Access PointsScope & Sequence Focus Calendar

Geometry

Overview Focus Access Points Assessed Weekly Assignments

OVERVIEW:

Students will apply geometric concepts in modeling situations. Students will explore geometric theories and related vocabulary. Students will investigate, model, and practice different geometric concepts involving triangles, circles, 2D and 3D shapes.

Essential Understanding: (Concrete)

Students will construct

Congruence

MAFS.912.G-CO.1.AP.1a Identify precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

MAFS.912.G-CO.3.AP.9a Measure lengths of line segments and angles to establish the facts about the angles created when parallel lines are cut by a transversal and the points on a perpendicular bisector.

MAFS.912.G-CO.4.AP.12a Copy a segment.

MAFS.912.G-CO.4.AP.12c Bisect a segment.

MAFS.912.G-CO.4.AP.12e Construct perpendicular lines, including the perpendicular bisector of a line segment.

MAFS.912.G-CO.4.AP.12f Construct a line parallel to a given line through a point not on the line.

Geometric Properties with Equations

MAFS.912.G-GPE.2.AP.6a Given two points, find the

Unit 1

Line Segment

Weekly Assignment 1: Create a line segment using two points.

(MAFS.912.G.-CO.4.AP.12a)

Weekly Assignment 2:

Indicate point ratios on a line segment (1/2, ¾).

(MAFS.912.G-GPE.2.AP.6a)

Weekly Assignment 3:

Construct a bisector of a segment using paper folding.

(MAFS.912.G-CO.4.AP.12c)

and manipulate line segments.

Students will categorize and classify shapes, such as triangles and parallelograms.

Students will identify, measure, and compare sides and angles of various shapes.

Students will define and demonstrate rotations, reflections, and translations.

Essential Understanding (Representation)

point on the line segment between the two points that divides the segment into a given ratio.

Congruence

MAFS.912.G-CO.1.AP.1a Identify precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

MAFS.912.G-CO.3.AP.9a Measure lengths of line segments and angles to establish the facts about the angles created when parallel lines are cut by a transversal line and the points on a perpendicular bisector.

Unit 2

Angles

Students will solve real world problems involving volume and area.

Students will apply concepts of transformations on a coordinate plane.

Students will create connections between real-world problems and geometric principles and concepts that can solve those problems.

MAFS.912.G-CO.4.AP.12b Copy an angle.

MAFS.912.G-CO.4.AP.12d Bisect an angle

Similarity, Right Triangles & Trigonometry

MAFS.912.G-SRT.3.AP.7a Explore the sine of an acute angle and the cosine of its complement and determine their relationship.

Weekly Assignment 4: Construct an angle bisector using paper folding.

(MAFS.912.G-CO.4.AP.12d)

Weekly Assignment 5: Recognize an acute angle.

(MAFS.912.G.SRT.3.AP.7a)

Essential Questions

How can you use the tools of geometry to solve real-world problems?

How can you use concepts of congruency or translation to solve real-world problems?

How can you use properties of triangles or quadrilaterals to solve real-world problems?

How can you use similarity and transformations to solve real-world problems?

How can you use volume formulas to solve real-world problems?

How can you use

Similarity, Right Triangles & Trigonometry

MAFS.912.G-SRT.1.AP.2a Determine if two figures are similar.

MAFS.912.G-SRT.1.AP.2b Given two figures, determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides.

Congruence

MAFS.912.G-CO.2.AP.7a Use definitions to demonstrate congruency and similarity in figures.

MAFS.912.G-CO.3.AP.11a Measure the angles and sides of parallelograms to establish facts about parallelograms.

Unit 3

Shapes

Weekly Assignment 6: Classify shapes that are

modeling to solve real-world problems?

Mathematical Practices:

MAFS.K12.MP.1.1

Make sense of problems and persevere in solving them.

*Make a plan!

Circles

MAFS.912.G-C.1.AP.1a Compare the ratio of diameter to circumference for several circles to establish all circles are similar.

similar.

(MAFS.912.G-SRT.1.AP.2a)

Weekly Assignment 7: Recognize shapes that are congruent.

