<p>Students will estimate a large number of items to form an idea about the relative size of a number. Students are going to:<br>- Skip counting to solve multiplication problems.<br>- Collaborate to find solutions to multiplication problems.<br>- Convert grouping problems into numerical expressions.</p>

<p>- How are mathematical representations of relationships made?<br>- How can the arrangement and visualization of data help reveal the relationship between quantities?<br>- What are some applications for expressions, equations, and inequalities in the quantification, modeling, solving, and/or analysis of mathematical situations?<br>- In what ways can mathematics facilitate efficient communication?<br>- What relationships in mathematical contexts can patterns be used to describe?<br>- How can we use probability and data analysis to make predictions?<br>- How can identifying regularity or repetition help with problem-solving efficiency?<br>- How do we represent, compare, quantify, and model numbers using mathematics?<br>- What qualifies a tool or strategy as suitable for a particular task?</p>

<p>- Estimate: To find an approximate answer.</p>

<p>- Suzanne Aker. (1992). <i>What comes in 2’s, 3’s and 4’s? </i>Aladdin.<br>- Paul Giganti, Jr. (1993). <i>Each Orange Had 8 Slices</i>. Greenwillow Books, 1993.<br>- construction paper<br>- markers<br>- journals or paper<br>- Sample School Multiplication Story Problems (M-3-2-2_School Multiplication Story Problems and KEY) (optional)<br>- Lesson 2 Exit Ticket (M-3-2-2_Lesson 2 Exit Ticket and KEY)</p>

<p>- Small-group work, workstations, and teacher-student conversations can all be used for ongoing formative assessment.&nbsp;<br>- Students' progress and mastery can be further assessed by using the Lesson 2 Exit Ticket (M-3-2-2_Lesson 2 Exit Ticket and KEY).</p>

<p>Formative assessment, explicit instruction, modeling, scaffolding, and active engagement<br>W: The teacher uses different techniques such as grouping, skip counting, proof drawing, repeated addition, word sentences, and number sentences to teach students the concept of simple multiplication. Students are taught to represent multiplication story problems in multiple ways so that they can solve them easily.<br>H: Students are taught how to use skip counting as a method for solving multiplication word problems. The teacher reads the problem aloud to the students, and then they work in pairs to come up with a list of related items. For example, pairs of gloves, boots, and so on. After this, they move on to working in groups of three and so on.<br>E: You can use drawings on the board to summarize this method for the class, using some of the skip-counting ideas that the students came up with. The teacher develops the concept of groups through the reading of Paul Giganti Jr.'s book, Each Orange Had Eight Slices. The instructor then goes over the object groupings in the book and various methods for calculating their totals.<br>R: The instructor shows the multiplication problem-solving poster and completes a word problem using the instructions provided. This will compile all of the various approaches to solving a multiplication story problem.<br>E: Give the students two word problems to solve using the steps for solving multiplication problems. There are numerous examples of multiplication story problems available as resources.<br>T: To make multiplication lessons more approachable, teachers can assign students to work in pairs and solve multiplication problems using skip counting. They can also provide students with more multiplication story problems with two factors from the Sample School Multiplication Story Problems sheet. For students who are ready for a bigger challenge, they can try multiplication problems with three factors.&nbsp;<br>O: This lesson aims to teach multiplication through a progression of well-known skip-counting methods and grouping</p>

