MEASUREMENT / CONSUMER ARITHMETIC 3. GEOMETRY 4. STATISTICS AND DATA HANDLING 5. ALGEBRA, PATTERNS AND FUNCTIONS
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.
GRADE 8: NUMBER: THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: INTEGERS; FRACTIONS; PERCENTAGES TERM: ONE UNIT: ONE DURATION: TWO WEEKS
Focus Questions:
1. What are different ways of getting zero?
2. How relevant are fractions and percentages in our daily life?
Learning
Outcomes
Specific Objectives Key Concepts Strategies Skills Resources Assessment
Demonstrate
proficiency with
calculations /
connection
between
operations
1. Add or subtract any two negative or positive integers.
2. Simplify
expressions
involving fractions
in combinations of
the four basic
operations
3. Calculate a
specified
percentage of a
given quantity as a
percentage of
another
4. Express one
quantity as a
percentage of
another.
Integers
Inverses for
addition
Fractions
Percentages
If to begin we are given any two integers and a single operation of
addition, then there are infinite ways to get 0 e.g.
1 + -1 = 0
2 + -2 = 0
n + -n = 0 for any positive integer n
Begin such a pattern that students can continue class discussion to establish
that there is a negative integer associated with every positive integer.
Students use the number line to add or subtract any two negatives or
positive numbers also, or positive and a negative number
Language: if two numbers a, b behave such that a + b = 0, then a and
b are called additive inverses of each other (or inverses of addition
Students will create and sole more cases in order to generalize the above
idea that there are infinitely many ways to generate any integer.
Students will use the number line to add or subtract any negative and/or
positive numbers
Teacher will further provide opportunity to decompose a given integer
into the sum of two integers; or the subtraction of two integers.
Give students a combination of the four (4) operations in calculating
fractions
e.g. 2/3 + 5/7 x 14/15 (BOMDAS)
Teacher provide word problems as following; Suppose John walks
20% of a 10 km journey. What distance did he walk? Guide students
to use the proportion or unitary method.
Students will solve similar problems which may involve other
quantities as time, mass, and volume.
Calculating number line
Text books
Bank of
questions
Coloured
counters, e.g.
for negative
one (-1), and
green for
positive 0ne
(+1)
Worksheet
Exercise in
textbooks
GRADE 8: NUMBER: THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: COMPUTATION
ESTIMATION; SEQUENCE; RATIO; PROPORTION TERM: ONE UNIT: TWO DURATION: TWO WEEKS
Focus Questions:
1. Why is estimation relevant?
2. How are ratio and proportion relevant in our day to day activities?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Demonstrate
proficiency with
calculations
Investigate whole
numbers using
sequences
1. Estimate sums and products of whole
numbers to the nearest hundreds and to
the nearest thousands.
2. Identify patterns in number sequences.
Estimation
Sequence
Operations
Given a set of numbers, students will find the
sum then give the answer correct to the nearest
hundreds or thousands
Given two numbers students will find the
products then estimate the answer correct to the
nearest hundreds or thousands.
Provide a set of numbers and have students
identify the pattern then provide additional
terms.
Estimating
Identifying
Calculating
Text book
Worksheet with
problems
Worksheet\
Create and solve
problems using
fractions as a way to
write ratio
3. Share a quantity in a give ratio
4. Calculate the missing components in
equivalent ratios
5. Calculate the ratio in which a given
quantity has been shared
6. Solve problems involving direct
proportion using the unitary method.
Ratio
Proportion
Increase the level of difficulty in sharing in
given ration e.g. Share $4500 between Bob,
Oliver and Nigel in the ratio 3:7:5
More difficult problem involving direct and
inverse proportion e.g. How long will it take 2
men to fence a play field if 5 men can do the
same job in 6 days
Sharing
Calculating
Bank of
questions
Worksheet with
word problem
GRADE 8: NUMBER: THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: SETS OF NUMBERS TERM: ONE UNIT: THREE DURATION: TWO WEEKS
Focus Questions:
1. What are real numbers?
2. Why are indices important?
Learning
Outcomes
Specific Objectives Key Concepts Strategies Skills Resources Assessment
Demonstrate a
basic
understanding of
number systems
with emphasis on
real numbers
1. Define the set of real
numbers.
