Guided Lessons

# Figuring Out Function Tables

Get your students talking about number patterns and rules with this introductory lesson on function tables. Use this lesson as a pre-lesson to Input and Output Boxes or teach it on its own.
This lesson can be used as a pre-lesson for theInput and Output BoxesLesson plan.

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This lesson can be used as a pre-lesson for theInput and Output BoxesLesson plan.

Students will be able to generate a number pattern and make observations about the numbers.

##### Language

Students will be able to identify and discuss the number that does not belong in the function table using sentence starters.

(3 minutes)
• Write the term Number patternIn the centre of a Frayer Model and display it on the document camera.
• Have students turn and talk to a partner about their background knowledge of this term. Tell students to think of a definition and examples of number patterns to discuss with their partner.
• Invite students to share their background knowledge and begin filling out the model with the correct definition and students' insights into the concept. Celebrate accurate descriptions and examples mentioned in students' discussions. Encourage students to state the definition of "number pattern" in their home language (L1). Complete the model by adding an image and non-examples.
• Tell students that today they will practise discovering number patterns and the corresponding rule to discover which number does not belong in a function table.
(8 minutes)
• Define Function tableTo students by showing them the vocabulary card. Show students some simple examples of function tables and mention that sometimes they are also called input-output tables.
• Continue introducing the remaining vocabulary terms to students by inviting volunteers to read the word aloud, its definition, and describe the image that matches the word.
• Write out the following word problem on the board and read it aloud to students: "Norah's dentist told her to brush her teeth for 2 minutes every night. How many minutes will she spend brushing her teeth in 5 days?"
• Tell students that one way to solve this problem is by drawing an input-output table and writing out a number pattern. Model how to do this with two columns titled input and output. In the input column, write 1, 2, 3, 4, 5 in each row to represent the days. In the output column column, write 2, 4, 6, 8, 10 in each row to represent minutes spent brushing teeth. Say, "I notice that the pattern from each input to output is plus 2. Therefore, Norah spends 10 minutes brushing her teeth in five days. If we continue to follow this rule, could we figure out how many minutes she spends brushing her teeth in 10 days? 15 days?" Gather students' insight and discuss.
• Remind students that a function table, or input-output table, can have a rule that involves any of the four main maths operations (refer to the vocabulary card to remind them of this concept). This means that the rule could have addition, subtraction, multiplication, or division so it is important that they think of all connections or relationships between the input and output numbers.
• Tell students that another key point to remember is that once the rule has been established (e.g., plus 2, minus 4, times 5, etc.), any number that enters as an input must follow the rule to get the correct output. The whole table must be consistent with the rule being applied to every row.
• Ask students if they have any questions or concerns and address them.
• Ask students this question and have them discuss with their partner: Why do we write the number pattern into a table format? ("I think we write a number pattern in a table format so that we can...")
• Engage students' in a brief discussion and lead them to the understanding that we use the table format so that we can clearly see the relationship between the numbers. It is a way of keeping the numbers, or data, organized.
(10 minutes)
• Distribute the Which Number Doesn't Belong in the Function Table? worksheet and display a teacher copy on the document camera.
• Read aloud the teaching points and instructions at the top of the worksheet. Have some volunteer students rephrase the key points in their own words to the whole class.
• Model how to solve the first problem on the worksheet. Think aloud as you figure out the rule for the number pattern, and circle the number that does not belong in the table. Make sure you explain your reasoning using the sentence starters provided.
• Place students into effective partnerships and have them solve the second and third problems.
• Review the problems as a whole group by asking one set of partners to come up to the document camera to share their maths thinking.
• Check to see if other students got different answers and discuss the differences.
• Allow students in the "audience" to ask questions or provide feedback. Notice if anyone uses a different strategy to solve the same problem (i.e., if anyone uses the inverse operation to check their answers). Provide the following questions and sentence starters to help students interact with each other regarding the function tables:
• "I don't understand the part about... Could you explain it again?"
• "How do you know you got the right answer?"
• "I like how you... I would add..."
(12 minutes)
• Have students solve problems 4, 5, and 6 independently. Circulate to offer assistance as needed.
• Place students with a new partner and have them share their answers to the remaining problems.
• Display the previous questions and sentence starters, and instruct students to provide feedback to their partner about their work.
• Tell students to do the "You Try It!" section at the bottom of the worksheet on their own. Tell them to make a function table with one number that does not belong in the table.
• Have them share their own function table from this section with their partner so that the partner can identify the incorrect number and explain their reasoning. Encourage students to use their own words to explain.

Beginning

• Have students repeat the directions in their home language (L1) or in English (L2) before beginning the work.
• Give students access to bilingual glossaries and online dictionaries for them to look up unfamiliar words throughout the lesson.
• Place students with more advanced ELs for partner work.
• Pull aside a small group of students as they work on the group work and guide them through the process.
• Allow students to work on the formative assessment with a helpful partner.

• Encourage students to say their answers without using the sentence frames/stems.
• Allow students to be the first to share their ideas or rephrase their classmates' contributions to class discussions.
• Have students create and display a word/phrase bank with helpful terms from the lesson for reference purposes, with images if applicable.
(4 minutes)
• Hand out a sticky note to each student and instruct them to complete the following sentence starter: "A function table is ____. It is used to ____."
(3 minutes)
• Tell students to share their answers verbally with their table group. Have each table group choose one representative to share their sentences aloud with the whole class.
• Reiterate the importance of being able to identify number patterns in function tables and to see how numbers relate to each other. Having this skill prepares them for more complex maths concepts such as algebra.