YEAR 8 Mathematics. Assessment 2: Pythagoras Theorem and Geometry

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Finds correct answer Finds correct answer YEAR 8 Mathematics Assessment : Pythagoras Theorem and Geometry Name: Class: DUE DATE: Thursday 9 th June (Week 10) MARK : Pythagoras (Ques 1-3): /13

1 Finds correct answer Finds correct answer YEAR 8 Mathematics Assessment : Pythagoras Theorem and Geometry Name: Class: DUE DATE: Thursday 9 th June (Week 10) MARK : Pythagoras (Ques 1-3): /13 ASSESSMENT NAME : Assignment Pythagoras Theorem and Geometry WEIGHTING : 30 % Geometry lines (Ques 4-6): /11 Triangles and Quads (Ques 7, 8) /9 TOTAL: /33 SYLLABUS OUTCOMES TO BE ASSESSED : MA 4-1 MG applies Pythagoras theorem to calculate side-lengths of right-angled triangles, and solve related problems MA 4-18 MG identifies and uses angle relationships, including those related to transversals of sets of parallel lines MA 4-17 MG classifies, describes and uses the properties of triangles and quadrilaterals DIRECTIVES TO BE ASSESSED : Applies: uses relevant information and skills for a given situation Calculate: find the value; the numerical answer Solve: to find the answer to or explanation for effectively dealing with a problem Describes: gives a detailed account in words of mathematical context Uses: applies, utilises, employs in a particular situation Identifies: establishes or indicates key information TASK DESCRIPTION: You are to complete an assignment on Pythagoras Theorem and Geometry as instructed in this booklet. All working out should be shown to earn full. All written answers should be written in the spaces provided. Draw all diagrams neatly, using a ruler and pencil, in the spaces provided. 1

2 PYTHAGORAS THEOREM Question 1: a) Draw a right-angled triangle. Correctly draws a neat triangle with a right-angle in it Draws a messy triangle with a right-angle in it Incorrect diagram or no attempt 0 b) Measure the dimensions (side lengths) and write them on the diagram. Labels with correct dimensions Incorrect dimensions or no attempt 0 c) Show that Pythagoras Theorem is approximately true for this right-triangle. Question : Shows correct approximate correlation with working out Shows correct correlation showing no working out A ladder is leaned against a wall. The base of the ladder sits metres away from the wall and the top of the ladder rests against the wall 4 metres above ground level. a) Draw a diagram showing this information. Correctly draws a neat diagram labelled with the correct dimensions. Draws diagram with incorrect dimensions Incorrect diagram or no attempt 0

3 b) Calculate the length of the ladder. Finds correct length showing full working out Finds correct length showing no working out Incorrect answer, correct working out Question 3: Another ladder rests against a different wall. This ladder is 5 meters long and the top of the ladder rests against the wall 4 metres above ground level. a) Draw a diagram showing this information. Correctly draws a neat diagram labelled with the correct dimensions. Draws diagram with incorrect dimensions Incorrect diagram or no attempt 0 b) Calculate how far the base of the ladder sits from the wall. Finds correct distance showing full working out Finds correct distance showing no working out Incorrect answer, correct working out 3

4 GEOMETRY Question 4 a) Draw a pair of parallel lines with a transversal. Correctly draws a pair of parallel lines with a traversal Correctly draws a pair of parallel lines without a traversal Incorrect diagram or no attempt 0 b) Measure the size of all 8 angles formed and write these angles on the diagram. Measures correctly, within acceptable tolerance (+/- 5 degrees) and labels correctly Has one or two obviously incorrect measurements or labels incorrectly c) What do you notice about the relationship between the angle sizes, approximately? Correct relationship Using incorrect measurements but otherwise reasonable relationship 4

5 Question 5 Draw a pair of perpendicular lines. Correctly draws a pair of perpendicular lines Question 6 a) Draw a pair of intersecting lines. Correctly draws a pair of intersecting lines b) Measure all 4 angles formed and write these on the diagram. Correctly measures all angles within acceptable tolerance (+/- 5 degrees) c) What do you notice about the angle sizes? Correct relatonship Using incorrect measurements but otherwise reasonable correlation 5

6 Question 7 a) Draw an isosceles triangle. Correctly draws an isosceles triangle b) Write the length of each side on the diagram. Correctly labels each side c) Measure all 3 angles and write these on the diagram. Correctly measures all angles within acceptable tolerance (+/- 5 degrees) d) What do you notice about the angles? Correct correlation Using incorrect measurements but otherwise reasonable correlation e) To the nearest 10 degrees, what do the angles add up to? 6

7 Question 8 a) Draw a square Correctly draws a square b) Write its side lengths on the diagram Correctly writes lengths, regardless of shape drawn c) Draw the two diagonals. Correctly draws diagonals d) To the nearest 5 degrees, what angle do the diagonals intersect at? Correctly measures angles * Remember you can always seek assistance in the maths staffroom every Friday for Tutoring if you need additional help. 7

8 ASSESSMENT CRITERIA STUDENT CHECKLIST: Have you attempted all questions? shown all working? drawn all diagrams neatly with the correct equipment and labelled them as required? 8

THE PYTHAGOREAN SPIRAL PROJECT

THE PYTHAGOREAN SPIRAL PROJECT A Pythagorean Spiral is a series of right triangles arranged in a spiral configuration such that the hypotenuse of one right triangle is a leg of the next right triangle.