the kings chessboard problem - math geek mama · 2015. 4. 25. · the king’s chessboard problem:...

The King’s Chessboard Problem

and Discussion Questions

Based on the book The King’s Chessboard by

David Birch

Created by Bethany @ MathGeekMama.com

Teaching Tips:

• This is a classic mathematical problem that can be a lot of fun to think through, and the results are often surprising to students who have never seen it! I have used this problem to introduce exponential functions, but it could also be a good example of a geometric series.

• Because this deals with such large numbers, the first question asks how many grains of rice would be on the 64th square (not how many would there be total-although that would be a great bonus question!)

• I’ve then included some further questions for students to think about and discuss. An answer key is provided.

• Also included in this download is a similar problem that makes it a little more relatable to students. I’ve included two formats, so you can decide how much support you want to give students as they solve it. o One page is left blank (so they can figure out how

to organize the information themselves). The second page has tables already set up for them, they just have to do the math and figure out which pay scale is better!

o There is an answer key for the second problem as well.

Enjoy! J

© www.MathGeekMama.com

The King’s Chessboard Problem: In The King’s Chessboard, the wise man requests as his reward 1 grain of rice for the first square on the chessboard, two grains of rice for the second square, four grains of rice for the next

square, then eight grains of rice, and so on, for all 64 squares on the chessboard.

1. How many grains of rice will he receive on the 64th day? Show your reasoning below.


The King’s Chessboard Problem:

2. How would you determine the total amount of grains of rice for all 64 days? 3. Were you surprised at how quickly the numbers grew? Why or why not? 4. Can you think of another way you might have figured out the solution in question 1? Describe another method. 5. Do you know what this kind of function is called or can you write a mathematical formula to represent how you figured it out?


The King’s Chessboard Problem: In The King’s Chessboard, the wise man requests as his reward 1 grain of rice for the first square on the chessboard, two grains of rice for the second square, four grains of rice for the next

square, then eight grains of rice, and so on, for all 64 squares on the chessboard.

Answer Key 1. How many grains of rice will he receive on the 64th day? Show your reasoning below. 9,223,372,036,854,775,808 2. How would you determine the total amount of grains of rice for all 64 days? Add each of the 64 days together (Bonus: the total for all 64 days is 18,466,744,073,709,551,615 3. Were you surprised at how quickly the numbers grew? Why or why not? Answers will vary. 4. Can you think of another way you might have figured out the solution in question 1? Describe another method. Answers will vary, but there are a variety of ways to solve, such as making a list, creating a table, using exponents, etc. 5. Do you know what this kind of function is called or can you write a mathematical formula to represent how you figured it out? Exponential function; y = 2x


Your First Job Offer: You are finally offered your very first job! But the pay is up to you. You have the choice between receiving $100 on the first day, $200 on the second day and so on (each day is $100 more than the last) OR you can

receive 1 cent on the first day, 2 cents the second day, 4 cents the third day, and so on, doubling your pay each day. Which do you choose?


I choose choice ___________ because ______________________ ________________________________________________________



Total Pay with the First Choice:


Monday Tuesday Wednesday Thursday Friday Saturday Sunday Total

Week 1 $100 $200

Week 2

Week 3

Week 4

Week 5

Total for 5 weeks


Week 1 $0.01 $0.02 $0.04

Week 2

Week 3

Week 4

Week 5

Total for 5 weeks

Total Pay with the Second Choice:




Answer Key Total Pay with the First Choice:


Total Pay with the Second Choice:



Week 1 $100 $200

$2800

Week 2

$7700

Week 3

$12,600

Week 4

$17,500

Week 5

$22,400

Total for 5 weeks

$63,000


Week 1 $0.01 $0.02 $0.04 $1.67

Week 2

$162.56

Week 3

$20,807.68

Week 4

$2,663,383.04

Week 5

$340,913,029.12

Total for 5 weeks

$343,597,384.10

Thank you for downloading this resource from

www.MathGeekMama.com!

I sincerely hope you find this resource to be helpful and enjoyable for you and your

students! I only ask that you abide by Math Geek Mama’s terms of use, as this

resource is intended for personal use in the home or classroom only. Please do not

link directly the pdf file, edit the resource in any way, store them on your website, or

print this resource to sell/distribute to others.

If you enjoyed this resource, I’d love to connect with you at my website, TpT store or

on facebook, twitter or pinterest!

All clip art and fonts courtesy of:

Brittney Murphy Design

the kings chessboard problem - math geek mama · 2015. 4. 25. · the king’s chessboard problem:...

Documents