Square Number / Pythagorean Theorem TEST Review
- 1. !!! Oh MY! What’s on the test ? !! Squared Numbers / Pythagorean Theorem Review We are at that that time in our unit where I will be assessing your progress in the form of a test. Your test will be graded based on our new system of assessment: ! 1(working below), 2(emerging thinking), 3(meeting) or a 4(exceeding) for each of! the 4 content subjects below. Use this list of criteria to properly gage your! review. Remember math students are always expected to: demonstrate their! knowledge of content, show step-by-step detail of their problem solving and to! communicate their thinking to the reader as if they have no math background. Lingley Math 8 When? Monday, October 20th, 2014 Concept 3 (Meeting) 4 (Exceeding) Evaluate square roots and square numbers. * Multiply numbers from 1 to 12 by themselves in order to obtain square numbers as products. ! * Understanding how squaring a number and a square root are opposite operations. * Square whole numbers from greater than 12 in order to obtain square numbers as products. ! * Complete complex equations using multiple square roots and exponents. ! * Numbers ending in 1, 4, 5, 6, 9, 00 are sometimes square. ! * Prime Factorization Approximation of Square Roots. * Evaluate the approximation of a square root to one decimal place, and provide proof for your answer by multiplying. ! * Identify which two consecutive square numbers a value lies between. * Adjusting the approximation of a square root value to more than one decimal place. ! * Simplification of a non-square number using radical form. Ex: √75 = 5√3 (Factor out the square root) Find the missing length of a Right Angle Triangle (RAT) using the Pythagorean Theorem. * Show visual evidence of understanding that the PT indicates that the sum of the areas around legs equals the area around the hypotenuse. ! * Solving for an unknown side length in a RAT that is not the hypotenuse by use of subtraction. ! * Approximation of square roots.! * Proper units are used. * Solve a question that involves an application of multiple pythagorean theorems. ! * Final Answers are as precise as possible. Ex: Two-digits after the decimal for approximations rather than one. Proper use of Pythagorean Triples. * Understand that the smallest PTriple appears in a RAT with side lengths that measure 3,4,5. ! * Multiples of 3,4,5 will also yield a right angle triangle. ! * Given specific side lengths, determine if a triangle is a right angle triangle. * Determine the missing value in a pythagorean triple. ! * Given larger specific side lengths, determine if a triangle is a right angle triangle. 1 2 3 4
- 2. !!! Find the missing side lengths in these right angle triangles. ! ! !!!!!!! ? √20 cm ? Approximate the following squared roots: √15 , √57 , √72 , √125 —> Try simplifying the last two square roots using radical simplification. Ex: √27 = 3√3 ! ! Using Prime factorization, find √324 and √625! ! Suppose you were given these numbers that represent the side lengths of a right angle triangle: 46, 88, 110. Explain how you would identify the hypotenuse. ! ! The first two numbers in a pythagorean triple are 32 and 24. What is the third and largest number in this triple? ! ! Sarah constructed a triangle with side lengths that measure 9, 30 and 35. She wants to know if this is a right angle triangle. How can you prove to her that she is correct in her thinking or incorrect. ! ! On grid paper, draw a line that measures √25 units long. ! ! During Hurricane Arthur, many trees in downtown Fredericton snapped. The vertical line to the right represents the tree still standing and the diagonal represents the broken top of the tree. What was the original height of the tree? ! ! Find the perimeter of the triangle below. ! Lingley Math 8 How do I prepare for this test? Review Video Tutorials on Wikispace Review Math Journal Notes from Class Do review problems on back of sheet Text book Review Extra Help Friday 12:25 Review Questions 1 5 cm 12 cm 5 cm 11 cm ? 4 cm ? 12 4√13 2 3 4 5 6 7 6 m 2 m 8 9 5 u 12 u 15 u
- 3. !!! Lingley Math 8