SAMPLE. a) Type of angle: Estimated size: Actual size: b) Type of angle: Estimated size: Actual size: c) Type of angle: Estimated size: Actual size:

Transcription

1

2 Egypt is famous for many things, including pyramids, pharaohs, mummies and,of course, camels! Travellers used to (and sometimes still do get around Egypt on camels. Q1! Identify each angle on the camels decorated saddle as acute, right, obtuse or reflex. Estimate the size of each and then, using a protractor, find the exact answer. e) a) c) f) a) Type of angle: Estimated size: Actual size: b) Type of angle: Estimated size: Actual size: c) Type of angle: Estimated size: Actual size: d) Type of angle: Estimated size: Actual size: e) Type of angle: Estimated size: Actual size: f) Type of angle: Estimated size: Actual size: g) Type of angle: Estimated size: Actual size: b) d) g)

3 The Egyptian pyramids are one of the most popular tourist attractions in Egypt. They were built by the ancient Egyptians as tombs for their Pharaohs and Queens. Q1 The pyramid below is marked with two parallel lines and two transversals. Label the pairs of angles as co-interior, alternate, corresponding, supplementary or vertically opposite angles. Some of them have no relationship make sure you label these not related! A B C D E F G H I J K L M N A and B: A and F: B and E: G and K: I and N: I and F: M and G: J and B: P and O: E and M: K and H: K and F: D and G: L and P: O P

4 Q2 Using the image from Question One, decide if the following are true or false: A = F A = B A = D D = O L + G = H + K B = G E + B = A + F B + F = I + M N M = F E G + K = O + P J = O K + G + F + J = C + H + L + O P + K + L = G + C + H I + N = K + P J + F = P + G E + I = L + H Q3 Below are several triangles. Decide which pairs of letters are complementary angles. A B F C 100 Isoceles triangle G E H 50 I Isoceles triangle

5 Ancient Egypt was ruled by Pharaohs until approximately 30BC. Egypt was divided into several countries, each ruled by a different Pharaoh. Q1 Below is a list of coordinates, some given as numbers and some as problems. Solve the unknown angles or answer the questions where necessary. Once you ve solved them all, plot them on the Cartesian plane on the next page, connecting the points as you go. An isosceles triangle: 87.5 o X 0 3 Total angle = 30 O Use the angle from the following triangle in the equation below: 30 o 3 Y 3 2 = 15y = y 182 o How many vertices are on one face of a triangular pyramid? 0 How many edges are on the base of a square based pyramid? 84 o o 5 o

6 Q2 Horizontally reflect everything on the Cartesian plane. What is the image? Tip One grid square = One unit

7

8 Firstly, thank you for your support of Mighty Minds and our resources. We endeavour to create highquality resources that are both educational and engaging, and results have shown that this approach works. To assist you in using this resource, we have compiled some brief tips and reminders below. About this resource This Mighty Minds Fundamentals Lesson focusses on one subtopic from the NAPLAN Tests and presents this skill through a theme from the Australian Curriculum (History, Science or Geography). This lesson is also targeted at a certain skill level, to ensure that your students are completing work that is suited to them. How to use this resource Our Fundamentals Lessons are split into two main sections, each of which contain different types of resources. The student workbook contains The main title page; and The blank student worksheets for students to complete. The teacher resources section contains This set of instructions; The Teacher s Guide, which offers information that may be needed to teach the lesson; The Item Description, which gives a brief overview of the lesson and its aims, as well as extension ideas; The student answer sheets, which show model responses on the student worksheets to ensure that answers to the questions are clear; The teacher s answer sheets, which provide a more detailed explanation of the model responses or answers; and Finally, the end of lesson marker. We suggest that you print the student workbook (the first set of pages) for the students. If students are completing this lesson for homework, you may also like to provide them with the student answer pages. Feedback and contacting us We love feedback. Our policy is that if you us with suggested changes to any lesson, we will complete those changes and send you the revised lesson free of charge. Just send your feedback to resources@mightyminds.com.au and we ll get back to you as soon as we can.

