<p>This lesson focuses on applying multiplication and division to solve real-world problems. For every problem, students are required to write a number sentence that includes the solution. Students are going to:&nbsp;<br>- Use contextual cues to distinguish between division and multiplication problems in the real world.&nbsp;<br>- Convert real-world issues into numerical sentences involving multiplication or division, then use the product or quotient to find the solution.</p>

<p>- What are the mathematical representations for relationships?&nbsp;<br>- What are some applications for expressions, equations, and inequalities in the quantification, modeling, solving, and/or analysis of mathematical situations?&nbsp;<br>- How does effective communication benefit from mathematics?&nbsp;<br>- How do we represent, compare, quantify, and model numbers using mathematics?</p>

<p>- Division: The mathematical operation of splitting a quantity into equal groups. (For example, 8 ÷ 2 = 4 because splitting 8 into 2 equal groups results in 2 groups of 4.)&nbsp;<br>- Equation: A statement of equality between two mathematical expressions.</p>

<p>- Color tiles&nbsp;<br>- One copy of the Problem Solving worksheet (M-3-5-1_Problem Solving and KEY) per student&nbsp;<br>- One copy of the Multiply or Divide worksheet (M-3-5-1_Multiply or Divide and KEY) per student&nbsp;<br>- One copy of the Zero and Eight worksheet (M-3-5-1_Zero and Eight and KEY) per student&nbsp;<br>- One copy of the Lesson 1 Exit Ticket (M-3-5-1_Lesson 1 Exit Ticket and KEY) per student</p>

<p>- The Zero and Eight worksheets (M-3-5-1_Zero and Eight and KEY) can be used to assess students' comprehension of translating and resolving multiplication and division problems from real-world scenarios.&nbsp;<br>- Use the Multiply or Divide worksheet (M-3-5-1_Multiply or Divide and KEY) to quickly evaluate students' ability to determine which method to use when solving real-world problems for multiplication or division.&nbsp;<br>- Utilize the Lesson 1 Exit Ticket (M-3-5-1_Lesson 1 Exit Ticket and KEY) to assess students' comprehension of translating and resolving real-world division and multiplication problems on the fly.</p>

<p>Formative assessment, explicit instruction, modeling, scaffolding, and active engagement&nbsp;<br>W: Students will gain the ability to solve real-world problems by translating them into multiplication and division number sentences. The main goal is to assist students in identifying contextual cues and figuring out whether they point to division or multiplication.&nbsp;<br>H: Draw in students by posing real-world issues and requesting that they model the issues using colored tiles.&nbsp;<br>E: Assign students to work in pairs to construct appropriate division or multiplication number sentences and model the real-world problems. Examine these exercises to make sure students can extract the data, solve the problem, and write a proper number sentence. Assist students in learning to recognize contextual cues that point to division or multiplication by using the Multiply or Divide? worksheet.&nbsp;<br>R: As they finish the Zero and Eight worksheet, students will review the commutative and associative properties of multiplication. Students will need to convert real-world problems into multiplication and division number sentences and solve them during this in-class assignment.&nbsp;<br>E: The correctness of the students' answers on the worksheets Zero and Eight will be the basis for their evaluation. Additionally, a student's performance on the Lesson 1 Exit Ticket will be considered in evaluating them.&nbsp;<br>T: You can adapt the lesson to fit the needs of your students by using the ideas in the Extension section. There are suggestions in the Routine section for incorporating concept reviews of lessons at various points during the academic year. For students who are prepared for a challenge above and beyond the requirements of the standard, extensions are suggested.&nbsp;<br>O:&nbsp;This lesson's main goal is to have students convert real-world issues into division and multiplication number sentences and then solve them. To&nbsp;model the action in&nbsp;real-world problems, students first use color tiles as part of the scaffolded lesson plan. Students gain the ability to recognize contextual cues that point to the typical division or multiplication action. Students will get practice translating and resolving real-world issues using&nbsp;contextual cues.</p>

