<p>The link between place value and multiplication will be clear to the students. Students are going to:&nbsp;<br>- Learn how to depict and identify an array.&nbsp;<br>- Possess the ability to discriminate between an array's rows and columns.&nbsp;<br>- Use arrays to solve basic multiplication problems.</p>

<p>- How do we represent, compare, quantify, and model numbers using mathematics?&nbsp;<br>- What mathematical representations exist for relationships?&nbsp;<br>- What qualifies a tool or strategy as suitable for a particular task?&nbsp;<br>- How can information be presented and arranged to shed light on the relationship between different quantities?</p>

<p>- Array: A rectangular arrangement of objects in equal rows and equal columns.&nbsp;<br>- Factor: The number multiplied in a multiplication expression.</p>

<p>- My Full Moon Is Square by Elinor J. Pinczes. Houghton Mifflin, 2002<br>- twelve counters for each student (optional)<br>- 30 counters or cubes<br>- Looking at Arrays (M-3-2-3_Looking at Arrays and KEY)<br>- Arrays for 12 KEY (M-3-2-3_Arrays for 12 KEY)<br>- Fruit Array (M-3-2-3_Fruit Array)<br>- Number Cards (M-3-2-3_Number Cards), two copies with cards cut apart<br>- Number Card Mat (M-3-2-3_Number Card Mat)<br>- Spin and Spin Again Recording Sheet (M-3-2-3_Spin and Spin Again Recording Sheet)<br>- Spin and Spin Again Spinners (M-3-2-3_Spin and Spin Again Spinners)<br>- Spin and Spin Again Spinner Template (M-3-2-3_Spin and Spin Again Spinner Template) and paper clips to use as spinners<br>- Array Assessment (M-3-2-3_Array Assessment and KEY)</p>

<p>- Observe students working in small groups and at their workstations, and participate in teacher-student conversations to gauge their level of mastery.<br>- The M-3-2-3_Array Assessment and KEY formative assessment example can be utilized to gauge students' comprehension levels through paper-and-pencil assessments. There are many pages. Make your selection based on the results of your assessment.</p>

<p>Modeling, Active Participation, and Scaffolding&nbsp;<br>W: In addition to learning about arrays, students will continue to work on multiplication story problems as they learn how to use arrays as a useful tool for problem-solving.&nbsp;<br>H: To introduce the concept of arrays, the teacher reads My Full Moon Is Square by Elinor J. Pinczes. Though it centers on square arrays, it will explain the idea of organizing arrays.&nbsp;<br>E: The instructor explains to students about arrays, and clearly defines what constitutes a row and what a column. Students will practice distinguishing between rows and columns. The instructor provides an example of how to use an array in a solution and explains that it is an additional multiplication model. "Lookin' at Arrays" is a worksheet completed by students that serves as a basic overview of multiplication's commutative property.<br>R: The task at hand requires students to use a total of twelve counters to explore and discover the number of arrays they can produce. After the activity, a few students will be selected to present their findings to the class. This will help to clarify any doubts and provide a summary of what they have learned.<br>E: The instructor evaluates students' arrays and explains concepts. Group those who need additional practice for reinforcement.<br>T: The lesson can be adjusted to suit the unique needs of the class. The teacher can display group photos to the class and ask them to state how many people are in each group and the total number of people. To help students understand the commutative property of multiplication, teachers can assign them to create arrays based on word problems and then rotate those arrays to illustrate that 3×5 is the same as 5×3.&nbsp;<br>O: The lesson aims to demonstrate how to use arrays to solve multiplication problems and introduce the commutative property of multiplication.</p>

