All Activities U Anywhere Nim

# Anywhere Nim

Take turns counting up by 1 or 2. Whoever says "10" wins!

Ages: 3+
Players: 2+
Time: Under 10 Minutes
Type: number games
Location: Play Anywhere
Ages: 3+
Players: 2+
Time: Under 10 Minutes
Type: number games
Location: Play Anywhere

## Instructions

Waiting in line together? Driving? Cleaning together or picking up toys? This simple game works anywhere and can be modified for any age group or ability level.

Players take turns counting up from 1. On a turn, a player can say either 1 or 2 numbers. The player who says the target number of 10 wins the game.

For example, a game might play out like this:

Player A said 10, so they win the game!

There are many ways to change the rules of the games in order to practice different math skills. Players could skip-count, count to a higher target number, subtract instead of adding, or mix any of these. See Variations below for some specific ideas.

Anywhere Nim is a variation of the classic math game Nim (and so are other BA Playground activities, including Odd Knights as well as Bumper Cars).

Don't forget: it's Beast Academy Playground, not Beast Academy Study Hall. Change the rules, be silly, make mistakes, and try again. The Variations and Learning Notes are here for you if you want to dive deeper, but not all of them apply to learners of every age. The most important thing is to have fun.

## Variations d

### Different Rules:

• Start at 10 and count down to a target number of 0.
• Skip-count by 10s, with a target number of 100.
• Let players count up as many as 4 numbers on a turn, with a target number of 50.
• Choose two numbers randomly (e.g. by rolling dice, or using the players' ages, or picking two numbers from the license plate on the car in front of you) and allow players to choose which of the two numbers to add on a turn. Adjust the target number up appropriately to, say, 50. It may not be possible to reach the target number exactly, so a player can win by reaching or surpassing the target number.

### More Players:

Any of these versions can also be played with more players. Take turns. The player who says the target number wins.

## Classroom Tips d

Practice counting and strategy with Anywhere Nim, a quick game that's great for transitions in class, or waiting in line for lunch, or anywhere! Incorporate addition and subtraction by "adding" 1 or 2 (or more) rather than "counting up" (or "subtracting" rather than "counting down").

Discussion Questions

• At what point do you know who will win?
• What number or numbers let you know who can win?
• How would the game change if you counted by different numbers?
• How would the game change with a different target number?
• What variations can you think of?

• Level 2, Chapter 8: Strategies (+ & -)
• Level 3, Chapter 2: Skip-Counting (See Variations)
• Level 3, Chapter 8: Division (students learn Nim in this chapter)

See Variations and Learning Notes for more ideas on how to adapt this activity and incorporate it into your classroom.

## Learning Notes d

### Strategic Thinking:

After playing several rounds, see if young players notice at which point they know who will win. In the example above, Player B loses by saying 8 (since Player A is then able to say 9, 10), but Player B also would have lost if they had said 8, 9 (since Player A could have then said 10). That means that when Player A says 7, their win is already guaranteed! Noticing this allows players to change their focus from "I need to say 10" to "I need to say 7." Can kids figure out what number they should aim to say in order to guarantee they will be able to say 7?

Here's the answer: Since this version allows players to count up by 1 or 2 numbers on a turn, the "winning" numbers occur in multiples of 3 less than the target number. Whoever says 4 is guaranteed to be able to say 7, and is then guaranteed to be able to say 10. Similarly, whoever says 1 is guaranteed to be able to say 4. That means that Player A is always guaranteed a win if they play correctly!

After kids have figured out the version above, see if they can determine who will win some of the variations listed above. For example, who can guarantee a win if players can count up by as many as 4 on a turn with a target number of 50? (In this case, Player B can guarantee a win by counting up to each multiple of 5 on their turn.)

## What do you think of this activity?

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Materials
• none
Learning Goals
• counting
• strategic thinking
• skip-counting
Common Core Standards
• MP1
• MP2
• MP7
• K.CC.A.1
• K.CC.A.2
• 1.OA.C.5
• 2.OA.B.2
• 2.NBT.A.2

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