<p><strong>"Today, to&nbsp;better understand multiplication, we will listen to two stories and practice skip counting. In groups, we will formulate multiplication problems and then illustrate them in our own picture books."</strong><br><br>Raise the book titled "What Comes in 2s, 3s, and 4s?" by Suzanne Aker.<br><br><strong>"Now let's examine the cover. What do you think this book will be about?"</strong><br><br>Consider the book's predictions and recommendations from the students.<br><br>After reading the given narrative, divide your class into pairs or let them choose their own partners. <strong>"For this task, you will need to work in pairs and use your creativity to think of some products or things that are available in the same specific size groups. For instance, gloves and shoes are available in pairs. Can you come up with other items that are available in pairs, threes, fours, or even up to tens?"&nbsp;</strong><br><br><strong>"List down all the items that come in twos, threes, fours, and so on up through tens in your groups."</strong> Use the "random reporter" technique to call on various students to respond, and start documenting their responses on a chart pad or the board.<br><br><strong>"Is there anyone in the class who is proficient in skip counting? Someone who can help others understand it better?"</strong>&nbsp;For instance<strong>, "Robbie explained that the number of eyes on a person comes in twos. We can use this to skip counting and find out how many eyes there would be with eight people."</strong> As the students skip counting, write the numbers on the board, overhead projector, or chart pad. Write 1, 2, 3,... 8 above each number: (Ten, Four, Six, Eight,... sixteen). <strong>"We counted by twos, eight times, and the result was sixteen eyes on eight people."</strong><br><br>Next, draw eight sets of eyes on the board or projector. However, do not display them as an array yet.<br><br>(picture 1)<br>&nbsp;<br><strong>"I'm going to read you another book by Paul Giganti, Jr. called Each Orange Had Eight Slices. What do you suppose this book is about based on the cover?" </strong>Consider the book's predictions and recommendations from the students.<br><br>"As we read the story, please take note of the images and groupings of objects on each page." After reading the book, some examples of questions to pose are as follows:<br><br>"What did the book teach you?"<br><br>"How many petals were there?"<br><br>"How many ants were there on each petal?"<br><br>"How many ants were present on every petal? How did you determine that?"<br><br>"How many ants were present on every flower? Justify your answer with an explanation."<br><br>Post the following multiplication procedures on a poster.&nbsp;<br><br>(picture 2)<br><br><strong>"Let's use all the multiplication problem-solving techniques on the poster to solve another problem."</strong><br><br>(picture 3)<br><br><strong>"We will solve this word problem by reviewing the steps on our chart paper. Who wants to draw a proof of concept in front of the board?"</strong> Give students the task of creating their&nbsp;proof drawings for their papers and journals.<br><br>An illustration of a proof drawing:<br><br>(picture 4)<br><br><strong>"Put your skip count numbers in writing directly below your proof drawing. Write a repeated addition sentence beneath the skip count numbers at this point."</strong><br>(picture 5)<br><br>You asked for assistance with filling in the blanks for a group phrase while pointing to a poster. The sentence on the poster reads <strong>"Four five-member groups equal twenty,"</strong> under which you wrote the phrase "addition" on the board. You then instructed the students to write the same sentence in their papers or journals.<br>(picture 6)<br><br><strong>"I'm going to demonstrate how to write a multiplication number sentence now. I'll write the sentence in the same format as the grouping phrase, substituting math symbols for the words. Three numbers are already mathematical symbols: four, five, and twenty."</strong> With spaces between each, write 4, 5, and 20.<br><br><strong>"Is there a mathematical symbol that is equivalent to "groups of"?" </strong>Inform students if they are unfamiliar with the multiplication symbol. <strong>"This is the multiplication symbol for the phrase 'groups of'."</strong> Put a multiplication sign beneath the phrase "groups of."&nbsp;<br><br><strong>"What mathematical symbol might stand in for the phrase "is the same as"?"</strong> Most students are aware that the = symbol denotes the statement "is the same as." The 5 and the 20 should be written with an equal symbol.&nbsp;<br><br><strong>"I need help writing a sentence that provides the solution to the problem. Who can help me?" </strong>Students should be able to state, <i>"Pete's Pet Shop has 20 rabbits."</i><br><br>(picture 7)<br><br>Present the subsequent word puzzles using the overhead projector.<br><br>Rosie's collection of bugs included three spiders. Each spider had eight legs. In total, how many legs did the spiders have? <i>(24)</i><br><br>Del Shawn's bookcase has four shelves. On each shelf, there are six books. What is the total number of books? <i>(24)</i><br><br><strong>"Use the techniques of multiplication problem-solving to solve the following word problems in your journals. Raise your hand when you have solved the first problem so I can review your work."&nbsp;</strong><br><br>As you make your way around the classroom, please grade the assignments and assist students who need it. Once students have finished the first problem, they can start working on the second problem, which can also be used as a homework assignment.&nbsp;<br><br>If you would like to show additional problems to the class or if students need more practice, an optional problem set is available (M-3-2-2_School Multiplication Story Problems and KEY).<br><br><strong>Extension:</strong><br><br>Utilize the following strategies and activities to meet your students' needs all year long.<br><br><strong>Routine:</strong> Students who would like more practice can work with a partner. They should write a multiplication problem using one of the examples in their journal and solve it either through repeated addition or skip counting. Once they are done, they can share a few problems with the class using the random reporter method.<br><br><strong>Small group:</strong> Instruct students to form small groups and give each group construction paper and markers. Then, ask them to draw pictures of objects that come in pairs, threes, and so on. After completing the task, ask students to bind or staple the images into booklets. Students who need extra learning opportunities can make a picture book featuring groups of up to five or nine people.&nbsp;<br><br><strong>Expansion:</strong> For advanced students, give them three-factor multiplication problems. For example, "There are three oranges. Each orange has eight segments, with five seeds in each segment. How many seeds are there in total?"<br><br>This lesson aims to teach multiplication through well-known skip-counting techniques. In the Pete's Pet Shop problem, fives were used as the skip-counting number. The students then wrote down the skip counting as a repeated number sentence. After that, they wrote down the repeated addition of "_____ groups of ______ are the same as ______". Finally, they applied this knowledge to a conventional multiplication number sentence. By writing their answers to word problems in sentence format, students are better prepared to label word problem answers with units in subsequent years.</p>