# King's Chessboard

Lesson 8 of 10

## Objective: Students will be able to review multi-digit addition and reason abstractly and quantitatively.

## Big Idea: If a number is doubled everyday for 64 days will it be in the hundreds? Millions? Billions?

*45 minutes*

There are three critical areas of instruction in the Common Core standards and one is for students to be able to finalize fluency with multi-digit addition, subtraction, multiplication and division. The main focus of this lesson is for students to practice multi-digit addition with a fun, challenging and engaging activity and the story *The Kings Chessboard** by David Birch. I use these questions to direct my students thinking while reading.

- How do the illustrations and words help you understand the story?
- How does this story connect to what we are learning in math?
- What was the theme of the story?
- What message was the author trying to share?

After reading the part where the king wants to reward the wise man for his good services I point out the wise man asks to receive 1 grain of rice on the first day, 2 grains of rice on the second day and then 4, 8, 16 and so on. I write this on the board: 1, 2, 4, 8, 16.

This is the beginning of the year and we are also studying patterns. I am developing a pattern of learning for my students at the same time, *“Your brain is a pattern seeking device – look for patterns.”*

I ask, *“Is there a pattern in these numbers?”* You should hear answers such as they are doubling, they are multiplied by two.

I then ask if anyone knows how many squares there are on a chessboard. (64)

I ask another question, *“How many grains of rice do you think the king will have delivered on the 64 ^{th} day?”* Please talk with a neighbor and explain your thinking (MP2). “

*Why you think your answer is right?” Write your answer down in your math journal.*

At this point I stress to my students to not give the answer to their partner if they know it. I teach a multiage 4^{th} and 5^{th} grade class and my 5^{th} grade students will have done this lesson with me the year before. (In 15 years I have had one student who remembered the exact answer!) There is great benefit in using the same lesson with the same students. Students in 4^{th} grade are still developing fluency with multi-digit addition, as are some 5^{th} graders. For the fifth graders, this will be a review and refresh lesson. It also gives them practice being a teacher to their 4th grade partner. This is one teaching move that I reinforce with my students – Don’t give an answer if you can teach another how to find it themselves. Because there are 64 math problems to complete, it also establishes an environment where perseverance and patience is needed.

Once I had given time for the students to talk they move off to work the problems themselves. If your students don’t do this on their own you could set up a challenge to see what the number of grains of rice the king will have on the 64^{th} day.

Many students head for their calculators once the numbers get big but they will discover quickly the calculator will not fit the numbers and they will resort to paper and pencil. A main point your are going to want to make with your students is they need to work with a partner and check their work often (establishing another aspect of a hardworking learning environment). If they have made a mistake on step 5 all the other problems will be incorrect.

*Another, similar book that can be used is *One Grain of Rice* by Demi. You could also pair these books, which is a strategy recognized by the National Council of Teachers of English as more effective for transfer of learning.

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#### Student Reflection

*5 min*

It is important for *students* to reflect on their learning, thinking and behavior after a lesson such as this one. Students should reflect on their learning to increase comprehension; thinking to develop metacognition; behavior – better behavior equals less interruptions to learning.

Today I had them reflect verbally to establish a model of how to reflect. The first question I asked was, *“What did you learn about doubling numbers?”*

If you were a fly on the ceiling you would have heard answers such as:

*The numbers got big fast!*

*I didn’t think the answer would be that big!*

*I can’t believe my device couldn’t fit all the numbers! I had to actually do the math. *

*“Do you think the King learned his lesson to not let his pride get in the way?”* I use this example to remind student’s rewards should be intrinsic and not extrinsic.

*Yes, because he asked the wise man to help him other times.*

*Yes because he realized the wise man didn’t need something for the reward. It was the king who needed to give something to reward. *

* *“How did you help another person with their math?”

Many hands go up and there are answers such as:

*I helped by reading the number and Kayla put it in the calculator. At least until the calculator ran out of space.*

*I did the addition and then checked it with Xavier – he did his problems separately so we would know if we were right. *

*Hayden noticed that my partner and I had made a mistake way back on square 12 and he helped us fix it. *

#### Resources

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- LESSON 1: Sibling Statistics
- LESSON 2: The Math Curse
- LESSON 3: Favorites Survey Part 1
- LESSON 4: Favorites Survey Part 2
- LESSON 5: Favorites Survey Part 3
- LESSON 6: Palindrome Patterns (Part 1)
- LESSON 7: Palindrome Patterns (Part 2)
- LESSON 8: King's Chessboard
- LESSON 9: Problem Solving Strategies Introduction
- LESSON 10: Table Leaders