(MAFS.912.G-CO.2.AP.7a)

Weekly Assignment 8: List characteristics of parallelograms.

(MAFS.912.G.CO.3.AP.11a)

*Try different approaches when your problem is hard.

*Solve your problem in more than one way.

*Check whether your solution makes sense.

MAFS.K12.MP.2.1

Reason abstractly and quantitatively.

*Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use.

Congruence

MAFS.912.G-CO.1.AP.1a Identify precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

MAFS.912.G-CO.4.AP.12b Copy an angle.

Geometric Properties with Equations

MAFS.912.G-GPE.2.AP.5a Using slope, prove lines are parallel or perpendicular.

Similarity, Right Triangles & Trigonometry

MAFS.912.G-SRT.1.AP.2a Determine if two figures are similar.

MAFS.912.G-SRT.1.AP.2b Given two figures, determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides.

MAFS.912.G-SRT.1.AP.3a Apply the angle-angle (AA)

Unit 4

Angle Measurements

Weekly Assignment 9: Recognize angle measurements on a triangle. (less than, more than or 90°)

(MAFS.912.G-CO.4.AP.12b)

MAFS.K12.MP.3.1

Construct viable arguments and critique the reasoning of others.

*Explain both what to do and why it works.

*Work to make sense of others’ mathematical thinking.

MAFS.K.12.MP.4.1

Model with mathematics.

criteria for triangle similarity on two triangles.

MAFS.912.G-SRT.2.AP.4a Establish facts about the lengths of segments of sides of a triangle when a line parallel to one side of the triangles divides the other two sides proportionally.

MAFS.912.G-SRT.2.AP.5a Apply the criteria for triangle congruence and/or similarity (angle-side-angle [ASA], side-angle-side [SAS], side-side-side [SSS], angle-angle [AA] to determine if geometric shapes that divide into triangles are or are not congruent and/or can be similar.

MAFS.912.G-SRT.3.AP.6a Using a corresponding angle of similar right triangles, show that the relationships of the side ratios are the same, which leads to the definition of trigonometric ratios for acute angles.

MAFS.912.G-SRT.3.AP.7a Explore the sine of an acute angle and the cosine of its complement and determine their relationship.

MAFS.912.G-SRT.3.AP.8a Apply both trigonometric ratios and Pythagorean Theorem to solve application problems involving right triangles.

Weekly Assignment 10: Categorize triangles with similar angles.

(MAFS.912.G-SRT.1.AP.3a)

Weekly Assignment 11: Sort given triangles based on angle measurement.

(MAFS.912.G-SRT.1.AP.2b)

Weekly Assignment 12: Determine the corresponding angles of similar right triangles.

(MAFS.912.G-SRT.3.AP.6a)

Weekly Assignment 13: Classify triangles based on side measurements.

(MAFS.912.G.CO.3.AP.10a)

Weekly Assignment 14: Divide a figure into triangles and determine if the triangles are similar.

(MAFS.912.G-SRT.2.AP.5a)

Weekly Assignment 15: Create a congruent

*Apply math to real-world situations.

*Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.

MAFS.K12.MP.5.1

Congruence

MAFS.912.G-CO.2.AP.8a Use the definition of congruence, based on rigid motion, to develop and explain the triangle congruence criteria; ASA, SSS, and SAS.

MAFS.912.G-CO.3.AP.10a Measure the angles and sides of equilateral, isosceles, and scalene triangles to establish facts about triangles.

MAFS.912.G-CO.4.AP.12d Bisect an angle.

triangle when given a model.

(MAFS.912.G-CO.2.AP.8a)

Use appropriate tools strategically.

*Choose appropriate tools for your problem.

*Use mathematical tools correctly and efficiently.

*Estimate and use what you know to check the answers you find using tools.

MAFS.K12.MP.6.1

Attend to precision.

*Communicate your mathematical thinking clearly and precisely.

*Use the level of precision you need for your problem.

*Be accurate when you count, measure, and

Geometric Properties with Equations

MAFS.912.G-GPE.2.AP.4a Use coordinates to prove simple geometric theorems algebraically.

MAFS.912.G-GPE.2.AP.5a Using slope, prove lines are parallel or perpendicular.

