<p>The purpose of this lesson is to provide students practice translating word sentences or phrases into mathematical language and vice versa. Students will also become familiar with signal words, which will aid in translation. Students will:&nbsp;<br>- rewrite verbal expressions/sentences into algebraic expressions and equations.&nbsp;<br>- review signal words for operations (e.g., add, subtract, more than, less than).&nbsp;</p>

<p>- How are relationships represented mathematically?<br>- How may data be arranged and represented to reveal the relationship between quantities?<br>- How are expressions, equations, and inequalities used to quantify, solve, model, and/or analyze mathematical problems?<br>- How can mathematics help us communicate more effectively?<br>- How can recognizing repetition or regularity assist in solving problems more efficiently?<br>- How can mathematics help to quantify, compare, depict, and model numbers?</p>

<p>- Coefficient: The numeric factor of a term with a variable.<br>- Distributive Property: The product of a number and a sum is equal to the sum of the individual products of addends and the number (e.g., <i>a(b + c) = ab + ac</i>).&nbsp;<br>- Expression: A variable or any combination of numbers, variables, and symbols that represent a mathematical relationship (e.g., 24 × 2 + 5 or 4<i>a</i>−9).<br>- Inequality: A mathematical sentence that contains an inequality symbol (&gt;, &lt;, ≤, ≥, or ≠) in which the terms on either side of the symbol are unequal.</p>

<p>- ABC Variables template (M-6-6-1_ABC Variables) made into a transparency or computer projection<br>- Signal Words When Writing Equations template (M-6-6-1_Signal Words Template)<br>- Ways to Show Multiplication and Division sheet (M-6-6-1_Ways to Show Multiplication and Division)<br>- Silent Pass with Variables worksheet (M-6-6-1_Silent Pass with Variables)<br>- Equations and Expressions Involving Variables worksheet (M-6-6-1_Equations &amp; Expressions Involving Variables and KEY)<br>- Routine Flash Card Example (M-6-6-1_Routine Flash Card Example)<br>- Exit Ticket (M-6-6-1_Exit Ticket and KEY)</p>

<p>- Ongoing formative evaluations can be done based on student engagement during large-group, small-group, pair, and individual work completed in class. Monitor students' grasp and recognition of variables.&nbsp;<br>- Exit Ticket (M-6-6-1_Exit Ticket and Key). Use exit tickets to quickly assess student comprehension at the end of the lesson. Give students 5 minutes or fewer to complete their tickets. Collect papers as students leave the classroom.</p>

<p>Scaffolding, Active Engagement, Modeling&nbsp;<br>W: Introduce the concept of variables to the class. Emphasize that a variable represents an unknown number.&nbsp;<br>H: Display the ABC Variables sheet from Resources folder and provide students examples of words to "add" together based on the sheet. Next, have them create equations using math word sentences. Distribute the Signal Words template to help students identify which words refer to which operation or symbol.&nbsp;<br>E: Encourage students to practice writing equations with variables (not yet solving the variables), some starting with the equation and writing it out in word form, and some starting with the word form and writing it as an equation.&nbsp;<br>R: Students will continue to write equations with variables, but will now include story problems.&nbsp;<br>E: Students will verify their answers by comparing them to those of their partners and discussing any disagreements among themselves or with another group for verification.&nbsp;<br>T: Adapt the lesson to the needs of the students. Students who need more experience can participate in small-group activities with tiered problems. Create flashcards with equations involving variables for extra practice or to use in class throughout the year. Divide the equations into parts if students are having trouble translating the entire equation. Expansion activities are supplied at the end of the lesson and are recommended for students who want to be challenged beyond the requirements of the standard. Students that are ready may be able to solve for the variable.&nbsp;<br>O: This lesson aims to teach students how to translate written expressions into symbolic expressions/equations.&nbsp;</p>

