<p>Students learn how to write and understand numerical expressions. Students will:&nbsp;<br>- match a numerical expression to a word phrase, then match a word phrase to a numerical expression.&nbsp;<br>- create a word phrase representing a numerical expression, as well as create a numerical expression representing a word phrase.&nbsp;</p>

<p>- How can mathematics help to quantify, compare, depict, and model numbers?<br>- How can mathematics help us communicate more effectively?<br>- How are expressions, equations, and inequalities used to quantify, solve, model, and/or analyze mathematical problems?</p>

<p>- Braces: Symbols used to group certain parts of a mathematical expression, { }.&nbsp;<br>- Brackets: Symbols used to group certain parts of a mathematical expression, [ ].&nbsp;<br>- Numerical Expressions: A mathematical combination of numbers, operations, and grouping symbols.&nbsp;<br>- Order of Operations: The steps used to evaluate a numerical expression: 1) Simplify the expressions inside grouping symbols. 2) Evaluate all powers. 3) Do all multiplications and/or divisions from left to right. 4) Do all additions and/or subtractions from left to right.&nbsp;<br>- Parentheses: Symbols used to group certain parts of a mathematical expression, ( ).</p>

<p>- Writing Numerical Expressions practice worksheet (M-5-6-3_Writing Numerical Expressions Practice Worksheet and KEY)<br>- Expression Matching Games 1, 2, and 3 (M-5-6-3_Expression Matching Games 1, 2, and 3)<br>- index cards</p>

<p>- Use expression matching games to assess whether students need additional teaching.&nbsp;<br>- The exit slip can be used to assess whether students understand how to write and evaluate numerical expressions.&nbsp;</p>

<p>Scaffolding, Active Engagement, Modeling, and Explicit Instruction&nbsp;<br>W: The lesson focuses on writing and understanding numerical expressions. The purpose is to help students translate between word phrases and mathematical phrases (known as expressions).&nbsp;<br>H: Introduce the situations about Amelia's cousins and the teacher's pencil and lead a discussion regarding them. Help students understand the importance of being able to translate between word phrases and the related number phrases or expressions.&nbsp;<br>E: Encourage students to write expressions for different situations. Ask students to share their written expressions with the class. Peer teaching is an extremely strong technique. The more exposure students have to different explanations of the same concept, the more likely they are to grasp and remember it. Encourage students to think about what words or phrases represent hints for each of the four basic operations: addition, subtraction, multiplication, and division.&nbsp;<br>R: Use three Matching Games to improve students' abilities to translate word phrases and numerical expressions. Students working in pairs can also check each other's thinking.&nbsp;<br>E: The Matching Games can test students' understanding as there is only one correct way to create five pairs of cards. Monitor student responses and clarify any misconceptions. Use the exit slip to evaluate an individual's understanding of both writing and interpreting numerical expressions.&nbsp;<br>T: To tailor the lesson to meet the needs of your students, refer to the Extension section for options.&nbsp;<br>O: The lesson prepares students to translate between word phrases and numerical expressions. The lesson begins with situations that need to be translated into numerical expressions and ends with matching activities that require students to translate between word phrases and numerical expressions. A focus on hint words and phrases for each operation improves students' ability to translate word problems into numerical expressions.&nbsp;</p>

