In this unit students will build upon their experiences with geometry in earlier grades. Seventh grade students use these skills to informally construct geometric figures.

Manipulatives, dynamic geometry, and tools like rulers and protractors will be particularly helpful with this unit. A particular focus in this unit is the construction of triangles when given combinations of measures of three angles and/or sides. Students will investigate which of these combinations create unique triangles, more than one triangle, or no triangle at all. Students will use the angle-angle criterion to determine similarity.

Angle relationships generated by intersecting lines including supplementary, complementary, adjacent, and vertical angles are also used in problem solving. Using these relationships, students will make conjectures and solve multistep problems with angles created by parallel lines cut by a transversal. They will also examine both angle sums of polygons and exterior angles.

Students will know and use formulas for the area and circumference of a circle and be able to determine the relationship between them.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Find the area and perimeter of the colored part of each of the six figures below. The purple, blue, orange, red, and green figures are composed of smal...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The students in Mr. Rivera's art class are designing a stained-glass window to hang in the school entryway. The window will be 2 feet tall and 5 feet w...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This 7th grade Math parent guide explains the content in straightforward terms so they can support their children’s learning at home and will encourage caretaker engagement with lessons.

Our Teacher Guides are meant to support the use of our online course and unit content. Please use these to accompany the use of our content and for ideas to support struggling learners, those needing extension and for additional resources.

An interactive applet and associated web page that demonstrate the area of a circle. A circle is shown with a point on the circumference that can be dragged to resize the circle. As the circle is resized, the radius and the area computation is shown changing in real time. The radius and formula can be hidden for class discussion. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

 Students will be asked to evaluate their local community and design and build a 3-dimensional circular space, building, or facility to meet their town's / city's / state's needs. Requirements: two written paragraphs, blueprints drafted on graph paper, a physical model, a Project Improvement Plan, and self reflection. 

Students compare the relationships between radius, diameter, circumference, and area by manipulating a circle and increasing or decreasing its size in this interactive from Illuminations. It also provides a problems section where students determine the answer to each question using the applet, a calculator, or paper and pencil. They must also indicate the proper units!

This task is to be used after students have been taught circles content including parts of a circle, the meaning of pi, circumference and area. This lesson was developed by NCDPI as part of the Academically and/or Intellectually Gifted Instructional Resources Project. This lesson plan has been vetted at the state level for standards alignment, AIG focus, and content accuracy.

Students review examples of finding circumference of a circle and complete practice exercises.

This task is to be used in a geometry unit after the area and circumference of circles is taught. This lesson was developed by NCDPI as part of the Academically and/or Intellectually Gifted Instructional Resources Project. This lesson plan has been vetted at the state level for standards alignment, AIG focus, and content accuracy.

The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. Similarly, the value of pi can be approximated by calculating the areas of inscribed and circumscribed polygons. This activity allows for the investigation and comparison of both methods.

In this lesson, students develop the definition of circle using diameter and radius. Students know that the distance around a circle is called the circumference and discover that the ratio of the circumference to the diameter of a circle is a special number called pi, written π. Students know the formula for the circumference C of a circle of diameter d and radius r. They use scale models to derive these formulas. Students use 22/7 and 3.14 as estimates for π and informally show that π is slightly greater than 3.

After a discussion about what a parachute is and how it works, students create parachutes using different materials that they think will work best. They test their designs, and then contribute to a class discussion (and possible journal writing) to report which paper materials worked best.

Students create model elevator carriages and calibrate them, similar to the work of design and quality control engineers. Students use measurements from rotary encoders to recreate the task of calibrating elevators for a high-rise building. They translate the rotations from an encoder to correspond to the heights of different floors in a hypothetical multi-story building. Students also determine the accuracy of their model elevators in getting passengers to their correct destinations.

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.

The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value.

This activity will allow students to measure the circumference, diameter, and radius of a circle in a hands-on way. By being able to manipulate a circle and stretch it out the idea of circumference will be more concrete. Students will use each other, desks, and chairs to create circles that can be measured.