Number patterns near squares — Tables & Multiplication Mastery

How it works

Middle square — “(a − d) × (a + d) = a² − d²”

1. Find the middle number (20 for 19 × 21) and the distance from it (1).
2. Square the middle number.
3. Take away the distance squared.

Use it for: Pairs like 29 × 31, 47 × 53, 97 × 103 — the pattern 3 × 5 = 15 = 4 × 4 − 1 works for every square.

Worked example: 48 × 52 = 2496

✏️ Practice

Work it out in your head or on paper, then tap your answer — or type it and press Check. Stuck? Press “Show me how”.

🏁 Lesson 18 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 💎 Square Spotter badge when you pass — and a certificate when you finish all 9 lessons of Module 3 · Multiplication strategies. You can still take the test without signing in.

🖨️ Multiplication Near Squares Worksheet

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)