<p>Students learn different methods for solving multiplication word problems. They will:&nbsp;<br>- create word problems that require multiplication.&nbsp;<br>- create or match a number sentence to a word problem that requires multiplication.&nbsp;<br>- identify different strategies and techniques for solving multiplication word problems.</p>

<p>- What are the mathematical representations for relationships?&nbsp;<br>- What makes a tool and/or strategy suitable for a certain task?&nbsp;</p>

<p>- Equivalence: The relationship between expressions which have an equal value.&nbsp;<br>- Multiple: The product of a given number and a whole number.</p>

<p>- Word Problem Template (M-4-2-1_Word Problem Template)<br>- Observation Checklist (M-4-2-1_Observation Checklist)<br>- Multiplication Practice worksheet and Multiplication Practice KEY (M-4-2-1_Multiplication Practice and M-4-2-1_Multiplication Practice KEY)<br>- base-ten blocks<br>- chart paper<br>- dry-erase boards</p>

<p>- Examine first group work to determine whether students have an overall understanding of problems that require multiplication to solve.&nbsp;<br>- Use dry-erase board activities to assess students' understanding of the two types of multiplication problems: sharing and grouping.&nbsp;<br>- Use the think-pair-share activity from the Extension's Routine section to determine whether students require extra instruction.&nbsp;<br>- Use the Observation Checklist to assess individual students' understanding of the content.&nbsp;<br>- Teacher observation can be used to guide the level of difficulty of instruction at any time during the lesson.&nbsp;</p>

<p>Scaffolding, Active Engagement, Modeling, and Explicit Instruction&nbsp;<br>W: The lesson focuses on answering multiplication word problems. Give students the topic of amusement parks and ask them to brainstorm some word problems.&nbsp;<br>H: Introduce amusement park word problems and engage students in a discussion. Help students comprehend that they can find the other number in the problem if they know one of the numbers and the link between them.&nbsp;<br>E: Encourage students to deal with problems using multiple methods. The more exposure they have to different methods, the more likely they are to use them. Reinforce student thinking about what vocabulary and contexts indicate that a word problem can be solved with multiplication.&nbsp;<br>R: After solving a problem, have students write the associated numerical sentence. This helps students connect the actual calculation to its symbolic representation. Allow students to practice and revise by working through stations.&nbsp;<br>E: Model multiplication problems for students and have them write the corresponding number sentences on a note card. Monitor student replies and clarify any misconceptions.&nbsp;<br>T: To adapt the lesson to your students' requirements, refer to the Extension section for options.&nbsp;<br>O: The lesson prepares students to solve multiplication problems using a variety of strategies. Because the lesson begins with tactile problem solving tools and then progresses to decomposing numbers, students can visualize the multiplication process, making it easier to translate to symbols on paper. Decomposing numbers prepares the way for the partial-products multiplication strategy and division.&nbsp;</p>

