## Description

- Overview:
- This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.

- Level:
- Lower Primary, Upper Primary, Middle School, High School
- Grades:
- Kindergarten, Grade 1, Grade 2, Grade 3, Grade 4, Grade 5, Grade 6, Grade 7, Grade 8, Grade 9, Grade 10, Grade 11, Grade 12
- Material Type:
- Assessment, Lesson Plan
- Provider:
- Shell Center for Mathematical Education, U.C. Berkeley
- Provider Set:
- Mathematics Assessment Project (MAP)
- Date Added:
- 04/26/2013

- License:
- Creative Commons Attribution Non-Commercial No Derivatives
- Media Format:
- Downloadable docs, Text/HTML

# Comments

## Standards

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Degree of Alignment: 3 Superior (1 user)

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Degree of Alignment: Not Rated (0 users)

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Degree of Alignment: Not Rated (0 users)

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Geometry: Similarity, Right Triangles, and TrigonometryCluster: Prove theorems involving similarity

Standard: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Degree of Alignment: Not Rated (0 users)

# Common Core State Standards Math

Grades 9-12,Functions: Building FunctionsCluster: Build a function that models a relationship between two quantities

Standard: Write a function that describes a relationship between two quantities.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Functions: Building Functions

Standard: Build a function that models a relationship between two quantities

Indicator: Write a function that describes a relationship between two quantities.*

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 x 8 equals the well remembered 7 x 5 + 7 x 3, in preparation for learning about the distributive property. In the expression x^2 + 9x + 14, older students can see the 14 as 2 x 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)^2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Similarity, Right Triangles, and Trigonometry

Standard: Prove theorems involving similarity

Indicator: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and"Óif there is a flaw in an argument"Óexplain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

## Evaluations

# Achieve OER

Average Score (3 Points Possible)Degree of Alignment | 3 (1 user) |

Quality of Explanation of the Subject Matter | 3 (1 user) |

Utility of Materials Designed to Support Teaching | 3 (1 user) |

Quality of Assessments | N/A |

Quality of Technological Interactivity | N/A |

Quality of Instructional and Practice Exercises | N/A |

Opportunities for Deeper Learning | N/A |

# Tags (9)

- Mathematics
- Geometry and measures
- Angles
- CCSS
- Common Core Math
- Common Core PD
- Geometry
- ODE Learning
- Polygons

This is a lesson and assessment task that has many teacher resources. It has ppt, student worksheets, assessment, and lesson plan. It strongly addresses CCSS 7.G.5. Students have to try different ways to find the unknown angle.

Rolling Cups unit presents a non-routine mathematical inquiry situation requiring students to develop experimental and analytical models of a physical situation and to generate and analyze data through the systematic control of variables.

Resources include common misconceptions associated with the target standards along with suggested instructional strategies to ensure students build conceptual understanding.

F-BF.1 – Rating: 3

G-SRT.5 – Rating: 2