| Curriculum Map 2006-2007 | |||
|
The Dwight School |
| Period | Content | Purpose/ Objectives | Activities & Resources | Areas of Interaction | Assessments | |
| BASIC GEOMETRY : | UNDEFINED TERMS and DEFINITIONS: points, lines and planes, segments, angles. POSTULATES: the angle and segment addition postulates. Deductive and inductive reasoning. Segments and angles and their measures. Using the distance formula, the mid-point formula, and Pythagoras'Theorem. Distinguishing acute, right, obtuse, straight and reflex angles. Estimation of an angle's measure. ALGEBRA REVIEW: using algebra to solve simple geometric problems involving angles, segments and their bisectors. |
To learn that in any system there will be undefined terms, and postulates which are not proved. To recognize simple patterns and see this as an example of inductive reasoning. To be able to estimate the measure of an angle and to calculate it using algebra. To be able to find mid-points, and the length of a line algebraically. To review basic algebra skills. |
Donald in Mathemagicland video Geometry(Larson et al) chapter one Straight edge, compasses, protractor. Finding patterns of numbers and shapes, seeing that there may be more than one way to continue a pattern. Estimating angles, and lengths. An exploration of taxi-cab geometry. Student-made questions: use initials to make a segment addition postulate problem |
What are the basic skills and terminology needed to study geometry? Homo faber: the occurrence of geometric patterns in art and in design. Environment: Patterns in the natural world. |
Formative: quizzes and classroom discussion word-wall Summative: end of chapter test |
|
| PROOF, PERPENDICULAR AND PARALLEL LINES : | Conditional and biconditional statements. Inverses, converses and contrapositives. Deductive reasoning. The Law of Syllogism. The Law of Detachment. The algebraic properties of equality. Symmetric, reflexive and transitive properties. Complements and supplements of angles. Simple two column proofs. Review of algebra: solving simple linear equations, testing whether a point is on a line. Finding the slope of a line and its equation. Finding the equation of a line through two given points. Properties of parallel lines: corresponding, alternate interior and exterior angles, vertical angles, transversals. Testing whether lines are parallel or perpendicular given their equations. |
To learn the difference between deductive and inductive reasoning. To be familiar with the algebraic properties of equality and with reflexive, symmetric and transitive properties. To be able to write a simple two column proof. To be able to solve simple problems involving parallel or perpendicular lines. To be able to solve simple problems involving co-ordinate geometry. To understand the concept of slope. |
Geometry Chapters two and three. Finding examples of conditional statements to illustrate deductive reasoning. Looking at relations (eg: is a cousin of or is taller than) to see if they are equivalence relations (reflexive, symmetric and transitive) Create a children's book (based on the books "If You Give a Pig a Pancake") using biconditional statements. Using simple algebra in problems involving parallel and perpendicular lines. |
How do you logically prove something to be always true? What are the properties of angles that are created by parallel and perpendicular lines? What is meant by parallel lines and transversals? What is the relationship between pairs of angles formed by a transversal that intersects parallel lines? How can we show when two lines must be parallel? Homo faber: the syllogism in Greek philosophy. When deductive reasoning is important. Environment: Parallel and perpendicular l;lines in the natural world. |
Formative: Book Project, Word Wall contributions, quizzes and class discussion Summative: End of topic tests. |
|
| CONGRUENT TRIANGLES : | Classification of triangles. Triangle sum theorem. Exterior angle theorem. The idea of a corollary. Finding the measure of angles in a triangle. Congruence. The SSS,SAS, AAS postulates for congruent triangles. Isosceles, equilateral and right triangles. Base angles theorem for isosceles triangles. Proofs involving co-ordinate geometry. Algebra review: distance between points. Combining like terms. Solving simple equations and inequalities. Absolute value equations and inequalities. |
To be able to classify triangles, test for congruency, and calculate angles in triangles. To be able to use the congruency postulates in simple two column proofs. To review and extend algebra skills. |
Geometry chapter four. Using protractors and compasses to construct triangles and see what is required for congruency. Finding all the angles of a triangle given some information, using simple algebra. The Greedy Triangle (children's book) |
What is meant by triangles being congruent? Why do we want to study this topic? How will this be connected to other areas of math? What criteria must be met for two triangles to be congruent? What are the properties of isosceles and equilateral triangles? What are the special properties of right triangles that you can use to prove that two right triangles are congruent? Homo faber: rigid structures and congruency: why triangles are used by architects. |
Formative: Quizzes. Class discussion Summative: End of topic test. |
|
