1.) Rational and Irrational Numbers on the Number Line
Grade 9 – Math A
Topic – Ordering of Rational and Irrational Numbers
Materials Needed – Number cards (index cards with numbers on them. There will be whole numbers, fractions, decimals, square roots, pi), number lines, graphing calculators, and worksheet (attached).
2.) Lesson Overview: Students will work with number lines and index cards with both rational and irrational numbers on them to order the numbers.
3.) Lesson Objectives:
a.) Students will be able to subdivide the real numbers into rational and irrational numbers.
b.) Students will be able to compare the values of rational numbers to other rational numbers and to irrational numbers.
c.) Students will connect that the absolute value of a number is that numbers distance from zero on the number line.
4.) NYS Standard Key Ideas:
2A. Understand and use rational and irrational numbers
2B. Recognize the order of real numbers.
5.) Anticipatory Set: Ask the students what is the last thing that they bought. Ask them what is more expensive? A car or a those items? The students will hopefully say, car. Then I will ask, how do we know that? Because it costs more. The price is more. The number associated with the dollar amount is more. It is important to be able to know things order so we can value it. If a car is $20,500 and a book costs $19.95, the car has more value, because 20,500 is greater than 19.95.
Instructor should say the following (or paraphrase). But what if we aren’t given nice numbers? What if we are given fractions? What if we are given square roots? What if the numbers we have contain Pi? Well, one simple way to remedy this problem is to use the graphing calculator to convert these numbers into decimals. So if we are asked, what is greater? Square root of 5 or 5/2? We can use the graphing calculator to show that 5/2 = 2.5 and Square root of 5 = 2.236, so 5/2 is greater. - This should take no more than 5 minutes.
6.) Developmental Activity: First of all, we need to review rational versus irrational numbers. Ask the students if they know what a rational number is? Explain that it is a number that can be expressed as a fraction, or a ratio (ratio is the prefix of rational). Then say, if rational numbers can be expressed as a fraction, than irrational numbers can not be expressed as a fraction.
Then, hand out calculators to the class. Explain that any number, no matter which number, can be expressed as a decimal. Have the students go to the “MODE” section and make sure that the second row is set to “FLOAT,” so the calculator does not round too soon. - This should take about 4-5 minutes.
Then, break the students up into groups of two or three, depending on the numbers. From there, hand out the packs of number cards to each pair (NOTE: The number cards will be separated prior to the class. There will be several packs of cards, with the packs consisting of 5 cards. There will be more than a pack per group). What each group will do is order the number cards by their value, and then graph them on a number line. NOTE: Explain to the students that since we are graphing a single number on the number line, we use a filled in circle. Once they are finished with one pack of cards, they will either exchange cards with another group or with the instructor, who will have extras. While they are doing this, go around to the groups and help them if they have any questions. - This section should take 15 – 20 minutes.
When each group has finished with all of the packs of numbers, we will move on to absolute values. Define that absolute value is simply the distance from zero on the number line. Also explain to them that the absolute value signs act like a parenthesis, in that you have to do what is inside of the absolute value signs first, and then find the absolute value. Then, show the students where to find the absolute value on the graphing calculator (MATH -> NUM -> abs( ). Then give examples to the class.
· How far from zero is the number 3? (Answer 3)
· How far from zero is -2? (Answer 2)
· How far from zero is 2 – 3? (Answer 1)
Then, introduce the absolute value notation with the handout. For the remaining time, the students will work on the handout independently. What they do not finish will be for homework. - This should take 10-15 minutes.
7.) Closure: With the class coming to an end, first, review rational and irrational numbers. Say that rational numbers can be expressed as a ratio of two numbers, also known as a fraction. Whole numbers are rational numbers, but just over 1. Explain that all rational numbers can be expressed as a decimal which terminates. Then say that irrational numbers are just the opposite. They can’t be expressed as fractions. They are non-repeating decimals. Also review that the best way to compare the value of rational and irrational numbers is the make them all decimals, and compare them that way. Then review absolute value. Review what the symbol looks like. Tell them that absolute value means the distance from zero on a number line. Review how to find it on a graphing calculator. – This should take about 5 minutes.
8.) Assessments: Collect both the number line sheet and the worksheet with the practice problems. For the number line sheet, check to see if all of the numbers are graphed correctly, and if they are in the correct order. For the other worksheet, see if the answers are correct. This way you will be able to see how much of the topic they understood.
Name ______Date ______
| -4 | = ______| 7 | = ______| 2-1 | = ______
| 0.234 | = ______| -4 - 3 | = ______| -2.34 | = ______
MATH A Questions