First Term Scheme of Work
Scheme of Work Overview
The first term of JSS 3 Mathematics strengthens algebra, set theory, proportional reasoning, and graphs. These lessons prepare students for senior secondary mathematics and examination-style thinking.
How to use this page: read each topic carefully, study the examples, answer the brain tests, and then attempt the full-term CBT quiz.
JSS 3 Mathematics First Term Scheme of Work
| Week | Topic | Core Content |
|---|
| 1 | Sets and Set Notation | Definition of sets, elements, roster form, set-builder notation. |
| 2 | Venn Diagrams | Union, intersection, complement and set problems. |
| 3 | Indices and Standard Form | Meaning of indices, laws of indices, standard form. |
| 4 | Algebraic Expressions | Terms, coefficients, simplifying expressions and substitution. |
| 5 | Linear Equations | Solving one-step and two-step equations. |
| 6 | Variation | Direct variation and inverse variation. |
| 7 | Graphs and Coordinates | Plotting points, reading graphs and straight line ideas. |
| 8 | Statistics and Data Interpretation | Mean, median, mode, range and presentation of data. |
| 9 | Revision | General revision and practice. |
| 10 | Examination | First-term assessment. |
Topic 1
Sets and Set Notation
A set is a well-defined collection of objects or elements. Set notation helps us list elements clearly, describe membership, and compare groups of items in mathematics.
Element
An object inside a set.
Roster form
Elements are listed inside braces.
Set-builder form
Describes the rule used to form the set.
Worked examples
Example 1
Question: Write the set of first three natural numbers.
Step 1: Natural numbers start from 1.
Step 2: The first three are 1, 2 and 3.
Step 3: Answer: {1, 2, 3}.
Example 2
Question: State whether 5 is an element of {2, 4, 5, 7}.
Step 1: Check the listed elements.
Step 2: 5 appears in the set.
Step 3: Answer: yes, 5 ∈ {2, 4, 5, 7}.
Example 3
Question: Write the set of even numbers less than 8.
Step 1: List even numbers below 8.
Step 2: They are 2, 4 and 6.
Step 3: Answer: {2, 4, 6}.
Example 4
Question: Describe the set {x : x is a vowel in the word MATHEMATICS}.
Step 1: Identify vowels in the word.
Step 2: The vowels are A and I.
Step 3: Answer: {A, I}.
Example 5
Question: What is the empty set?
Step 1: Think of a set with no elements.
Step 2: It is written as ∅ or {}.
Step 3: Answer: the empty set.
Example 6
Question: Write the set of letters in the word SUN.
Step 1: Identify the letters one by one.
Step 2: They are S, U and N.
Step 3: Answer: {S, U, N}.
Quick Brain Tests
1. A set with no elements?
Empty set.
2. Symbol for membership?
∈
3. Roster form uses what symbols?
Braces { }.
4. First three natural numbers?
{1, 2, 3}.
5. Set of vowels in A, E, I, O, U?
{A, E, I, O, U}.
Topic 2
Venn Diagrams
Venn diagrams show the relationship between sets using circles inside a rectangle. They help students understand union, intersection, complement and set counting problems.
Union
All elements in both sets.
Intersection
Common elements.
Complement
Elements not in the set.
Worked examples
Example 1
Question: A = {1, 2, 3}, B = {3, 4, 5}. Find A ∩ B.
Step 1: Find common elements.
Step 2: The common element is 3.
Step 3: Answer: {3}.
Example 2
Question: A = {1, 2, 3}, B = {3, 4, 5}. Find A ∪ B.
Step 1: Combine all distinct elements.
Step 2: Write 1, 2, 3, 4, 5.
Step 3: Answer: {1, 2, 3, 4, 5}.
Example 3
Question: If U = {1,2,3,4,5,6} and A = {2,4,6}, find A'.
Step 1: List all elements in U not in A.
Step 2: They are 1, 3 and 5.
Step 3: Answer: {1, 3, 5}.
Example 4
Question: If A has 3 elements and B has 4 elements, what does a Venn diagram help show?
Step 1: Compare the two sets visually.
Step 2: See common and separate elements.
Step 3: Answer: the relationship between the sets.
Example 5
Question: A = {2, 4, 6, 8} and B = {1, 2, 3, 4}. Find common elements.
Step 1: Compare both sets.
Step 2: Common numbers are 2 and 4.