2. Identify different subsets
of the real number system.
3. Identify the relationship
between the different
subsets of real numbers
4. Arrange integers
according to size on a
number line
5. Compare integers using
inequalities symbols.
Real numbers
Whole numbers
Integers
Natural
numbers
Rational
numbers
Provide students with a list of the sub-
sets of real numbers. Have students do
research to define each type. Using the
definitions of subset above, have
relationship between theme
e.g.
Real numbers
Rational Irrational
Numbers Numbers
Integers (2) Fractions
Negatives Whole Numbers
Integers
Zero Natural
numbers
Have students use the number line to
order and compare the integers
Researching
Identifying
Computing
Flow chart
Number line
Bank of question
Charts,
Flash cards
Loops
Worksheet
worksheet
GRADE 8: NUMBER: THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: NUMBER PROPERTIES TERM: ONE UNIT: FOUR DURATION: TWO WEEKS
Focus Questions:
1. Why is the important to do things in order?
2. How are number properties used to make problem solving easier?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment Demonstrate a basic
understanding of number
systems with emphasis
on laws of indices
1. Identify and differentiate between the
orders of operations (BOMDAS).
2. Define the number properties.
3. Apply the laws in performing the four
basic operations.
4. Use the properties to carry out
computation in problem-solving
situation
5. Define the laws of indices'; 1
6. a x a = a
7. Use the laws of indices of simplify
expressions with integral indices
laws of
Indices
Commutative
Associative
Distributive
Order of
operation
Instruct students in the different laws of indices
Given the laws, have students research their
meaning then write and example of each.
1. Commutative law: (i) a +- b" == b + a
(ii) a x b = b x a
2. Associative law: (i) (a + b) + C == a +- (b +
c)
(ii) (a x b) x c == a x (b x c)
3. Distributive law:
(i) a (b + c) == ab + ac (over addition)
(ii) a (b - c) = ab -- ac (over subtraction)
Given a problem with different operation
students will calculate according to the correct
order e.g. 5 + (12 – 4) ÷2
Review laws of indices have a class discussion
and further explanation on the board to show
the various operation to each law
e.g. commutative law 3 + 5 = 5 + 3 3 - 5 ≠ 5 - 3
3 × 5 = 5 × 3
3 ÷ 5 ≠ 5÷3
Therefore the law is only applicable for
addition and multiplication.
Use similar example with other laws
Calculating
Researching
Chart
displaying the
definition and
examples of
the various
laws
Text books
Worksheet
Exercise in text
books
GRADE 8: NUMBER: THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: BASES 2, 5, 8 TERM: ONE UNIT: FIVE DURATION: ONE WEEK
Focus Questions:
1. In what daily situation are number bases applicable?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment Demonstrate a basic
understanding of number
systems, with emphasis
on the bases 2, 5, and 8
1. Identify the place value of the digits in
bases 2,5 and 8
2. Perform simple operations in addition
and subtraction in bases 2,5 and 8
Bases 2, 5, 8 Refer to grade 7 (base 2, 5, 8)
Have students perform simple addition and
subtraction in the number bases 2. 5 and 8
e.g. 214 + 143 = 214
5 5 143
412
5
Calculating
Regrouping
Number line,
counters,
charts, flash
cards, loops.
