<p>This lesson teaches students to break down numbers into smaller parts and look for patterns that emerge. At the end of this lesson, students are going to:&nbsp;<br>- Calculate the decomposition of any number less than or equal to 10, then record the results using equations or drawings.</p>

<p>- How does effective communication benefit from mathematics?<br>- How are relationships mathematically represented?<br>- How can identifying regularity or repetition help with problem-solving efficiency?<br>- How do we represent, compare, quantify, and model numbers using mathematics?</p>

<p>- Addition: Putting numbers together.&nbsp;<br>- Equal: The same in value.&nbsp;<br>- Greater Than: More than.&nbsp;<br>- Less Than: Smaller, or not as many.&nbsp;<br>- Patterns: Designs, shapes, or objects that repeat.&nbsp;<br>- Total: The sum, or amount, in all.</p>

<p>- storybooks that show related sets and patterns, such as The Grouchy Ladybug, by Eric Carle and The Doorbell Rang, by Pat Hutchins<br>- counting manipulatives or dried beans<br>- small cups to hide small sets of objects<br>- leaf workmats (M-K-3-1_Leaves and Ladybugs)<br>- organized charts for counting and recording sets of the numbers 0 to 5 (M-K-3-1_Count Down, Count Up)</p>

<p>- To demonstrate that students have understood the fundamental concepts taught in the lesson, Count Down, Count Up (M-K-3-1_Count Down, Count Up) can be used as a record of student progress. When students can explain that the columns exhibit a decreasing and increasing pattern that changes by ones&nbsp;and that the combination in each row equals five, they are demonstrating understanding.&nbsp;<br>- Observations during the lesson can be used to make ongoing formative assessments, which should center on student participation and their ability to accurately record their work.</p>

<p>Direct Instruction, Modeling, Active Participation, and Scaffolding&nbsp;<br>W: Read one of the recommended tales about matching patterns that grow and shrink.&nbsp;<br>H: Give the ladybug worksheet to the class to use as a pattern activity and talk about the different kinds of patterns that the animals in the story exhibit.&nbsp;<br>E: Write a series of number sentences on chart paper listing all possible arrangements for the five ladybugs on the two leaves, emphasizing that the sums remain the same regardless of the arrangement of the addenda. (You can use this chart paper as an anchor chart.)&nbsp;<br>R: Take note of the pattern that the number sentences have created; the sum stays the same while one column grows and the other decreases.&nbsp;<br>E: Give the students the Count Down, Count Up worksheet, having them copy the number sentences from the board onto their worksheets. Instruct students to explain the pattern in their work.&nbsp;<br>T: Use the same pattern idea to calculate how many school days are left in the current week and how many are left to go. Additional suggestions, such as taking a more hands-on approach and enacting a narrative, are provided to highlight related pattern creations.&nbsp;<br>O: This lesson's main goal is to demonstrate how changing one set can have an impact on an associated set's overall object count.&nbsp;</p>

