Blank piece of scrap paper or white boards and erasable markers
Initiate this lesson by conceptualizing the relationship between seconds, minutes, hours, days, weeks, and years with students.
Ask students: How many seconds are in a minute? How many minutes are in an hour? How many hours are there in a day? How many days are there in a week? How many weeks are there in a year? Record the following as they are discovered:
This activity helps students understand how large the total number of grains of rice is before interacting with the story itself.
Ensure each student has access to a calculator before proceeding.
Tell students: I want you to predict how many years you think it would take to count to 100,000,000 if it took one second to count one number. This prediction is not about being correct but rather about internalizing and understanding how large numbers are when we attach meaning to them. The meaning we will be attaching to numbers today is time which is something we are all familiar with. Dealing with large numbers involves abstract thinking and reasoning.Today we are going to uncover how many years it would take to count to 100,000,000. Then later you will be challenged find out how many years it would take to count to a number in the billions!
As you collaboratively work through the following points, be sure to copy the bolded equations so children can see the growing equation.
Ask students: How many seconds are in one minute? When 60 seconds has been shared, continue by asking: Because there are 60 seconds in one minute, how many numbers could I count if it took me one second to say one number? Students should respond by saying that 60 numbers would be counted as there are 60 seconds in a minute and it takes one second to count one number. To make this more explicit ask students: What is 60 divided by one? Or how many times does one go into 60?
60 seconds/minute ´ 1 second to count each number = 60 numbers/minute
60 seconds/minute = 60 numbers/minute
Continue by asking students: How many minutes are in one hour? When sixty minutes has been shared continue by asking: If there are 60 minutes in one hour and we already know that we can say 60 words per minute, how many words might we be able to say in one hour?
Proceed by asking students: How many hours are there in one day? When 24 hours has been shared, continue by asking: Since there are 24 hours in one day and we already know that we can say 3,600 words per hour, how many words might we be able to say in one day?
Continue by asking students: How many days are there in one week? When seven days has been shared, continue by asking: Since there are seven days in one week and we already know that we can say 86,400 words per day, how many words would we say in one week?
Proceed by asking students: How many weeks are there in one year? When 52 weeks has been shared, continue by asking: Since there are 52 weeks in one year and we already know that we can say 604,800 words per week, how many words would we say in one year?
Ask students: Now that we have calculated how many numbers could be counted in a year if each word took one second to say, how can we determine how many years it will take to count to 100,000,000?
100,000,000 numbers total ¸ 31,449,600 numbers/year = 3.18 years
Bring closure to this section of the activity by asking students: What does 3.18 years mean? Students should share that if you were to count from one to 100,000,000 and it took you one second to say each word, it would take you 3.18 years to reach 100,000,000. Ask students: Was your prediction higher or lower? Does the time of 3.18 years to count to 100,000,000 surprise you?
Tell students: Now we are going read “One Grain of Rice”.While you are listening to the story, I want you to pay attention to the numbers and visualize what they look like in your mind when you hear them.
Alternatively, you can play the One Grain of Rice: Approaching Math Through Story Read Aloud
When you have finished reading the book to the class, ask: Does anyone remember how many grains of rice Rani had in total after 30 days? Students may not remember the exact number. Students may share that the number is in the billions.
Share the number with students verbally by telling them: After 30 days, Rani had a total of 1,073,741,823 grains of rice. We are going to compile the digits of this number together to make sure that we have each digit in its proper place value holder.
Say the number again and ask students: What number goes in the one’s column? They should say a three. Ask students: What number is this? Students should say three. Say the number again.
Ask: What number goes in the ten’s column? Students should say a two. Ask students: What number is this? Students should say 23. Continue asking the same question with the other place value column names until the entire number has been built.
Break students into pairs and tell them: Now you are going to work with your partner to determine how many years it would take to count to 1,073,741,823 if Rani could count one number every Remember that we already determined how many numbers could be counted in one year if it took one second to say one number.
1,073,741,823 numbers total ¸ 31,449,600 numbers/year = 34.14 years
During this time circulate around the classroom and to assist any pairs who made require further probing.
When pairs have finished, ask students: How do you know your answer is correct? See if they perform the reverse operation and use their answer and either 31,449,600 or 1,073,741,823 to reach either 31,449,600 or 1,073,741,823.
Conclude the lesson by telling students: Tomorrow, we will be exploring and uncovering patterns in the amount of rice Rani received over time. Tonight, I want you to think about how addition, subtraction, multiplication, and division can help us build and identify patterns in numbers.
Do students understand growing equations and how to manipulate them?
Do students understand the difference between face value and place value?
Do students understand the relationship between multiplication and division?