Worksheet
Exercise in text
books
GRADE 8: NUMBER: THEORY, CONCEPTS AND OPERATIONS
UNIT TITLE: SET NOTATION TERM: ONE UNIT: SIX DURATION: ONE WEEK
Focus Questions:
1. What are some examples of universal sets in our environment?
2. What is the difference between the union and the intersection of a set?
3. What is meant by the complement of a set?
Learning
Outcomes
Specific Objectives Key
Concepts
Strategies Skills Resources Assessment
Develop
understanding of
the relationship
among groups of
objects
1. Build universal sets, given a series of subsets.
2. Identify subsets of a given universal set.
3. Use the correct symbols to represent the Universal set
(U/€)
4. Identify members and non-members of a particular
named subset in a given universal set.
5. Identify and list the members of the complement of a
set.
6. - Use correct notation for the complement of a set.
a. Use shaded region in Venn diagram to show
the complement of a set.
7. Identify the elements found in the intersection of two
sets.
8. Use the correct symbol for intersection of sets.
9. Use shaded regions in Venn diagrams to show
intersection of set.
10. Identify the elements found in the union of two sets.
11. Use correct symbol for union of sets.
12. Use shaded regions on Venn diagram to represent
union of sets.
13. Determine elements of intersection and elements of
union of set from information given on Venn diagram
Union of sets
intersection
of sets
Review work done in grade 7
Use concrete objects to simplify the meaning
of the complement of a set. E.g. the students
in the class
Subset = {boys}
Complement of this is girl
A= {grade 8}
B= {grade 8 boys}
B1= {grade 8 girls}
Have students specific area on Venn diagram
e.g. shade A ∩ B
Observing
Identifying
Computing
Chart to show the
union,
intersection and
complement of
sets
Concrete objects
Text books
Worksheet
Exercise
from text books
A B
.
14. Use Venn diagram to show union and intersection of
sets.
15. Determine the number of elements in any given finite
set.
16. Use correct notation to represent the number of
elements in a set ∩ (B) = 4 means number of elements
in set B=4.
GRADE 8: NUMBER: THEORY, CONCEPTS AND OPERATIONS UNIT TITLE: TYPES; RELATIONSHIP; SUBSETS; VENN TERM: ONE UNIT: SEVEN DURATION: TWO WEEKS
Focus Questions:
1. What is the difference between infinite and finite set?
2. What is the different joint and disjoint sets?
3. How many subsets can be obtained from any given set?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Develop
understanding of the
relationship among
groups of objects
1. Differentiate between finite and infinite
sets.
2. Use set notation to list members of
finite and infinite sets.
3. Identify sets that are joint and disjoint.
21. Give examples of sets which are
disjoint.
4. Use symbols to show that the
intersection of a disjoint set is an empty
set, 5. Set A and set B are disjoint, therefore A
∩ B = Ø or {} 6.
Finite
and infinite
sets joint and
disjoint sets
Review and consolidate work done in grade 7 Listening
Identifying
Textbooks Worksheet
Develop
understanding of the
relationship among
groups of objects
7. List subsets of sets of up to four
elements.
8. Identify patterns found in listing subsets
number of
subsets in a set Review and consolidate work done in grade 7.
Introduce then give exercise to use the formulas
for finding the number of subsets in a given set.
Calculator Chart with
formula and
example
Worksheet
of sets with up to 4 elements and these
patterns to form and test conjectures.
9. Determine the number of subsets in a
set of no more than five elements.
(Number of subsets = 2n where n =
number of elements in the set).
10. Identify proper subsets of a given set,
11. Use correct notation to represent proper
subsets.
No. of subsets = 2n where n= number of
element in asset
e.g. A = {1,3,5}
No. of subsets in A = 2n
= 2³ = 2 × 2 × 2
= 8
GRADE 8: STATISTICS & DATA HANDLING
UNIT TITLE: DATA COLLECTION & MANAGEMENT TERM: TWO UNIT: ONE DURATION: FOUR WEEKS
Focus Questions:
1. What is a pie chart
2. How useful is a pie chart to display data?
3. What do frequency table and charts/graphs tell us?
4. How useful are averages?
Learning Outcomes Specific Objectives Key
Concepts
Strategies Skills Resources Assessment
Solve problems
involving collection,
display and analysis of
data
1. Construct instruments for data gathering
2. Plan statistical investigation.
3. Use instruments to gather data.
4. Select appropriate graphic mode of presenting
data.
