1 Start-Up/ Review ***************** ***** Note: Reteaching from Ready to Go On Quizzes indicate time built in for Intervention lessons/ student mastery of previously taught material. Wk 2 1.1: Understanding Points, Lines, and Planes; 1.2: Measuring and Constructing Segments; 1.3: Measuring and Constructing Angles; Quarter 1 Classroom rules, expectations, grading policy for the course. Intervention review Alg 1/ Math 7 traditional low-performance areas: Note: These are Key CAHSEE Standards 7th M&G 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. 7th M&G 2.2 Estimate and compute the area of more complex or irregular two and three dimensional figures by breaking the figures down into more basic geometric objects. 7th M&G 3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections. 7th M&G 3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. 1.0~Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 16.0~Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Use Edusoft to print a report of your particular student weaknesses in this area and determine your focus. 1.1, 1.2, 1.3 Undefined terms: point, line, and plane. Collinear, coplanar, segment, endpoint, ray, opposite rays, postulate, coordinate, distance, length, congruent segments, construction, between, midpoint, bisects, segment bisector, angle, vertex, interior of an angle, exterior of an angle, measure, degree, congruent angles, angle bisector Labs/ Enrichment Technology Lab - Properties w/ Points 1 st Construction Copying a Segment (1.2) Patty Paper - Segment Bisector 2 nd Construction Congruent Angles (1.3) 3 rd Construction Angle Bisector (1.3)
Quarter 1 Wk 3 1.4: Pairs of Angles; 1.5: Using Formulas in ; 1.6: Midpoint and Distance in the Coordinate Plane; 8.0~Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 13.0~Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. 15.0~Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 1.4 *Reteach 1.1 1.4 1.5, 1.6 Adjacent, vertical, complementary, and supplementary angles. Linear pair, base, height, diameter, radius, pi, coordinate plane, legs, hypotenuse Connecting to Algebra - Graphing in the Coordinate Plane Wk 4 1.6: Midpoint and Distance in the Coordinate Plane; 2.1: Using Inductive Reasoning to Make Conjectures; Wk 5 2.1: Using Inductive Reasoning to Make Conjectures; 2.2: Conditional Statements; 2.3: Using Deductive Reasoning to Verify Conjectures; 2.4: Bi-Conditional Statements and Definitions; 1.0~Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 3.0~Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 15.0~Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 1.0~Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 3.0~Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. 1.6 *Reteach 1.5, 1.6 *Unit 1 Test Review *Unit 1 Test 2.1 Coordinate plane, legs, hypotenuse, counter examples, conjectures 2.1 2.4 *Reteach 2.1 2.4 Counter examples, conjectures, inverse, converse, contrapositive, conditional, deductive reasoning Enrichment - 1.7: Transformations in the Coordinate Plane Connecting to Geo Venn Diagrams Geo Lab Solve Logic Puzzles
Wk 6 2.5: Algebraic Proof; 2.6: Geometric Proof; Quarter 1 1.0~Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. 2.0~Students write geometric proofs, including proofs by contradiction. 2.5, 2.6 *Reteach 2.5 2.6 Proof, equality, congruent, reflexive, symmetric, transitive, theorem, 2-column proof, complement, supplement Geo Lab Design Plans for Proofs Enrichment 2.7: Flowchart and Paragraph Proofs Wk 7 3.2: Angles Formed by Parallel Lines and Transversals; 3.3: Proving Lines Parallel 7.0~Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 16.0~Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. *Unit 2 Test Review *Unit 2 Test 3.2, 3.3 Interior, exterior, postulate, parallel, transversal, consecutive, converse, corresponding, alternate Enrichment 3.1: Lines and Angles Technology Lab Parallel lines and Transversals Wk 8 3.3: Proving Lines Parallel; 3.4: Perpendicular Lines; 3.5: Slopes of Lines; 2.0~Students write geometric proofs, including proofs by contradiction. 7.0~Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 16.0~Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 3.3, 3.4 *Reteach 3.2 3.4 3.5 Slope, rise, run, rate of change, opposite, reciprocals, converse, perpendicular bisector 4 th Construction Line Parallel to a Given Line through a Point off the Line (3.3) 5 th Construction Perpendicular Bisector of a Segment (3.4) 6 th Construction Line Perpendicular to a Given Line through a Given Point (Geo Lab) Technology Lab Parallel and Perpendicular Lines
