QaD Teacher Support Materials

Transcription

1 QaD Teacher Support Materials Focus: Develop skills at interpreting geometric diagrams and using them to solve problems. Instructions Remember to download the Weekly Class Report and use it to help plan the minute Weekly Follow-up lesson. Use the Weekly Class Report to determine which group students will be in for the Suggested Activities (score 0 or 1 = Red, score 2 or 3 = Yellow, score 4 or 5 = Green). Please refer to the QaD Teacher Guide, and also the Using the Teacher Support Materials Video to assist you in understanding and using the Weekly Class Report and the Teacher Support Materials. QaD Weekly Questions These are the questions completed by the students this week. Please refer to these as you look at the Weekly Class Report. Each student will also need a copy of these questions. Misconceptions Information (by Day) Use these with the Weekly Questions and the Weekly Class Report to better understand student errors. What TIMSS content and skills are assessed by Thursday s question? This table shows the content and skills that Thursday s question assesses. This is an international framework and may not align with your current curriculum. The QaD Thursday question attempts to assess long-term learning and higher order thinking. Summary, focus and purpose of QaD Weekly Follow-up Lesson (by Group) This table connects the Weekly Class Report to the Follow-up Lesson with differentiated information for the three ability groups. It provides a quick overview of the focus and intent of the Weekly Follow-up Lesson for each of the Red, Yellow and Green groups. Use the table to focus the lesson, plan the activities and organise the required equipment. Follow-up Lesson The Follow-up Lesson is the key component of the Teacher Support Materials document. The Follow-up Lesson has been specifically developed to address student needs according to demonstrated ability. It is recommended that the format of this Follow-up Lesson have three parts: Introduction (whole class) Suggested Activities (in colour groups) Student worksheets have been provided for each colour Group. Red Group Worksheet Yellow Group Worksheet Green Group Worksheet (Note: answers included on the page before the activities.) Explicit instruction in solving the QaD Thursday question (whole class)

2 QaD Weekly Questions Sunday Sultan is measuring angles in this right-angled triangle. He has measured and labelled one of the angles. What is the size of the angle x? A. 35 B. 45 C. 55 D. 90 Monday Fatima draws this shape. The lines AB and CD are parallel. Fatima measured a 35 angle in her shape. What is the size of the angle marked x? A. 25 B. 35 C. 55 D. 90

3 Tuesday T1 Week 1_Mathematics_G8_Interpreting Diagrams Aysha wants to calculate the area of the rectangle ABCD. She has drawn a line between the point B and the midpoint (M) of the line CD. What is the area of the rectangle ABCD? A. 10 cm 2 B. 20 cm 2 C. 30 cm 2 D. 40 cm 2 Wednesday In this diagram, the line AB is parallel to the line CD. Which of these statements is true? A. The line m is parallel to n and the same length as n. B. The line m is perpendicular to n and the same length as n. C. The line m is parallel to n and shorter than n. D. The line m is perpendicular to n and shorter than n.

4 Thursday T1 Week 1_Mathematics_G8_Interpreting Diagrams Ali has this net, which he folds into a prism. What is the surface area of Ali s prism? A. 48 cm 2 B. 96 cm 2 C. 108 cm 2 D. 120 cm 2

5 Misconception Information (by Day) Sunday A Key B Miscalculates the complement of 55 using 100 as sum instead of 90 C Uses given angle, or assumes the triangle is isosceles D Gives the right angle as the unknown Monday A B C D Miscalculates supplementary angle at C; or, chooses this as a plausible value Key Finds the supplementary angle at C Mistakes the right angle in the diagram as indicating value of angle x Tuesday A B C D Determines the area of triangle BCM Multiplies the two lengths given, or incorrectly determines the area of the triangle BCM (forgets to halve) Determines the area of the trapezium ABMD Key Wednesday A B C D Key Confuses the terms parallel and perpendicular Confuses the effect of these two shorter lines ending at parallel lines Confuses the effect of these two shorter lines ending at parallel lines, and the terms parallel and perpendicular Thursday A B C D Calculates volume instead of surface area Calculates surface area without the triangular ends Key Calculates surface area with rectangular instead of triangular ends