5. Organize data for presentation.
6. Construct appropriate graph to display
data.
7. Interpret data displayed on different types of
Pie chart
bar graph
line graph
table
Review work covered in grade 7
Introduce pie chart. Discuss.
Students collect relevant information and
construct pie chart then interpret the
information.
Students will display of the information in
other forms and compare the clarity of the
information
Students answer questions by analysing
the information displayed
Researching
Constructing
Interpreting
Analysing
Graph paper
Newspaper
Magazines
Books with
data
Chart with
examples of
graphs
Coloured
pencils
Geometry sets
Draw/interpret
Pie charts
project
oral
presentations
charts/graphs
8. Identify trends depicted on graphs/charts/tables.
Solve problems
involving collection,
display and analysis of
data
9. Construct frequency distribution tables from raw
data.
10. Interpret information in frequency distribution
tables.
11. Calculate the arithmetic mean for given sets of
data.
12. Identify the median and mode for given sets of
data.
13. Explain the relative advantage of mean, median
and mode
Frequency
Distribution;
Measures of
Central
Tendency
Average
Mean
Mode
Medium
Review and consolidate work done in
grade 7
Teacher presents raw data as a results of
students mark on a particular exercise for
explanation and practice
Students in groups will be engaged in
preparing project involving frequency
table, and measures of central tendency
using given data or what they found from
mini research
Manipulating
Calculating
Constructing
Interpreting
text books Worksheet
Exercises from
text books
project
oral
presentations
GRADE 8: GEOMETRY
UNIT TITLE: POINTS; LINE, ANGLES TERM: TWO UNIT: TWO DURATION: THREE WEEKS
Focus Questions:
1. What is meant by a perpendicular bisector?
2. What is meant by transversal?
3. What types of angles are formed when parallel lines are cut by a transversal?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Demonstrate spatial
sense and application
of geometric concepts,
properties and
relationships
1. Manipulate set squares to draw parallel
lines.
2. Construct the perpendicular bisector of a
line, using pair of compasses.
Bisecting line
Points
rays
Line segments,
lines.
Review work done in points, rays, line
segments and line in grade 7
Teach students how to use the set square to
draw parallel lines
Students will be taught to construct
perpendicular bisector to a line using a pair of
compasses
Manipulating
geometric
instruments
Constructing
Geometry sets
Coloured
pencils
Work sheet
instructing
students to
draw lines etc.
Demonstrate spatial
sense and application 3. Identify different types of related angles
formed when sets of parallel lines are cut
Transversal
Have students draw a pair of parallel lines, cut
these by a transversal. They will measure the
Observing
Drawing
Geometric
instruments
Worksheet
of geometric concepts,
properties and
relationships
by transversals
a. alternate, corresponding, vertically
opposite
b. supplemental, interior, adjacent
4. Explain the relationship between
alternate, corresponding, vertically
opposite, supplementary interior and
adjacent angles formed when a set of
parallel lines is cut by a transversal.
5. Find missing angles given various linear
relationships.
6. Identify different types of angles in the
environment.
7. Link reflex angle to acute, right angle,
obtuse and straight angles
8. Draw and measure reflex angles.
9. Construct angles of 30º, 45º, 60º, 90º,
120º
10. (Constructions should be done using
straight edges and pair of compasses
only)
Angles formed
when
(parallel) lines
are cut by a
transversal.
- Alternate
- Corresponding
etc.
