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Points, lines, planes, and precise definitions Measuring segments; segment addition Congruent segments and segment bisectors Midpoint on a number line and in the plane Angle measure, the protractor, classifying angles Angle addition, angle bisectors, and congruent angles Angle pairs: complementary, supplementary, linear pair, vertical Inductive reasoning, conjecture and counterexample Conditional statements and truth value Converse, inverse and contrapositive Biconditionals and the structure of a definition Deductive reasoning: detachment and syllogism Algebraic proof: justifying each step Proof formats; undefined term, postulate, theorem Indirect proof What a construction is: tools and rules Copying a segment and copying an angle The perpendicular bisector of a segment Bisecting an angle Perpendiculars through a point, on the line and off it A parallel line through an external point Constructing an equilateral triangle and a square Inscribing a regular hexagon in a circle Transformations as functions on points Rigid and non-rigid: what is preserved Translations: drawing, describing, defining Translations in the coordinate plane Reflections: drawing, describing, defining Reflections in the coordinate plane Rotations: drawing and describing Defining rotations; rotations in the coordinate plane Compositions of rigid motions Symmetry: carrying a figure onto itself Dilations: centre and scale factor Dilating lines, segments and angles Dilations in the coordinate plane Parallel lines, transversals, and the angle pairs formed Corresponding, alternate and same-side angles Proving lines parallel: the converses Unknown angle problems with parallel lines Triangle angle sum; the exterior angle theorem Perpendicular lines and their angle relationships Distance from a point to a line; distance between parallel lines The perpendicular bisector characterization The angle bisector characterization Congruence defined by rigid motions Congruent figures: the correspondence definition Corresponding parts of congruent figures The SSS criterion (by rigid motions) The SSS criterion (from the postulates) The SAS criterion (by rigid motions) The SAS criterion (from the postulates) The ASA and AAS criteria (by rigid motions) The ASA and AAS criteria (from the postulates) Why SSA is not a criterion Right triangle congruence: HL Choosing a criterion from a marked figure CPCTC Multi-step and overlapping-triangle proofs Isosceles and equilateral triangles The triangle midsegment theorem and its applications Perpendicular bisectors of a triangle; the circumcenter Angle bisectors of a triangle; the incenter Medians and the centroid Altitudes and the orthocenter Side–angle inequalities in one triangle The triangle inequality and the Hinge Theorem Interior and exterior angle sums of a polygon Properties of parallelograms: sides, angles, diagonals Proving a quadrilateral is a parallelogram Rectangles, rhombuses and squares Trapezoids: the midsegment theorem and isosceles trapezoids Kites Classifying quadrilaterals; mixed proofs Scale drawings and scale factor Similarity transformations; the definition of similar Similar figures: equal angles and proportional sides Similar triangles: equal angles and proportional sides The AA criterion (by rigid motions) The AA criterion (from the postulates) The SSS and SAS similarity criteria Triangle proportionality and its converse Three parallel lines and the angle bisector Indirect measurement and similar-figure problems The altitude to the hypotenuse and the geometric mean Proving the Pythagorean theorem The converse; classifying triangles by side lengths Pythagorean applications and triples 45-45-90 triangles 30-60-90 triangles Trigonometric ratios defined by similarity Sine and cosine of complementary angles Using the ratios to find a side length Inverse trigonometric ratios: finding an angle Solving right triangles; angles of elevation and depression Area of a triangle as one half ab sin C Circle vocabulary; all circles are similar Central angles and arc measure Arcs and chords Perpendicular bisectors of chords Inscribed angles Inscribed angles on a diameter; inscribed polygons Tangent lines and the radius Tangent segments; the inscribed and circumscribed circles of a triangle Angles from chords, secants, and tangents Segment relationships: power of a point Cyclic quadrilaterals Arc length and radian measure Area of a sector The distance and midpoint formulas Slope criteria for parallel and perpendicular lines, and why they hold Writing equations of parallel and perpendicular lines Partitioning a directed segment Perimeter and area from coordinates Classifying triangles on the coordinate plane Classifying quadrilaterals on the coordinate plane Setting up a coordinate proof: placing a general figure Writing coordinate proofs Deriving the equation of a circle Completing the square; centre, radius, key features A curve built from a point and a line Area of triangles and parallelograms Area of trapezoids, rhombuses and kites Area of regular polygons: the apothem Area of composite two-dimensional figures Circumference and area of a circle Three-dimensional figures: naming, nets, Euler’s formula Cross-sections and solids of revolution Surface area of prisms and cylinders: lateral and total Surface area of pyramids, cones and spheres Volume of prisms and cylinders; Cavalieri’s principle Volume of pyramids, cones and spheres Scaling: k, k², k³, and change in one dimension only Surface area and volume of composite solids Density and geometric design problems

Standards for

About this project

Volume of pyramids, cones and spheres

Presets — a starting point; add or drop any task afterwards

Same practice at every level

Warm-up — 3 tasks
Bridge — 3 tasks
One third of which prism — 3 tasks
The sphere, by subtraction — 3 tasks
Going Deeper — 8 tasks
Practice — 24 tasks
Summary — 5 tasks
Cool-down — 3 tasks

Leave room at the top of the first sheet for the student’s name, date and period

The cool-down’s leaf keeps a line for the student’s name whatever you choose here: it is torn off and handed in, so it is always signed.

Start each activity on a new sheet Put the cool-down on its own leaf, headed with the lesson and a line for the student’s name Ask the student, at the foot of the cool-down, how well he thinks he understood — five steps to circle and a line to say why I will print double-sided

This tells the site how you mean to print, so that it can leave a sheet blank and keep the cool-down on the front of a leaf. It does not print anything double-sided by itself — you still choose that in your own printer dialogue.

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