<p>The lesson's main objectives are to teach students how to break down numbers into smaller subsets and how changes in one set can impact related sets' object counts even when the total number of objects stays unchanged. The lesson starts with a story and a follow-up exercise that demonstrates how to move an object from one set to another while keeping the total number of objects constant. Students talk about how one set gets smaller while the other gets bigger by the same amount. Students then document their work in charts to further illustrate the connections between the sets and the matching addition sentences. They enumerate every possible combination that can add up to five using patterns.<br><br><strong>"Today, I'm going to share a story with you about a grumpy ladybug that I really hate to tell. When I'm done reading the story, we'll discuss its patterns. Next, we'll use leaves and ladybugs to illustrate a different kind of pattern."</strong><br><br>Students listen and look at the pictures while you read The Grouchy Ladybug.<br><br><strong>"What patterns do you notice in the images or the story?"</strong><br><br>After asking them to turn and discuss with a partner, invite them to present their ideas to the class. (<i>The ladybugs' spotted patterns vary. Other animals have patterns as well.</i>)<br><br><strong>"That's correct, indeed. The patterns that you see on the animals in the story are one type of pattern. What sort of animal size pattern does the narrative illustrate?"</strong><br><br>After asking them to turn and discuss with a partner, invite them to present their ideas to the class. (<i>The animals grow in size until the whale returns the grumpy ladybug to the first leaf.</i>)<br><br><strong>"You've gotten really good at identifying and characterizing patterns. You can now record your work and create other kinds of patterns. We need our own leaves and ladybugs before we can create any of the alterations to the patterns."</strong> Give students copies of the ladybug worksheet (M-K-3-1_Leaves and Ladybugs) and instruct them to cut apart the ladybug strip located at the bottom of the page. [Note: To assist students in making connections between patterns in the book and new patterns they will be discovering, this activity may be conducted after alternate book selections with a brief introduction.]<br><br><strong>"How many ladybugs do you have?"</strong> (5) <strong>"You can arrange your ladybugs in any way on the leaves."</strong> Make it clear to students that they are not yet ready to glue the ladybugs to the paper. You could also take a stroll and see if any students are experimenting with different arrangements for the ladybugs already.<strong> "Now, take a moment to observe how other people have applied their ladybugs to the leaves. Did everyone follow the same procedure?"</strong> (<i>I placed four ladybugs on the other leaf and one on the first. There are two ladybugs on one leaf and three on the other</i>.) Use an overhead projector, interactive whiteboard, flannel board, anchor chart, or other tool to demonstrate student responses as they share their arrangements with the class.<br><br>Write addition sentences on the board to correspond with the first two responses, emphasizing to students that each sum equals 5.<br><br><strong>"We can arrange the ladybugs in two different ways to show five in total. How can we ensure that we include every possible way to create five?" </strong>Give students time to talk about their ideas for experimenting with various setups and documenting the outcomes. Have the students consider whether they could place every ladybug on a single leaf and still display the sum of five&nbsp;if they are not thinking of using 0 as an addendum. After that, carry on with the next organized task.<br><br><strong>"Let's try it this way. Place every single ladybug on the first leaf. What is the number of ladybugs on the second leaf?</strong> <i>(0)</i><strong> "The number sentence is 5 + 0 = 5. Place one ladybug on the second leaf after moving it from the first. "What is the number sentence shown now?"</strong> <i>(1 + 4) = (5)</i><br><br><strong>"Okay. Move a second ladybug from the first to the second leaf at this point. What is the next number sentence?"</strong> <i>(3 + 2 = 5)</i><br><br>Once students get to 0 + 5 = 5, have them move one ladybug at a time. Posting each number sentence on the board will make it easier for students to follow the pattern while they work and to talk about it once they have created every possible combination.<br><br><strong>"Check out our collection of numerical expressions. Do you think we covered all of the possibilities for arranging the five ladybugs? How do you know?"</strong> (<i>We must have used all of the ways because we only moved one ladybug at a time.</i>)<br><br><strong>"That's a good idea. Additionally, you can examine the arrangement of our number sentences on the board. In each number sentence, pay attention to the first number. When we move the ladybugs, what happens to that number?"</strong>(<i>The number decreases. Every time, there is one less.</i>)<br><br><strong>"That is accurate, but now notice the second figure in each sentence. What happens to it?"</strong> (<i>It grows bigger.</i>)<br><br><strong>"Ah, right. The pattern here is evolving. As the number of ladybugs on the first leaf decreases, the number increases on the second leaf. The first leaf's numbers are 5, 4, 3, 2, 1, 0, and the second leaf's numbers are 0, 1, 2, 3, 4, 5. We listed every conceivable way to make five, according to the pattern."</strong><br><br><strong>"We will now collaborate to document our ladybug pattern on a chart. Keep in mind that there are a total of five ladybugs. Five circles will be used in each row to symbolize the five ladybugs."</strong> Provide a copy of the M-K-3-1_Count Down, Count Up worksheet to every student so they can keep track of their progress. <strong>"I've started the first row for you. "In the first box, trace the five circles. Since all five circles are displayed in that row, there are no circles to trace in the second box. Next, draw a line through the numbers to indicate that there are five circles and none at all. As you work, keep in mind that every row needs a total of five circles."