Quarter 1 Wk 9 3.6: Lines in the Coordinate Plane 4.1: Classifying Triangles and exterior angles of triangles and polygons to classify figures and solve problems. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 3.6 *Reteach 3.5, 3.6 *Unit 3 Test Review *Unit 3 Test 4.1 Intersecting, coincide, classify, equation, along with acute, equiangular, right, obtuse, equilateral, isosceles, and scalene triangles Geo Lab Develop the Triangle Sum Theorem Wk 10 4.2: Angle Relationships; 4.3: Congruent Triangles; 4.4: Triangle Congruence: SSS & SAS; 2.0~Students write geometric proofs, including proofs by contradiction. 5.0~Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. and exterior angles of triangles and polygons to classify figures and solve problems. 13.0~Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. 4.2, 4.3 *Reteach 4.1 4.3 4.4 Corollary, interior, exterior, interior angle, exterior angle, remote interior angle, corresponding angles, sides, polygons, congruence Geo Lab Explore SSS and SAS Triangle Congruence End Quarter 1
Quarter 2 Wk 11 4.4: Triangle Congruence SSS, SAS; 4.5: Triangle Congruence ASA, AAS, HL; 4.7: Introduction to Coordinate Proof; 2.0~Students write geometric proofs, including proofs by contradiction. 4.0~Students prove basic theorems involving congruence and similarity. 5.0~Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. 16.0~Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 4.4, 4.5, 4.7 Triangle rigidity, included angle, included side, CPCTC Technology Lab Predict Other Triangle Congruence Relationships Connecting to Algebra Quadratic Equations Wk 12 4.8: Isosceles and Equilateral Triangles; 5.1: Perpendicular and Angle Bisectors; 2.0~Students write geometric proofs, including proofs by contradiction. 4.0~Students prove basic theorems involving congruence and similarity. and exterior angles of triangles and polygons to classify figures and solve problems. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 4.8 *Reteach 4.4 4.8 *Unit 4 Test Review *Unit 4 Test 5.1 Legs, vertex, angle, base, base angles, isosceles and equilateral triangles, equidistant, locus, perpendicular and angle bisectors
Quarter 2 Wk 13 5.1: Perpendicular and Angle Bisectors; 5.4: The Triangle Mid-segment Theorem; 5.5: Indirect Proof and Inequalities in One Triangle; Wk 14 5.7: The Pythagorean Theorem; 5.8: Applying Special Right Triangles; 8.2: Trigonometric Ratios; 2.0~Students write geometric proofs, including proofs by contradiction. 6.0~Students know and are able to use the triangle inequality theorem. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 6.0~Students know and are able to use the triangle inequality theorem. and exterior angles of triangles and polygons to classify figures and solve problems. 14.0~Students prove the Pythagorean theorem. 15.0~Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. 18.0~Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin ( x )) 2 + (cos( x )) 2 = 1. 19.0~Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. 20.0~Students know and are able to use angle and side relationships in problems with special right triangles, such as 30, 60, and 90 triangles and 45, 45, and 90 triangles. 5.1, 5.4, 5.5 *Reteach 5.1, 5.4, 5.5 Equidistant, locus, perpendicular and angle bisectors, proof by contradiction 5.7, 5.8, 8.2 Pythagorean triple, trigonometric ratios, sine, cosine, tangent Construction of a Midsegment of a Triangle Geo Lab Explore Triangle Inequalities Connecting Geo to Algebra Simplest Radical Form Geo Lab Hands on Proof of the Pythagorean Theorem Enrichment 5.6: Inequalities in Two Triangles Enrichment 8.1: Similarity in Right Triangles
