Math (Multi-Digit Operations & Word Problems) Syllabus

Granular syllabus for multi-digit addition, subtraction, multiplication, division, and word problems for Noorani Level 3.

Learning Objectives

By the end of this component, the student should be able to:

Add and subtract 2- and 3-digit numbers with and without regrouping (carrying/borrowing).
Multiply 1- and 2-digit numbers (tables 1–10 and simple 2-digit by 1-digit).
Divide 2-digit numbers by 1-digit (no remainder, then with remainder); understand quotient and remainder.
Solve one- and two-step word problems using the four operations and check reasonableness of answers.

Syllabus Structure (Phases 1–4)

This syllabus builds on Level 2 Math (1–100, place value, basic operations). It extends to larger numbers, all four operations, and structured word-problem solving.

Phase 1: Multi-Digit Addition & Subtraction (With Regrouping)

Consolidate place value and introduce carrying (addition) and borrowing (subtraction) for 2- and 3-digit numbers.

Addition: 2-digit + 2-digit, then 3-digit + 2-digit and 3-digit + 3-digit; align by place value; carry to tens/hundreds.
Subtraction: 2-digit − 2-digit, then 3-digit − 2-digit and 3-digit − 3-digit; borrow from tens/hundreds when needed.
Use base-10 blocks or place-value charts initially; then standard vertical algorithm only.
Mastery: student correctly solves 5 out of 6 problems (2- and 3-digit add/sub) with regrouping, showing work.

Phase 2: Multiplication (Tables & 2-Digit × 1-Digit)

Memorize multiplication tables 1–10 and apply to 2-digit × 1-digit (including regrouping).

Tables: daily drill (orally and written) for 2–5, then 6–10; mixed practice; timed quizzes once per week.
Meaning: "3 × 4 means 3 groups of 4"; use arrays or repeated addition to reinforce.
2-digit × 1-digit: e.g., 24 × 3, 17 × 5; multiply ones first, then tens; carry if product ≥ 10.
Mastery: student knows tables 1–10 and correctly computes 4 out of 5 problems like 34 × 2, 19 × 4.

Phase 3: Division (2-Digit ÷ 1-Digit, Quotient & Remainder)

Divide 2-digit numbers by 1-digit; interpret remainder and check using multiplication.

Division as sharing or grouping: 12 ÷ 3 = 4; link to multiplication (3 × 4 = 12).
2-digit ÷ 1-digit, no remainder: e.g., 36 ÷ 3, 48 ÷ 4; use long-division format (or short division) with clear steps.
With remainder: e.g., 17 ÷ 5 = 3 R 2; meaning of remainder ("2 left over"); when remainder is zero vs not.
Check: quotient × divisor + remainder = dividend.
Mastery: student correctly solves 4 out of 5 divisions (with and without remainder) and checks one problem.

Phase 4: Word Problems (One- and Two-Step, All Operations)

Read a short scenario, identify the operation(s), set up number sentence(s), solve, and state the answer in context.

One-step: addition (total), subtraction (difference, left over), multiplication (total in equal groups), division (share equally, how many each).
Two-step: e.g., "Buy 3 pens at 5 taka each, then pay 20 taka; how much change?" — multiply then subtract.
Key words and phrases: total, left, how many more, each, per, share, altogether — but always check the situation, not just keywords.
Write number sentence(s); solve; write answer with unit (e.g., 12 taka, 4 pens); check if the answer is reasonable.
Mastery: student solves 2 one-step and 1 two-step word problem correctly (correct operation and answer with unit) in a short assessment.

Recommended Daily Time Allocation

For the Math (multi-digit operations, word problems) block (around 35–40 minutes) in Noorani Level 3:

5–8 minutes: mental math or table drill (addition/subtraction facts or multiplication tables).
12–15 minutes: main lesson — one operation (e.g., 3-digit subtraction with borrowing) or mixed practice; model then guided then independent.
10–12 minutes: word problems — read together, identify operation(s), solve 1–2 problems as class, then 1–2 individually.
5–8 minutes: correct work, discuss errors, and assign 4–6 practice sums or 1–2 word problems for next day.