6 What TIMSS content and skills are assessed by Thursday s question? Cognitive Area Cognitive Skill Strand Content Area TIMSS Topic Applying Implement Geometry Geometric Shapes and Measurement 2. Identify two-dimensional shapes and use their geometric properties to solve problems, including those involving perimeter, circumference, area, and the Pythagorean Theorem (see TIMSS 2019 Mathematics Framework, IEA) Summary, focus and purpose of QaD Weekly Follow-up Lesson (by Group) Focus: Develop skills at interpreting geometric diagrams and using them to solve problems. What does the Class Report show? This week s Follow-up Lesson learning focus This week s Follow-up Lesson activity focus Red (score 0 or 1) Yellow (score 2 or 3) Green (score 4 or 5) Has not attempted, or chosen answers that look most obvious but are incorrect. Practicing interpreting geometric diagrams involving angle and area calculations. Interpret geometric diagrams to find unknown angles, lengths and areas. Identify important features of geometric diagrams. Understands simple diagrams and interpretations of diagrams but finds questions requiring extrapolation from limited information more difficult. Practicing interpreting geometric diagrams involving angle and area calculations. Interpret geometric diagrams to find unknown angles, lengths and areas. Identify important features of geometric diagrams. Cog. Skills Applying (Determine) Applying (Represent/Model) Strategies Identify important Identify important features of diagrams features of diagrams Find many/all unknowns Find many/all unknowns in diagrams in diagrams Preparation Materials Copy of Questions for each student Red Group Worksheet note that the worksheet is two pages in length and should be copied back-to back. Copy of Questions for each student Yellow Group Worksheet note that the worksheet is two pages in length and should be copied back-to back. Able to solve most diagrammatic problems extension with more complex problems is suggested. Practicing interpreting geometric diagrams involving angle and area calculations including more complex algebraic contexts. Interpret geometric diagrams to find unknown angles, lengths and areas. Identify important features of geometric diagrams. Incorporate other areas of mathematics to help solve problems. Applying (Implement) Identify important features of diagrams Find many/all unknowns in diagrams Copy of Questions for each student Green Group Worksheet note that the worksheet is three pages in length and should be copied back-to back.

7 Follow-up Lesson (15-20 minutes) 1. Introduction (whole class): a) Introduce the focus of the Lesson: Develop skills at interpreting geometric diagrams and using them to solve problems and remind students that the Question-a-Day questions they did over the last week were related to interpreting geometric diagrams. b) Go through the Vocabulary and explain the meaning of all words listed c) Go through the Remember! points and remind students of what they need to do when answering questions. Vocabulary Parallel lines Perpendicular lines Any two lines that are exactly the same distance apart along their entire lengths Any two lines that cross at an angle of exactly 90 Remember! Read the question carefully Look for clue words must Read all the answers Eliminate impossible or unlikely answers. 2. Suggested Activities (in colour groups): Red (score 0 or 1) Yellow (score 2 or 3) Green (score 4 or 5) 1. Read through Sunday and Monday questions. For Sunday question, why 1. Read through Tuesday question. Ask students why B is incorrect? 1. Read through Wednesday question. Ask students to explain their is A correct? Why are the other answers incorrect? For Monday question allow the students to explain their answer. 2. Students work in pairs (or larger groups) and complete Red Group Worksheet. For angles question, remind students of the rules that they can use to find unknown angles. For shapes with more sides such as the 5-sided shape have them try and break this shape up intro triangles. For area question, encourage students to identify all of the parts of the shape triangles and rectangles and then determine the area of these parts 2. Students work in pairs (or larger groups) and complete Yellow Group Worksheet. For angles question, remind students of the rules that they can use to find unknown angles. For shapes with more sides such as the 5-sided shape have them try and break this shape up intro triangles. For area question, encourage students to break this shape up into smaller parts rectangles and triangles. answers. 2. Students work in pairs (or larger groups) and complete Green Group Worksheet. For angles question, remind students of the rules that they can use to find unknown angles. For shapes with more sides such as the 5-sided shape have them try and break this shape up intro triangles. For hexagon questions, remind students of the definition of a rhombus For the area question, encourage students to break the shape up into smaller parts rectangles. The solution includes an algebraic approach but students can solve this by inspection.

