A paper number line can be the whole playing field for two people. NRICH’s Strike It Out supplies the published competitive game used here. Our proposed hosting arrangement adds a separate equation record and a practice fragment, without claiming a winning strategy, a completed play session or a learning outcome.

Prepare one line and one shared record

Write the integers from 0 through 20 once, in order, along a line with enough space to cross a number or circle it clearly. Put a second blank sheet beside it for equations. Choose pencils suited to the surface and participants. A printed commercial worksheet or special scoring board is unnecessary.

Agree which player begins and who writes each equation. The shared record is an organizational proposal: it documents calculations without changing which moves are legal. Keep drinks and unrelated notes away from the playing sheet so a crossed mark cannot easily be mistaken for a casual pen stroke.

Explain what the next player inherits

Under NRICH’s rules, the first player crosses two numbers and circles their sum or difference. The next player must cross the previously circled number and another unused number, then circle the new result. Numbers remain within the 0–20 line. Crossed numbers cannot be reused; the circled result is available specifically as the next turn’s required starting number. A player unable to make a legal calculation loses.

The circled number therefore has a different job from a crossed number. Do not mark every number involved with the same symbol. The arithmetic result needs to be an available number, rather than a number already crossed out. Addition and subtraction are the operations used here; multiplication or a rule requiring alternating operations would change this chosen version.

Try a fragment before making the real board

On a separate practice line, show 3 + 5 = 8: cross 3 and 5, then circle 8. Next, 8 + 4 = 12 crosses the carried 8 and unused 4, leaving 12 circled. Then 12 − 2 = 10 crosses 12 and 2 and circles 10. These three calculations illustrate continuation only; they are not a complete game or a recommended opening.

Point to the marks after each calculation and check them against the written equation. When the players understand that correspondence, set the practice sheet aside and begin on an untouched line. Leaving the example marks on the real line would remove choices before the first actual player had a turn.

Let the stopping rule end the session

During play, keep the equation record beside the current line and take turns making the required move. When a player cannot make a legal calculation, the published competitive result settles that game. Do not replace it with a cooperative target, a reward for the largest number or a speed score. Those would require a different agreement.

A second game can begin on a fresh line so previous marks do not carry over. Before buying a reusable number board, ask whether the existing paper record already makes turns legible. A wipe-clean version would need suitable pens and its own care directions. This arrangement promises neither improved arithmetic nor a certain duration; it offers a complete, consistently marked game with a clear ending.

Sources & further reading

Published sources for the details and examples discussed in this story.