Core Ideas

• Recognize and use characteristics, properties, and relationships of two- and three-dimensional geometric shapes and apply appropriate techniques to determine measurements.
• Begin to describe and classify two- and three-dimensional shapes according to common attributes and/or parts of their shapes.
• Compare the length, weight, and volume of objects by using direct comparison or non-standard units.
• Develop an understanding of the standard units of measuring time.

Core Ideas

• Recognize and use characteristics, properties, and relationships of two- and three-dimensional geometric shapes and apply appropriate techniques to determine measurements.
• Describe and classify two- and three-dimensional shapes according to their attributes and/or parts of their shapes
• Develop an understanding of how shapes can be put together or taken apart to form other shapes.
• Develop an understanding of line symmetry.
• Understand how to measure using non-standard and standard units.
• Select an appropriate unit and tool for the attribute being measured (length, volume, weight, area, time).
• Use number concepts in geometric contexts.

MARS Tasks

Don's Shapes

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Don's Shapes" Toolkit Packet (large file)

Core Ideas

• Recognize and use characteristics, properties, and relationships of two-dimensional geometric shapes and apply appropriate techniques to determine measurements.
• Choose appropriate units and tools for particular tasks and use these units and tools to estimate and measure (length, weight, temperature, time, and capacity).
• Identify and compare attributes of two-dimensional shapes and develop vocabulary to describe the attributes.
• Calculate perimeter and area and be able to distinguish between the two measures. (Area may be measured by covering a figure with squares.)
• Use visualization, spatial reasoning, and geometric modeling to solve problems.
• Recognize geometric ideas and relationships and apply them to problems.

MARS Tasks

Looking Glass Land

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Looking Glass Land" Toolkit Packet (large file)

Time to Get Clean

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Time to Get Clean" Toolkit Packet (large file)

Core Ideas

• Use characteristics, properties, and relationships of two-dimensional geometric shapes and apply appropriate techniques to determine measurements. Examine, compare, and analyze attributes of geometric figures.
• Classify two-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles.
• Understand line symmetry and predict the results of sliding, flipping, or turning two-dimensional figures.
• Investigate, describe, and reason about the results of combining and subdividing figures.
• Understand and use appropriate techniques to determine measurement.

MARS Tasks

Quilt Making

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Quilt Making" Toolkit Packet (large file)

Core Ideas

• Analyze characteristics and properties of two- and three-dimensional geometric shapes, understand attributes, and apply appropriate techniques, tools, and formulas to determine measurements.
• Understand such attributes as length, area, weight, volume, and angle size and select the appropriate type of unit for measuring each attribute. (Volume may be measured by filling an object.)
• Develop, understand, and use methods to find the area of rectangles and use that understanding of rectangles to find areas of triangles and parallelograms.
• Develop strategies for estimating or calculating the perimeters and areas of irregular shapes.
• Identify, compare, and analyze attributes of two- and three-dimensional shapes, and develop vocabulary to describe the attributes.
• Explore and determine what happens to perimeter and area of a two-dimensional figure when its shape is changed in some way.

MARS Tasks

Shopping Bags

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Shopping Bags" Toolkit Packet (large file)

Core Ideas

• Analyze characteristics and properties of two- and three-dimensional geometric shapes; use symmetry to predict and describe the results of sliding, flipping and turning two-dimensional shapes; and apply the appropriate techniques, tools, and formulas to determine measurements.
• Describe, classify, and understand relationships among types of two- and three-dimensional objects, using their defining properties.
• Develop, understand, and use formulas to determine the area of triangles, quadrilaterals, and the circumference and area of circles.
• Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes.
• Understand line and rotational symmetry and predict the results of these transformations.
• Select and apply techniques and tools to accurately find length, area, and angle measures to appropriate levels of precision.

MARS Tasks

Snail Pace

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Snail Pace" Toolkit Packet (large file)

Area & Perimeter

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Area & Perimeter" Toolkit Packet (large file)

Core Ideas

• Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; apply congruence and similarity to analyze mathematical situations; and apply appropriate techniques, tools, and formulas to determine measurements.
• Understand relationships among the angles, side lengths, perimeters, and areas of similar objects.
• Develop and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence and similarity.
• Solve problems involving similarity and scale factors, using proportional reasoning.

MARS Tasks

Pizza Crusts

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Pizza Crusts" Toolkit Packet (large file)

• See Related Classroom Video Visit: Area & Perimeter
  Antoinette Villarin leads a lesson asking students to identify successful strategies for finding the area and perimeter of various sized pizzas. The multimedia documentation of Villarin's teaching includes a pre-teaching planning conversation between Villarin, Suzanne McSpadden, math coach, and Patricia Ferrant, the teacher of record for the documented class. The documentation also includes a follow-up faculty debrief with observing teachers and an interview with participating students. VIDEO >>

Winter Hat

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Winter Hat" Toolkit Packet (large file)

Core Ideas

• Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; apply transformations and use symmetry to analyze mathematical situations; and apply appropriate techniques, tools, and formulas to determine measurements.
• Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.
• Understand relationships among the angles, side lengths, perimeter, areas, and volumes of similar objects.
• Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
• Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

MARS Tasks

Patterns in Prague

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Patterns in Prague" Toolkit Packet (large file)

Core Ideas

• Describe spatial relationships using coordinate geometry; develop mathematical arguments about geometric relationships; understand measurable attributes of objects; and understand the units, systems, and process of measurement.
• Investigate conjectures and solve problems involving two-dimensional objects represented with Cartesian coordinates.
• Solve problems that involve measurement units and scale factors.
• Use geometric models to gain insights into, and answer questions in, other areas of mathematics.

Core Ideas

• Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and apply appropriate techniques, tools, and formulas to determine measurements.
• Understand and use formulas for the area, surface area, and volume of geometric figures, including spheres and cylinders.
• Explore relationships among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.
• Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, and function notation.
• Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools.
• Visualize three-dimensional objects from different perspectives and analyze their cross-sections.

MARS Tasks

Glasses

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Glasses" Toolkit Packet (large file)

Circles & Squares

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Circle & Squares" Toolkit Packet (large file)

Triangles

• Task
• Rubric
• Core Mathematical Ideas and Challenges
• Questions for Teacher Reflection
• Discussion of Successful Examples of Student Work
• Discussion of Student Misconceptions
• Graph and Analysis of the MARS Task Data
• Summary of Student Understandings and Misunderstandings
• Implications for Instruction
• Entire "Triangles" Toolkit Packet (large file)