Unit 1: Foundations of Geometry
Unit 1: Essential Questions
In this unit we are going to address questions such as: How do we describe geometric figures? How do we measure geometric figures? What do we understand the differences and similarities between equality and congruence?
Summary of Key Lesson Topics
Identify points, lines and planes.
Use ruler and segment addition postulates to find distances.
Identify midpoint and congruent segments to find distances
Measure, Estimate, and Classify Angles
Describe Angle Pair Relationships
Classify Polygons
Find the Perimeter, Circumference, and Area
Math Standards Introduced
Most of this section is review of prior standards taught in earlier grades. However, there is much overlap between the earlier grade standards and the high school geometry standards.
High School Common Core:
CCSS.MATH.CONTENT.HSG.CO.A.1: Know 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.
Grade 4 Common Core:
CCSS.MATH.CONTENT.4.MD.C.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
CCSS.MATH.CONTENT.4.MD.C.7: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
Pre-requisite Skills
This unit is 99% review of prior grades starting with 4th grade. You have been practicing the essential components of geometry for last six years. In 8th grade you were introduced to the concepts of congruency and similarity. By 9th grade you have been evaluating expressions and solving linear equations with variables on both sides. You will need all these algebra and geometry skills as the foundations of this course.
Below are the common core standards first introduced in grade 4 and which we will be revisiting in Unit 1 of High School Geometry. However, if you are interested in seeing the progression of standards across the grade then click here.
CCLS - Math: 4.MD.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
CCLS - Math: 4.MD.6: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
CCLS - Math: 4.MD.7: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
Lesson Objectives and Resources
Day 1:
How do we identify points, lines and planes?
Students will be able to…
Identify and label undefined terms points, lines, and planes.
Identify and label defined terms line segments and rays, as well as endpoints.
Study Resources:
Geometry Textbook: Chapter 1 Lesson 1.1
Day 2:
How do we identify collinear and coplanar points?
Students will be able to…
Identify collinear and coplanar points
Review how to identify and label undefined terms points, lines, and planes.
Study Resources: Same as Day 1
Day 3:
How do we use Segment postulates to find lengths?
Students will be able to…
Use the ruler and segment addition postulates to identify distances (lengths) between two points.
Calculate segment lengths and calculate flight distances.
Study Resources:
Day 4:
How do we find unknown lengths using congruent segments, segment midpoints and bisectors?
Students will be able to…
Identify congruent segments in the coordinate plane.
Identify segment midpoints and bisectors to calculate missing lengths using algebra
Study Resources:
Geometry Textbook: Chapter 1 Lesson 1.2 (congruence) and Lesson 1.3
- (skipped distance or midpoint formulas for a later date. )
Day 5:
How do we name, measure and estimate angles?
Students will be able to…
name and measure angles
estimate measurements of angles
Study Resources:
Geometry Textbook: Chapter 1 Lesson 1.4
Video: How do we measure angles
Additional Video Resources:
Day 6:
How do we classify angles?
Students will be able to…
Classify angles
Review estimating angles
Study Resources:
Geometry Textbook: Chapter 1 Lesson 1.4
Additional Video Resources:
Day 7:
How do we use the angle addition postulate to measure angles?
Students will be able to…
use the angle addition postulate to find angles measures
identify congruent angles to measure unknown angles
Study Resources:
Geometry Textbook: Chapter 1 Lesson 1.4
Mid-Unit Review
How do we review lessons 1 through 7?
Students will be able to review ...
Define, identify, and name points, lines, planes, segments and rays
Identify and name collinear and coplanar points
Find measure of unknown segment lengths using the segment addition postulate
Identify and use congruent segments, and segment bisectors to measure segments
Define, name, measure, and estimate angles
Classify angles
Identify and use congruent angles and angle addition postulate to measure angles