## Description

- Overview:
- This lesson unit is intended to help teachers assess how well students can: Understand the concepts of length and area; use the concept of area in proving why two areas are or are not equal; and construct their own examples and counterexamples to help justify or refute conjectures.

- 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-world and mathematical problems involving area, surface area, and volume

Standard: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Degree of Alignment: 3 Superior (1 user)

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: 2 Strong (1 user)

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: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

Degree of Alignment: Not Rated (0 users)

Cluster: Prove geometric theorems

Standard: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Degree of Alignment: Not Rated (0 users)

Cluster: Prove geometric theorems

Standard: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Degree of Alignment: Not Rated (0 users)

Cluster: Prove geometric theorems

Standard: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: Prove geometric theorems

Indicator: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry: Congruence

Standard: Prove geometric theorems

Indicator: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

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: Congruence

Standard: Prove geometric theorems

Indicator: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Solve real-world and mathematical problems involving area, surface area, and volume

Indicator: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

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 | 2.5 (1 user) |

Quality of Explanation of the Subject Matter | 2 (1 user) |

Utility of Materials Designed to Support Teaching | 2 (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 (10)

- Mathematics
- Geometry and measures
- Area
- CCSS
- Common Core Math
- Common Core PD
- Geometry
- Length
- ODE Learning
- Math Literacy Lessons

Designing Candy Cartons (Grade 6): Students represent three-dimensional candy cartons using nets. They design a box to fit a given an upper limit (the total surface area must fit on a single sheet of paper) that will hold a given volume of candy.

Students are required to draw either an accurate full sized or scale drawing net including flaps necessary for carton construction.

After completing the task, students can analyze sample student work to deepen conceptual understanding.

6.G.4: Rating 3

Applying Angle Theorems (Grade 7):

Students use geometric properties to solve problems. The assessment problems provides information about students understanding of geometric properties. Misconceptions are addressed as students analyze peer solutions. Analysis of student work incorporates Standards for Mathematical practice 3: students critique the reasoning of others.

7.G.6: Rating 2