Download Grade 8 Mathematics Curriculum

Grade 8 Mathematics Curriculum
2014-2015
North Jersey Arts and Science Charter Schools
Unit 2 Summary: Geometry
Essential Questions
1.
Big Ideas
How can we understand congruence and similarity?
1.
Understand congruence and similarity using physical models,
transparencies, or geometry software.
Learning Outcomes (CCSS)
8.G.1: Verify experimentally the properties of rotations, reflections, and translations:
8.G.1a:: Lines are taken to lines, and line segments to line segments of the same length.
8.G.1b: Angles are taken to angles of the same measure.
8.G.1c: Parallel lines are taken to parallel lines.
8.G.2: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and
translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.4: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations,
and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.
8.G.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears
to form a line, and give an argument in terms of transversals why this is so.
Local Standards (LS) #16-31 are taught in this unit.
Prior Knowledge Expected
•
•
•
•
•
Geometric measurement: understand concepts of angle and measure angles (4.MD.C.5)
Draw and identify lines and angles, and classify shapes by properties of their lines and angles (4.G.A.1) (4.G.A.2) (4.G.A.3)
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume (7.G.B.5)
Understand ratio concepts and use ratio reasoning to solve problems (6.RP.A.2)
Analyze proportional relationships and use them to solve real-world and mathematical problems (7.RP.A.2) (7.RP.A.3)
Assessment Summary
Grade 8 Curriculum
Unit 2: Geometry
Unit 2 Summary: Geometry
1.
2.
Mid-Unit Assessment (LS # 16 – 23)
End-of-Unit Assessment (LS # 24-31)
(Scope and Sequence on the next page)
Grade 8 Curriculum
Unit 2: Geometry
Unit 2: Geometry
Periods*
1
1
1
4
3
CCSS
8.G.1
8.G.3
8.G.1
8.G.3
8.G.1
8.G.3
8.G.2
8.G.1a,b,c
LS
S16
S17
S18
S19
S20
Grade 8 Curriculum
Student Friendly Language
Know what translations are and describe their effects on two-dimensional
figures using coordinates.
Know what reflections are and describe their effects on two-dimensional
figures using coordinates.
Know what rotations are and describe their effects on two-dimensional figures
using coordinates.
Rotate, reflect, and translate figures to determine if they are congruent and
describe the sequence.
Rotate, reflect, and translate lines, line segments, angles, and parallel lines
Resources
Textbook
Lesson 9-1
Links
Unit 2 Activity 2
Other
EngageNY M2 L1, L2, L3
Georgia Unit 1
Assessment
Skill Check 16
Textbook
Lesson 9-2
Links
Unit 2 Activity 2
Other
EngageNY M2 L4
Georgia Unit 1
Assessment
Skill Check 17
Textbook
Lesson 9-3
Links
Unit 2 Activity 2
Other
EngageNY M2 L5
Georgia Unit 1
Assessment
Skill Check 18
Textbook
Lesson 9-4
Links
Cutting it Out
Other
EngageNY M2 L10, L11
Georgia Unit 1
Assessment
Skill Check 19
Textbook
Lesson 9-4
Unit 2: Geometry
Unit 2: Geometry
Periods*
CCSS
LS
Student Friendly Language
keeping them the same length
2
2
2
1
8.G.3
8.G.4
8.G.4
8.G.4
8.G.4
S21
S22
S23
S24
Grade 8 Curriculum
Explain what dilations are (enlargement and reduction) and describe their
effects on two-dimensional figures using coordinates.
Resources
Links
Congruent Segments
Other
EngageNY M2 L3
Georgia Unit 1
Assessment
Skill Check 20
Textbook
Lesson 10-1
Links
Dilation
Other
EngageNY M3 L # 1-7
Georgia Unit 1
Assessment
Skill Check 21
Textbook
Lesson 10-1
Links
Blew up the candy bar
Other
EngageNY M3 L # 1-7
Georgia Unit 1
Assessment
Skill Check 22
Textbook
Lesson 10-2
Links
In Your Shadow
Other
EngageNY M3 L8
Georgia Unit 1
Assessment
Skill Check 23
Textbook
Lesson 10-3
Links
Slope & Triangles
Find the scale factor of a two-dimensional figure using coordinates
Draw two similar two-dimensional figures and describe the sequence that
shows the similarity between them.
Show how similar triangles and slope are related
Unit 2: Geometry
Unit 2: Geometry
Periods*
2
3
1
CCSS
8.G.4
8.G.5
8.G.5
LS
S25
S26
S27
Grade 8 Curriculum
Student Friendly Language
Use transformations and similarity to solve problems
Identify congruent angles when two parallel lines are cut by a transversal.
Resources
Other
EngageNY M3 L 9
Georgia Unit 1
Assessment
Skill Check 24
Textbook
Lesson 10-4
Links
Miles of Tiles
Other
EngageNY M3 L12
Georgia Unit 1
Assessment
Skill Check 25
Textbook
Lesson 11-1
Links
Find the angle
Other
EngageNY M2 L12
Georgia Unit 1
Assessment
Skill Check 26
Textbook
Lesson 11-2
Links
Missing Angle
Other
EngageNY M2 L12
Georgia Unit 1
Assessment
Skill Check 27
Reason how congruent angles can determine whether a line is parallel
Unit 2: Geometry
Unit 2: Geometry
Periods*
1
1
1
2
CCSS
8.G.5
8.G.5
8.G.5
8.G.4
LS
S28
S29
S30
S31
Grade 8 Curriculum
Student Friendly Language
Resources
Textbook
Lesson 11-3
Links
Missing Angle
Other
EngageNY M2 L13
Georgia Unit 1
Assessment
Skill Check 28
Textbook
Lesson 11-4
Links
Tile Patterns
Other
EngageNY M2 L14
Georgia Unit 1
Assessment
Skill Check 29
Textbook
Lesson 11-5
Links
Congruency
Find the measure of the missing angle in a triangle.
Find the measure of any exterior angle of a triangle.
Recognize that two triangles with two pairs of congruent angles will be similar to
Other
each other.
EngageNY M2 L14
Georgia Unit 1
Assessment
Skill Check 30
Textbook
Lesson 11-6
Links
Tile Patterns
Other
EngageNY M2 L13
Georgia Unit 1
Assessment
Skill Check 31
Use relationships between angles to solve complex problems
Unit 2: Geometry