<p><strong>Creating a Multiplication and Division Model with Manipulatives</strong><br><br><strong>"Today, we'll talk about how to turn real-world problem situations into number sentences. After that, we'll solve the number sentences. First, let's work with some manipulatives. I'll be distributing some colored tiles. Find a partner. About 40 colored tiles will be distributed to each pair of students."</strong><br><br>To finish this task, students should work in pairs. Provide every student pair with a minimum of 40 color tiles.<br><br>Assign each student a copy of the Problem Solving worksheet (M-3-5-1_Problem Solving and KEY).<br><br>Ask for a volunteer: <strong>"Will someone please read the first example aloud?" </strong>Once a student has read the problem, have them describe the circumstances. <strong>"Could you please explain the problem aloud?" </strong>It is likely that students will be able to explain at least some of the issues. Once the important details (who and what) have been mentioned, ask follow-up questions to the students. Then, use short phrases to write the information on the board.<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; There are 3 kids.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;Each kid has 6 cars.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; How many cars in all?<br><br>Ask students to model this problem. <strong>"Work together with your partner and use color tiles to model this problem."</strong><br><br>After they're done, ask one pair of students to show how they used color tiles to model the problem. Next, give an example of how to sketch a picture of the model. On their practice worksheet, have students draw the model. (In order to symbolize the three children, you might want to draw a person next to each group.)<br><img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 17.10.41.png" width="394" height="125"><br>Now, ask the class, <strong>"What number sentence can we write for this problem?"</strong>. Some students will probably propose 6+6+6 or 3×6=18. It is important to focus on the multiplication number sentence and prompt students to consider it as a substitute representation for repeated addition.<br><br>Also, remind students that the number sentence 3×6=18&nbsp;is appropriate because the sentence can be read as “3 groups of 6 are equal to 18." Although 3×6 = 6×3 according to the commutative property, the number sentence 6×3=18 is inappropriate because there aren't six groups of three cars. Students can distinguish between division and multiplication word problems by understanding what multiplication means, which can be taught by having them read the equation as three groups of six.<br><br><strong>"Let's now slightly modify the issue. Or, let's say we are aware that three children will receive an equal share of the eighteen toy cars. For this problem, what number sentence can we write?" </strong>Help students understand that since we are dividing a given number into equal groups, this situation requires division (18 ÷ 3 = 6). Additionally, highlight how the new division problem (18 ÷ 3 = 6) and the original multiplication problem (3 × 6 = 18) have&nbsp;opposite relationships."<br><br>Provided with the Problem Solving worksheet (M-3-5-1_Problem Solving and KEY), have students work in pairs to complete it.<br><br>After the students have finished the worksheet, have them write the matching number sentence and model each problem in pairs. When students solve problems in the real world, they frequently find it difficult to decide which operation to apply. Make sure to pose the question,<strong> "How did you know what operation to use? </strong>"to the pair of students or the class as a whole for each problem. How can you determine which method to use to solve the problem—multiplication or division? (When there was repeated addition, I divided the number into equal groups; otherwise, I multiplied it.) Language used to explain these distinctions includes the following: division is used when there is a single large group that you wish to divide into several groups of equal size, and multiplication is used when there are several groups of equal size and you want to find the total amount.<br><br><strong>Translating Words to Multiplication or Division Problems</strong><br><br>Students frequently find that translating sentences into mathematical symbols is the most difficult part of solving real-world problems. The goal of this exercise is to teach students how to recognize important terms that denote division or multiplication.<br><br>Give each student a copy of the worksheet Multiply or Divide? (M-3-5-1_Multiply or Divide and KEY).<br><br>Present the worksheet. <strong>"Observe that the worksheet has two columns. Word problems are listed in the column to the left. The right column contains number sentences. Kindly collaborate in pairs once more. Put the right number of sentences in the word problem. Take caution. Observe how similar many number sentences are, like this one. Determining whether the issue is one of multiplication or division is the aim. Let's examine the first one together." </strong>Commence as follows: <strong>"What number sentence, in your opinion, best sums up number one?" </strong>(B)<strong> "Why do you suppose the first problem is a multiplication problem?"