## 7th Grade Measurement and Geometry

MG 1.1

**Tested on the CAHSEE**Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).

Velocity & Acceleration: **Sea World Physics**

Measuring Speed with iMovie – Using a digital camcorder, iMovie, and a spreadsheet program, students measure the speed of a variety of objects (running, walking, throwing a ball). They use a spreadsheet and the number of video frames per second to compute the speed in miles per hour. **iMovie and spreadsheet activity.**

The Race – This **math applet** from PBS Teachers Online provides a visual and a graphical comparison of actual speed and average speed over an entire race. Within the problem there is a link to an interactive that relates a visual image of a race with its graphical representation.

Comparing Mixtures: Mixing Orange Juice – From PBS Teachers Online. Students use a** java applet **to “mix orange juice” concentrates with cans of water as they solve problems on ratio and proportion and explore “orangeyness” of their mixtures. Addresses the misconception that proportionality is based on additive relationships.

Units of Measurement – **Powerpoint jeopardy game.**

Ratio and Earned Dollars – **Math Playground Word Problem**. How much money did each of two web site designers make? Onscreen audio and visual help is provided in setting up the problem and solving it. Once the problem is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

Quick Landscaping – **Math Playground Word Problem**. (Area and proportional reasoning). How long will it take Jamie to mow a square lawn if we know the time it takes him to mow a smaller lawn? Onscreen audio and visual help is provided in setting up the problem and solving it. Once the problem is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

**Tested on the CAHSEE**Construct and read drawings and models made to scale.

Great Cartoon Blow-Up Activity. **Students practice drawing to scale** and create blow-ups of their favorite Flinestone characters while learning about ratio of simultude.

Scales, Ratio & Proportion – **Video tutorial** on working with scale drawings from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. You may need to set up a free user account to access this site and see all topics. Designed as a homework help tutorial, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the video.

Body Ratios – Modeling Middle School Mathematics project (MMSM) is **a professional development program using video lessons and Web-based Internet materials to examine mathematical concepts**. Video clips and full transcripts are provided of actual classroom situations in which the lesson is taught. In this lesson on ratios and scaled drawings, educators use the story of Gulliver’s Travels to pose the problem: how to make a shirt for someone who is much bigger.

Ratio & Proportion – **Tutorial/Practice** from the Math League.

Introduction to Ratios – Math.com **interactive tutoring and practice**.

Estimator – **Interactivate activity**. Solve problems involving scale factors, using ratio and proportion; Students practice estimation skills by determining the number of objects, length, or area.

Scale Factors – Figure This! Math Challenge #61 : Statue of Liberty. One of a series of NCTM standards-aligned **math challenges** designed for students to work out with their families. Available in English and Spanish. Learn about similarity and scaling by measuring the length of your nose and your arm in the same units. Then apply this knowledge to find out if the Statue of Liberty’s nose is too long. (English/Spanish).

**Key Standard tested on the CAHSEE**Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.

Distance, Rate & Time – For fee, **Brainpop movie and interactive quiz**.

Going Nowhere Fast – **Math Playground video word problems**. Students must solve a swimming pool problem fill and draining problem that involves work, rate and time. Onscreen audio and visual help is provided in setting up the problem and solving it. Once the problem is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

Rate of Work Problems – How long does it take Bart vs Homer to wash the family car? **Colorful PowerPoint** covering rate-of-work math problems that involve the entire Simpson family.

**Tested on the CAHSEE**Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

What on Earth is Greater Than? – **Lesson Plan**

Surface Area and Volume – **Manipulate** a three-dimensional polyhedron to experiment with surface area and volume.

Circle: Perimeter, Circumference and Area – **Resize a rectangle, circle, or square and find its perimeter or circumference and area.** Superimpose a grid on the figure to estimate its area.

Find the Area of a Shape – **Investigate** area of parallelograms, triangles, trapezoids and circles with colorful manipulatives and answer questions to test understanding.

Designing Packages – Modeling Middle School Mathematics lesson and activity uses QuickTime video of actual teacher, group and student work to **model best practices in teaching mathematics**. A full transcript of the video is provided. In this activity, students learn what surface area and volume mean mathematically by designing packages that will house 24 blocks (representing toys) and calculating the surface area of prisms.

Shape Explorer – Students test their skills at calculating the area and perimeter of a given figure. **Includes exploration questions and teacher coaching materials.** (Shodor.org)

Learn about Length, Perimeter, Area, and Volume of Similar Objects by Using Interactive Figures – This** interactive activity** allows users to explore the relationship between volume and surface area of a given shape.

Using Spreadsheets to find area and perimeter – **Classroom spreadsheet exercises, activities and instructions for teachers.**

Length, Perimeter, Area & Volume – **NCTM Illuminations Interactive**. Students experiment with rectangles of different shapes and scale factors relative to side lengths and observe and interpret changes in perimeter and area. In Part II, they also learn about side length, volume, and surface are of similar solids.

Automatic Circle, Sphere & Cylinder Calculator (Includes Formulas)

Classify Polygons – **Annenberg Media/Learning.org activity**. Tutorial and practice in grouping polygons according to certain properties.

**Tested on the CAHSEE**Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.

Pyramids – **Tutorial, examples and workout problems** for calculating the volume of a pyramid.