<p><strong>“In today's lesson, we'll be using multiplication to solve word problems. First, create a list of important terms or phrases connected to the concept of multiplication. These will serve as clues, guiding us when to use multiplication. Now, can anyone think of any words or phrases that could be telling us to multiply?”</strong></p><p>Allow students to brainstorm and call out key words or phrases while you write their ideas on the board or overhead. (Examples include times, per, each, and product.)</p><p><strong>"We'll look at some examples of word problems that need multiplication. Remember, if we see words from our list in a problem, it could be a clue to utilize multiplication!"&nbsp;</strong></p><p>Present the following word problem.&nbsp;</p><p>Kelly bought three strips of tickets at the amusement park. Each strip had four tickets. What number of tickets did Kelly have?&nbsp;<br><strong>"First of all, what are the 'clues' in the problem that indicate we need to multiply?"</strong> (<i>the word "each"</i>)<br><br><strong>“Work with your friend to create two different ways of solving this problem.”</strong></p><p>Allow students a few minutes to develop two distinct solution methods. When they're completed, ask volunteers to discuss their methods and note them on chart paper. Methods include repeated addition (4 + 4 + 4 = 12), skip counting by 4s (4, 8, 12), making a multiplication equation (3 × 4 = 12), and modeling with counters or chips and counting up the sum.&nbsp;<br><br><strong>“These are all good methods, and it is important to understand them all, but right now we are going to focus on writing multiplication equations.”</strong></p><p>Give every student a dry-erase board. Present the following problems to the students. For each problem, have them write a multiplication number sentence for the word problem on their dry-erase boards and hold them up. Remind students that when writing a number sentence for a multiplication problem, they must include a multiplication symbol and an equal sign.&nbsp;</p><p>The man selling cotton candy had five pink bags. There were four times as many green bags as pink. How many green bags of cotton candy did the men have to sell?&nbsp;<br>The man selling cotton candy had 15 bags to sell. Each bag cost $3, and he sold them all. How much did he receive?&nbsp;<br>There were five roller coasters in the amusement park. There were six times more children's rides than roller coasters. How many children's rides were there?&nbsp;<br><strong>"Can someone explain how they know when to apply multiplication to solve a word problem? What clues are useful to you?"</strong> (<i>the keywords</i>)&nbsp;</p><p><strong>“Now, try to create your own multiplication word problem. If we keep with the amusement park theme, can you come up with a word problem requiring multiplication? Consider the people, rides, games, food, tickets, and souvenir shops you might see in an amusement park. Take a few moments with those around you to see if you can create a word problem that requires multiplication. Then, record your problem on a chart paper.”</strong></p><p>Ask volunteers to discuss their problems. Discuss as a class whether or not each example is a word problem requiring multiplication. If so, ask students to write the multiplication number sentence required for the solution. If these problems are authentic, they can be utilized as a review throughout the unit.</p><p><strong>"We just practiced solving multiplication word problems by writing multiplication equations." Now we'll look about few other ways for using base-ten blocks. Let's try an example together."&nbsp;</strong></p><p>Present the following problem.</p><p>An amusement park ride has 12 cars. Each car can carry three people. How many people can the ride carry?<br>Provide students with base-ten blocks. Encourage students to use the blocks (in multiple ways) to solve the problem. Then, have students record the process they utilized, as well as the number sentences for their solutions. Ask students to share their solutions. Two possible strategies are to form three-cube groups and then count up by threes 12 times, or to create a list of 12 threes to add (repeated addition). Other students may think (6 × 3 + 6 × 3). Students use their knowledge of multiplication facts to break apart products into sums of simpler products. Students may not understand 12 × 3, yet they can divide 12 into two groups of six. Another approach might be to break apart, or decompose, 12 to (10 + 2) and think (10 × 3) + (2 × 3).<br><br>As students discuss their solutions, remind out that each answer contains 10 groups of three, with two further groups of three to be added. Write the following numerical sentence for students to see: (10 × 3) + (2 × 3) = 36.&nbsp;<br><br><strong>"Is the equation true or false? (10 × 3) + (2 × 3) = 12 × 3. Why?"</strong> (<i>True. Both sides of the equation total 36.</i>) <strong>"What is another number sentence that is the same as 12 × 3?"</strong> Encourage students to recognize that any method of dividing up the 12 into a total of two addends and multiplying each addend by three will work. (<i>Examples are (9 × 3) + (3 × 3), (8 × 3) + (4 × 3), and so on.</i>)<br><br>Create additional issues based on the amusement park context.<br><br>An amusement park ride's seats are arranged in long rows. There are 12 seats in each row. There are four rows. How many kids can ride?&nbsp;<br>Tickets for the rides are bought in books of 15 tickets each. There are 5 kids that want to ride the rides. An parent bought five books, so that each child may have one. How many tickets did the adult buy in total?