Quarter 2 Wk 15 8.2: Trigonometric Ratios; 8.3: Solving Right Triangles; Wk 16 6.1: Properties and Attributes of Polygons; 6.2: Properties of Parallelograms; 6.3: Conditions for Parallelograms; 15.0~Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. 18.0~Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2 + (cos( x )) 2 = 1. 19.0~Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. 20.0~Students know and are able to use angle and side relationships in problems with special right triangles, such as 30, 60, and 90 triangles and 45, 45, and 90 triangles. 7.0~Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. and exterior angles of triangles and polygons to classify figures and solve problems. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 8.2, 8.3 *Reteach 5.7, 5.8, 8.2, 8.3 *Unit 5 Test Review *Unit 5 Test Trigonometric ratio, sine, cosine, tangent 6.1 6.3 *Reteach 6.1-6.3 Side of a polygon, vertex of a polygon, diagonal, regular polygon, concave, convex, parallelogram, quadrilateral Enrichment 8.4: Angles of Elevation and Depression Enrichment 8.5: Law of Sines and Cosines Enrichment 8.6: Vectors Geo Lab Indirect Measurement Using Trigonometry - Clinometer Geo Lab Construct Regular Polygons Geo Lab Explore Properties of Parallelograms
Quarter 2 Wk 17 6.4: Properties of Special Parallelograms; 6.5: conditions for Special Parallelograms; 6.5: Properties of Kites and Trapezoids; 2.0~Students write geometric proofs, including proofs by contradiction. 7.0~Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. and exterior angles of triangles and polygons to classify figures and solve problems. 15.0~Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. 6.4 6.6 *Reteach 6.4-6.6 Rectangle, rhombus, square, kite, trapezoid, base of a trapezoid, leg of trapezoid, base angle of a trapezoid, isosceles trapezoid, midsegment of a trapezoid Technology Lab Predict Conditions for Special Parallelograms Technology Lab Explore Isosceles Trapezoids Wk 18 *Unit 6 Test Review *Unit 6 Test *Final Exam Review Chapters 1 6, 8 Wk 19 *Final Exam Review Chapters 1 6, 8 *Final Exam End Quarter 2 End Semester 1
Quarter 3 Wk 1 7.1: Ratio and Proportion; 7.2: Ratios in Similar Polygons; 7.3: Triangle Similarity: AA, SSS, SAS 5.0~Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles. and exterior angles of triangles and polygons to classify figures and solve problems. 7.1 7.3 *Reteach 7.1-7.3 Reflexive, symmetric, transitive Technology Lab Explore the Golden Ratio Technology Lab Predict Triangle Similarity Relationships Wk 2 7.4: Applying Properties of Similar Triangles; 7.5: Using Proportional Relationships; 7.0~Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 8.0~Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 11.0~Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. and exterior angles of triangles and polygons to classify figures and solve problems. 16.0~Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 7.4, 7.5 Indirect measurement, scale, scale drawing, perimeter, area Tech Lab Investigate Angle Bisectors of a Triangle
Quarter 3 Wk 3 9.1: Developing Formulas for Triangles and Quadrilaterals; 8.0~Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 10.0~Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. *Reteach 7.4, 7.5 *Unit 7 Test Review *Unit 7 Test 9.1 Area of a parallelogram, triangle, trapezoid, rhombus, and kite Wk 4 9.1: Developing Formulas for Triangles and Quadrilaterals; 9.3: Composite Figures; 9.4: Perimeter and Area in the Coordinate Plane; 8.0~Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 10.0~Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. 12.0~Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. 9.1, 9.3, 9.4 *Reteach 9.1 9.4 *Unit 9 Test Review *Unit 9 Test Geo Lab Develop p Enrichment 9.2: Developing Formulas for Circles and Regular Polygons Enrichment 9.5: Effects of Changing Dimensions Proportionally Enrichment 9.6: Geometric Probability Ready to Go On Quiz