Step 3: Answer: {2, 4}.
Example 6
Question: What does the universal set contain?
Step 1: Think of all elements under discussion.
Step 2: It is the complete collection for the problem.
Step 3: Answer: all elements in the context.
Quick Brain Tests
1. Common elements in two sets?
Intersection.
2. All elements from both sets?
Union.
3. Symbol for intersection?
∩
4. Symbol for union?
∪
5. A rectangle in Venn diagram represents?
Universal set.
Topic 4
Algebraic Expressions
Algebraic expressions are combinations of numbers, letters and operations without an equal sign. They are used to represent relationships and to simplify mathematical statements.
Term
A part of an expression separated by + or −.
Coefficient
The number multiplying a variable.
Like terms
Terms with the same variables and powers.
Worked examples
Example 1
Question: Simplify 3x + 2x.
Step 1: Add the coefficients.
Step 2: 3 + 2 = 5.
Step 3: Answer: 5x.
Example 2
Question: Simplify 4a + 3b + 2a.
Step 1: Group like terms 4a and 2a.
Step 2: 4a + 2a = 6a.
Step 3: Answer: 6a + 3b.
Example 3
Question: Simplify 2y + 7y - 5y.
Step 1: Add and subtract coefficients.
Step 2: 2 + 7 - 5 = 4.
Step 3: Answer: 4y.
Example 4
Question: Simplify 5m + 2m + m.
Step 1: Write m as 1m.
Step 2: 5 + 2 + 1 = 8.
Step 3: Answer: 8m.
Example 5
Question: Expand 2(x + 5).
Step 1: Multiply 2 by x.
Step 2: Multiply 2 by 5.
Step 3: Answer: 2x + 10.
Example 6
Question: Expand 3(t - 4).
Step 1: Multiply 3 by t.
Step 2: Multiply 3 by -4.
Step 3: Answer: 3t - 12.
Quick Brain Tests
1. Like term of 4x?
2x, 3x, 5x etc.
2. 2a + 3a?
5a.
3. Expand 4(x + 1)?
4x + 4.
4. Expand 5(a - 2)?
5a - 10.
5. Coefficient of x in 7x?
7.
Topic 5
Linear Equations
Linear equations are equations in which the highest power of the variable is one. They can be solved by using inverse operations to isolate the variable.
One-step
One operation is needed.
Two-step
Two operations are needed.
Check
Substitute the answer to verify it.
Worked examples
Example 1
Question: x + 5 = 12
Step 1: Subtract 5 from both sides.
Step 2: x = 12 - 5.
Step 3: x = 7.
Example 2
Question: y - 4 = 9
Step 1: Add 4 to both sides.
Step 2: y = 9 + 4.
Step 3: y = 13.
Example 3
Question: 3n = 21
Step 1: Divide both sides by 3.
Step 2: n = 21 ÷ 3.
Step 3: n = 7.
Example 4
Question: a / 5 = 6
Step 1: Multiply both sides by 5.
Step 2: a = 6 × 5.
Step 3: a = 30.
Example 5
Question: 2x = 18
Step 1: Divide both sides by 2.
Step 2: x = 18 ÷ 2.
Step 3: x = 9.
Example 6
Question: m + 8 = 20
Step 1: Subtract 8 from both sides.
Step 2: m = 20 - 8.
Step 3: m = 12.
Quick Brain Tests
1. x + 3 = 10, x?
7.
2. 5p = 35, p?
7.
3. y - 6 = 2, y?
8.
4. 4a = 28, a?
7.
5. n / 4 = 5, n?
20.
Topic 6
Variation
Variation describes how one quantity changes with another. Direct variation means they increase or decrease together, while inverse variation means one increases as the other decreases.
Direct variation
y is proportional to x.
Inverse variation
y varies as 1/x.
Constant
A fixed value that links the quantities.
Worked examples
Example 1
Question: If y varies directly as x and y = 6 when x = 2, find the constant.
Step 1: Use y = kx.
Step 2: 6 = 2k.
Step 3: k = 3.
Example 2
Question: If y = 15 when x = 5, find y when x = 8.
Step 1: Find k: 15 = 5k, so k = 3.
Step 2: Use y = 3x.
Step 3: y = 3 × 8 = 24.
Example 3
Question: If y varies inversely as x and y = 4 when x = 3, find the constant.
Step 1: Use y = k/x.
