Square the Five

What This Drill Trains

Numbers ending in 5 square to a pattern you can trust: the ending is always 25, and the front comes from multiplying the leading digit by the next integer. Learning this removes a whole family of problems from “hard” to “instant,” which frees attention for messier squares later.

How to Think During the Round

For a number like 75: take the tens digit 7, multiply by (7+1)=8 to get 56, then append 25 → 5625. Same rule for 15, 25, 35, …, 95. Remember why it works briefly: (10a + 5)² = 100a(a+1) + 25 — that is exactly “a(a+1) followed by 25.”

You have 60 seconds. Accuracy still outranks raw speed: one calm method repeated well beats a streak of guesses. After the timer ends, notice which problems felt sticky — that short review is where real improvement happens.

Worked Examples

Study these before you press Start. Try to recreate the thinking without looking at the answer first.

Common Mistakes

• Multiplying the leading digit by itself instead of by (digit + 1).
• Appending 5 or 15 instead of 25.
• Applying the rule to numbers that do not end in 5.

Practice Tips

• Memorize the chant: “times next, then twenty-five.”
• Check 15²=225 and 45²=2025 once before a timed round to prime the pattern.
• After mastery, move to approximate square roots for the reverse skill.

Suggested Session Plan

1. Read the method section once if this skill is new.
2. Cover the answers and re-solve the three worked examples aloud.
3. Start the timed round and stick to one strategy.
4. Replay once, then write down any fact or pattern you missed.
5. If the same error repeats, open the full lesson for more examples and a practice set with an answer key.

Full explanation, extra worked examples, and practice problems for this skill: open the related stage lesson .

Prefer a structured curriculum instead of random drills? Browse all learning stages or read the complete mental arithmetic guide . More timed drills live on the games hub.