9 When two lines meet, they form an angle. Angles are measured in degrees, and the name of an angle depends on its size. The types of angle students will likely come will either be: Acute (less than 90 ) Right (exactly 90 ) Obtuse (greater than 90 but less than180 ) Measuring Angles Angle sizes are measured with a protractor, which looks like this: When measuring an angle, line the point where the two lines intersect up with the middle section (yellow) so that the angle s bottom arm points to 0. Whichever number the top arm aligns with is the size of the angle. This teaching guide is continued on the next page...

10 ...This teaching guide is continued from the previous page. For example: This acute angle is roughly 44. This acute angle is exactly 90, so is a right angle. This obtuse angle is roughly 149. Triangles The sum of angles in a triangle is 180 and there is also 180 in a straight line. Often students are asked to calculate the value of a missing angle in a triangle. Missing angles are usually represented a letter from either the Latin alphabet (a-z) or a Greek symbol, usually theta, which looks like this:. e.g. 45 Missing angle = (right angle) = 45

11 Item Description Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date. Crazy Camels, Perfect Pyramids and Fantastic Pharaohs Activity Description: This lesson is split into three activities which focus on geometry with a factual Egyptian theme; a key part of the Australian curriculum for history. Activity One, Crazy Camels, has students identify types of angles, estimate angle size and use a protractor to work out the actual size. Activity Two, Perfect Pyramids, requires students to label corresponding, alternative, co-interior, complementary and supplementary angles. Activity Three, Fantastic Pharaohs, has students solve various geometric problems and use the answers to plot on a Cartesian plane. They then use basic transformations to complete a Cartesian image. Purpose of Activity: To extend students knowledge of geometric problems as well as deepen their knowledge of ancient and modern Egypt. KLAs: Mathematics, History CCEs: Recognising letters, words and other symbols (α1) Translating from one form to another (α7) Identifying shapes in two and three dimensions (α51) Graphing (π15) Sketching/drawing (π60) Calculating with or without calculators (Ф16) Estimating numerical magnitude (Ф17) Suggested Time Allocation: This lesson is designed to take approximately one hour to complete 20 minutes per activity. Teaching Notes: Students will require a protractor and a ruler to complete this activity. Activity One can be extended by getting students to work out the corresponding reflex, acute or obtuse angle to the one they already worked out. This will help students to understand how the relationship between the two works. This Item Description is continued on the next page...

12 Item Description continued This Item Description is continued from the previous page. Crazy Camels, Perfect Pyramids and Fantastic Pharaohs Teaching Notes (cont d): To extend Activity Two, students could estimate and measure the angles labelled to increase their awareness of different angle sizes. If students are struggling with reflecting the image in Activity Three encourage them to think of it as a mirror as this will help them to visualise what it is supposed to look like. Follow Up/ Class Discussion Questions: When do you see angles being used is everyday life? Has anyone ever ridden a camel? Who has been to Egypt? What is known about the way Pharaohs ruled in Ancient Egypt?

13 Egypt is famous for many things, including pyramids, pharaohs, mummies and,of course, camels! Travellers used to (and sometimes still do) get around Egypt on camels. Q1! Identify each angle on the camels decorated saddle as acute, right, obtuse or reflex. Estimate the size of each and then, using a protractor, find the exact answer. a) Type of angle: Acute Estimated size: 20 o Actual size: 30 o b) Type of angle: Obtuse Estimated size: 100 o Actual size: c) Type of angle: Obtuse Estimated size: 140 o Actual size: e) a) c) f) b) d) g) 105 o 138 o d) Type of angle: Acute Estimated size: 60 o Actual size: e) Type of angle: Acute Estimated size: 60 o Actual size: f) Type of angle: Reflex Estimated size: 350 o Actual size: 56 o 53 o 340 o g) Type of angle: Right Estimated size: 90 o Actual size: 90 o

14 Crazy Camels Question One: In this question students had to identify angles as acute, obtuse, right or reflex. They then had to estimate the size and finally work out the actual size of each angle using a protractor. Because of the nature of estimation, students answers could vary for these answers however as long as it is reasonable it is deemed correct. A model response is shown below: Model Response: a) Acute 20 o 30 o b) Obtuse 100 o 105 o c) Obtuse 140 o 138 o d) Acute 60 o 56 o e) Acute 60 o 53 o f) Reflex 350 o 340 o g) Right 90 o 90 o This teacher s answer guide is continued on the next page...

