In this unit, students develop in-depth understanding of volume and surface area. Students should understand volume as a measure of filling and surface area as a measure of wrapping an object. Students should have the opportunity to generate their own strategies for finding volume and surface area. Students will be able to use patterns and rules/formulas for finding surface area and volume of three-dimensional shapes.

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 deals with the area of a kite, (a quadrilateral with two distinct pairs of equal adjacent sides). The applet shows a kite and the user can reshape it by dragging any vertex. The other vertices move automatically to ensure it always remains a kite. As the vertices are dragged, the area is continuously recalculated and displayed. The kite is filled with a grid of unit squares so that the students can estimate the area. The on-screen calculation can be hidden until the estimates are done. The web page lists two different ways to compute the area of a kite. 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.

Find the area of a complex figure by dividing it into simpler shapes, such as rectangles, squares, triangles, and trapezoids.

A web page and interactive applet showing the ways to calculate the area of a trapezoid. The user can drag the vertices of the trapezoid and the other points change automatically to ensure it remains a trapezoid. A grid inside the shape allows students to estimate the area visually, then check against the actual computed area. The text on the page gives three different ways to calculate the area with a formula for each. The applet uses one of the methods to compute the area in real time, so it changes as the trapezoid is reshaped with the mouse. A companion page is http://www.mathopenref.com/trapezoid.html showing the definition and properties of a trapezoid. 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.

In this lesson, students determine the area of composite figures in real-life contextual situations using composition and decomposition of polygons and circular regions.

Through this earth science curricular unit, student teams are presented with the scenario that an asteroid will impact the Earth. In response, their challenge is to design the location and size of underground caverns to shelter the people from an uninhabitable Earth for one year. Driven by this adventure scenario, student teams 1) explore general and geological maps of their fictional state called Alabraska, 2) determine the area of their classroom to help determine the necessary cavern size, 3) learn about map scales, 4) test rocks, 5) identify important and not-so-important rock properties for underground caverns, and 6) choose a final location and size.

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. The activities involved provide valuable experience in problem solving with spatial-visual relationships.

To display the results from the previous activity, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved. They problem solve and apply their understanding of see-saws and lever systems to create balanced mobiles.

Through a five-lesson series that includes numerous hands-on activities, students are introduced to the importance and pervasiveness of bridges for connecting people to resources, places and other people, with references to many historical and current-day examples. In learning about bridge types arch, beam, truss and suspension students explore the effect of tensile and compressive forces. Students investigate the calculations that go into designing bridges; they learn about loads and cross-sectional areas by designing and testing the strength of model piers. Geology and soils are explored as they discover the importance of foundations, bearing pressure and settlement considerations in the creation of dependable bridges and structures. Students learn about brittle and ductile material properties. Students also learn about the many cost factors that comprise the economic considerations of bridge building. Bridges are unique challenges that take advantage of the creative nature of engineering.

The students will be split into small, cooperative groups and build a city following specific guidelines. The students will learn how a city is constructed with angles, intersections, parallel, intersecting, and transversal streets. They will understand that buildings are located at particular points which are considered alternate interior or exterior angles, corresponding angles, etc.

 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. 

In this lesson, students compute volumes of three-dimensional objects composed of right prisms by using the fact that volume is additive.

Students Imagine constructing an open-topped water tank from a square metal sheet. They investigate the relationship between the maximum volume of the tank and the size of the squares cut from the corners, build models and collect data.

In this lesson, students determine the area of composite figures and of missing regions using composition and decomposition of polygons.

In this lesson, students determine the surface area of three-dimensional figures, including both composite figures and those missing sections.

In this lesson, students determine the surface area of three-dimensional figures, those that are composite figures and those that have missing sections.

In this lesson, students use the formula V = bh to determine the volume of a right prism. Students identify the base and compute the area of the base by decomposing it into pieces.

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.