- Adjacent
- Vertically
opposite
- Supplementary
- Co-interior
angles formed. Discuss the findings to relation
to the types of angles formed.
e.g. alternate angels are equal
a b
c d
d = e
d and e are
alternate angles
e f
g h
Draw students attention to the letters which we
associated with the types of angles
e.g
for alternate angles
Given a diagram, students will fined the
missing angles and give reasons for answers
60º
x
What is angle x? Give reasons
Calculating
Coloured
pencils
Exercise in text
books
GRADE 8: GEOMETRY
UNIT TITLE: CIRCLES TERM: TWO UNIT: THREE DURATION: THREE WEEKS
Focus Questions:
1. What is the relationship between radius diameter and circumference of a circle?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Demonstrate spatial
sense and application
of geometric concepts,
properties and
relationships
1. Review attributes of a circle (radius,
diameter, and circumference). Explain the
relationship between diameter and
circumference.
2. Calculate the circumference of a circle,
given its diameter or radius.
3. Calculate the radius of a circle, given the
circumference.
4. Solve problems involving circumference,
diameter and radius.
Find the
radius,
diameter and
circumference
of a circle
Have students use strings and ruler to measure
the circumference and diameter of different
round objects. Divide the circumference by the
diameter.
e.g.
Object Diameter Cir. Cir. ÷
Diameter
Coin
Plate
Milk
tin
This exercise will allow students to understand the
meaning of pi
From this exercise, the formula C = d can be
Or C = r obtained
Students will be engaged in calculating the
circumference of a circle when give the
radius or diameter and vice versa
Measuring
calculating
Manipulating
Strings
Cylindrical
objects
Rules
Worksheet with
circles to calculate
radius etc
Exercise form text
books
GRADE 8: ALGEBRA. PATTERNS & FUNCTIONS
UNIT TITLE: SYMBOLS; EQUATIONS TERM: THREE UNIT: ONE DURATION: TWO WEEKS
Focus Questions:
1. What is meant by algebra expression?
2. What is the different between an expression and an equation?
3. How is factorization helpful in algebra
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Demonstrate
knowledge of and
application of patterns
and relationship
1. Express simple verbal phrases and
statements using algebraic symbols.
2. Create simple verbal phrases and
statements to represent given algebraic
expressions or equations.
3. Simplify algebraic expressions
involving addition and subtraction
(using like and unlike terms).
4. Simplify and expand algebraic
expressions using the distributive law:
4 (e.g. x (2+y)-2x
5 2x+xy-2x=xy 5. Simplify algebraic fractions
involving multiplication and
division only. 6. X = 1
4 2
7. 5. Find the L. C.D. of simple algebraic
fractions.
8. e.g.: 4 and 2x L.C.D. = 4x
i. x 4
ii. 3 and 5x
iii. 2x 8 LC.D. = '8X
9. Factorize simple algebraic
expressions using the distributive
law.
4 e.g.: (a) 2x+6=2(x+3)
i. (b) 4x+6y+8x+9
ii. 12x + 6y + 9
iii. 3(4x + 2y + 3)
10. Substitute numbers for variables in
algebraic expressions and find numeric
value of these expressions. (Expression
should contain more than one operation
and build on work done in Grade 7). 11. Use laws of indices to simplify
Algebraic
expressions
- addition
- subtraction
- multiplication
- division
factorization
substitution
Lowest Common
Denominator
Given a statement, students will be able to
formulate algebraic expressions. E.g. a man
has x cows and y sheep. How many animals
does he have altogether?
Ans. (x + y) animals
When 5 is added to a number, the result is 1.
What is the number? X + 5 = 14
Given an algebraic expression students will
write a statement. E.g. (x – 4) marbles. A boy
had x marbles. He gave his friend 4. How
many had he left?
Use a similar situation for an equation e.g. y
– 2 = 4 students will express this in work
Given a set of algebraic terms students will
add and subtract like terms. e.g. 2a + 3b + 5a – b
2a + 5a + 3b - b
7a + 2b
Have students apply the concepts of the
distributive law to algebra
e.g. 2(3x + y)
6x + 2y
Given algebraic equations involving fractions
students will simply them. e.g. x = 1 (by cross multiplication)
= 2x = 4 (divide both sides by 2)
2x = 4
2 2
X = 2
Or x = 1
4 2 (by LDC)
X = 2 = x = 2
4
Calculating
Textbooks Worksheet
Exercise in
textbook
algebraic expressions indices. (Use multiplication, division and powers only).
