Fiza
Class 1–7 Mathematics Foundation → Class 8 Readiness
Why This Programme?
Fiza has entered Class 8 but requires substantial strengthening of the mathematical concepts normally developed from Classes 1–7. Therefore, the immediate objective is not to rush through the Class 8 syllabus.
The objective is to identify and repair the missing mathematical skills systematically so that she can eventually understand and solve Class 8 Mathematics independently.
Number Sense → Four Operations → Division → Fractions → Decimals → Integers → Ratio → Algebra → Geometry → Class 8
Do Not Teach Seven Classes as Seven Separate Years
Fiza does not need to mechanically complete every textbook from Class 1 to Class 7. The programme focuses on the prerequisite skills that are necessary for later Mathematics.
Weeks 1–2 — Rebuild the Number Foundation
- Counting and number recognition
- Number names
- Before, after and between numbers
- Greater than, less than and equal to
- Ascending and descending order
- Odd and even numbers
- Ones and tens
- Addition within 100
- Subtraction within 100
- Hundreds, tens and ones
- Numbers up to 1,000
- Expanded form
- Addition with carrying
- Subtraction with borrowing
- Repeated addition
- Introduction to multiplication
- Tables 2–5
- Division as equal sharing
Weeks 3–4 — Multiplication & Division
- Tables 2–10
- Random table recall
- Multiplication facts
- 2-digit × 1-digit
- 3-digit × 1-digit
- Vertical multiplication
- Multiplication word problems
- Division as sharing
- Division as grouping
- Relationship between multiplication and division
- 2-digit ÷ 1-digit
- 3-digit ÷ 1-digit
- Division with remainders
- Dividend, divisor, quotient and remainder
- Introduction to long division
Weeks 5–6 — Strong Written Arithmetic
- Numbers up to 10,000
- Place value
- Expanded and standard form
- Addition
- Subtraction
- Multiplication
- Division
- Estimation
- Multi-step word problems
- Meaning of a fraction
- Numerator and denominator
- Proper and improper fractions
- Equivalent fractions
- Like fractions
- Comparing fractions
- Addition of like fractions
- Subtraction of like fractions
Weeks 7–9 — Fractions, Decimals & Factors
- Tenths
- Hundredths
- Decimal place value
- Comparing decimals
- Ordering decimals
- Addition and subtraction of decimals
- Multiplication involving simple decimals
- Simplest form
- Equivalent fractions
- Unlike fractions
- Addition of unlike fractions
- Subtraction of unlike fractions
- Multiplication of fractions
- Simple division of fractions
- Factors
- Multiples
- Prime numbers
- Composite numbers
- Divisibility rules
- HCF
- LCM
Weeks 10–12 — Integers, Ratio & Algebra
- Positive numbers
- Negative numbers
- Number line
- Comparing integers
- Addition of integers
- Subtraction of integers
- Multiplication of integers
- Division of integers
- Meaning of ratio
- Writing ratios
- Equivalent ratios
- Proportion
- Unitary method
- Percentage
- Basic percentage problems
- Variables
- Constants
- Terms
- Coefficients
- Algebraic expressions
- Missing-number equations
- Simple equations
- Substitution
Weeks 13–15 — Class 7 Foundation
- Fractions as rational numbers
- Positive and negative rational numbers
- Comparison
- Addition
- Subtraction
- Multiplication
- Division
- Terms and coefficients
- Like and unlike terms
- Addition of algebraic expressions
- Subtraction of algebraic expressions
- Simple equations
- Word problems involving equations
- Lines and angles
- Types of angles
- Triangles
- Quadrilaterals
- Basic properties of shapes
- Perimeter
- Area
Week 16 — Diagnostic Assessment & Repair
The final week should not simply be another chapter. It should identify which skills have become secure and which still require targeted teaching.
- Number sense test
- Addition and subtraction test
- Multiplication test
- Division and long-division test
- Fractions test
- Decimals test
- Integers test
- Ratio and percentage test
- Algebra test
- Geometry and mensuration test
- Mixed Class 7 readiness test
Fiza’s Daily Mathematics Routine
A consistent routine is more important than completing a large number of questions in one sitting.
Division & Long Division
Division should receive additional attention in Fiza’s programme. She should not merely memorise the long-division procedure. She should understand the relationship between multiplication and division.
Equal Sharing → Equal Groups → Division Facts → 2-digit Division → 3-digit Division → Remainders → Long Division → Word Problems → Checking Answers
When Should Fiza Move to the Next Level?
| Performance | Decision |
|---|---|
| 80–100% | Skill is sufficiently secure. Move forward. |
| 60–79% | Continue with revision and additional practice. |
| Below 60% | Return to the prerequisite skill and reteach. |
Fiza’s Error Log
Every repeated mistake should be recorded rather than simply marked wrong. This will help identify the actual learning gap.
- Question number
- Type of mistake
- Why the mistake occurred
- Correct method
- Date of reattempt
- Whether the student solved it independently
Bridge to Class 8 Mathematics
After the foundation programme, Fiza should gradually begin Class 8 Mathematics alongside targeted revision of any remaining weak prerequisite skills.
✓ Comfortable with four basic operations
✓ Tables sufficiently fluent
✓ Can perform long division
✓ Understands fractions
✓ Can work with decimals
✓ Understands integers
✓ Can solve basic ratio and percentage questions
✓ Can simplify basic expressions
✓ Can solve simple equations
✓ Understands basic geometry and mensuration
Measure Progress by Skills, Not by Class Labels
Fiza should never be made to feel that she is being “sent back” to Class 1. This is a Mathematics Foundation & Skill-Building Programme.
The objective is to close learning gaps, build confidence and gradually bring her to the level where she can participate meaningfully in Class 8 Mathematics.