<p><strong>"Today we will look at expressions that contain variables. A variable is a letter that represents an unknown number in an expression. Remember that an expression differs from an equation. An expression does not contain the equal sign. When you solve for a variable, you discover the number value the variable represents. Symbolic expressions with variables are utilized in accounting, building, and even in science. The purpose of this lesson is to be able to look at a written statement and convert it into a symbolic expression with a variable."</strong><br><br>Display the ABC Variables template (M-6-6-1_ABC Variables) for students to see. <strong>"Look at the alphabet letters in the top row. The bottom row shows that each letter has been given a value. What is the value of the expression </strong><i><strong>h + a + p + p + y</strong></i><strong>?"</strong> Allow students to work together to discover the value of this expression. Ask students to explain how they solved this expression. Record your responses on the board (<i>Possible answer: 11 + 1 + 2(17) + 25 = 71</i>). Say, <strong>"Variables can be substituted for values. Once we have the values of the variables, we may evaluate the expression. Let's take another example: </strong><i><strong>m + a + t + h</strong></i><strong>."</strong> Allow students to work together to discover the value of this expression. Ask students to explain how they evaluate this expression. Record your responses on the board. (<i>Possible answer: 15 + 1 + 21 + 11 = 48</i>)&nbsp;<br><br><strong>"Now you are going to look at some statements and practice translating each of them into a symbolic equation that contains a variable."</strong>&nbsp;<br><br>Write this on the board: <i>Twelve more than a number equals fifty-two</i>. As you go through each part of the statement, write the equation on the whiteboard. Say, <strong>"In order to write this as a symbolic equation, we must first break the statement apart and translate it into numbers and symbols. </strong><i><strong>Twelve more than</strong></i><strong> indicates that we are adding, thus the equation will begin with 12+. The following part of the statement is </strong><i><strong>a number</strong></i><strong>. This would be the variable. We might choose any letter for the variable. The equation so far is 12 + </strong><i><strong>n</strong></i><strong>. The final part of the statement is </strong><i><strong>fifty-two</strong></i><strong>. This tells me where the equal sign should be, so the equation is 12 + </strong><i><strong>n</strong></i><strong> = 52."</strong>&nbsp;<br><br><strong>"Let's look at another example where we read a statement and then turn it into a symbolic equation that contains numbers, symbols, and variables."</strong> Write the following on the board: <i>Six is fifteen less than three times a number</i>. As you explain each step, write it down for students to see. <strong>"I can start by separating the statement into parts:&nbsp;</strong><br><br><strong>"</strong><i><strong>Six is | fifteen less than | three times | a number</strong></i><strong>.&nbsp;</strong><br><br><strong>"I can translate </strong><i><strong>Six is</strong></i><strong> into </strong><i><strong>6 =</strong></i><br><br><strong>"This is subtraction, but </strong><i><strong>fifteen less than</strong></i><strong> means I have to remove 15 from the initial number.&nbsp;</strong><br><br><strong>"The phrase </strong><i><strong>three times</strong></i><strong> can be interpreted as </strong><i><strong>3 ×</strong></i><strong>&nbsp;</strong><br><br><strong>"The phrase </strong><i><strong>a number</strong></i><strong> can be interpreted as the variable </strong><i><strong>m</strong></i><strong>.&nbsp;</strong><br><br><strong>"So, the equation would be 6 = 3 × </strong><i><strong>m</strong></i><strong> − 15."</strong>&nbsp;<br><br>Divide students into small groups and give each one a copy of the Signal Words Template (M-6-6-1_Signal Words Template). Encourage students to come up with signal words that will assist them recognize the operation being referred to in a written expression. Once the groups have had a chance to brainstorm, make a class list on chart paper. As an alternative, make a class list on chart paper and have students transfer the information to their templates. This will be an important resource for students to refer to throughout the lesson/unit.&nbsp;<br><br>At this point, it would be good to show students various ways to represent multiplication. Distribute the Ways to Show Multiplication and Division worksheet (M-6-6-1_Ways to Show Multiplication and Division) and encourage students to use it as a resource throughout the lesson.