Relevance/Connections 8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). 8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √is irrational. 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Student Outcomes Students will be able to identify and describe rational and irrational numbers. Prior Knowledge Needed to Support This Learning 7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 2b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. 2d. Convert a rational number to a decimal using long division; and know that the decimal form of a rational number terminates in 0s or eventually repeats. Method for determining student readiness for the lesson Use the warm-up as a starting point to determine students’ abilities to identify characteristics of numbers. Learning Experience Component Details Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency? Warm Up Teacher Notes: Definition of Natural Numbers: Natural numbers are 1, 2, 3, 4, 5, 6… Definition of Whole Numbers: Whole numbers are 0, 1, 2, 3, 4, 5, 6… Definition of Integers: A positive or negative number that can be written without fractions or decimal components. …-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …
Explain why fractions and decimals can be in the same group. Are whole numbers integers? Explain. Are decimals or fractions part of the integer group? Why do you think that? Motivation We want the students to be able to identify and describe rational and irrational numbers. Use the comic strip to capture their interest. Tell them that by the end of class they will understand the meaning behind the comic. (Attachment #5) Activity 1 UDL Components Multiple Means of Representation Multiple Means for Action and Expression Multiple Means for Engagement Key Questions Formative Assessment Summary UDL Components: Principle I: Representation is present in the activity as students write their conclusions on chart paper for the gallery walk. Principle II: Expression is present in the activity as the students use the Think, Pair, Share activity to express in their own words what they perceive to be the ways to group numbers. Principle III: Engagement is present in the activity as they explain to others what they are thinking about the activity. Students compare rational and irrational numbers using the Think, Pair, Share activity and persevere until the whole group agrees. (SMP#1) Students need to communicate clearly on the posters so that everyone understands each others’ thinking. (SMP#6)