8 3. Explicit instruction in solving the QaD Thursday question (whole class): The following provides a suggested step-by-step approach to solving Thursday s question. Read the Thursday question aloud to all students. Then use a question-answer approach to go through the problem. Teacher: Students: Teacher: Students: Teacher: Students: (5) Teacher: Students: Teacher: Students: Teacher: What do we have to find? (the surface area of a prism) What information do we have? (a net for the prism, with some lengths marked) How can we do this? We don t need to know anything about the prism. (Although, we can fold this net up into a triangular prism). A net represents all of the faces of a particular prism. The surface area of a prism is the total combined area of all of the faces. So, we should be able to calculate the area of each face of the net and then add them all together. How many faces area there? What shapes are the faces? (3 rectangles and 2 triangle) What are the lengths of the rectangles? (4 cm 8 cm, 5 cm 8 cm, and 3 cm 8 cm) So, what are the areas of the rectangles? Students: (32 cm 2, 40 cm 2, and 24 cm 2 ) Teacher: Students: Teacher: Students: Teacher: What are the base and height lengths of the triangles? (They are both 3 cm 4 cm) So, what are the areas of the triangles? (6 cm 2 each) So, what is the total area of the net? Students: ( = 108 cm 2 ) Teacher: Which is option C.

9 Answers to Red Group Worksheet See separate worksheet solutions document. Answers to Yellow Group Worksheet See separate worksheet solutions document. Answers to Green Group Worksheet See separate worksheet solutions document.

10 Red Group Worksheet: T1 Week 1_Mathematics_G8_Interpreting Diagrams Instructions Mark any pairs of parallel lines you can see by placing a tick on each line Write in the sizes of all the angles that you can determine Circle all of the rules that you used to determine any of the angles: Angles at a point Angles on a straight line Angles that add up to 90 Angles in a triangle Angles in a quadrilateral Vertically opposite angles Angles on parallel lines

11 Instructions Area: cm 2 Area: cm 2 Calculate the area of each of the small rectangles and triangles in this diagram. Write your answers on the diagram. Area: cm 2 What is the length and width of the large rectangle that makes up the entire shape? Length cm Area: cm 2 Width cm Area: cm 2 What is the area of the large rectangle? cm 2 Area: cm 2 What is the area of the shaded shape in this diagram? cm 2

12 Yellow Group Worksheet: Instructions Mark any pairs of parallel lines you can see by placing a tick on each line Write in the sizes of all the angles that you can determine Circle all of the rules that you used to determine any of the angles: Angles at a point Angles on a straight line Angles that add up to 90 Angles in a triangle Angles in a quadrilateral Vertically opposite angles Angles on parallel lines

13 Instructions Calculate the areas of the two white shapes in this diagram. These shapes are divided into small rectangles and triangles by the dashed lines. Determine the areas of each of the small rectangles and triangles and combine these to find the areas of the white shapes. Write your answers on the diagram. What is the length and width of the large rectangle that makes up the entire shape? Length cm Width cm What is the area of the large rectangle? (The two dashed lines divide this large rectangle into quarters) cm 2 What is the area of the shaded shape in this diagram? cm 2

14 Green Group Worksheet: Instructions Mark any pairs of parallel lines you can see by placing a tick on each line Write in the sizes of all the angles that you can determine Circle all of the rules that you used to determine any of the angles: Angles at a point Angles on a straight line Angles that add up to 90 Angles in a triangle Angles in a quadrilateral Vertically opposite angles Angles on parallel lines

15 Instructions ABCDEF is a hexagon formed by shapes drawn on the sides of an equilateral triangle ABO with a side length of 10. Two equal-sized rhombuses are drawn on each side of ABO. The acute angles in the rhombuses are 75. The top of the two rhombuses are joined by a line of length 14.1 The resulting final shape is a hexagon. Write all the angles and lengths you can for this shape. What is the perimeter of the hexagon?

16 Instructions The area of the quadrilateral shape BCDE is 60% of the area of the quadrilateral shape ABEF. What is the unknown length x?

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