12. Laws of indices: an × a
m = a
n + m 13. Example: a2
× a4 = a
2 + 4 = a
6
=
Have students factorize simple algebraic
expressions
e.g. 5a + 5b 4xy + 6 xz
= 5 (a+b) 2x (2y + 3z)
GRADE 8: MEASUREMENT
UNIT TITLE: METRIC SYSTEM; SI UNITS; LENGTH TERM: THREE UNIT: TWO DURATION: ONE WEEK
Focus Questions:
1. Why is measurement relevant for daily life?
2. What is meant by perimeter?
3. How can we utilize the perimeter in our lives?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Demonstrate an
understanding of and
application of concepts
and skills associated
with measurement using
formulas and calculators
1. Explain the need for scales in
measurement
2. and for standard units of measurement
3. Compare metric and imperial units
4. Measure and record using SI units
5. Volume
6. Mass
7. Temperature
8. time
scales
standard units
metric and
imperial units
Review and consolidate work done in grade 7
Guided discussion on the
Measuring
Recording
Thermometer
Clock
Scale
Measuring
cylinder
Worksheet
Exercise texts
Demonstrate an
understanding of and
application of concepts
and skills associated
with measurement using
formulas and calculators
9. Calibrate instruments for measuring
length
10. Make corrections for zero errors when
using defective instruments.
11. Determine perimeter of regular two-
dimensional shapes
12. Determine perimeter of composite
shapes.
13. Solve word problems involving lengths
and perimeters of 2 D shapes.
14. Convert units of length within the SI and
imperial systems.
Measuring
length
Perimeter
Conversion
tables
Take students through a series of exercises
which will show them that a line of any length
can be drawn starting at any point on the ruler
e.g. beginning at 4 (on the ruler) you line is 6
cm long. Where do you stop?
Given the length of the sides of any regular or
irregular shapes, have students find its
perimeter.
Given a word problem, students will find the
length, width or perimeter. E.g. the perimeter
of a rectangle is 44 cm. What is the length if
the width is 10 cm?
Measuring
Calculating
Comprehending
Estimating
Ruler
Charts with
2D – shapes
Textbooks
Worksheets
Observation
Quiz
GRADE 8: MEASUREMENT
UNIT TITLE: AREA TERM: THREE UNIT: THREE DURATION: ONE WEEK Focus Questions:
1. Why is area important in our everyday life?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment Demonstrate an
understanding of and
application of concepts
and skills associated
with measurement using
formulas
1. Calculate the area of common two-
dimensional shapes.
2. Construct cube using squares (cut -outs)
3. Construct cuboids using cut-outs of
squares and rectangles. d) Dissect cube to
form nets.
4. Dissect cuboids to form nets.
5. Construct cylinders using cut-outs of
rectangles and circle g) Dissect cylinders
to form nets.
6. Calculate surface area of cubes, cuboids
and cylinders by adding area component
2-D shapes.
Areas
Square unit
e.g. m²
nets
Using squared paper, have students outline
rectangles, squares, triangle having specific
perimeters. Then have students count the
squares to find the area of each shape.
Use the above activity to have students derive
the formula to find the area of
(a) rectangle
(b) squares
(c) triangles
Have students use cut-outs of squares,
rectangles, circle to construct cubes, cuboids,
and cylinders. Students will also construct the
above solids from given nets.
Discuss meaning of surface area. Using
examples of cuboids in the class e.g. a box, a
students use previous knowledge to find the
area of each sides then add to find the surface
area.
Calculating
Constructing
Measuring
Squared paper
Ruler
Cut-out and/or
nets of shapes
Solids
Worksheet
Observation
Textbook
exercises
GRADE 8: MEASUREMENT
Unit Title: Volume TIME; TEMP.; MASS Term: THREE Unit: FIVE Duration: TWO WEEKS
Focus Questions:
1. 1. What is the relationship between volume and capacity?