Step 2: 4 = k/3.
Step 3: k = 12.
Example 4
Question: If y = 12 when x = 4, what is y when x = 6 in direct variation?
Step 1: Find k: 12 = 4k, so k = 3.
Step 2: y = 3x.
Step 3: y = 18.
Example 5
Question: If y = 10 when x = 2 in inverse variation, find y when x = 5.
Step 1: Find k: 10 = k/2, so k = 20.
Step 2: y = 20/5.
Step 3: y = 4.
Example 6
Question: State whether p varies directly or inversely with q if p = kq.
Step 1: Compare with the formulas.
Step 2: p = kq matches direct variation.
Step 3: Answer: direct variation.
Quick Brain Tests
1. y = kx means?
Direct variation.
2. y = k/x means?
Inverse variation.
3. If x increases and y increases together?
Direct variation.
4. If x increases and y decreases?
Inverse variation.
5. Constant is?
A fixed value linking variables.
Topic 7
Graphs and Coordinates
Graphs and coordinates help us display and locate information on a plane. This topic prepares students to interpret data visually and understand simple patterns in mathematics.
Ordered pair
Coordinates written as (x, y).
Worked examples
Example 1
Question: What are coordinates?
Step 1: They are numbers used to locate a point.
Step 2: They are written as (x, y).
Step 3: Answer: ordered pair values.
Example 2
Question: What point is 3 units right and 2 units up?
Step 1: Right means x = 3.
Step 2: Up means y = 2.
Step 3: Answer: (3, 2).
Example 3
Question: What is the x-axis?
Step 1: Think of the horizontal line.
Step 2: It is the x-axis.
Step 3: Answer: horizontal axis.
Example 4
Question: What is the y-axis?
Step 1: Think of the vertical line.
Step 2: It is the y-axis.
Step 3: Answer: vertical axis.
Example 5
Question: Plot the point (4, 1).
Step 1: Move 4 units on x-axis.
Step 2: Move 1 unit up.
Step 3: Point is (4, 1).
Example 6
Question: What point lies 2 units left and 3 units down?
Step 1: Left means negative x.
Step 2: Down means negative y.
Step 3: Answer: (-2, -3).
Quick Brain Tests
1. Horizontal axis?
x-axis.
2. Vertical axis?
y-axis.
3. Coordinates format?
(x, y).
4. Point 2 right and 1 up?
(2, 1).
5. Graphs help show?
Data visually.
Topic 8
Statistics and Data Interpretation
Statistics is the study of data collection, organization, presentation and interpretation. It helps students understand patterns, compare quantities and make informed conclusions.
Mean
Add all values and divide by the number of values.
Median
The middle value when data is arranged.
Mode
The most frequent value.
Worked examples
Example 1
Question: Find the mode of 2, 3, 3, 4, 5.
Step 1: Count repeats.
Step 2: 3 appears most often.
Step 3: Answer: 3.
Example 2
Question: Find the median of 2, 4, 6, 8, 10.
Step 1: Arrange in order.
Step 2: Identify the middle value.
Step 3: Answer: 6.
Example 3
Question: Find the mean of 2, 4, 6.
Step 1: Add the numbers: 2 + 4 + 6 = 12.
Step 2: Divide by 3.
Step 3: Answer: 4.
Example 4
Question: Find the range of 2, 5, 7, 10.
Step 1: Find the highest value: 10.
Step 2: Find the lowest value: 2.
Step 3: Range = 10 - 2 = 8.
Example 5
Question: Why do we use tables?
Step 1: Tables arrange data neatly.
Step 2: They make comparison easy.
Step 3: Answer: to present data clearly.
Example 6
Question: Name one method of collecting data.
Step 1: Recall common methods.
Step 2: Questionnaire is one method.
Step 3: Answer: questionnaire.
Quick Brain Tests
1. Most frequent value?
Mode.
2. Middle value?
Median.
3. Average value?
Mean.
4. Highest minus lowest is?
Range.
5. Data collection tool?
Questionnaire.
External Resources
Recommended learning links
These links support wider learning and improve discoverability around the topic.
CuemathExtra problem-solving support.
DesmosVisual math exploration.
CBT Practice Test
30 questions | Timed quiz | Corrections appear after submission.
20:00
The email button opens a draft to edwinogielibrary@gmail.com so the score can be sent quickly after submission.
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