| PROPERTIES OF TRIANGLES : | Constructing angle and perpendicular bisectors. Using these to find the incenter and circumcenter of triangles. Centroids, altitudes, medians and orthocenters. The midsegment theorem. Triangle inequality theorem. Largest angle opposite longest side.Simple problems involving these concepts. |
to be able to construct angle bisectors and perpendicular bisectors. To learn more of the properties of a triangle.The significance of the centroid, incenter, circumcenter and orthocenter. |
Compasses, protractor. Geometry Chapter five. Constructing angle and perpendicular bisectors. Finding the incenter, orthocenter, circumcenter, and centroid of a triangle by construction. |
Homo faber: Centroids and centers of gravity, in electrocardiograph readings (page 283). |
Formative: Consruction of circumcenters of triangles etc. |
|
| QUADRILATERALS : | Polygons: regular, convex, concave.Names of polygons. Quadrilaterals: interior angles. Parallelograms. Proving a quadrilateral is a parallelogram. Rhombuses, rectangles, squares, trapezoids and kites:their properties. Areas of triangles and quadrilaterals. Algebra review: solving equations using the distributive rule, and fractional equations. |
To be able to identify and describe polygons. To be able to prove that a quadrilateral is a particular type. To be able to write simple proofs involving the properties of quadrilaterals. To be able to write proofs using co-ordinate geometry. Learn how to find the area of different quadrilaterals. To review and extend equation solving skills. |
Geometry chapter six. Making patterns using quadrilaterals: tesselations. |
How are quadrilaterals classified? What is meant by convex polygons? How are the interior and exterior angle theorems developed? (cut-out triangle activity) Environment: examples of quadrilaterals in the natural world. Homo faber: the use of quadrilaterals in construction. |
Formative: quizzes and class discussion Summative: end of topic test |
|
| SIMILARITY : | Using ratios and proportion. Cross product and reciprocal properties. Solving algebraic and geometric proportions. Similar polygons and similar triangles. Similarity theorems and their relation to the triangle congruency theorems. Triangle proportionality theorems. Solving problems in geometry using proportionality. Algebra review: simplifying radicals, solving quadratics. |
To learn how to find the ratio of two quantities and to use proportions to solve problems. To understand the properties of proportions. To be able to prove the similarity of two triangles and use proportionality in solving problems. |
Geometry Chapter eight Tackling simple two column proofs involving similarity and proportion. Solving quadratic equations. simplifying radical expressions. |
How can I measure the height of the school? How do architects make blue prints? Homo faber: using similar triangles to find the height of a tall building. |
Summative: end of topic test |
|
| RIGHT TRIANGLES AND TRIGONOMETRY : | Geometric mean theorems. The Pythagorean theorem and its converse. Verifying right triangles. Special right triangles. Sines, cosines and tangents. Angle of elevation and depression. Solving right triangles. |
To extend knowledge of the Pythagorean theorem and be able to use it in solving simple problems. To become familiar with some Pythagorean triples. |
Geometry chapter nine Activities showing different ways to prove Pythagoras' theorem |
Homo faber: importance of Pythagoras' theorem and practical uses of trigonometry in measuring distances, including the distance of the moon from the earth. |
Formative: quizzes and classwork Summative: end of topic test |
|
| CIRCLES : | Investigating fractals (p590). Circles: center,radius,diameter, chord, secant, tangent. Properties of tangents and radii. Angles in the same segment are equal. Angle at center is twice the angle at the circumference. Cyclic quadrilaterals have opposite angles supplementary. Segment lengths in circles. The equation of a circle. Algebra review: simple word problems, percent problems, simplifying rational expressions. |
To learn the geometric properties of a circle. To be able to write simple proofs involving circles and use the circle theorems to find the measure of angles in circles. To review and extend algebra skills. |
Geometry chapter ten. Geometer's sketchpad |
Homo faber: satellite signal transmission. Locating beacons (page 609) |
Formative: quizzes and classwork Summative: end of topic test |
|
| AREA and VOLUME : | Interior and exterior angles of polygons. Area and perimeter of triangles, parallelograms and circles. Arc length of circles. Area of a sector and segment of a circle. The concept of a prism and how its volume can be found. Surface area and volume of cuboids and spheres. Volumes of cones and pyramids. Using similarity and scale factors. Review for final examination. |
To be able to find the angles of different polygons from given information. To understand the concepts of area and volume and be able to find the area and volumes of a variety of plane figures or solids. To review the work of the year in preparation for the final examination. |
Geometry chapters eleven and twelve. Skills Review Handbook (page 783) |
Homo faber and environment: the importance of area and volume in exploring the natural world and in man made objects. |
Quizzes. Class discussions Final examination |
|
|
|||
| «Previous Year |