The King's Chessboard by David Birch
Algebra and Patterns
Patterns, doubling, number sense
Lesson Created by:
Tracy Tauschek, Woodrow Wilson Elementary, Manhattan, KS
- The King's Chessboard by David Birch, small paper chessboards for each student, bag of rice, plastic cups, measuring spoons, and measuring cups
1. Launching the Lesson
- Read the beginning of the book to the students. Up to the point in which the King makes the deal with the wise man.
- Write the beginning of the pattern on the board. (1, 2, 4, 8,) Ask the students to determine how the pattern is created. What are different ways they can explain the pattern? (Double, times 2, add the number to itself)
- Challenge students to estimate how much rice will be given to the wise man by the end of the agreement. This is 64 days of doubling. Give students a small-copied chessboard so they can have a visual picture of the number of squares and to write on if they choose. Only give the students a limited amount of time to discourage attempt to get an exact answer. Let students share their estimations.
- Finish reading the book.
2. Developing the Lesson
- Allow time for students to comment on math concepts they noticed in the book.
- The wise man used the rice to feed the villagers challenge the students to find out on what day there would be enough rice to feed our class. Show them the bag of rice and ask them what information they need to find out what day they would have enough rice. Allow the students to brainstorm as a class, keep a list on the board.
- Lead the student to understand the need to figure out how many people are eating, how much rice each person eats, how to convert form a serving size to number of grains of rice.
- Have the students count a small amount of rice (such as a tablespoon) then figure out how many spoonfuls fit into a cup or ½ half cup. Put he same measurement of rice into a cup or on a plate for students to count. Have groups of students help you convert the spoonful to a bigger measurement (such as cup) by pouring spoonful of rice into the cup.
Write the count of each student down. Then as a class write them in numerical order and find the average number of grain of rice in a spoonful. You will need to continue to multiply that number in order to get a count of number of grains of rice you will need to feed the class. For example you could multiple the number in a spoonful by how many spoonfuls were needed to make a ¼ cup (one serving) then multiply that by the number of people eating rice. Have the student brainstorm as a class what process they will need to follow to get the correct answer.
- After determining the number of grains of rice needed to feed our class the students need to find our on what day we will have at least that much rice. Some students may have already done this as they were estimating. Give time f student o work the problem of doubling the pattern until they have enough rice to feed the class. Students who are finished could be writing conclusions.
- Students may want to make up their own "reward" using a pattern.
- You could cook the correct amount of rice in a steamer. This takes about an hour.