<p><strong>"Today we will continue our work with multiplication. A problem that needs to be solved will be presented to you, and you must find a solution. Although we have been working on problems all year, you will be given new challenges to solve today."</strong><br><br>Show the cover of Elinor J. Pinczes' book <i>My Full Moon Is Square</i> to the students.<br><br><strong>"I'd like to read you a book before we start working with arrays. Let's examine the front. What topic do you anticipate the book to cover?"</strong><br><br>Consider the book's predictions and recommendations from the students.<br><br><strong>"The title of the book is </strong><i><strong>My Full Moon Is Square</strong></i><strong> by Elinor J. Pinczes. I want you to take note of the moon's changes on each page as we read the story."&nbsp;</strong><br><br>Ask students questions about the book and the changes they observed in the moon after you have finished reading it. Possible sample questions are as follows:<br><br>What did you learn from the book?&nbsp;<br>What observations did you make about the moon?&nbsp;<br>What makes you believe that the moon is a square in the title?&nbsp;<br>What was the arrangement of the fireflies?<br><br><strong>"The fireflies were organised. Each of them was arranged in columns and rows. An array is what the fireflies were arranged into."&nbsp;</strong><br><br>Understanding how to multiply using an array model is crucial, as it is connected to numerous mathematical ideas. Algebraic properties, such as the commutative property, can be demonstrated using the array model.<br><br><strong>"An array is a collection of items arranged in rows and columns, similar to boxes, pictures, and other objects. Arrays are useful for visualizing a problem or determining the total number of objects by looking at the array."</strong><br><br><strong>"Today, we will be continuing our work on multiplication but using a different model, the array model. We will examine the similarities and differences between the grouping model and the array model as a class. To start, let's create a chart that shows the various multiplication models we have used in our classroom."</strong> You can begin working on this chart before the lesson.<br><br>(picture 1)<br><br>To understand arrays, it's essential for students to grasp the difference between rows and columns. Emphasize that columns are vertical while rows are horizontal, and columns are always counted after rows.&nbsp;<br><br>As part of the class activity, please draw the following star constellation on the chart: If some students are not familiar with arrays, make sure to explain the concept by including the details mentioned above.<br><br>(picture 2)<br><br><br>An array contains:<br><br>both columns and rows<br>rows with an equal number of objects spaced evenly apart.<br>columns with an equal number of objects spaced evenly apart.<br><br>Request that students describe their array in a number sentence. Remind the students that columns are counted after rows. Put the following in the chart:<br>(picture 3)<br><br><br><strong>"As we've covered a little bit more of the array model, is there anything else you'd like to share about what you found in the book we read before class?"</strong><br><br>(Students may have responded, "The fireflies created a display—the moon. As the story progressed, it continued to change.") Ask the pupils if they noticed the change in the moon. Did they notice that the 3-by-5 model above is shaped like a rectangle, whereas the arrays in the books were just squares? The arrays in the book have the same number of rows and columns and form squares rather than rectangles when drawn. This is why they are referred to as square arrays.<br><br>1 × 1, 2 × 2, 3 × 3 …<br><br>Distribute copies of the worksheet titled "M-3-2-3_Looking at Arrays and KEY". Instruct the students to examine each array and note down the number of rows and columns it has. Encourage them to draw a circle around each row or column. Also, ask them to write a multiplication equation for each array.&nbsp;<br><br>Next, direct their attention towards the last two arrays and ask them to note that even though they have different looks, they both equal 12. Explain to them that the equation 4x3=3x4 is a commutative property. Although the arrays appear differently, each equation contains the same number of objects.&nbsp;<br><br>Finally, provide each student with thirty counters or cubes and ask them to set them up in a corner of their desks. Ask them to create arrays according to the information you provide. While they work, inspect their work by going around to see it.<br><br>Some examples of prompts are:<br><br>Show me three rows of two.<br>Put your desk in four rows of five.<br>Construct a 6-by-3 grid.<br>Sam was carrying two bags. There were five apples in each bag. What array model would I use to represent this problem?<br>Cindy had six granola bars on each of her four granola bar plates. What was the total number of granola bars she had on each plate? To illustrate your response, use an array model.<br><br>Students should discuss their ideas and share their array models.<br><br><strong>"I will be assigning a task to each person to complete independently. While you work on the task, I will come over to say hello. You will have to explain your approach to completing the assignment. It's okay if you can't figure it out entirely. Please write your response on paper. During the final ten minutes of class, the whole class will review the tasks together."</strong><br><br>Ensure that each student has twelve counters or more.<br><br><strong>"Your task is to find as many array models as possible that add up to 12. For the first few minutes, please work on this task alone. After a few minutes, you will be able to show your work to a partner. You can share your work when I tell you to. Remember to record your results."</strong><br><br>Ensure that the students comprehend what is being taught by moving around and observing each of them.<br><br>Encourage students to work in pairs and compare their recordings and assignments. At the end of the lesson (M-3-2-3_Arrays for 12 KEY), select a few students to present their work using the board, overhead projector, or other projection system.<br><br>Throughout the task, you will have the opportunity to assess students through questions and discussions. You may need to divide the class into smaller groups to explain the material more effectively. Alternatively, you can evaluate their learning at a later time.<br><br>To establish the connections between the various models used in division and multiplication, students will need to practice multiplication problems extensively.<br><br><strong>Extension:</strong><br><br>To meet your students' needs throughout the year, implement the strategies and activities listed below.<br><br>Routine: Show students a picture of groups of fruit arrays (M-3-2-3_Fruit Array). Ask students to state how many people there are overall and in each group. Students could state:<br><br><i>"The oranges form a 3-by-2 array. That comes to a total of six oranges."</i><br><br><i>"Six oranges is equivalent to three groups of two."</i><br><br>Throughout the year, the image can be altered to reflect the interests of the students.<br><br><strong>Mini-Lesson:</strong> Give the students a multiplication problem.<br><strong>"Stanley put some hamburgers on the grill. He arranged the hamburgers into three rows, five in each row. On the grill, how many hamburgers were there?"</strong><br><br>Ask students to use circle counters to construct an array. Talk about the constructed arrays. A 3-by-5 array and a 5-by-3 array are similar, but some students won't notice that. To help students see this similarity, stack the arrays on top of one another. Take the conversation to the commutative property. Do this several times.<br><br><strong>Small Group: </strong>Each student in the small group should be given a laminated Number Card Mat (M-3-2-3_Number Card Mat). Shuffle two sets of Number Cards (M-3-2-3_Number Cards) before piling them. Ask students to select two cards at random and place them on their mats. Instruct each student to create an array using the two number cards as a basis. Once the first array is complete, ask the student to switch the cards and create a second array.<br><br>It is possible to assign the same numbers to each student. Assess their problem-solving skills and clarify any misunderstandings.<br><br><strong>Workstation:</strong> To organize a classroom activity, you can group the students into small teams or set up different workstations around the room. Each student will need a recording sheet (M-3-2-3_Spin and Spin Again Recording Sheet) and a paper clip or spinner component, in addition to the Spin and Spin Again spinners (M-3-2-3_Spin and Spin Again Spinners).<br><br>Players will need to write down the multiplication sentence after spinning both spinners on their recording sheet. They will also need to draw a dot array for every multiplication sentence. (To change the numbers in the spinners, see M-3-2-3_Spin and Spin Again Spinner Template)<br><br>These classes are designed to progress from teaching the relative size of a number to estimating a large number of items. The last step involves using visual aids and hands-on activities.</p>