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.

The purpose of this lesson is to introduce the unit on geometry in grade 5 math.

Included is a YouTube video to support Grade 5 Blended Learning Math - Unit 6.0: Geometry - Introduction.

The purpose of this lesson is to explore and describe shapes.

Included is a YouTube video to support Grade 5 Blended Learning Math - Unit 6.1: Geometry - Describing Shapes.

The purpose of this lesson is to explore quadrilaterals.

Included is a YouTube video to support Grade 5 Blended Learning Math - Unit 6.3: Geometry - Investigating Quadrilaterals.

The purpose of this lesson is to explore triangles.

Included is a YouTube video to support Grade 6 Blended Learning Math - Unit 6.1: Geometry - Exploring Triangles.

Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.

A web page and interactive applet show how to compute the perimeter of a trapezoid. A trapezoid is shown that can be resized by dragging its vertices. As you drag, the perimeter is continuously recalculated. Text on the page explains that the perimeter is the sum of the sides. For those who prefer it, in a formula that is given. 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 reference book project at http://www.mathopenref.com.

These logic number puzzles help students develop strong number sense as they work, clue by clue, to identify the digits of the missing number. The mixed-skills clues incorporate even-odd, less than-greater than, operations (sum, difference), multiples of 5 and 10, geometric terms (octagaon, pentagon, hexagon, quadrilateral, trapezoid, parallelogram), money (quarters, nickels) and measurement (cup, pint, quart, gallon). Students must squeeze every bit of knowledge from each clue to eliminate possible digits until they finally identify the missing digits.

A web page and interactive applet showing the definition and properties of a trapezoid. The applet shows a trapezoid where the user can drag any vertex. The other points then move in such a way that the figure remains a trapezoid at all times. A control to hide the details allows a classroom discussion where students can try to infer what the properties are as it is reshaped by the discussion leader. Text on the page has the formal definition and properties of the trapezoid with links to related pages. A companion page is http://www.mathopenref.com/trapezoidarea.html showing the ways to calculate the area 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.

An interactive applet and associated web page that show the definition and properties of a trapezoid in coordinate geometry. The applet has a trapezoid with draggable vertices. As the user re-sizes the trapezoid the applet continuously recalculates its altitude and median from the vertex coordinates. The trapezoid can be rotated on the plane to show the more complex cases. The grid, coordinates and calculations can be turned on and off for class problem solving. The applet can be printed in the state it appears on the screen to make handouts. The web page has a full definition of a trapezoid when the coordinates of the points defining it are known, and has links to other pages relating to coordinate geometry. 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.

An interactive applet and associated web page showing how to find the area and perimeter of a trapezoid from the coordinates of its vertices. The trapezoid can be either parallel to the axes or rotated. The grid and coordinates can be turned on and off. The area and perimeter calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the method for determining area and perimeter, a worked example and has links to other pages relating to coordinate geometry. 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.

An interactive applet and associated web page that demonstrate the median line of a trapezoid (line linking midpoints of non-parallel sides). The applet shows a trapezoid with all vertices draggable. As you drag any vertex, the figure changes to remain trapezoid, and the median line id continually repositioned to remain correct. It can be seen visually that the median remains parallel to the bases and a formula shows that its length is the average of the bases. 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.