Area of a Trapezoid – The Web-Based Math Education (WBE) site offers **colorful, interactive tutorials** in 9 topic areas of 7th & 8th grade math. Each is divided into 10 or more sub-topics. The Area & Perimeter of a Trapezoid activity allows students to move the four vertices of a figure to make their own trapezoid and creates awareness that the area of a trapezoid can be calculated by adding the areas of the two triangles together. There are diagram exercises to complete, questions to answer (immediate feedback is given), and a summary writing activity, complete with writing tablet.

**Tested on the CAHSEE**Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.

Surface Area of a Tetrahedron – Using a digital camcorder and iMovie, students practice reciprocal teaching by **making a 3-minute movie** on a real world application of math.

Volume of a Cube – **NCTM Illuminations Interactive**. Students determine the volume of a box by manipulating unit cubes.

Surface Area and Volume – Students **manipulate** three-dimensional polyhedra to experiment with surface area and volume. Includes worksheets and discussion.(Shodor.org)

Similar Solids – A **PowerPoint presentation** explaining the scale factor and other properties of similar solids.

Covering the Plane with Rep-Tiles – In this **activity**, students discover and explore a special kind of tiling of the plane. Rep-tiles are geometric figures such that n copies can fit together to form a larger, similar figure.

Linking Length, Perimeter, Area, and Volume – **Five lessons**: The first is an online pre-activity to build students’ understanding of ratio, proportion and similarity. Another online pre-activity follows with similarity and scale factor. The third lesson involves students comparing perimeter and area ratios of similar rectangles with various scale factors using an e-manipultive which is the basis for the fourth and fifth lessons. The fourth lesson focuses on the relationship between scale factor and volume. The final lesson highlights the surface area for rectangular prisms in relationship to scale factor.

Surface Area and Volume – This **lesson** is designed to introduce students to surface area and volume.

Student-made videos – These **movies **were made by students to teach a math concept.

**Tested on the CAHSEE**Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft] = [144 in], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in] = [16.38 cm].

Side Length, Volume, and Surface Area of Similar Solids – **Java Applet** that lets the user manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes.

Comparison of volumes with Similar Solids – ** Lesson, practice and teacher resources** for determining volumes of similar solids (Regents Exam Prep).

**Tested on the CAHSEE**Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

Points in the Coordinated Plane – plot order pairs, x and y values and work within quadrants. **Guided practice and exploration**.

Coordinates Game – **Java Activity** allows the user to plot points on the coordinate plane and to read the coordinates of a point plotted by the computer.

Maze Game – **Users practice their point plotting skills** by moving a robot through a minefield to a target location. Moves are accomplished by specifying the coordinates of the new location. In order to win, the path must not cross a mine.

Mathsnet: Interactive Rotations, Reflections and Translations – Students **observe **reflected shapes, **answer quiz** questions on reflection, **practice** creating reflections and mirror lines. Includes sections for investigating rotations and translations.

**Key standard**

**tested on the CAHSEE**Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.

Pythagorean Theorem – **Video tutorial on understanding the Pythagorean theorem**. One of over 30 topics specifically covering problem areas of middle school math. You may need to set up a free user account to access this site and see all topics. Designed as a homework help tutorial, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the video.

Geoboard: Pythagorean Theorem – **guided practice and exploration** using and interactive geoboard.

Pythagorean Explorer – **Find** the length of a triangle and check answers.

Walk through a visual proof of the Pythagorean theorem

Figure out the Pythagorean Theorem – This lesson is intended for students to work on their own and provides** java applets** for them to figure out the theorem on their own and understand it. It includes, tips, practice problems using onscreen manipulatives and history about Pythagoras.

Explore Learning: Pythagorean theorem – **Interactive guided exploration**.

Pythagorean theorem – What is it and how does it work? **PowerPoint presentation** walkthrough suitiable for teacher presentation or student review.

Squaring the Triangle – learn how the Pythagorean Theorem works through **investigating** the standard geometric proof.

**Key Standard tested on the CAHSEE**Demonstrate an understanding of conditions that indicate two geometric figures are congruent and what congruence means about relationships between the sides and angles of two figures.

Congruence Tutorial and Math Applet – Students **manipulate** shapes to show that they can be fitted exactly over each other by rotation, translation and reflection. Shows multiple examples of congruence (side-angle-side, angle-side-angle, side-side-side.

Congruence Theorems – **Explore** the conditions that guarantee uniqueness of a triangle, quadrilateral, or pentagon regardless of location or orientation. Each set of conditions results in a new congruence theorem.

Explore Learning: Congruence in Right Triangles –** Exploration**: Apply constraints to right triangles, drag their vertices and determine conditions of congruence.

Proving Triangles Congruent – **guided practice and exploration.**

Congruent triangles – This **virtual manipulative** allows students to construct two triangles from various combinations of sides and angles. You can choose to work with any one of four different cases.

**Key Standard**Identify elements of the three dimensional geometric objects (e.g. diagonals of rectangular solids) and describe how two or more objects are related in space (e.g. skew lines, the possible ways three planes might intersect).

Investigating Parallel Lines and Planes – **exploration and guided practice** with parallel, intersecting and skew lines.

Points, Lines & Intersections – **Definitions, explanations and examples** for lines, points, intersections, line segments, rays, endpoints and parallel lines.

Geometry in Tessellations – Students **examine** tessellations and their geometric properties. The activity and discussion may be used to develop students’ understanding of lines, planes, angles, and polygons.

A Math Dictionary: Skewed Lines – **Description of skew lines along with a visual representation**. Use the links to related terms, everyday examples, more information, and the interactive checkpoint involving skew lines located in the left-hand column.

Last Updated (Wednesday, 10 March 2010 11:19)