MAFS.912.G-GPE.2.AP.7a Use the distance formula to calculate perimeter and area of polygons plotted on a coordinate plane.

Congruence

MAFS.912.G-CO.4.AP.12e Construct perpendicular lines, including the perpendicular bisector of a line segment.

calculate.

MAFS.K12.MP.7.1

Look for and make use of structure.

*Find, extend, analyze, and create patterns.

*Use patterns and structures to solve

MAFS.912.G-CO.4.AP.12f Construct a line parallel to a given line through a point not on the line.

Similarity, Right Triangles & Trigonometry

MAFS.912.G-SRT.1.AP.1b Given a center and a scale factor, verify experimentally that when performing dilations of a line segment, the pre-image, the segment which becomes the image is longer or shorter based on the ratio given by the scale factor. Unit 5

Graphing

Weekly Assignment 16: Determine if lines are parallel or perpendicular based on a given slope and model.

(MAFS.912.G-GPE.2.AP.5a)

Weekly Assignment 17: Plot four ordered pairs on a grid.

(MAFS.912.G-GPE.2.AP.4a)

Weekly Assignment 18: Compute the perimeter of a polygon using a coordinate plane after

problems.

MAFS.K12.MP.8.1

Look for and express regularity in repeated reasoning.

*Use patterns and structures to create and explain rules and shortcuts.

*Use properties, rules, and shortcuts to solve problems.

*Reflect on your thinking before, during, and after you solve a problem.

Congruence

MAFS.912.G-CO.1.AP.2a Represent transformations in the plane using, e.g., transparencies and geometry software.

MAFS.912.G-CO.1.AP.2b Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

MAFS.912.G-CO.1.AP.3a Describe the rotations and reflections of a rectangle, parallelogram, trapezoid, or regular polygon that maps each figure onto itself.

MAFS.912.G-CO.1.AP.4a Using previous comparisons and descriptions of transformations, develop and understand the meaning of rotations, reflections, and translations based on angles, circles, perpendicular lines, parallel lines, and line segments.

MAFS.912.G-CO.1.AP.5a Transform a geometric figure given a rotation, reflection, or translation using graph paper, tracing paper, or geometric software.

MAFS.912.G-CO.1.AP.5b Create sequences of transformations that map a geometric figure on to itself and another geometric figure.

plotting four points.

(MAFS.912.G.-GPE.2.AP.7a)

MAFS.912.G-CO.2.AP.6a Use descriptions of rigid motion and transformed geometric figures to predict the effects rigid motion has on figures in the coordinate plane.

MAFS.912.G-CO.2.AP.6b Knowing that rigid transformations preserve size and shape or distance and angle, use this fact to connect the idea of congruency and develop the definition of congruent.

Similarity, Right Triangles & Trigonometry

MAFS.912.G-SRT.1.AP.1a Given a center and a scale factor, verify experimentally that when dilating a figure in a coordinate plane, a segment of the pre-image that does not pass through the center of the dilation, is parallel to its image when the dilation is performed. However, a segment that passes through the center remains unchanged.

MAFS.912.G-SRT.1.AP.1b Given a center and a scale factor, verify experimentally that when performing dilations of a line segment, the pre-image, the segment which becomes the image is longer or shorter based on the ratio given by the scale factor.

Unit 6

Geometric Transformations

Weekly Assignment 19: Define rotation, reflection, and translation.

(MAFS.912.G-CO.1.AP.4a)

Weekly Assignment 20: Investigate translations versus a horizontal stretch.

(MAFS.912.G-CO.1.AP.2b)

Weekly Assignment 21: Represent translations on different quadrants in a plane.

(MAFS.912.G-CO.1.AP.2a)

Weekly Assignment 22: Show the resulting image of a given combination of transformations

(reflection then rotation)

(MAFS.912.G-CO.1.AP.5b)

Weekly Assignment 23: Determine the sequence of two combined transformations to a shape (when given a starting picture and a resulting picture).

(MAFS.912.G-CO.2.AP.6b)

Weekly Assignment 24: Apply a translation to a shape on a coordinate grid with an ordered pair (left, down).

