5 minute read
Launch
Students recognize that organizing objects is useful for comparing the size of groups.
Gather students and display the scattered yellow bears and blue bears.
I will show you yellow bears and blue bears. See if you can tell just by looking whether there are more yellow bears or more blue bears.
Show the bears only for a few seconds.
Facilitate a brief discussion by using questions such as the following:
• Are there more yellow bears or blue bears?
• Is it easy or hard to tell which group has more? Why?
Repeat with the rows of blue bears and yellow bears.
Then display the scattered bears and rows of bears side by side.
Language Support
Consider using strategic, flexible grouping throughout the module.
• Pair students who have different levels of mathematical proficiency.
• Pair students who have different levels of English language proficiency.
• Join pairs of students to form small groups of four.
As applicable, complement any of these groupings by pairing students who speak the same native language.
Draw attention to the usefulness of organization by asking the following question. Is it easier to compare the bears in the first picture or in the second? Why?
It is easier in the second picture, because there are extra yellow bears on the bottom line.
Revoice the correct answer using the term organize in your response. The second picture makes comparing easier, because the bears are organized or lined up.
Transition to the next segment by framing the work. Today, we will organize Unifix Cubes to help us count and compare.
Learn Count a Set
Materials—S: Bag of Unifix Cubes
Students explore ways to organize and count a collection.
Distribute a bag of cubes to each student, and prompt them to count the items in their bags. Tell students that mathematicians take their time. Provide limited guidance so that you may circulate and informally assess the following counting behaviors:
• Do students show one-to-one correspondence (say one and only one number word per cube)?
• Do students understand that the last number said when counting is the total?
• Do students organize their count in some way?
• Do students say the counting sequence fluently?
Identify two or three students who have varied approaches to organizing and counting, such as organizing in a line or in an array or by using 5-groups, as shown.
Invite the students you identified to share their work with the class. Use prompts such as the following to show the value of organization.
Teacher Note
The following terms within this lesson are familiar from kindergarten:
• Organize
• Compare
• Is more than
• Is greater than
Tell us how you organized and counted.
How did organizing help our friend count?
It was easy for them to know what they already counted. It helped them count each one (cube) only once. They didn’t skip any when they lined them up.
Organize to Count and Compare
Materials—T: Large number path, Unifix Cubes; S: Large number path Students use a number path to organize, count, and compare.
Distribute a number path, numbered side up, to each student.
Model counting to 5 by using a number path. Have students follow along on their own paths. Start at 1, place a cube on each number, and count out loud. When the class reaches 5, invite students to clear their number paths and repeat the process to organize and count their own collections.
Differentiation: Support
Consider making brief mention of incorrect counting behaviors, such as
• placing more than 1 cube in a space,
• skipping numbers on the number path as you place cubes, or
• starting at a number other than 1 when placing cubes.
Invite students to begin. As they finish, guide a class discussion.
Peek at the number under your last cube. That number is the total. Tell a partner your total.
How does the number path help you organize your cubes?
The cubes are in a line now. Each cube has its own spot.
How does using the number path make it easier to find the total?
The number under the last cube shows the total, so I don’t have to count. Have students set their work aside and turn their attention to the class number path. Place 9 cubes along the top and 7 cubes of another color along the bottom.
Promoting the Standards for Mathematical Practice
When students use the number path and are careful to start at 1, not skip any spaces, and only put 1 item in each space, they attend to precision (MP6).
Ask the following questions to promote MP6:
• When using the number path, what do you need to be extra careful with?
• What mistakes are easy to make when using the number path?
Ask students how many there are of each color. Then ask which color has more.
How can we tell there are more green cubes?
The green line of cubes is longer.
9 is more than 7.
We can match each blue cube with a green cube. 2 green cubes don’t have a match, or a partner, because there are more green cubes.
Tell students that we can also compare totals on the number path without using cubes. On the number path, circle the total of each color group, and then remove the cubes as shown. Point to the circled numbers as you refer to them.
Differentiation: Challenge
Consider asking the following questions:
• If you didn’t have a number path, how would you compare two amounts?
• Which numbers on the number path are greater than 7? Which numbers on the path are greater than 9?
7 is one total, and 9 is the other total.
Without cubes, how can we tell that 9 is more than 7?
9 comes after 7.
9 objects are more than 7 objects.
Display the prepared sentence frame and use it to compare the totals: 9 is greater than 7 .
We say 9 is greater than 7. Let’s say this statement together. 9 is greater than 7.
If students are ready, briefly introduce the greater than symbol (>) by recording a comparison on a whiteboard, such as 9 > 7.
Although the concept of difference is not taught until module 2, some students may notice how many more or how many fewer there are in one set than another.
For these students, ask the following questions:
• How many extra blue cubes are there?
• How many more green cubes would we need to make the groups the same?
Have students return to their cubes and work with a partner to compare totals by using one or both of their number paths. Listen to student conversations, and prompt them to use the language more than or greater than as they discuss.
If time allows, consider having students trade bags of cubes to count and compare by using their number paths.
Problem Set
Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex.
In lesson 1, students may benefit from the support of guided practice, and the directions may be read aloud. Help students recognize the word count in print. Invite students to underline it as you read it aloud. Please note that students will continue to use their cubes and number path.
Teacher Note
The Problem Set transitions students from counting concretely with cubes to pictorial practice.
Notice that the image of the dogs adds the complexity of a scattered arrangement. If students need a strategy to organize and count accurately, suggest they use their pencils to mark and count each dog.
Some students may need to continue to organize and count cubes in lieu of counting static images.
