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Input/Output Tables

Lesson Plan

Input/Output Tables

Objectives

Students will work with input/output tables. Students will:

  • find the rule for an input/output table.
  • use the rule to find the missing elements in the table.

Essential Questions

How can data be organized and represented to provide insight into the relationship between quantities?
How can mathematics support effective communication?
How can patterns be used to describe relationships in mathematical situations?
How can probability and data analysis be used to make predictions?
How can recognizing repetition or regularity assist in solving problems more efficiently?
How is mathematics used to quantify, compare, represent, and model numbers?
  • How is mathematics used to quantify, compare, represent, and model numbers?
  • How are relationships represented mathematically?
  • How can patterns be used to describe relationships in mathematical situations?
  • How can recognizing repetition or regularity assist in solving problems more efficiently?
  • How can data be organized and represented to provide insight into the relationship between quantities?

Vocabulary

  • Factor: The number or variable multiplied in a multiplication expression.
  • Function: A relation in which each value of an independent variable is associated with a unique value of the dependent variable.
  • Multiple: A number that is the product of a given integer and another integer (e.g., 6 and 9 are multiples of 3).
  • Patterns: Regularities in situations such as those in nature, events, shapes, designs and sets of numbers (e.g., spirals on pineapples, geometric designs in quilts, the number sequence 3, 6, 9, 12, . . .).

Duration

60–90 minutes

Prerequisite Skills

Prerequisite Skills haven't been entered into the lesson plan.

Materials

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

  • IXL activity that asks students to determine the rules used in input/output tables and type missing values into the tables.

http://ca.ixl.com/math/grade-4/input-output-tables-with-addition-subtraction-multiplication-and-division

  • IXL activity that provides brief contexts and rules written with variables, and asks students to type missing values into the tables.

http://ca.ixl.com/math/grade-4/function-tables

 

Formative Assessment

  • View
    • Use the Think-Pair-Share activity to assess students’ abilities to connect function tables to real-world functions.
    • Use the Journal Entry activity to determine students’ ability to conceptually describe the meaning of an input/output table, criteria of such a table, and an example.
    • Use the Lesson 3 Exit Ticket to quickly evaluate students’ mastery.

Suggested Instructional Supports

  • View
    Scaffolding, Active Engagement, Metacognition, Modeling, Explicit Instruction, Formative Assessment
    W: Students will find rules for input/output tables and use the rules to find the missing elements in the tables. 
    H: Use of the function table applet should hook students into the learning. Students may examine the appearance of function tables and analyze the relationship between the input and output values. 
    E: The focus of the lesson is on finding rules for input/output tables and using the rules to find the missing elements. Students will first explore function tables using a function table applet. Next, students will brainstorm real-world information that may be represented by such tables. Students will then work through examples, identifying the rules and then using the rules to find the missing elements. Finally, students will be asked to convey their understanding of function tables in writing. 
    R: Opportunities for discussion start at the beginning of the lesson, with the Virtual Applet and Think-Pair-Share activities. The Journal Entry activity will require students to connect ideas and convey conceptual understanding, using words. This will allow students to review, rethink, and revise their understanding of patterns in function tables as needed. 
    E: Observation during the journaling activity will help in identifying areas of strength and weakness. Students will be evaluated using the Lesson 3 Exit Ticket at the close of the lesson.  
    T: Use the Extension section to tailor the lesson to meet the needs of student. The Routine section is designed to provide opportunities for reviewing lesson concepts throughout the year. The Small Groups section is intended for use by students who may benefit from additional practice and instruction opportunities. The Expansion section contains ideas for students who are prepared to move beyond the requirements of the standard. 
    O: The lesson is scaffolded so that students are first given time to explore input/output tables and the relationship between the input and output values, while also brainstorming examples of such data as shown in the real world. They will then determine rules for input/output tables and find missing elements in tables. 

Instructional Procedures

  • View

    Virtual Applet Activity

    Provide students an opportunity to explore a virtual function table. This applet allows students to drag values into the input column, observe values in the output column, determine the rule, and use that rule to determine missing values in the table. Give students about 10 minutes to work with the applet. Students may be arranged in pairs. Encourage students to think of questions and discuss them with their partner and the whole class. The function machine applet may be found at: http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html?open=instructions&from=grade_g_3.html.

    Think-Pair-Share Activity

    Ask students to brainstorm real-world information that may be placed in input/output tables. After students have brainstormed for 2–3 minutes, pair each student with a partner. Partners should exchange ideas for about 3 minutes. Bring the class back together. One partner from each group should share the ideas with the whole class. Encourage questions and debate.

    Show some examples of partially-completed input/output tables. Students will determine the rule and apply the rule to fill in the missing values. Shown below are some possible examples.

     

    Example 1

     

    “What is the rule used to create the table?” (The rule is “Add 2.”) Students may look for the relationship between the input values or the relationship between the output values. Explain that the rule relates each input value to the matching output value.

    “What number will we put in the first box?” Give students plenty of time to think about what operation they should use. (The first box will contain a number that is 2 less than 12. So, the number is 10.) “What number will we put in the second box?” (The second box will contain a number that is 2 more than 13, or 15.)

    The guiding questions for the remaining examples may be similar to those asked for the previous example. The rule and values, as well as explanations, will be briefly provided below.

    Example 2

     

    Rule: Multiply by 2.

    The first box will contain a number that is half of 22, or 11. The second box will contain a number that is two times 13, or 26. The third box will contain a number that is half of 36, or 18.

     

    Example 3

     

    Rule: Subtract 4.

    The first box will contain a number that is 4 more than 5, or 9. The second box will contain a number that is 4 less than 14, or 10. The third box will contain a number that is 4 more than
    15, or 19.

     

    Example 4

     

    Rule: Multiply by 5.

    The first box will contain a number that is 5 times 10, or 50. The second box will contain a number that is equal to the quotient of 65 and 5, or 13. The third box will contain a number that is 5 times 18, or 90.

     

     

     

     

     

     

     

    Example 5

     

    Rule: Add 8.

    The first box will contain a number that is 8 more than 12, or 20. The second box will contain a number that is 8 less than 26, or 18. The third box will contain a number that is 8 more than 24, or 32.

     

    Journal Entry Activity

    Have students write a brief entry on the definition of an input/output table. Students should explain how the input values relate to the output values and provide at least one example.

    Have students complete the Lesson 3 Exit Ticket (M-4-6-3_Lesson 3 Exit Ticket and KEY.docx) at the close of the lesson to evaluate students’ level of understanding.

     

    Extension:

    • Routine: During the school year, students will use input/output (function) tables to create graphs of functions. The relationship between the input values, or x-values, and the output values, or y-values, should be examined.
    • Small Groups: Students who need additional practice may by pulled into small groups to work on the Small Group Practice worksheet (M-4-6-3_Small Group Practice and KEY.docx). Students can work on the worksheet together or work individually and compare answers when done.
    • Expansion: Students who are prepared for a challenge beyond the requirements of the standard may be asked to use a Microsoft Excel spreadsheet to create a function table. They will enter input values and use a rule to create output values. For example, a student may enter the following values into column A: 1, 2, 3, 4, 5, 6, 7, and 8. The student could then click in B1 and enter the formula, =A1 + 2. The spreadsheet would show an output value of 3. This formula can then be copied to other cells.

Related Instructional Videos

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Final 06/28/2013
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