(MAFS.912.G-CO.1.AP.5a)

Geometric Properties with Equations

MAFS.912.G-GPE.1.AP.1a Given the center and the radius of a circle, use the Pythagorean Theorem to find the equation of the circle.

MAFS.912.G-GPE.1.AP.1b Given the equation, find the center and the radius of a circle.

Circles

MAFS.912.G-C.1.AP.1a Compare the ratio of diameter to circumference for several circles to establish all circles are similar.

MAFS.912.G-C.1.AP.5a Find the arc length of a circle.

Geometric Measurement and Dimension

MAFS.912.G-GMD.1.AP.1a Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection.

Unit 7

Geometric Properties

Circles

MAFS.912.G-C.1.AP.3a Construct the inscribed and circumscribed circles of a triangle.

Congruence

MAFS.912.G-CO.4.AP.13a Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.

Geometric Measurement and Dimension

MAFS.912.G-GMD.1.AP.1a Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection.

Weekly Assignment 25: Distinguish between the center, radius, diameter, and circumference of a circle.

(MAFS.912.G-GPE.1.AP.1b)

Weekly Assignment 26: Using a string, measure the arc length of a circle.

(MAFS.912.G-C.1.AP.5a)

Weekly Assignment 27: Connect at least three diameter measurements to different sized circles they belong with.

(MAFS.912.G-C.1.AP.1a)

Unit 8

Circles

Weekly Assignments 28 & 29: Create different shapes inscribed in a circle.

Geometric Measurement & Dimension

MAFS.912.G-GMD.1.AP.1a Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection.

MAFS.912.G-GMD.1.AP.3a Use appropriate formulas to calculate volume for cylinders, pyramids, and cones.

MAFS.912.G-GMD.2.AP.4a Identify shapes created by cross sections of two-dimensional and three-dimensional figures.

(MAFS.912.G-CO.4.AP.13.a)

Circles

MAFS.912.G-C.2.AP.5c Apply the formula to the area of a

Unit 9

Geometric Dimension

Weekly Assignment 30: Identify three-dimensional shapes that can be created using circles.

(MAFS.912.G-GMD.1.AP.1a)

sector (e.g., area of a slice of pie).

Geometric Properties with Equations

MAFS.912.G-GPE.1.AP.1a Given the center and the radius of a circle, use the Pythagorean Theorem to find the equation of the circle.

Geometric Measurement & Dimension

MAFS.912.G-GMD.1.AP.1a Describe why the formulas work for a circle or cylinder (circumference of a circle, area of a circle, volume of a cylinder) based on a dissection.

MAFS.912.G-GMD.1.AP.3a Use appropriate formulas to calculate volume for cylinders, pyramids, and cones.

MAFS.912.G-GMD.2.AP.4a Identify shapes created by cross sections of two-dimensional and three-dimensional figures.

Modeling with Geometry

MAFS.912.G-MG.1.AP.1a Describe the relationship between the attributes of a figure and the changes in the area or volume when one attribute is changed.

Weekly Assignment 31: Discover two-dimensional shapes from a cross section of three-dimensional shapes (square-cube).

(MAFS.912.G-GMD.2.AP.4a)

MAFS.912.G-MG.1.AP.2a Recognize the relationship between density and area; density and volume using real-world models.

MAFS.912.G-MG.1.AP.3a Apply the formula of geometric figures to solve design problems (e.g., designing an object or structure to satisfy physical restraints or minimize cost).

Unit 10

2D & 3D Area

Weekly Assignment 32: Sequence the steps needed to solve the area of a sector.

(MAFS.912.G-C.2.AP.5c)

Weekly Assignment 33: Calculate the volume to a three dimensional shape following a formula model.

(MAFS.912.G-GMD.1.AP.3a)

Weekly Assignment 34: Explore how changes in one attribute will affect volume.

(MAFS.912.G-GMD.1.AP.1a)

Weekly Assignment 35: Explore the density of set items in containers of different sizes.

(MAFS.912.G-MG.1.AP.2a)

Weekly Assignment 36: Apply the knowledge of area to calculate measurement in real life scenarios.

(MAFS.912.G-MG.1.AP.3a)