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: Campus: Clark Jr High Author(s):Montgomery, Donaldson, Luelf, Anderson, Lincoln Date Created / Revised: 1/2/17 Six Weeks Period: 4 Grade Level & Course: 8th Math Timeline: 13 days Unit Title: Unit 08: Angle and Triangle Relationships involving Real Numbers Stated Objectives: TEK # and SE Lesson # 1 of 1 8.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. 8.2: The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to: 8.2A: Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers. 8.2B:Approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line. 8.2D: Order a set of real numbers arising from mathematical and real-world contexts 8.6: The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to: 8.6C: Use models and diagrams to explain the Pythagorean theorem 8.10B: Differentiate between transformations that preserve congruence and those that do not. 8.10C: Explain the effect of translations, reflections over the x- or yaxis, and rotations limited to 90°, 180°, 270°, and 360° as applied to twodimensional shapes on a coordinate plane using an algebraic repr esentation. 8.10D: Model the effect on linear and area measurements of dilated two-dimensional shapes. See Instructional Focus Document (IFD) for TEK Specificity Key Understandings Visual representations can be used to represent relationships between sets and subsets of numbers. The value of an irrational number can be approximated using the relationship between perfect squares of consecutive integers. A number line is composed of an infinite series of points that are labeled according to a specified unit length and its distance from zero. The sum of the area of the squares of the legs of a right triangle is equivalent to the area of the square of the hypotenuse. A right triangle can be formed from any two points on a non-horizontal, non-vertical line by drawing a vertical line from one point and a horizontal line from the other point until the lines intersect. A special relationship exists between the measures of the interior angles of a triangle and their related exterior angles. Misconceptions Students may mislabel the hypotenuse as a or b rather than labeling it as c. Some students may think the Pythagorean relationship can be used on all triangles instead of only right triangles. Key Vocabulary Adjacent angles – angles that share a common vertex and side Angle – two rays with a common end point (the vertex) Angle-angle criterion for triangles – if two angles in one triangle are congruent to two angles in another triangle, then the measure of the third angle in both triangles are congruent Axes – the vertical and horizontal lines that act as a reference when plotting points on a coordinate plane Complementary angles – two angles whose sum of angle measures equals 90 degrees Congruent angles – angles whose angle measurements are equal Coordinate plane – a two-dimensional plane on which to plot points, lines, and curves Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n} Degree – the measure of an angle where each degree represents of a circle Exterior angles of a triangle – angles that are outside of a triangle between one side of a triangle and the extension of the adjacent side Hypotenuse – the longest side of a right triangle, the side opposite the right angle Integers – the set of counting (natural numbers), their opposites, and zero {-n, …, -3, -2, -1, 0, 1, 2, 3, ..., n}. The set of integers is denoted by the symbol Z. Interior angles of a triangle – angles that are inside of a triangle, formed by two sides of the triangle Intersecting lines – lines that meet or cross at a point Irrational numbers – the set of numbers that cannot be expressed as a fraction , where a and b are integers and b ≠ 0 Legs – the two shortest sides of a right triangle Order numbers – to arrange a set of numbers based on their numerical value Origin – the starting point in locating points on a coordinate plane Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart Place value – the value of a digit as determined by its location in a number such as ones, tens, hundreds, one thousands, ten thousands, etc. Quadrants – any of the four areas created by dividing a plane with an x-axis and y-axis Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0, which includes the subsets of integers, whole numbers, and counting (natural) numbers (e.g., -3, 0, 2, - , , etc.). The set of rational numbers is denoted by the symbol Q. Real numbers – the set of rational and irrational numbers. The set of real numbers is denoted by the symbol R. Right triangle – a triangle with one right angle (exactly 90 degrees) and two acute angles Square root – a factor of a number that, when squared, equals the original number Supplementary angles – two angles whose sum of angle measures equals 180 degrees Transversal – a line that intersects two or more lines Triangle – a polygon with three sides and three vertices Vertical angles – a pair of non-overlapping angles that are opposite and congruent to each other when two lines intersect Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n} Ascending Consecutive Converse Corresponding angles Descending Formula Informal argument Interval Number line Open number line Ordered pair Perfect square Pythagorean theorem Radical symbol Repeating decimal Square Terminating decimal x-axis x-coordinate y-axis y-coordinate Suggested Day 5E Model Instructional Procedures (Engage, Explore, Explain, Extend/Elaborate, Evaluate) Materials, Resources, Notes Day 1 Warm Up: Relating Rational Numbers #1-3 Relating Rational Numbers Real Numbers Examining Real Numbers Exploring Real Numbers Day 2 Warm Up: Rational Numbers Application Irrational Numbers Irrational Numbers Interactive Bundle – Notes Irrational Number Interactive Bundle – Task Cards Examining Real Numbers Exploring Real Numbers Rational Numbers Application Irrational Numbers Interactive Bundle – Notes Irrational Number Interactive Bundle – Task Cards Day 3 Irrational Numbers Irrational Numbers Interactive Bundle – Word Problems (as a class) Irrational Numbers Interactive Bundle – Independent Practice – Approximating Square Roots Irrational Numbers Interactive Bundle – Word Problems (as a class) Irrational Numbers Interactive Bundle – Independent Practice – Approximating Square Roots Day 4 Real Number Review Day 5 Real Number Quiz Ready to go on – Go Math pg 27 Ready to go on – Go Math pg 27 Day 6 Pythagorean Theorem Go Math Differentiated Instruction Reading Strategies – pg 150 Understanding Pythagorean Theorem Notes – ppt Examples and Non Examples of Pythagorean Theorem Differentiated Instruction Reading Strategies Understanding Pythagorean Theorem Notes – ppt Examples and Non Examples of Pythagorean Theorem Day 7 Pythagorean Theorem in Three Dimensions - 8.1 pg 223 Go Math Example 2 – pg 223 Go Math Your Turn #6 - pg 224 Go Math Differentiated Instruction Practice D – pg 148 Go Math Differentiated Instruction Practice D Day 8 Converse of the Pythagorean Theorem – 8.2 pg 227 Identifying a Right Triangle Go Math Example 1 – pg 228 Go Math Your Turn #2-5 – pg 228 Go Math Differentiated Instruction Practice C Using the Converse of the Pythagorean Theorem – pg 229 Go Math Example 2 – pg 229 Go Math Your Turn #6-8 – pg 229 Go Math Differentiated Instruction Practice C Day 9 Distance between Two Points – 8.3 pg 233 Go Math Example 1 – pg 233 Go Math Your Turn #1 – pg 233 Go Math Explore Activity – pg 234 Distance Formula – Coloring Activity Finding the Distance Between Two Points Go Math Example 2 – pg 235 Go Math Your Turn – pg 236 Distance Formula – Coloring Activity Day 10 Pythagorean Theorem Quiz – Ready to Go On? Pg 239 Day 11 Unit Review Day 12 Unit Test Day 13 Review Unit Test Accommodations for Special Populations Accommodations for instruction will be provided as stated on each student’s (IEP) Individual Education Plan for special education, 504, at risk, and ESL/Bilingual. Ready to Go On? Module Quiz