Summary
This lesson introduces identifying and classifying numbers with an emphasis on the subsets of real numbers. Students will recall proper and improper fractions, repeating and terminating decimals, integers, and counting numbers. Students will learn about the symbols used to represent complex, real, rational, and natural numbers and integers and organize numbers into a graphic organizer.
Essential Question(s)
Why and how do we classify numbers?
Snapshot
Engage
Students describe groups of numbers with which they are already familiar.
Explore
Students explore categorizing numbers.
Explain
Students formalize descriptions of types of numbers and place examples in a graphic organizer.
Extend
Students determine which set(s) of numbers each given number belongs.
Evaluate
Students reflect on their learning by using the Muddiest Point strategy.
Materials
Lesson Slides (attached)
Describing Numbers handout (attached; one per group; printed front only)
Exploring Types of Numbers handout (attached; one per group; printed front only)
Naming Types of Numbers handout (attached; one per student; printed front only)
Naming Types of Numbers (Sample Response) document (attached; for teacher use)
Classifying Numbers handout (attached; one per student; printed front only)
Classifying Numbers (Key) document (attached; for teacher use)
Pencils
Colored pencils (optional)
Engage
10 Minute(s)
Introduce the lesson using the attached Lesson Slides. Display slide 3 to share the lesson's essential question with students. Go to slide 4 to share the lesson's learning objective. Review each of these with students to the extent you feel necessary.
Let the students know that class is starting with a review challenge. Have students find a partner or assign students partners.
Display slide 5 and distribute the Describing Numbers handout to each group. Direct pairs to write a description for each set of numbers and to be specific enough that their description only applies to that one set of numbers. Give them approximately 5 minutes to complete this task. Encourage students to do their best and to only work with their partner. Explain that this is the time for them to show you what they know.
As pairs work, circulate the room. Use student responses to determine how much time to spend sharing the sample responses on the following slides.
Show slide 6 and have students compare their description with the description of integers on the slide. Remind students that what is on the slide is one of multiple right ways to describe that set of numbers.
Transition through slides 7–11 and have students compare their descriptions for counting numbers, proper fractions, improper fractions, terminating decimals, and repeating decimals with what is on the slides.
If time allows, ask for volunteers to share what important differences they noticed between what they have written and what is shown on the slides.
What words did you use that were used on the slides as well?
Even if the words used are different, did you still describe the set of numbers as precisely as what is shown on the slides?
Where did you make some mistakes in your descriptions? How could you fix those mistakes without copying the description from the slides?
Explore
10 Minute(s)
Display slide 12 and pass out the attached Exploring Types of Numbers handout to each pair. Direct students to try their best to come up with three numbers for each type of number in the graphic organizer on the handout.
After a few minutes, have students share their examples with another pair, creating a small group, using the Inverted Pyramid strategy. Remind students that they will likely not have the same examples, but guide them to discuss why they selected the numbers they selected.
Explain
20 Minute(s)
Display slide 13 and give each student a copy of the Naming Types of Numbers handout. Explain to students the symbols that are used to represent the sets: complex numbers, real numbers, rational numbers, integers, and natural numbers.
Direct students’ attention to the bottom of their handout and introduce the descriptions for the following sets of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, imaginary numbers, and complex numbers.
Now that students have a description for each set of numbers, have students get back into their small groups to compare their Exploring Types of Numbers handout from earlier with these descriptions.
Continuing the Inverted Pyramid strategy, bring the class together for a whole class discussion. Starting with the set of natural numbers and working your way out, ask each group to give one example for each set of numbers. Have the class record these examples on their Naming Types of Numbers handout. Repeat this for the other sets of numbers. Complete the handout as a class by adding at least 3 examples for each set of numbers. Help students better understand the idea of subsets by writing the same number in more than one set. For example, 9 is a natural number and a rational number, so include it in both of those sets. Use the Naming Types of Numbers (Sample Response) document as a guide if needed.
Have students add their completed Naming Types of Numbers handout to their math notebooks if that is a classroom norm.
Extend
10 Minute(s)
Display slide 14 and inform students it is time for them to apply what they have learned. Pass out a copy of the attached Classifying Numbers handout to each student.
Challenge students to work independently to determine to which set(s) each number belongs.
Evaluate
5 Minute(s)
Go to slide 15. Have students reflect on the lesson and their overall understanding of the content using the Muddiest Point strategy. Have students answer the following questions:
Crystal Clear: What do you think is the easiest part of classifying numbers?
Muddiest Point: What do you think is the most confusing part of classifying numbers?
You can collect responses in a variety of ways depending on your class. Sticky notes, pieces of paper, or digital posts are a few examples.
Resources
K20 Center. (n.d.). Inverted pyramid. Strategies. https://learn.k20center.ou.edu/strategy/173
K20 Center. (n.d.). Muddiest point. Strategies. https://learn.k20center.ou.edu/strategy/109