2. Why do you think it is important to know time?
3. How can we tell how hot or cold something is?
4. What is meant by mass?
Learning
Outcomes
Specific Objectives Key
Concepts
Strategies Skills Resources Assessment
Demonstrate an
understanding of
and application of
concepts and skills
associated with
measurement
using formulas
1. Differentiate between volume and capacity
2. Recognize the relationship between volume
and capacity.
3. Calculate volume of regular solids -cubes,
cuboids and Cylinders
4. Measure volume of irregular solids.
5. Solve problems involving volume of regular
and irregular
Volume
unit used:
cm³
Capacity
unit used
e.g. litre
Use a square container with a liquid. E.g. water. Discuss to
help students to understand the difference between volume
and capacity.
Given the length, width and height of e.g. a cuboids, have
students calculate its volume
Teacher can demonstrate to students the process used to find
the volume of irregular solids
Measuring
Calculating
Containers
Measuring
cylinders
Irregular
solids
Water
String
Observation
worksheets
Demonstrate an
understanding of
and application of
concepts and skills
associated with
measurement
using formulas
6. Use stop-watch to time various events.
7. Convert intervals in days to months, months to
years etc.
8. Solve problems involving distance, time and
speed
9. Convert units of temperature from Cº to ºF and
vice versa.
10. b) Solve problems involving temperature
changes.
11. Estimate mass in SI and imperial units.
12. Convert units of mass within the SI and
imperial system (large to small and vice versa)
13. Pose/construct problems involving mass.
14. Solve problems involving mass.
Time
Temperat
ure
Mass
Have students use stop-watch to time any event e.g. running
Create situations to show the relationship between days,
weeks, months and years and have students convert from on
to the other
Provide students with the appropriate information then have
them calculate the distance, speed or time. E.g. A bus
traveled at an average speed of 48 km/h for 5 hours. What
distance did the bus travel?
D = ST
= 48km × 5
= 240km
Use similar problems to calculate speed and or time
Given a Celsius/Fahrenheit scale, have students compare
different temperature. E.g. 30ºC = 86Fº. Follow this exercise,
teacher can provide the formula and have students convert form
one temperature to the next. Visa versa
Converting
Calculating
Comparing
Stop-watch
Calendar
Worksheet
Quiz
Observation
Chart with
Celsius scale
and
Fahrenheit
Scale
Thermometer
GRADE 8: CONSUMER ARITHMETIC
UNIT TITLE: PROFIT/LOSS, DISCOUNT TERM: THREE UNIT: SEVEN DURATION: ONE WEEK
Focus Questions:
1. How much money can be gained or lost on sale of goods or services?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Create and solve
problems involving
common currencies /
money and
percentages
1. Calculate the profit/loss on a transaction
as an amount of money or as a percent
2. Calculate the selling price of an article,
given the cost price and the profit/loss,
as an amount of money or a percent
3. Calculate the cost price of an article,
given the selling price and profit/loss as
an amount of money
Profit;
Loss
Selling price
Cost price
Let students use the articles in advertisements
to identify terms related to profit and loss
Students can use the information generate in
the articles to generate meanings for the terms.
Help students to refine the meanings form a
mathematical perspective
Let students use the information in the articles
to develop problems related to the profit and
loss. Have them solve the problems.
Ensure that students develop an understanding
of profit that is greater than 100%. Let them,
for examples; explore the prices of items in
boutiques.
Exercises:
Cost Price Selling
Price
Profit % Loss %
Project: Example: present with a situation
where they are to run a school booth selling a
food item that they must prepare. Let them do
the necessary research related to cost of
ingredients, quantities to be prepared. Ask them
to determine the minimum unit price that would
allow them to make a profit.