Quarter 3 Wk 5 10.1: Solid ; 10.3: Formulas in 3-D; 10.4: Surface Area of Prisms and Cylinders; 10.5: Surface Area of Pyramids and Cones; 10.6: Volume of Prisms and Cylinders; 10.7: Volume of Pyramids and Cones; 8.0~Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 9.0~Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. 11.0~Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. 10.1/10.3 10.7 Face, edge, vertex, prism, cylinder, pyramid, cone, cube, net, cross section, polyhedron, space, lateral face, lateral edge, right prism, oblique prism, altitude, surface area, lateral surface, axis of a cylinder, right cylinder, oblique cylinder, vertex of a pyramid, regular pyramid, slant height of a regular pyramid, altitude of a pyramid, vertex of a cone, axis of a cone, right cone, oblique cone, slant height of a right cone, altitude of a come, volume Enrichment 10.2: Representations of 3-D figures Wk 6 10.8: Spheres; 8.0~Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 9.0~Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. 11.0~Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. 10.8 *Reteach 10.4 10.8 *Unit 10 Test Review *Unit 10 Test Sphere, center of a sphere, radius of a sphere, hemisphere
Quarter 3 Wk 7 11.1: Lines that Intersect Circles; 11.2: Arcs and Chords; 11.4: Inscribed Angles; Wk 8 11.4: Inscribed Angles; 11.5: Angle Relationship in Circles; 11.6: Segment Relationships in Circles; 7.0~Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 8.0~Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. 16.0~Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 21.0~Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. 7.0~Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 21.0~Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. 11.1, 11.2, 11.4 *Reteach 11.1, 11.2 Interior of a circle, exterior of a circle, chord, secant, tangent of a circle, point of tangency, congruent circles, concentric circles, tangent circles, common tangent, central angle, arc, minor arc, major arc, semicircle, adjacent arcs, congruent arcs, sector of a circle, segment of a circle, arc length 11.4-11.6 *Reteach 11.4 11.6 *Unit 11 Test Review *Unit 11 Test Inscribed angle, intercepted arc, subtend, secant segment, external secant segment, tangent segment Constructions Center of a Circle Constructions Tangent to a circle from an Exterior Point Tech Lab Explore Angle Relationships in Circles Tech Lab Explore Segment Relationships in Circles Enrichment: 11.7 Circles in the Coordinate Plane
Quarter 3 Wk 9 12.1: Reflections; 12.2: Translations; 12.3: Rotations; 22.0~Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. 12.1 12.3 *Reteach 12.1 12.3 *Unit 12 Test Review *Unit 12 Test Isometry, reflection, rotation, translation, transformation Patty Paper Translate a Figure Enrichment 12.4: Compositions of Transformations Enrichment 12.5: Symmetry Enrichment 12.7: Dilations 10 CST Review (Testing usually done in weeks 11/12 of Semester 2 Key Standards: (32% of CST) 4.0 Students prove basic theorems involving congruence and similarity 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. 12.0 Students find and use measures of sides and of Interior and Exterior angles of triangles and polygons to classify figures and solve problems. 21.0 students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. End of Quarter 3
Quarter 4 Wk 11 Projected CST Week (If CST occurs in Week 12 instead, continue review and ensure mastery of power standards.) *Review for CST *CST NOTE : Throughout Quarter 4, we are preparing students for Algebra II success. In order to accomplish this, coordinate geometry should be woven through the following weekly topics. Wk 12 Linear Functions Wk 13 Properties of Exponents Wk 14 Radical Expressions Algebra 1 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). Algebra 1 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. Algebra 1 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. Tie into Special Right Triangles Algebra 1 Chapter 5 Algebra 1 Chapter 7.3, 7.4, 7.5 Algebra 1 Chapter 11.1, 11.2, 11.3, 11.4
Quarter 4 Wk 15 Add/ subtract/ multiple/ divide polynomials Algebra 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. Holt Chapter 7.7, 7.8, 7.9 Wk 16 Factoring Wk 17 Review for Semester Final Exam Wk 18 Review for Final Exam/ Senior Final Exams Algebra 11.0 Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials Key Standards for Review: 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles 10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. 12.0- Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. 16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. 21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. Holt Chapter 8 Wk 19 Freshmen/ Sophomore/ Junior Final Exams End of Quarter 4 ~ Semester 2