CTE Architecture: Framing a House

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning - and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

Material Type: Activity/Lab, Assessment, Homework/Assignment, Lesson Plan

Modeling Conditional Probabilities 1: Lucky Dip

This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

Material Type: Assessment, Lesson Plan

Modeling: Making Matchsticks

This lesson unit is intended to help you assess how well students are able to: interpret a situation and represent the variables mathematically; select appropriate mathematical methods; interpret and evaluate the data generated; and communicate their reasoning clearly.

Material Type: Assessment, Lesson Plan

Modeling: Rolling Cups

This lesson unit is intended to help teachers assess how well students are able to: choose appropriate mathematics to solve a non-routine problem; generate useful data by systematically controlling variables; and develop experimental and analytical models of a physical situation.

Material Type: Assessment, Lesson Plan

Music and Sports

In this group task students collect data and analyze from the class to answer the question "is there an association between whether a student plays a sport and whether he or she plays a musical instrument? "

Material Type: Activity/Lab

Author: Illustrative Mathematics

Sports Equipment Set

The purpose of this task is to present students with a context that can naturally be represented with an inequality and to explore the relationship between the context and the mathematical representation of that context; thus, this is an intended as an instructional task.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Using Dimensions: Designing a Sports Bag

This lesson unit is intended to help you assess how well students are able to: recognize and use common 2D representations of 3D objects and identify and use the appropriate formula for finding the circumference of a circle.

Material Type: Assessment, Lesson Plan

Author: http://map.mathshell.org/

Throwing a Ball

Although this task is quite straightforward, it has a couple of aspects designed to encourage students to attend to the structure of the equation and the meaning of the variables in it. It fosters flexibility in seeing the same equation in two different ways, and it requires students to attend to the meaning of the variables in the preamble and extract the values from the descriptions.

Material Type: Activity/Lab

Author: Illustrative Mathematics

G-MG Tennis Balls in a Can

This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a Ňdouble-naped coneÓ with vertex at the center of the sphere and bases equal to the bases of the cylinder.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Calories in a sports drink

This problem involves the meaning of numbers found on labels. When the level of accuracy is not given we need to make assumptions based on how the information is reported. The goal of the task is to stimulate a conversation about rounding and about how to record numbers with an appropriate level of accuracy, tying in directly to the standard N-Q.3. It is therefore better suited for instruction than for assessment purposes.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Parabolas and Inverse Functions

This task assumes students have an understanding of the relationship between functions and equations. Using this knowledge, the students are prompted to try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, this means that the function does not have an inverse.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Finding Parabolas Through Two Points

In this task students have the opportunity to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Material Type: Activity/Lab

Author: Illustrative Mathematics

Graphs of Quadratic Functions

This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Red Rover Robotics

This lesson will start with a brief history of robotics and explain how robots are beneficial to science and society. The lesson then will explore how robots have been used in recent space exploration efforts. The engineering design of the two Mars rovers, Spirit and Opportunity, will be used as prime examples. Finally, the maneuverability of their robotic arms and the functionality of their tools will be discussed.

Material Type: Activity/Lab, Lesson Plan

Authors: Chris Yakacki, Daria Kotys-Schwartz, Geoffrey Hill, Janet Yowell, Malinda Schaefer Zarske

Robot Races

This task requires graphing time and distance.

Material Type: Activity/Lab

Author: Illustrative Mathematics

Strong-Arm Tactics

Students generally do not know the complexity that goes into building and programming a robotic arm. In actuality, creating such an arm comes from a design that involves mechanical, electrical, and computer science engineers. This activity allows students to control a robotic arm from both a machine's and a computer science engineer's perspective by letting them perform a simple task with a few entertaining instructions and constraints.

Material Type: Activity/Lab, Lesson Plan

Authors: Chris Yakacki, Daria Kotys-Schwartz, Geoffrey Hill, Janet Yowell, Malinda Schaefer Zarske

Mission to Mars

The Mission to Mars curricular unit introduces students to Mars the Red Planet. Students discover why scientists are so interested in studying this mysterious planet. Many interesting facts about Mars are revealed, and the history of Martian exploration is reviewed. Students will learn about the development of robotics and how robots are beneficial to science, society and the exploration of space. Details on engineers' involvement in space exploration are presented. Furthermore, students will learn how orbits allow astronauts to move from planet to planet and what type of equipment is used by scientists and engineers to safely explore space. Lastly, the specific details on and human risks for a possible future manned mission to Mars (and back to Earth again!) are discussed.

Material Type: Activity/Lab, Lesson Plan

Drawing to Scale: Designing a Garden

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

Material Type: Assessment, Lesson Plan

Drawing Board

The Drawing Board consists of a marking pen that remains stationary and a platform that swings beneath the pen, acting as a pendulum. As the platform swings, the pen marks a sheet of paper that is fastened to the platform, generating beautiful repetitive patterns. These colorful designs contain hidden lessons in physics. This resource includes instructions for making a large-scale Drawing Board as well.

Material Type: Activity/Lab

Floor Plan

The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing.

Material Type: Activity/Lab

Author: Illustrative Mathematics