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Input and Output Boxes
Students will be able to generate a number pattern and make observations about the numbers.
- Ask students the following questions: "Where do you see patterns? Is anyone wearing a pattern? Does anyone see a pattern in the classroom?" Write or draw their responses on the board and give them an example of patterns if necessary.
- Gather background knowledge by asking students to work in pairs to find patterns on a multiplication chart (e.g., all rows and columns that have even factors will produce an even product, rows, and columns for 5 all have products that end in 0 or 5, etc.).
- Ask students to think about how finding patterns helps in counting or remembering their multiplication facts. Allow them to share in partners and choose someone to share aloud with the class.
Explicit Instruction/Teacher modeling(8 minutes)
- Tell students that today they'll learn how to find and explain number patterns using T-charts. Display problem 1 from the First Functions Table worksheet and model how to find the input given the stated rule.
- Explain that the input is the number they start with and the output results after using an operation (e.g., x, -, +, ÷) to alter the input. Explain that the rule in the middle column shows the operation you applied in a given row.
- Model completing problem 2 and highlight how you used inverse operations (i.e., adding to get the input instead of subtracting to get the output) to get the input.
- Display problem 3 and ask for volunteers to tell you the steps you must follow to complete the table. Ask follow-up questions, like, "Why can't I add? How do I find the input since it's missing?"
- Ask for volunteers to share their ideas about some patterns that arise after you've applied the rule.
Guided Practice(20 minutes)
- Create your own input and output table with missing numbers and a stated rule. Think aloud your process. (Tip: you can start with the input, find the output, and then erase the input so that the students know how to have missing inputs.) Check your answers using inverse operations as well.
- Separate students into groups of three to four and give them a piece of construction paper to share. Ask them to create an input and output table that is missing information yet still has enough information for another group to complete the chart.
- Have students switch their papers with another group and find the missing information.
- Ask group members: "Did you have enough information to solve the problem? If not, what essential information was missing? Was it too easy or hard, and why or why not?" Have group members share their impressions of the other group's table.
- Discuss the number pattern and observe any patterns seen in the input or outputs (e.g., counting up, skip counting, all even or odd numbers, etc.).
Independent working time(12 minutes)
- Distribute the First Functions Table worksheet and read the instructions to the students.
- Ask students to complete the remaining questions on their own. Then allow them to turn to their elbow partner to compare answers and speak about the patterns they see between a table's inputs or outputs. Have them change their answers in a new color.
- Allow students to use a 100s and/or multiplication chart to identify the patterns and make observations about the numbers.
- Pre-teach vocabulary terms such as "level," "sequence," "operations," and "pattern" before the lesson or reinforce their meanings in small-groups during the group work section.
- Use visuals or manipulatives to represent the mathematical expressions as necessary.
- Ask students to create a table with rules that alternate. For instance, the number pattern could be to add 4 then subtract 5 to each of the inputs, or the rule can alternate between two rules. Have them share these patterns with their group members and explain their thought process.
- Challenge them to create a word problem that requires students to show their reasoning using a table diagram with inputs and/or outputs.
- Write an input and output table on the board with the rule and some inputs and outputs missing.
- Tell students to work on the back of their worksheet to find the rule and the missing numbers. Have them write down any patterns in the numbers they see in the table.
- Monitor student answers and offer corrections and encouragements as needed.
Review and closing(5 minutes)
- Read the following word problem and write it on the board: "The students received free books once a week for 6 weeks. Every batch contained 10 books. How many books did they have by the end of the 6th week?"
- Ask students to turn and talk to their partner about how they could solve this problem using an input and output table.
- What is the rule? (x10)
- What's the starting number? (number 1, for week 1)
- What is the answer to the question? (60 books)
- Ask students how being familiar with patterns can help them solve mathematical problems. What are some other uses for patterns? (e.g., building structures, sewing and crocheting, symmetry, coding, designs, etc.)