&nbsp;<br>Karl rode three rides before lunch and five times as many after lunch. Karl took how many rides in total?&nbsp;<br>A game at the amusement park cost $0.25. Karl wanted to play the game three times. How much will it cost to play three times?<br><strong>"For each word problem, identify the key words that indicate multiplication and then write three equal multiplication equations that could be used."</strong> Examine performance and explanations. Post some of the methods that students use on chart paper and have them discuss the similarities. Encourage students to use decomposing numbers to answer multiplication problems. For example, consider the following problems: 12 × 4 = (10 × 4) + (2 × 4), 15 × 5 = (10 × 5) + (5 × 5), and so on.</p><p><strong>Station Rotation</strong></p><p>Set up three workstations for students. Station 1 will feature word problems focused on equation writing. Station 2 will allow students to practice writing word problems. Station 3 will concentrate on writing numbers in expanded notation (the distributive property of addition). Monitor student progress as they work at each station. Provide interventions and support as needed. Keep track of the student's understanding using the Observation Checklist (M-4-2-1_Observation Checklist).</p><p><strong>Station 1: Writing Equations</strong></p><p>Please provide the following word problems for Station 1. Ask students to answer the problems using a variety of strategies and as many different equations as possible. Use the first word problem below to demonstrate how equations have equal signs.&nbsp;</p><p>In a package of chocolate chip cookies, Alice counted 15 cookies in each row and there were 3 rows in the package. How many chocolate chip cookies were within the package?&nbsp;<br><i>3 × 15 = 15 + 15 + 15 = _______.</i><br>Students counted eight mysteries on the class bookcase. There were three times more realistic fiction books than mysteries. How many realistic fiction books were on the classroom shelves?&nbsp;<br>A farmer planted 16 rows of tomatoes. The farmer put five tomato plants in each row. What number of tomato plants did the farmer plant?</p><p><strong>Station 2: Writing Multiplication Word Problems</strong></p><p>In Station 2, students will use the Word Problem Template (M-4-2-1_Word Problem Template) to create two separate word problems that require multiplication to solve. Ask them to demonstrate at least two strategies for solving each problem.<br><br><strong>Station 3: Writing Numbers in Expanded Notation (Distributive Property over Addition)</strong></p><p>For Station 3, give students the following number sentences and ask them to explain whether they are true or false, and how they know.<br><br>(10 × 4) + (3 × 4) = 13 × 4<br>24 × 4 = (20 × 2) + (4 × 2)<br>18 × 6 = (10 × 6) + (8 × 6)</p><p>Use base-ten blocks to simulate a multiplication problem. Ask students to write the number sentence that corresponds to the model on a dry-erase board and hold it up. Repeat by demonstrating two or three extra examples for students. Then, have students describe to a partner how they would answer a problem such as 14 x 5. Observe and listen to students to make sure they understand. Correct any misunderstandings.&nbsp;</p><p>Ask students to solve 18 ×7 as a journal response. Then, ask them to explain what they did and why they did each step. Finally, ask students to explain why they used the strategy they did to solve the problem.<br><br><strong>Extension:</strong></p><p><strong>Routine:</strong> Create a two-digit by one-digit multiplication problem on the board. Have students think about and write down two possible ways to express the problem. Pair students up and have them share representations. Discuss the results. This think-pair-share game can be used as a warm-up before another class session or as a way to end this lesson.</p><p><strong>Expansion:</strong> Have students create a poster demonstrating various methods for solving one-digit by two-digit multiplication problems. They can separate each strategy into its own column and title it. Alternatively, have students who have mastered the concept explain strategies to those who need help.&nbsp;<br>Students can use expanded notation to answer multiplication problems: 18 × 6 = (10 × 6) + (10 × 6) - (2 × 6). Ask students to explain why this works. Dividing 18 into 10s may help solve this problem. One group of ten is not enough; two groups of ten are too much. Students should notice that, rather than using 18 groups of six as the original problem stated, estimation is used. Since the number of groups is overestimated by two, the two extra groups of six must be subtracted. Once students can explain why this strategy works, have them try to come up with more multiplication problems where this method may be applied. Students can then swap multiplication problems with a partner and attempt to solve them using extended notation.<br><br><strong>Small Group:</strong> Use the Multiplication Practice Worksheet (M-4-2-1_Multiplication Practice). This worksheet was made specifically for small groups of students.&nbsp;</p><p><strong>Technology Connection:</strong> Use the Rags-to-Riches game to teach students about two-digit multiplication. This game focuses on tens and place value. Students practice multiplication skills and obtain immediate results. See Rags to Riches at <a href="http://www.quia.com/rr/10206.html.">http://www.quia.com/rr/10206.html.</a></p>