</strong> (There are fifteen pies or groups; each pie or group contains three apples; the objective is to ascertain the total number of apples in all of the of the pies.) Assist students in concentrating on multiplication as a means of calculating the total in situations where there are multiple equal groups. Verify if the color tiles from the prior exercise are still available to the pupils. To determine whether the problem calls for multiplication or division, some students might want to model it using the tiles. <strong>"Now, finish the worksheet with your partners."</strong><br><br>Once students have completed the practice worksheet, it is crucial that they discuss each problem in pairs. It's important to highlight how they decided whether to divide or multiply the data.<br><br>Ask students to elaborate on the appropriate number sentence for every problem they encounter. Since number 3 is the first division problem, here is a summary of how you might want to talk about it.<strong> "In your opinion, what number sentence best represents number three?"</strong> Many groups will likely say G. <strong>"Why do you believe that the third problem is a division problem?" </strong>Have a student or students explain it to you. The common response from students is, <strong>"There are a total of 14 bananas; the goal is to determine how many bananas each monkey gets to eat. The total number of bananas must be divided into 2 equal groups for the 2 monkeys."</strong> Encourage your students to concentrate on division by having them start with the total and divide it into equal groups.<br><br>[Note: There are two ways that division can happen. Finding the number of people in each group is the aim of division, which can take the form of splitting the total into a predetermined number of groups. This is the outcome of the monkey puzzle. There were two equal groups of the total of fourteen bananas, and the answer was the number of bananas in each group. Another way division can occur is if the total is split up into groups of a given size, with the objective being to determine the maximum number of groups that can be formed. Problem number eight is the same kind. Identifying how many groups there will be is the objective. There are eight pencils in total, and the pencils are grouped into twos. Students will be prepared for both types of division even if they are unaware of the minor variations in how division can be presented if they concentrate on division as being given the entire amount and dividing it into equal groups.]<br><br>All students should receive copies of the Zero and Eight worksheet (M-3-5-1_Zero and Eight and KEY). Give the students this worksheet to finish, either at home or in class. Utilize the worksheet to evaluate students' comprehension of translating and resolving multiplication and division problems from the real world.<br><br><strong>Extension:</strong><br><br>As the lesson needs to be adjusted, use the suggestions listed below. Ideas for reviewing lesson concepts throughout the year are provided in the Routine section. For those who would benefit from them, the Small Group section provides extra practice opportunities. For students who are up for a challenge beyond what the standard requires, there are opportunities in the Expansion section.<br><br><strong>Routine: </strong>Ask students to come up with real-world problems involving division and multiplication throughout the school year. How many cookies can each student have, for instance, if there are 48 cookies and 24 students?<br><br><strong>Small Group: </strong>Students who require more practice might be divided into groups of two or three to work on modeling word problems with manipulatives. Help students recognize that "separating into equal groups" is division and "combining equal groups" is multiplication. Additional division and multiplication word problems are available on this website for use with small groups.<br><br><a href="http://www.beaconlearningcenter.com/WebLessons/CameronsTrip/default.htm">http://www.beaconlearningcenter.com/WebLessons/CameronsTrip/default.htm</a>&nbsp;<br><br>Expansion: For students seeking a more challenging online experience, the three websites listed below are recommended. Students must solve multistep real-world problems in each of them. Students must perform two operations in many of them as well. http://www.prongo.com/farm/game.html<br><br><a href="http://www.studyzone.org/testprep/math4/d/twostep4p.cfm">http://www.studyzone.org/testprep/math4/d/twostep4p.cfm</a>&nbsp;<br><a href="http://www.mathplayground.com/WordProblemsWithKatie2.html">http://www.mathplayground.com/WordProblemsWithKatie2.html</a></p>