Calculating Newspaper
advertisements
Flyers
Simple
business
reports
Worksheet:
completing
tables to show
cost price;
selling price;
profit %; loss %
Exercise in
textbooks
Project
Create and solve
problems involving
common currencies /
money and
percentages
4. Use appropriate terms to describe
transactions involving discounts
5. Calculate the value of a discount as (a)
an amount of money; (b) a percent of a
marked price
6. Calculate the sale/discount price of an
article given the marked price and the
discount as (a) an amount of money; (b)
Discount
Discount price
Marked price
Sales price
Selling price
Let students use the articles in advertisements
to identify terms related to profit and loss
Ensure students develop meanings for the terms
by analyzing several advertisements.
Discount- the amount you subtract from the
marked price of an articles or from a bill
Marked Price- The price at which an articles is
to be sold
Calculating Advertisements
in the form of
flyers,
newspaper
inserts, radio
and TV
advertisements.
Worksheet
Exercise in
textbooks
a percent of a marked price
7. Calculate the marked price of an article
given the sales/discount price and the
discount as an amount of money
Discount Price- The price at which an articles is
sold after a discount has been taken off.
Sale Price is the same as discount price.
Let students identify situations in which
discounts may be given. Let them use these
situations to develop problems for the class to
solve
GRADE 8: CONSUMER ARITHMETIC
UNIT TITLE: CURRENCY/WAGES/SALARIES, BILLS TERM: THREE UNIT: EIGHT DURATION: ? WEEK
Focus Questions:
1. What is the currency exchange internationally?
2. How much do workers make?
3. How much is spent?
Learning Outcomes Specific Objectives Key Concepts Strategies Skills Resources Assessment
Create and solve
problems involving
common currencies /
money and
percentages
1. Read and interpret exchange rates
2. Convert from home currency to foreign
currency and vice versa
3. Use appropriate terms to describe
situations related to payment for
employment
4. Calculate the following:
5. Basic wages
6. Overtime wages
7. Total wages/salaries for a given period
of time
8. Hourly/weekly rates
Wage
Salary
Basic wage
Hourly wage
Hourly rate
Overtime
Time and a
half double
time
Let student’s collect/idnetify examples of goods
that are priced in the home currency.
Let them use the banks’ exchange rate to convert
the foreign currency to the home or visa versa.
Have them compare the quantities. In cases where
there is a discrepancy, explain that this probably
results from duties/taxes which have been added
on for payment by residents.
Problems can focus on travel situations and the
cost of items. Examples Mrs. John purchases
travelers’ cheques in the amount of US$110. The
exchange rate was EC $1 = US$40. How much
did she pay in EC$ for the travelers cheques. She
traveled to the USA and on her return had US$15
left. Calculate the EC$ equivalent for the
remainder.
Encourage students to use the unitary methods to
carry out conversions.
E.g.
US $0.40 = EC $1.00
US $1.00= $1.00
0.40
US $110 = $1.00 x 100
0.40 1
Let students carry out a survey among family
members or various companies to determine the
ways in employees are paid and the various
salaries/wages
Let students discuss their findings. Use the
discussion to develop meaning for the relevant
vocabulary.
Present students with the payment schemes for
Calculating
Copies of banks
exchange rates.
Exchange rates
listed in
newspapers
Worksheet
Exercise in
textbooks
two or more companies. Have them determine for
which company they would like to work.
Create and solve
problems involving
common currencies /
money and
percentages
9. Use vocabulary associated with bills
10. Calculate the following:
11. Total cost of items
12. Sales tax and service charge
13. Discount to be deducted from bills,
given the discount as a percent
14. Unit cost of items
Total cost
Unit cost
Sales tax
Service charge
Let students collect and mount classroom display
of a variety of bills
Guide students to identify the various
costs/charges on the bills. Let students label the
parts of the bills.
Have students analyse the bills to determine how
the various costs/charges are calculated. Let them
make a summary of their discoveries.
Let students make up bills of their own based on
family experiences and use these bills to generate