Lesson Plan Title: Exploring Real Numbers
Concept/Topic to Teach: Classification of numbers and sets of numbers. Inspiration software: Diagram view overview.
Standards Addressed: Alabama Course of Study mathematics eighth grade content standard 1.
Specific Objectives: Students will be able to classify any given number as a member of the set(s) of natural numbers, whole numbers, integers, rational numbers or irrational numbers.
Students will be able to create a concept map of the real number system with notes and examples in each set.
Required Materials: Text book: Pre-algebra by Prentice Hall, Inspiration software, computers (scheduled lab time), calculators, white board, expo marker, paper, and pencil.
Anticipatory Set (Lead-In): Students raise your hand if you have ever played with Lego blocks. Call on a few students and see what kind of Lego sets that they have or had. Establish thru discussions the different sets in which you can buy legos: standard sets, jumbo sets, deluxe sets, and unique sets. Explain that if you own the jumbo set that you have everything that comes in the standard set plus pieces that only come in the jumbo set. Also, if you own the deluxe set that you have every piece that comes in the jumbo set, the standard set and pieces that only come in the deluxe set. After discussion of legos ask students if they realize that numbers come in sets just like legos. Tell students that after today that they will be able to determine exactly what set or sets that a number belongs to. First, I want everyone to think for a minute about the first thing you did with numbers. Raise your hand when you think you know. Call on students until you get the answer, “counting”. Have a student to count for the class. Stop the student at some point and ask if counting is a natural thing for them to do now. Good, because the first set of numbers we learn about is the set of natural numbers.
Step-By-Step Procedures for Teaching the Lesson: Draw a circle on the board and place inside the name, “Natural Numbers”, along with the pattern: 1, 2, 3, … . Explain to students that, “…”, means that the pattern continues in the same way. The set of natural numbers has all the counting numbers in it all the way to positive infinitely. Ask students if they know what number was added to their counting numbers, which they now know is called the set of natural numbers. Call on students until you get the answer zero. Draw another circle on the board label inside the circle, “Whole Numbers”, along with the pattern: 0, 1, 2, 3, … . Explain that the set of whole numbers is like having the standard set of legos which is like the natural set of numbers plus one extra piece. Explain that the natural set of numbers is a subset of the whole numbers. Make sure students know the difference in the two sets. Explain to students that all the numbers we have discussed so far has been positive numbers. The next set of numbers we will talk about is called the set of integers. This set doubles compared to the set of whole numbers. It not only includes the set of positive whole numbers, but all the negative whole numbers. Draw another circle on the board labeled, “Integers”, along with the pattern: …, -3, -2, -1, 0, 1, 2, 3, … . Explain this is like owning the jumbo set of legos. In this set you have all the natural numbers, all the positive whole number and all the negative whole numbers. Ask students what kind of numbers we have not talked about yet. Call on students until you get fractions and decimals as answers. Fractions and decimals belong to the set of numbers called rational numbers. Draw another circle on the board and label it “Rational numbers”. Inside of this circle write the subsets natural numbers, whole numbers, integers, fractions and decimals. Explain not all decimals belong to this set of rational numbers. Say to class: “Remember when you learned about repeating decimals?” Tell me what you remember about repeating decimals. Give time for students to comment. Then ask, “Did you ever have a division problem where the answer kept going on and on without a repeating pattern. Give time for students to comment. Explain that decimals that go on and on do not belong to the set of rational numbers. They belong to last set of numbers that we are going to discuss. This set is called the irrational numbers and it is like the unique set in that it only contains numbers that does not terminate or have a repeating pattern. Draw another circle labeled, “Irrational Numbers”, Write in the circle, numbers without a repeating pattern or numbers that do not terminate. Put several irrational numbers on the board. Have students to simplify the irrational numbers to decimals using their calculators. Continue with examples until students understand what irrational numbers are. Draw one more circle above the other circles. Draw lines from all the other circles to the one above. Conclude, Class this is the set of all the sets, the super deluxe set that contains all other sets. It is, drum roll, “The Real Number System”. Ask if there are any questions or confusion on what we have learned today. Answer any questions and give more examples if needed. Take students to computer lab during scheduled time and have students watch Diagram View overview of Inspiration software. Students are to work in their cooperative groups to learn Inspiration software and produce a concept map of their choice. (Groups are chosen every two months for computer use in the class room). Monitor and assist in pointing out tools in which they will need to build their concept map.
Guided Practice/Monitoring: Write the numbers 7, -5, ¾, -1/3, 10/5, 14/5, square root of 2, square root of 9. Ask the students which set or sets of numbers, does the number 7 belong to. Call on students until you get all the sets. Take each number and do the same thing. If the number is a fraction, then the student must first evaluate. They do this by dividing the top number by the bottom number on the calculator. This is a must to determine if the number has a repeating pattern or terminates. Students are to evaluate all square roots using their calculators to see if they get a terminating or repeating pattern before naming the sets. After I demonstrate several on the board, I put a few more numbers on the board and have students to write the set or sets of number each belong to and have them to raise their hands when they think they have the correct answers. I walk around the room monitoring and checking answer while giving feedback.
Closure (Reflect Anticipatory Set): Class we have learned about the Real Number System today. It has 5 subsets: 1) the set of natural numbers, which is your counting numbers, 2) the set of whole numbers, which is the set of natural numbers plus “0”, 3) the set of integers, which includes all the natural numbers, all the whole numbers, and all the negative whole numbers, 4) the set of rational numbers, which is the set of natural numbers, the set of whole numbers, the set of integers, fractions, and decimals that has a repeating pattern or terminates, and the last set 5) the set of irrational numbers, which contains the numbers that do not have a repeating pattern and does not terminate.
Assessment Based on Objectives: - With 80% accuracy students will be able to create a concept map of the real number system including notes and examples in each set. Rubric for the assessment is also handed out to the students before they start their project.
Adaptations (For Students With Special Needs): For below level learners hand out a hand drawn diagram of the real number system already labeled and assist students in placing examples of all types of real numbers on the diagram.
Extensions (For Advanced Students): Newspaper scavenger hunt: Examples of numbers can be found in many newspaper and magazines that are read every day. Look through newspapers and magazines to find the following items. When you locate an item, cut it out and fasten it to poster board or a notebook. Be sure to label each item.
· An integer greater than 100
· An integer less than 100
· A number written in words
· A percent
· A positive rational number
· A negative rational number
· An irrational number
· A decimal (not money)
· A numeral less than 1
· A negative integer
· A negative non-integer
· A whole number
Possible Connections to Other Subjects: In geometry directions sometimes imply for a specific type of numerical answer. Concept map building could be used in any subject.
Reflection: Using the Lego sets for examples gets the students attention, because all students at some time or another have played with Lego blocks. They are used in elementary for following patterns of color and shape at our school. Students seem to quickly learn what subsets are. Students loved the Inspiration software and asked many questions about the Real Number System to make sure they built the concept map correctly. More interaction with the students would be an improvement. The next time I teach this lesson, I will have a note card with a specific number written on it such as: 2, -9, ¾, -7.34, -5.123342467823456 (enough digits across the top of the note card so that students realize that the number is non-terminating), etc. Each student will be assigned a note card. I will have sections marked off in the room for each of the subsets of the real number system. When I call out a subset any student that has a note card with a number written on it that is a member must go and stand in that section and tell their number. Over all the lesson works well.