15 The Egyptian pyramids are one of the most popular tourist attractions in Egypt. They were built by the ancient Egyptians as tombs for their Pharaohs and Queens. Q1 The pyramid below is marked with two parallel lines and two transversals. Label the pairs of angles as co-interior, alternate, corresponding, supplementary or vertically opposite angles. Some of them have no relationship make sure you label these not related! A B C D E F G H I J K L M N A and B: Supplementary A and F: B and E: Vertically opposite G and K: I and N: Vertically opposite I and F: O P Vertically opposite Co-interior Alternate M and G: Not related J and B: P and O: Supplementary E and M: K and H: Co-interior K and F: D and G: Vertically opposite L and P: Corresponding Corresponding Not related Supplementary

16 Q2 Using the image from Question One, decide if the following are true or false: A = F A = D L + G = H + K E + B = A + F N M = F E J = O P + K + L = G + C + H J + F = P + G B + F = I + M G + K = O + P K + G + F + J = C + H + L + O I + N = K + P E + I = L + H Q3 Below are several triangles. Decide which pairs of letters are complementary angles. A B F A = B D = O B = G A and B, F and G, C and I and E and I C 100 Isosceles triangle G E H 50 I Isosceles triangle

17 Perfect Pyramids Question One: In this question students were required to identify pairs of angles from the lines shown below as cointerior, alternate, corresponding, supplementary, vertically opposite or not related. Model Response: A and B: Supplementary A and F: Vertically opposite B and E: Vertically opposite G and K: Co-interior I and N: Vertically opposite I and F: Alternate M and G: Not related J and B: Corresponding P and O: Supplementary E and M: Corresponding K and H: Co-interior K and F: Not related D and G: Vertically opposite L and P: Supplementary Question Two: A B E F C D G H I J K L M N O P In this question students were told to use the same diagram from Question One and answer true or false to a series of equations. As long as students understood which types of angles were equivalent, this should have been a simple task. Students should also have recognised that the shape formed by F, G, J and K was a quadrilateral and therefore the sum of these angles was 360. A model response is shown overleaf. This teacher s answer guide is continued on the next page...

18 ...This teacher s answer guide is continued from the previous page. Question Two (cont d): Model Response: A = F A = B A = D D = O L + G = H + K B = G E + B = A + F B + F = I + M N M = F E G + K = O + P J = O K + G + F + J = C + H + L + O P + K + L = G + C + H I + N = K + P J + F = P + G E + I = L + H Question Three: Students were provided with the following shapes and asked to identify which pairs of letters were complementary angles. Complementary angles add to 90. Therefore, two angles (other than the right angle) within a right angle triangle will be complementary. Model Response: A and B, F and G, C and I and E and I A F B C 100 Isosceles triangle G H E 50 I Isosceles triangle

19 Ancient Egypt was ruled by Pharaohs until approximately 30BC. Egypt was divided into several countries, each ruled by a different Pharaoh. Q1 Below is a list of coordinates, some given as numbers and some as problems. Solve the unknown angles or answer the questions where necessary. Once you ve solved them all, plot them on the Cartesian plane on the next page, connecting the points as you go. An isosceles triangle: 87.5 o X 0 3 Total angle = 30 O Use the angle from the following triangle in the equation below: 30 o 3 Y 3 2 = 15y = y 182 o How many vertices are on one face of a triangular pyramid? 3 0 How many edges are on the base of a square based pyramid? 4 84 o o 2 5 o

20 Q2 Horizontally reflect everything on the Cartesian plane. What is the image? Tip One grid square = One unit A Pharaoh

21 Fantastic Pharaohs Question One: Students were required to answer a series of geometric questions to find coordinates to plot on a Cartesian plane. These question revolved around finding unknown answers but also used algebra and general knowledge. The answers and Cartesian plane is shown below: Correct Responses: (0,6), (3,5), (5,3), (3.5,0), (3.5,-4), (2.5,-5), (2,-5), (2,0), (2.5,3), (0,4) This teacher s answer guide is continued on the next page...

22 ...This teacher s answer guide is continued from the previous page. Question Two: In this question students were required to horizontally reflect everything on the Cartesian plane and name what it resembles. The image resembles a pharaoh, as shown below. Model Response:

23