&nbsp;<br><br>To improve students' ability to write equations with variables, separate them into small groups and distribute a copy of the Silent Pass with Variables worksheet (M-6-6-1_Silent Pass with Variables). Place a copy of the worksheet in the center of each group. <strong>"The best approach to improve your ability to write equations with variables is through practice. We'll participate in an activity called Silent Pass with Variables. Each individual in your group should use a distinct color so that it is easy to distinguish which questions each person has answered. You will answer one question on your worksheet in your designated color. When you're finished, trade papers with someone in your group, correct any errors, and then respond to a new question. When you're completed, trade papers again, making sure to get a new sheet, and repeat the process until time is up."</strong> (Set time limit at 10 to 15 minutes.) <strong>"Try to answer as many questions as possible in the time given. Before you begin, let me remind you of the title…SILENT Pass with Variables."</strong><br><br>Monitor the students' performance as they complete this task. You can tell which students are struggling by looking at which color distinguishes them. When the time is up, gather the class and go over any questions that students need answered. Remind students that there may be more than one correct answer when writing an expression or equation due to the various ways to express the operations of addition, subtraction, multiplication, and division. Refer to the Signal Words template that the students created on chart paper.&nbsp;<br><br>Use this opportunity to determine what may be confusing to students. Review items on the Silent Pass worksheet. Allow students time to think of questions. They will most likely want to know about alternative wording for some of the written expressions.<br><br>In the following assignment, students will work independently to create symbolic equations with numbers, variables, and symbols. Expressions will be incorporated in word problems.&nbsp;<br><br>Give each student a copy of the Equations &amp; Expressions Involving Variables worksheet (M-6-6-1_Equations &amp; Expressions Involving Variables and KEY).&nbsp;<br>Remind students that before they can solve any problems, they must first recognize the relationship being expressed by breaking down the expression or equation into smaller parts.&nbsp;<br>Ask students to choose which component of the expression or equation should be represented by a variable.&nbsp;<br>Tell them to write a symbolic expression in response to the problem's question.<br>Remind students that they don't need to solve the equation. Students are practicing writing symbolic equations.&nbsp;<br>During this activity, students will have the opportunity to update and refine their ideas on this concept. Be available to provide immediate assistance to students who may require urging to complete the process of writing expressions or equations containing variables.&nbsp;<br><br>After students have completed the worksheet, gather them together to discuss generalizations about when to use addition, subtraction, multiplication, and division. (<i>Possible responses: Adding is when you combine items; "less than" implies you subtract, but you must be careful which number comes first; "times" a number is multiplication; and when you need equal parts, you divide.</i>) Allow students to pair up and compare their responses to the Equations &amp; Expressions Involving Variables worksheet. If their responses do not agree, have students talk to another pair of students to figure out why their answers differ. Examine student engagement and performance. Set up a place where you will be available to assist students who are having difficulties understanding the concepts, even with the help of their classmates. Observe and gather small groups to correct misconceptions.<br><br><strong>Extension:</strong><br><br>This lesson is intended to introduce students to the concept of translating written expressions into symbolic expressions or equations. At this point, students are not required to solve such problems. There may be instances in this lesson when an explanation of how to use parenthesis in mathematical expressions or equations is required. Lesson 3 provides a more in-depth look at order of operations and properties.&nbsp;<br><br>The following are some suggestions for tailoring this activity to the needs of your class.<br><br><strong>Routine:</strong> Create a set of flashcards that may be represented as expressions or equations involving variables, similar to those used in this lesson. (For a sample, see M-6-6-1_Routine Flash Card Example).<br><br><strong>Small Group, Tiered Problems:</strong> The difficulty of the problems varies according on the student's proficiency. For students who struggle with translating written statements to expressions/equations containing a variable, break the sentences down so they can examine at smaller pieces at a time (for example, <i>four times | a number | is | forty-eight</i>).&nbsp;<br><br><strong>Expansion:</strong> Students that are skilled at translating statements into symbolic expressions/equations can practice solving for the unknown variable. At this stage, students can solve using whatever strategy makes sense to them. For example, students can use guess and check to see if they can discover numbers that can be replaced for the variables in order to make the equation true.</p>