Irrational Numbers Teacher Resources

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You'll need scissors, glue sticks, and mini whiteboards for this activity on rational and irrational numbers. Learners work in groups to classify a variety of expressions as rational or irrational. They are also given a mock discussion about an expression and must explain why they agree or disagree with each part of the conversation. The detailed lesson plan includes worksheets, PowerPoint, helpful suggestions, and an in-depth answer key. Learners must be familiar with the definitions of rational and irrational numbers before beginning.
This detailed lesson plan is a great way to explore the difference between rational and irrational numbers. Learners work in pairs to write the decimal expansions of fractions and irrational numbers and describe the distinguishing characteristics they see. Includes detailed notes for facilitators, worksheet, and an answer key.
Learners complete addition and multiplication tables that include rational and irrational numbers. They also answer a series of questions about the sums and products of irrational and rational numbers. One suggested modification would be to make the tables larger to give pupils more room to write or have them write answers on their own paper.
In this algebra worksheet, students solve rational numbers using addition, subtraction and multiplication. They identify the rules of solving rational and irrational numbers. There are 50 questions on 6 pages.
Students identify properties of circles and irrational numbers. For this geometry lesson, students research Pi and explain why we round irrational numbers. They describe the many different ways people tried to come up with a value for Pi.
This video defines rational numbers. Through the definition and examples, learners should comprehend that irrational numbers are numbers that cannot become simple fractions. The video uses examples of very common irrational numbers, such as pi, to back up their definition. Appropriate for in-class or at-home use.
Is 4 plus the square root of 2 rational or irrational? After your class has gained a basic grasp of rational and irrational numbers, use this worksheet to push them a little further in their understanding. Learners must identify sums and quotients as irrational or rational and justify their answers mathematically. The difficulty level is quite high, and some problems include variables.
Does a calculator give you the exact value of the square root of 2? Here, learners must decide if 1.414236 is equal to the square root of 2. They must also explain why the square root of 2 could never be equal to a terminating decimal. Learners must be familiar with rational and irrational numbers before beginning.
Let your mathematicians create their own rational and irrational numbers and organize a group number line to display their place value. The activity provides a code that allows learners to find the numbers associated with their names before estimating the square roots. There can be multiple variations on the activity, including the detail of finding the square root, or just finding the numbers the radical falls between. The activity includes sample answers and follow-up questions.
Mathematicians need to know that not all numbers are rational. We approximate irrational number with rational numbers. That is why a calculator may be misleading. This task give learners an opportunity to see how rounding a number and then multiplying it is not the same as multiplying a number and rounding it. 
Is the circumference of a circle always, sometimes, or never rational? Learners answer questions individually and also work in groups to look at sums and products of rational and irrational numbers. They must also be able to use the Pythagorean theorem to answer several of the questions. Additionally, they consider if providing a few examples is enough to be sure a statement is always true. The detailed lesson plan includes a PowerPoint and many helpful suggestions to facilitate the lesson.
Which numbers are rational and which are irrational? Play an initial speed round with a linked online game to see where kids are at with this concept (you should have already covered it at the basic level). Challenge scholars to consider how to graph irrational numbers (think about the fact that they never stop). The linked online explanation does a great job of illustrating this concept; however it is extremely text-heavy so you may want to address this yourself. Next, give kids some guided practice. You can use the online problems or the attached worksheet. Consider having kids go back to the original fast-paced online game to see if they improve. The "First Million Digits" link is interesting if you have some extra time, but the remediation links may not operate.
Sal works through several problems involving rational and irrational numbers, and shows how to find the difference. This video is a good stepping stone for those who are preparing to take on more challenging algebra work.
There are four irrational numbers that participants need to graph. Pi(π),      -(½ x π), and √17 are easy to approximate with common rational numbers. On the other hand, the commentary describing the irrational number 2√2 is not clear. It might be easier to list the squares of rational numbers that the class would know:  1.12 = 1.21, 1.22 = 1.44, 1.32 = 1.69, 1.52= 2.25. A close rational approximation for √2 is 1.4, therefore 2√2 ≈ 2.8.
Fourth graders use the story of the discovery of irrational numbers to explore the different classes of numbers, the different ways in which numbers may be represented, and how to classify different numbers into their particular class.
Young leearners identify subsets of the real number system and play a number game to identify natural numbers, whole numbers, integers, rational and irrational numbers.
Young mathematicians examine and discuss the concepts of integers, rational numbers, irrational numbers, and real numbers. They list examples of each term and order numerical examples.
Students identify rational and irrational numbers and their use in mathematical functions. Through demonstration, students discover the difference between rational and irrational numbers and their use. Using estimation skills students decide upon the best estimate for imperfect squares.
Seventh graders solve problems using order of operation. For this algebra lesson, 7th graders compare and contrast rational and irrational numbers. They create a T-chart to help differentiate between the two.
Here is a worksheet that examines the difference between rational and irrational numbers. Assignees assess 11 problems, determining which numbers are irrational, comparing decimals to fractions, and ordering various types of numbers on a number line. This is a well-rounded assignment to apply as homework or a test.

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