Ask students: Who can share how addition, subtraction, multiplication, and division can help us build and identify patterns in numbers? Students may share that patterns can grow, shrink, increase, and/or decrease.
Continue, saying: Recognizing and identifying patterns help us make predictions based on our observations to solve problems. Today, we are going to become number pattern explorers to understand how one grain of rice became 1,073,741,823 over the span of 30 days.
Project Appendix B and tell students: On the board you will see “Days 1-10” of “Grains of Rice Received” and “Total Grains of Rice”. What is the difference between “Grains of Rice Received” and “Total Grains of Rice”?
Allow students to share their answers.
Say: The “Grains of Rice Received” column represents how many grains of rice Rani was given each day. This column is always less than the “Total Grains of Rice” column. Who can share why the “Grains of Rice Received” column is always less than the “Total Grains of Rice” column after “Day 1” where the columns are equal?
Allow students to share their ideas.
Say: On Day 1 the columns are equal because there was no previous day’s total for Day 1 “Grains of Rice Received” to be added to. Each day the “Grains of Rice Received” column is added to the previous day’s “Total Grains of Rice” value.
Continue by demonstrating this to students. Point to the table and say: On Day 1 Rani received one grain of rice. What is Rani’s total grains of rice on Day 1? Students should respond by saying 1.
Point to “Day 2” and say: If Rani received double the amount of rice than they did on Day 1, how many pieces of rice will Rani receive on Day 2? Students should say two because one doubled is two.
Say: How can we determine Rani’s “Total Grains of Rice” for Day 2? Allow students to share their responses.
Say: Rani will have three grains of rice after two days because on Day 1, the “Total Grains of Rice” was one and then we add the two grains that Rani received on Day 2.
Hand out a copy of Appendix C to each student. Say: You will now have five minutes to find as many patterns as you can! You are encouraged to mark up this page and record patterns when you identify them. Remember patterns can occur vertically within the same column and horizontally across different rows. Your five minutes of exploring for patterns starts now!
During this time, circulate the classroom to ensure all students are comprehending the task.
When the five minutes are up, tell students: We are now going to share the patterns we found. Appendix C should still be projected on the board. As students share their identified patterns, mark up the table for students to observe (use Appendix B as reference). Allow students to share the patterns they identified within the table and help them uncover ones they may have missed.
Continue, saying: Now you are going to independently fill in the blanks for Days 11 to 20 using the patterns we have identified and discussed.
Handout Appendix D, giving students 10 minutes to work on the table. When 10 minutes are up, project Appendix D and review the activity together.
Say: In pairs, you are now going to apply your learning using the patterns we have identified. Your task is to complete the columns “Grains of Rice Received” and “Total Grains of Rice” from Days 21 to 30. When you are done, write a sentence using words describing each pattern you and your partner used on the back of the sheet.
Before students work in pairs, ensure the task is understood. Ask: How will you determine the values for Day 21? Students should respond that they will reference the values for “Day 20” and use patterns to determine “Day 21” values.
As a group, take up Appendix D and get students to share what strategies they used to complete the table.
What prior knowledge do students have about growing patterns?
What language is being used when students share patterns they found?
Do students understand that patterns involve repeating the same function?