The focus of the lesson is on decomposing a number in multiple ways and recognizing that a change in one set affects the number of objects in a related set when the total number of objects remains constant. The lesson begins with a story and follow-up activity that shows a pattern of moving an object from one set to the other while maintaining a consistent total number of objects. Students discuss how one set decreases as the other set increases by the same amount. Then students record their work in charts to further show the relationship between the sets, also relating the addition sentences that match. They use patterns to list all of the possible combinations that equal 5.
“Today I will read you a story about a Grouchy Ladybug who does not like to share. After I read the story, we will discuss the patterns in the story. Then we will use leaves and ladybugs to show another type of pattern.”
Read The Grouchy Ladybug as students listen and look at the pictures.
“What patterns do you see in the story or the pictures?”
Ask students to turn and talk with a partner, then share their ideas with the class. (The ladybugs have different patterns of spots. Some of the other animals have patterns, too.)
“Yes, that’s right. One kind of pattern in the story is the designs that you can see on the animals. What kind of pattern does the story show about the sizes of the animals?”
Ask students to turn and talk with a partner, then share their ideas with the class. (The animals get bigger until the whale flips the grouchy ladybug back to the first leaf.)
“You have become very good at seeing patterns and describing them. Now you are ready to make other types of patterns and record your work. We will make some patterns that change, but first we will need some leaves and ladybugs of our own.” Distribute copies of the ladybug worksheet (M-K-3-1_Leaves and Ladybugs.docx) to students and have them cut apart the strip of ladybugs at the bottom of the page. [Note: This activity may follow alternate book selections with a simple introduction to help students connect patterns in the book and new patterns that they will be discovering.]
“How many ladybugs do you have?” (5) “Place your ladybugs on the leaves any way you want.” Make sure students understand that they are not yet supposed to glue the ladybugs onto the paper. You might also walk around to observe whether any students are already experimenting with more than one way to arrange the ladybugs. “Now look around to see how others put their ladybugs on the leaves. Did everyone do it the same way?” (I put one ladybug on the first leaf and four on the other leaf. My ladybugs are three on one leaf and two on the other leaf.) As students share their arrangements, model their responses for the class (via overhead projector, interactive whiteboard, flannel board, anchor chart, etc.).
Write addition sentences on the board to match the first two responses given, pointing out to students that each sum is 5.
“These are two of the ways we can arrange the ladybugs to show five in all. What could we do to make sure we list all of the ways to make five?” Allow time for students to discuss their ideas for trying different arrangements and recording the results. If students do not think of using 0 as an addend, ask whether they could put all of the ladybugs on the same leaf and still show a sum of 5. Then continue with the following structured activity.
“Let’s try it this way. Put all of your ladybugs on the first leaf. How many ladybugs are on the second leaf?” (0) “The number sentence is 5 + 0 = 5. Now move one ladybug from the first leaf to the second leaf. Now what is the number sentence shown?” (4 + 1 = 5)
“Good. Now move another ladybug from the first leaf to the second leaf. What is the number sentence now?” (3 + 2 = 5)
Continue having students move one ladybug at a time until they reach 0 + 5 = 5. Writing each number sentence on the board will help students keep up with the pattern as they work, and discuss the pattern when they have made all possible combinations.
“Look at our list of number sentences. Do you think we listed all of the ways to arrange the five ladybugs? How do you know?” (We only moved one ladybug at a time, so we must have used all of the ways.)
“That’s good thinking. You can also look at the pattern of our number sentences on the board. Look at the first number in each number sentence. What happens to that number as we move the ladybugs?” (The number gets smaller. It is one less each time.)
“That’s true, but now look at the second number in each sentence. What happens to it?” (It gets larger.)
“Right. This is a changing pattern. As the number of ladybugs gets smaller on the first leaf, the number gets larger on the second leaf. The numbers for the first leaf are 5, 4, 3, 2, 1, 0, and the numbers for the second leaf are 0, 1, 2, 3, 4, 5. The pattern tells us that we listed every possible way to make 5.”
“Now we are going to record our ladybug pattern on a chart together. Remember that there are five ladybugs in all. Each row will have five circles to represent the five ladybugs.” Give each student a copy of the Count Down, Count Up worksheet (M-K-3-1_Count Down, Count Up.docx) for recording his/her work. “The first row has been started for you. Trace the five circles in the first box. There are no circles to trace in the second box because all five circles are already shown in that row. Then trace the numbers to show that there are five circles and zero circles. Remember as you work that each row must have five circles in all.”