</strong><br><br><strong>"Try completing the following row. Before you continue, I will review your work. Remember the pattern we used to make the ladybugs. As the number in the first column decreases by one, the number in the second column increases by one." </strong>As soon as students start working independently, move around the classroom. Encourage students to continue methodically by offering support and guidance. Additionally, don't hesitate to offer assistance to students who appear lost or who fail to finish the drawings or numbers. In case students seem perplexed by the sixth row, kindly remind them that the numbers in the first column drop to zero instead of just one.<br><br>Ask six students to stand and explain the results displayed on each row sequentially after they have finished their charts. After that, instruct additional groups of six students to alternate in the same way until every student has had a chance to explain a row on the chart. Point out to students that each row represents a single way to make five, a number sentence with five as the total, or a pattern using five that is either decreasing or increasing. Each student's chart should end up with a left column of circles and the numbers 5, 4, 3, 2, 1, and 0 and a right column of circles and the numbers 0, 1, 2, 3, 4, and 5.<br><br><strong>Extension:</strong><br>To meet the needs of your students, utilize the following activities and strategies:<br><br><strong>Routine: </strong>Utilize a calendar in the classroom to compare the number of school days that have already passed with those that have not yet occurred. For instance, if it's Tuesday of a five-day school week, then two days have already passed, and three days are still to come. After students are comfortable with this procedure, expand the practice to include the hours of each school day, the days of the month, or the days leading up to a special occasion.<br><br><strong>Remediation: </strong>Try a more tactile approach and fewer items overall if students have trouble understanding the decreasing/increasing relationship of the changing pattern. When you place or move objects in students' hands, instruct them to keep their eyes closed. If your students are easily distracted, you may want to consider using a blindfold to help them focus on the tactile sense instead of opening their eyes to look around. Use little items, like rough little rocks or smooth dried beans, that are small enough to fit in a child's hand and have a distinct texture.<br><br>Instruct a student to count the dried beans or other small objects by touch instead of by sight by placing three in his or her left hand. Ask the student to count the number of beans in their left hand (3), right hand (0), and all hands (3). Let the student&nbsp;use their eyes to verify these responses. Next, take one bean out of the student's left hand and put it in their right, all while keeping their eyes closed. To determine the altered quantity of beans in each hand, ask the student to use touch. Move one bean at a time until all of the beans are in the correct hand, then continue by allowing visual confirmation of responses. After that, ask your students&nbsp;to explain what transpired about each hand's amount of beans. In response, it should be clear that the beans remain three for every combination, that the rate is decreasing or increasing one at a time, and that the actions on the one hand have an impact on the total on the other.<br><br><strong>Small Group:</strong> Distribute five dried beans or other small manipulatives and one small cup to each group of students. Each player is informed that there are five beans total when they place all of the beans under the cup to begin the game. Without revealing the quantity of beans still in the cup, one player removes zero to five beans. After that player reveals the beans they have taken, the subsequent player has to state how many beans are still under the cup. After that, the cup can be moved to confirm or adjust the response. After they have all had a turn, the students take turns taking out the beans or guessing. You can change the total number of beans to any number between three and ten once you've used up all five possible combinations.<br><br><strong>Expansion:</strong> Read a book or tell a story to the class that demonstrates a different type of number pattern, such as The Doorbell Rang by Pat Hutchins. In this tale, two kids are going to share a dozen cookies, but then someone rings the doorbell and more kids show up to take cookies. While the first two kids figure out how much change in cookie amounts each makes, more guests show up. Finally, 12 children arrive to share 12 cookies, but the doorbell rings again. Luckily, Grandmother comes in with more cookies this time.<br><br>Should you choose to utilize the recommended book, go over it once more and have a class perform it. To symbolize the cookies at first, two students will each hold six objects. Once more students arrive, ask them to share the cookies until a total of 12 students have received one cookie each.<br><br>It is still possible to discuss and act out the story without the book. Make a chart with two columns on the board, titled "Children" and "Cookies." Put the numbers 2, 3, 4, 6, and 12 in the first column. Assign 12 counters to two students equally. Restate that two kids receive six cookies apiece, writing the result (6) at the top of the second column and pointing to the numbers. Then assign a set of three students a total of twelve counters to share. Ask them to identify which number they each own (4). Once more, note this number in the chart. Next, move on to groups of four, six, and twelve students, recording the outcomes of each sharing scenario. Finally, go over with the class how each column's numbers vary. Simply teaching children that one column increases while the other decreases is more important at this point than it is for them to grasp division or multiplication concepts.</p>