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geometry week 1 and 2 geometry week 1 and 2
- 1. Geometry-shapes n space 1-Unpack, repack 2-Designteaching activities & assessment 6C Maths Proceses s The Van Hiele 1- Geometric language and properties of two- dimensional and three-dimensional shapes 2- Right angle, acute angle and obtuse angle on basic two-dimensional shapes 3- Parallel lines and perpendicular lines on basic two- dimensional shapes 4- Axes of symmetry of two-dimensional shapes 5- Classification of two-dimensional and three- dimensional shapes 6- Nets of three-dimensional shapes 7- Determine area and perimeter of two- dimensional shapes using squared grid and formulae 8- Determine volume of three-dimensional shapes using unit cubes and formulae 9- Cartesian Coordinate System – first quadrant 10- Applications of Space in daily life
- 2. The Van HieleModel: •Pierre Marie van Hiele-Geldof and Dina van Hiele- investigated children's progression in Euclidean geometry. •Five stages of geometric understanding: • Visualization, • Analysis, • Informal Deduction, • Deduction, • and Rigor •Understanding these stages helps teachers design
- 3. The Van HieleModel: •Pierre Marie van Hiele-Geldof and Dina van Hiele- investigated children's progression in Euclidean geometry. •Five stages of geometric understanding: •Stage 0: Visualization - Recognizing and naming figures. •Stage 1: Analysis - Describing attributes of figures. •Stage 2: Informal Deduction - Classifying and generalizing figures. •Stage 3: Deduction - Developing proofs using postulates. •Stage 4: Rigor - Working in various geometric systems. •Progression influenced more by instruction than age. •Understanding these stages helps teachers design appropriate geometry activities.
- 4. Group Task (need7 groups) • Plan teaching activity using suitable tools that applying 6C/Mathematical Processes/Van Hiele for one of these: 1- Right angle, acute angle and obtuse angle on basic 2D shapes 2- Parallel lines and perpendicular lines on basic 2D shapes 3- Axes of symmetry of 2D shapes 4- Classification of 2D and 3D shapes, - Nets of 3D shapes 5- Determine area and perimeter of 2D shapes using squared grid and formulae 6- Determine volume of 3D shapes using unit cubes and formulae 7 - Cartesian Coordinate System – first quadrant
- 5. Group Task (need7 groups) • Plan teaching activity (applying 6C/Mathematical Processes/Van Hiele) • Create the suitable tool • Demonstrate the teaching activity to your classmate (record) • Get feedback and suggest improvement (if needed)
- 6. *every student mustpass through each of the stages of geometric thinking * Primary school-not expected to use deductive proofs . 1-Visualization • recognize and label common plane figures such as circles, squares, triangles, and rectangles • simple solids such as cubes, spheres, pyramids, and cones and name them with those labels or with less formal names such as boxes and balls. • =>may categorize all shapes with curved surfaces as circles- rectangles as squares. • Misconception-all the triangles are equilateral triangles Add Text Get a modern PowerPoint Presentation that is beautifully designed. Add Text • organize two- and three- dimensional figures according to their characteristics Add Text • students become more proficient in describing the attributes shape • Starts starts introduce correct term • learn to identify the unique characteristics of all plane and solid figures through work with various geometric situations and materials. Add Text • after elementary school. • A typical high school geometry course is designed to fully develop students’ deduction abilities with the postulate- theorem-proof of Euclidean geometry. Through manipulation of real objects and graphic representations, they name and describe geometric shapes and figures and their characteristics, relationships, position, and properties. But still can involve activity -create deduction 2. Analysis 3. Informal deduction 4. Deduction 5. Rigor
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- 9. Right angle, acuteangle and obtuse angle
- 10. Another idea: • Usepaper plates on which the center has been marked. • Students cut straight lines from the outside edge to the center to make acute, right, and obtuse angles. • Pose challenges to older children such as these: • “Can you cut a plate so that you have one obtuse and three acute angles? • Can you cut a single plate so you have a right, an acute, and an obtuse angle?”
- 11. Symmetry • each sideof the symmetry line is a mirror image of the other. Every example of line symmetry produces mirror images that can be “folded” along the symmetry line onto one another. Misconception- if a figure is divided into two congruent parts by a line, then the line must be a symmetry line. Help them- they should have many experiences examining figures such as a rectangle with a diagonal, in which the line divides the rectangle into two congruent parts, but the diagonal is not a symmetry line. In this case the diagonal fails the fold test.
- 14. Triangles classified bytheir sides are equilateral, isosceles, or scalene. Equilateral triangles have three equal, or congruent, sides; isosceles triangles have two congruent sides; and scalene triangles have no congruent sides. Tri- angles can also be classified by their angles. Right triangles have a 90 angle. All angles in acute triangles are less than 90 obtuse triangles have one angle larger than 90
- 16. The coordinate gridcan also be used to mark off a picture for a scale drawing. The picture is enlarged by drawing each piece of the grid on a large square and reassembling the result. Figure 17.19 shows a picture and portions of its enlarged version using coordinate squares. This activity can also be used with older children when studying symmetry. The original figure and its enlargement are similar to each other.
- 23. To avoid confusion betweenarea and perimeter, use the illustration of fields and fences to explain these concepts and pose problems about area and perimeter in these terms. Perimeter VS Area we find the square to be the superior solution, requiring the minimum amount of fencing for the given area.
- 24. find the superior solution, requiring the minimum amount of fencingfor the Max area. • The first challenge is to find as many different fields as possible that can be enclosed within a given amount of fencing. • The second challenge si the reverse problem: keep the area fixed and find the different perimeters. - what amounts of fencing would be required to enclose differently shaped fields all with the same area?