<p>Students will work with input and output tables. Students will:&nbsp;<br>- identify the rule for an input/output table.<br>- use the rule to find any missing elements in the table.</p>

<p>- How may data be arranged and represented to reveal the link between quantities?<br>- How can mathematics help us communicate more effectively?&nbsp;<br>- How may patterns be used to describe mathematical relationships?&nbsp;<br>- How can probability and data analysis be used to make predictions?&nbsp;<br>- How may detecting repetition or regularity assist in solving problems more efficiently?<br>- How can mathematics help to quantify, compare, depict, and model numbers?</p>

<p>- Factor: The number or variable multiplied in a multiplication expression.&nbsp;<br>- Function: A relation in which each value of an independent variable is associated with a unique value of the dependent variable.&nbsp;<br>- Multiple: A number that is the product of a given integer and another integer (e.g., 6 and 9 are multiples of 3).&nbsp;<br>- 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, . . .).</p>

<p>- one copy of the Lesson 3 Exit Ticket (M-4-6-3_Lesson 3 Exit Ticket and KEY) for each student<br>- copies of the Small Group Practice worksheet (M-4-6-3_Small Group Practice and KEY) as needed</p>

<p>- Use the Think-Pair-Share activity to evaluate students' ability to relate function tables to real-world functions.&nbsp;<br>- Use the Journal Entry assignment to assess students' conceptual understanding of an input/output table, its criteria, and an example.&nbsp;<br>- Use the Lesson 3 Exit Ticket to quickly assess students mastery.</p>

<p>Scaffolding, Active Engagement, Metacognition, Modeling, Explicit Instruction, and Formative Assessment&nbsp;<br>W: Students will apply input/output table rules to identify missing elements.&nbsp;<br>H: Using the function table applet can engage students in learning. Students can explore the appearance of function tables and analyze the relationship between input and output values.&nbsp;<br>E: The course focuses on identifying rules for input/output tables and using them to find missing elements. Students will initially experiment with function tables using an applet. Next, students will brainstorm real-world facts that could be represented by such tables. Students will next work through examples, identifying the concepts and applying them to find the missing elements. Finally, students will be required to express their comprehension of function tables in writing.&nbsp;<br>R: The Virtual Applet and Think-Pair-Share activities provide opportunities for discussion at the start of the class. Students will use words to connect ideas and show conceptual understanding in the Journal Entry activity. This will allow students to review, reconsider, and change their understanding of patterns in function tables as necessary.&nbsp;<br>E: Observation during journaling activity can help discover strengths and weaknesses. Students will be evaluated using the Lesson 3 Exit Ticket at the end of the lesson.&nbsp;<br>T: Use the Extension section to customize the lesson to match the needs of the student. The Routine part is intended to provide opportunities to review course concepts throughout the year. The Small Groups part is meant for those who would benefit from further practice and teaching. The Expansion section provides ideas for students who are willing to go above and beyond the normal criteria.&nbsp;<br>O: The lesson is scaffolded to allow students to study input/output tables and their relationship, as well as generate real-world situations. They will next develop rules for input/output tables and identify missing elements.&nbsp;</p>

<p><strong>Virtual Applet Activity&nbsp;</strong><br><br>Give students the opportunity to examine 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 then apply that rule to find missing values in the table. Allow students approximately 10 minutes to work with the applet. Students may be arranged in pairs. Encourage students to brainstorm questions and discuss them with their partner and the entire class. The function machine applet is available at: <a href="http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html?open=instructions&amp;from=grade_g_3.html">http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html?open=instructions&amp;from=grade_g_3.html</a>.&nbsp;<br><br><strong>Think-Pair-Share Activity</strong><br><br>Instruct students to brainstorm real-world information that could be used in input/output tables. After students have brainstormed for 2-3 minutes, assign each student a partner. Partners should exchange ideas for around 3 minutes. Bring the class back together. One partner from each group should discuss their ideas with the entire class. Encourage questioning and discussion.&nbsp;<br><br>Provide some samples of partially completed input/output tables. Students will establish the rule and use it to fill in the missing values. Here are some possible examples.<br><br><strong>Example 1</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_63.png" width="360" height="184"><br><strong>"What is the rule used to create the table?"</strong> (<i>The rule is "Add 2."</i>) Students may look for a relationship between the input and output values. Explain how the rule relates each input value to its corresponding output value.&nbsp;<br><br><strong>"What number will we put in the first box?"</strong> Allow students plenty of time to consider which operation they should use. (<i>The first box will hold a number that is 2 less than 12. So the number is 10.</i>) <strong>"What number will we put in the second box?"</strong> (<i>The second box will have a number that is 2 more than 13, or 15</i>).<br><br>The guiding questions for the subsequent examples may be similar to those posed in the previous one. The rule, values, and explanations will be described briefly below.<br><br><strong>Example 2</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_64.png" width="360" height="183"><br><br>Rule: Multiply by 2.<br><br>The first box will hold a number that is half of 22, or 11. The second box will have a number that is two times 13, or 26. The third box will hold a number that is half of 36, or 18.<br><br><strong>Example 3</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_65.png" width="360" height="184"><br><br>Rule: Subtract 4.<br><br>The first box will have a number that is 4 more than 5 or 9. The second box will have a number that is 4 less than 14 or 10. The third box will have a number 4 more than 15, or 19.<br><br><strong>Example 4</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_66.png" width="361" height="182"><br><br>Rule: Multiply by 5.<br><br>The first box will contain a number that is 5 times 10, or 50. The second box will hold a number equal to the quotient of 65 and 5, or 13. The third box will have a number that is 5 times 18, or 90.<br><br><strong>Example 5</strong><br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screenshot_67.png" width="359" height="177"><br><br>Rule: Add 8.<br><br>The first box will have a number that is 8 more than 12 or 20. The second box will hold a value that is 8 less than 26, or 18. The third box will hold a number that is 8 more than 24, or 32.<br><br><strong>Journal Entry Activity</strong><br><br>Ask students to write a brief entry about the definition of an input/output table. Students should explain how the input values correspond to the output values, using at least one example.<br><br>Students should complete the Lesson 3 Exit Ticket (M-4-6-3_Lesson 3 Exit Ticket and KEY) at the end of the lesson to assess their level of knowledge.<br><br><strong>Extension:</strong></p><p><strong>Routine:</strong> Throughout the school year, students will use input/output (function) tables to generate function graphs. The relationship between the input values (x-values) and the output values (y-values) should be investigated.&nbsp;</p><p><strong>Small Groups:</strong> Students who require further practice may be divided into small groups to complete the Small Group Practice worksheet (M-4-6-3_Small Group Practice and KEY). Students can complete the task together or independently, and then compare their answers.&nbsp;</p><p><strong>Expansion:</strong> Students who are prepared to take on a task that goes beyond the standard's criteria may be requested to develop a function table using Microsoft Excel. They will enter input values and then apply a rule to generate output values. For example, a student could input the following values in column A: 1, 2, 3, 4, 5, 6, 7, and 8. Student could then click in B1 and enter the formula, =A1 + 2. The spreadsheet would display an output value of 3. The formula can then be duplicated into other cells.</p>