Curriculum Documents by Quarter - Mathematics Grade 10

Unit of Study 1: Geometry Unit 1
Standards
Essential Questions

Learning Objectives

Understand meanings of operations and how they relate to one another.

Understand patterns, relations, and functions.

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

Apply transformations and use symmetry to analyze mathematical situations.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Create and use representations to organize, record, and communicate mathematical ideas.

What are different ways of representing numbers?

How do patterns and relationships help us understand mathematical situations?

How do we represent patterns and relationships in everyday life?

How can change be analyzed?

Vocabulary

 

Learning Outcomes

  • Students learn how to find and describe a pattern. 
  • Students understand and use the basic terms of geometry.
  • Students use postulate and formulas to measure angles and line segments.
  • Students classify and identify angles.
  • Students find the perimeter and area of common plane figures.
  • Students recognize, analyze and use definitions, postulates and theorems.
  • Students write reasons for steps in a proof.
  • Students write different types of proofs.

Unit of Study 2: Geometry Unit 2

 

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

Apply transformations and use symmetry to analyze mathematical situations.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Create and use representations to organize, record, and communicate mathematical ideas.

What are different ways of representing, organizing, and relating numbers to mathematical operations?

How do we understand and represent patterns, relationships, and change?

What are the characteristics, properties, and applications of multi-dimensional shapes?

How do we collect, organize, display, and analyze data?

Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?

How can mathematical thinking be effectively communicated to different audiences?

How are mathematical concepts related to one another, other disciplines, and to the real world?

Vocabulary

   

Learning Outcomes

  • Students learn how to identify relationships between lines and angles.
  • Students identify and write different types of proofs.
  • Students learn to classify angles and find their measures.
  • Students learn to identify and prove two triangles are congruent using postulates and theorems.
  • Students identify and use properties of triangles to describe them.

Unit of Study 3: Geometry Unit 3

 Understand meanings of
operations and how they relate
to one another.

 Understand patterns,
relations, and functions.

 Analyze characteristics
and properties of two- and
three-dimensional geometric
shapes and develop
mathematical arguments about
geometric relationships.

 Specify locations and
describe spatial relationships
using coordinate geometry and
other representational systems.

 Apply transformations
and use symmetry to analyze
mathematical situations.


 Use visualization, spatial
reasoning, and geometric
modeling to solve problems.

 Create and use
representations to organize,
record, and communicate
mathematical ideas.

 

  • What are different ways of representing, organizing, and relating numbers to mathematical operations?
  • How do we understand and represent patterns, relationships, and change?
  • How do we collect, organize, display, and analyze data? 
  • Which strategies and mathematical operations are used to solve problems and arguments, and how can we develop and improve them?
  • How can mathematical thinking be effectively communicated to different audiences? 
  • How are mathematical concepts related to one another, other disciplines, and to the real world?

Vocabulary

  

Learning Outcomes

  • Three ways to describe motion of geometric figures in the plane.
  • How to use transformations in real-life situations, such as making a kaleidoscope or designing a border pattern.
  • Four ways to prove triangles are similar given information about their sides and angles.
  • How to use similar polygons to solve real-life problems
  • Properties related to general right triangles, similar right triangles, and special right triangles.'
  • Applications of right triangles, including trigonometry, or triangle measurement, and vectors.
  • How to use arcs, angles, and segments in circles to solve real-life problems.
  • How to use the graph of an equation of a circle to model real-life situations.
  • How to find angle measures and areas of polygons.
  • How to compare perimeters and areas of similar figures.
  • How to find the circumference and area of a circle and to find other measures.

Unit of Study 4:Geometry Unit 4

 

 

Vocabulary

 

Learning Outcomes

  • How to calculate the surface area and volume of various solids.
  • How to use surface area and volume in real-life situations, such as finding the amount of wax needed to make a candle.

 

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