<p><strong>"In mathematics, we frequently have to rewrite words and phrases with numbers and symbols. Today, we'll practice writing and analyzing mathematical phrases - more often called mathematical expressions."</strong>&nbsp;<br><br>Present the following situations:&nbsp;<br><br><strong>"Lija has four cousins. Amelia has three less than five times as many cousins as Lija. How many cousins does Amelia have?&nbsp;</strong><br><strong>Hans has six pencils, and Russell has twelve pencils. The teacher bought three times as many pencils as Hans and Russell have together. How many pencils did the teacher buy?</strong>"<br>Now teach students how to write expressions that describe these situations. Many students will probably want to find the answers, which is fine. However, it is important to help them in writing the numerical expression that accurately reflects the situation. A student's ability to translate words into mathematical symbols and numerals is important during problem solving.&nbsp;<br><br>Ask students for ideas on how to write an expression for the number of Amelia's cousins. If there are numerous ideas, write them down on the whiteboard. Work together as a class to decide which of the expressions is correct. This will need students to apply their working knowledge of the order of operations from the previous lesson. (Both 4 × 5 - 3 and 5 × 4 -3 are correct expressions.)<br><br>Ask students, <strong>"What clues did you find in the situation that helped you write the expression? What specific words served as clues for you?"</strong> Students are likely to say "times as many" to signify multiplication. Students are also likely to say "less than" to signify subtraction.&nbsp;<br><br>Mathematical expressions are similar to phrases in English class in that they lack "punctuation" (for example, an equal sign). Mathematical equations, like sentences in English class, have "punctuation" (for example, an equal sign in math). So, 4 × 5 is an expression, but 4 × 5 = 20 is an equation.<br><br>In the second situation, ask for ideas on how to write an expression for the number of pencils the teacher bought. Work as a class to identify which of the expressions created by the students are correct. In this situation, students should use parenthesis to indicate that the sum of 6 and 12 must be computed first, followed by a multiplication by 3. As a result, students' understanding of the order of operations is very important to this lesson.&nbsp;<br><br>Ask students, <strong>"What clues did you find in the situation that helped you write the expression? What specific words served as clues for you?"</strong> Students will likely to say "times as many" (multiplication) and "together" (addition).<br><br>Help students review some key words before moving on. <strong>"The four basic operations are addition, subtraction, multiplication, and division. The result of each operation has its own term. The result of adding two numbers is a sum. The result of subtraction is a difference. The result of multiplying two numbers is a product. The result of dividing two numbers is a quotient."</strong> Write the following table on the board and have students record it in their math notebooks. The final column of the table will be completed once students have finished the Writing Numerical Expressions practice worksheet.</p><figure class="image"><img style="aspect-ratio:472/352;" src="https://storage.googleapis.com/worksheetzone/images/Screenshot_40.png" width="472" height="352"></figure><p>Now, distribute the Writing Numerical Expressions Practice Worksheet (M-5-6-3_Writing Numerical Expressions Practice Worksheet and KEY). Ask students to work in pairs to create expressions for each of the six situations. Keep track of students' progress while they work.&nbsp;<br><br>Provide interventions and support as needed. English language learners and other students who struggle with literacy abilities may require additional support translating between words and symbols. Focus on the important words and phrases listed in the table above. You can also display these words and phrases on a word wall in your classroom.<br><br>Ask six students to volunteer to write the expressions on the board for every situation. Ask the other students to confirm if they have the same expressions. If they have a different expression, ask them to record it on the board as well. Note that each situation can be represented by two or three expressions (the KEY is also included in M-5-6-3_Writing Numerical Expressions Practice Worksheet and KEY). Ask the class to use the order of operations to ensure that the various expressions they have written for a certain situation all have the same value.<br><br>After students have completed the Writing Numerical Expressions Practice Worksheet, ask them to identify any additional "clue" words or phrases to fill out the table's final column. <strong>"Review the situation. Did you notice any other key words or phrases in these situations that indicated a specific operation?"</strong> Students are likely to recognize some of the words and phrases included in the third column. If not, suggest ideas and help them in determining the situation from the Writing Numerical Expressions Practice Worksheet in which the word or phrase was used.</p><figure class="image"><img style="aspect-ratio:473/354;" src="https://storage.googleapis.com/worksheetzone/images/Screenshot_41.png" width="473" height="354"></figure><p>The Expression Matching Games 1, 2, and 3 (M-5-6-3_Expression Matching Games 1, 2, and 3) provide more practice interpreting numerical expressions.&nbsp;<br><br>Each pair of students will need a copy of all three versions of the game. It is important to prepare these in advance since the 10 cards in each game set must be cut out before play can begin. If possible, make a copy of each game set on a different color paper. This will help to keep the various versions of the game separate.<br><br>Ask students to work in pairs. Distribute Expression Matching Game 1 and introduce it as follows. <strong>"We'll play a matching game to practice interpreting numerical expressions. The matching game consists of 10 cards. Five of the cards include a word phrase, while the other five feature a mathematical phrase or expression on them. The goal is to match each word phrase to its matching mathematical expression. To begin, place all 10 cards on the table, with the writing showing. Work together to find all of the matching sets of cards."</strong><br><br>Once all groups have completed Expression Matching Game 1, ask students which expressions were the most difficult to match with their phrases. If students do not find it difficult, be sure to discuss the phrase "four less than the sum of 7 and 3," which is frequently the most difficult for students. Students often think this should be written as 4 - (7 + 3). Remind students that the order of a subtraction problem is important. Finding "four less than" 20, for example, implies subtracting 4 from 20, which is written as 20 – 4.<br><br>Now assign Expression Matching Games 2 and 3 to each pair of students. For Game 2, you might want to suggest students place the 10 cards so that the writing is not visible. Students may then take turns flipping two cards. If the two cards they uncover are a match, they keep them. The student with the most matches at the end of the game is considered the winner. A third Expression Matching Game is also provided. The difficulty level improves somewhat from Game 2 to Game 3.<br><br>With 5 to 8 minutes remaining in the class time, hand out index cards to each student. Ask students to describe the expression 7 + 8 × 3 using a word phrase. Also, use the phrase "4 less than the product of 9 and 2". Ask students to create a mathematical expression that represents this phrase.&nbsp;<br><br>Collect all of the "exit slips" before the students leave the classroom. Review the exit slips before the next class period to discover typical mistakes students make and specific students who need additional support. (7 + 8 × 3 could be described as 7 more than the product of 8 and 3. The expression 9 × 2 – 4 or (9 × 2) - 4 can represent "4 less than the product of 9 and 2".)<br><br><strong>Extension:&nbsp;</strong><br><br>Use the strategies and activities below to meet your students' needs during the lesson and throughout the year.&nbsp;<br><br><strong>Routine:</strong> To refresh students on lesson concepts throughout the year, try the Video Tutorial—Interpreting Numerical Expressions. This website features a video lesson. It focuses on helping students write words to describe expressions, including phrases like "product," "less than," and so on: <a href="http://hoodamath.com/tutorials/5thgrade/Interpreting_Numerical_Expressions_by_Writing_them_in_Sentences.php">http://hoodamath.com/tutorials/5thgrade/Interpreting_Numerical_Expressions_by_Writing_them_in_Sentences.php</a>&nbsp;<br><br><strong>Small Group:</strong> This online activity allows students to practice writing and interpreting expressions: <a href="http://www.mathgoodies.com/lessons/vol7/expressions.html">http://www.mathgoodies.com/lessons/vol7/expressions.html</a>&nbsp;<br><br><strong>Expansion:</strong> Students looking for a new challenge will find this website useful. This online activity encourages students to write equations rather than just expressions, as in this lesson: <a href="http://www.mathgoodies.com/lessons/vol7/equations.html">http://www.mathgoodies.com/lessons/vol7/equations.html</a></p>