“Try filling in the next row. Then I will check your work before you go on. Keep in mind the pattern that we used for the ladybugs. As the number gets smaller by one in the first column, it gets larger by one in the second column.” Move about the room as students begin to work on their own. Provide reassurance as students progress in an organized pattern, and give hints to students who seem confused about how to proceed or to those who forget to complete the drawings or the numbers. If students appear puzzled about the sixth row, remind them that the first column numbers decrease to zero, not just to one.
When students have completed their charts, ask six students to stand and take turns explaining the results shown on each row in order. Then ask other groups of six students to take turns in the same manner until each student has had at least one opportunity to explain a row of the chart. Students should point out that each row shows one way to make 5, a number sentence with a total of 5, or a decreasing/increasing pattern using 5. The final result of each student’s chart should show a left column of circles and numbers 5, 4, 3, 2, 1, 0 and a right column of circles and numbers 0, 1, 2, 3, 4, 5.
Extension:
Use the activities and strategies listed below to tailor the lesson to meet the needs of your students.
- Routine: Use a classroom calendar to discuss the number of school days in each week and to compare those that are in the past or present with those yet to come. For example, if today is Tuesday in a 5-day school week, 2 days are in the past or present and 3 days are yet to come. Once students become very familiar with this process, extend the routine to include the days of the month, the days until a special event, or even the hours of each school day.
- Remediation: If students struggle with the decreasing/increasing relationship of the changing pattern, try a more tactile approach and reduce the total number of items. Tell students to keep their eyes closed while you place or move some objects in their hands. For students who are easily distracted, you might want to use a blindfold to help them isolate the sense of touch rather than opening their eyes to look around. Use small objects that will fit in a child’s hand and that have specific recognizable texture, such as smooth dried beans or rough small rocks.
Place three dried beans or other small objects in a student’s left hand and ask him/her to count the beans by touch rather than by looking at them. Have the student identify the number of beans in the left hand (3), the number of beans in the right hand (0), and the number in all (3). Allow the student to confirm these answers by looking. Then with the student’s eyes closed again, remove one bean from the left hand and place it into the right hand. Have the student use touch to identify the changed number of beans in each hand. Continue the process of moving one bean at a time and allowing visual confirmation of answers until all of the beans are in the right hand. Then ask the student to explain what happened to the number of beans in each hand. Responses should indicate an understanding that the decreasing/increasing rate is by one at a time, that what happens in one hand effects the total in the other hand, and that the sum of the beans remains three for each combination.
- Small Group: Give each group of students five dried beans or other small manipulatives and one small cup. To play the game, all of the beans are placed under the cup, and each player is told that there are five beans in all. One player takes zero to five beans from under the cup, without showing the number of beans that remain. That player shows the beans that s/he took, and the next player must tell the number of beans that are still under the cup. Then the cup can be moved to verify or correct the answer. Students take turns removing beans or making a guess until everyone has had at least one turn. When the combinations to five have been exhausted, the total number of beans can be changed to any number between three and ten.
- Expansion: Read a book to the class or tell about a story that shows a different type of number pattern, such as The Doorbell Rang by Pat Hutchins. In this story, two children plan to share 12 cookies, but then the doorbell rings and more children arrive to share the cookies. Other visitors continue to arrive as the first two children calculate how the number of cookies for each changes. Finally, 12 children are present to share 12 cookies, but the doorbell rings again. Thankfully, this time Grandmother enters with more cookies.
If you use the suggested book, read it again and have a group of students act it out. In the beginning, two students will hold six items each to represent the cookies. Then as others arrive, have students share the cookies again until you reach a total of 12 students with one cookie each.
Even without the book, the story can be discussed and acted out. Draw a two-column chart on the board and label the columns Children and Cookies. In the first column, write the numbers 2, 3, 4, 6, and 12. Ask two students to share 12 counters equally. Record the result (6) at the top of the second column and point to the numbers as you restate that two children get six cookies each. Then give 12 counters to a group of three students for sharing. Have them state the number each of them has (4). Again, record this number in the chart. Then continue with groups of 4 students, 6 students, and 12 students, recording the results of each sharing situation. Finally, discuss with students how the numbers in each column change. It is not important for students to understand division or multiplication concepts at this time, but simply that one column increases while the other decreases.
