Same or Different? is a routine that provides students opportunities to construct arguments when comparing objects, such as numbers or shapes.

A routine like Same or Different? provides accessible opportunities for even youngest students to learn how to talk about various features of mathematical objects – quantity, shape, color, orientation, and arrangement, to name a few.

This real world word problem requires students to figure out the scale ratio and unit rate.

This task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task models a satellite orbiting the earth in communication with two control stations located miles apart on earthsŐ surface.

An interactive applet and associated web page that demonstrate the properties of scalene triangles. The applet presents a scalene triangle where any vertex can be dragged to reshape it. As it is dragged, the length of the sides and interior angles are continuously changed. If a change is made that causes two sides to be the same length, they are highlighted and the message 'not scalene' appears. The massages and measures can be turned off for class discussions. The text on the page has links to other pages defining each angle type in depth. 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 a secant to a circle. (not trig). The applet shows a circle and a secant line. The points where the secant cross the circle are both draggable. As you drag each, the secant line moves. If you carefully make the two points coincide, it shows a message that this is now a tangent line. 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 main areas of focus in the second grade math curriculum are: understanding the base-ten system within 1,000, including place value and skip-counting in fives, tens, and hundreds; developing fluency with addition and subtraction, including solving word problems; regrouping in addition and subtraction; describing and analyzing shapes; using and understanding standard units of measure; working with money and time; and introducing multiplication.

The worksheets and printables for second grade math available on this page will enhance any classroom's math curriculum. These engaging second grade math worksheets cover the basics of counting and ordering as well as addition and subtraction, and include exciting introductions to geometry and algebra for future self-assurance in math.

An interactive applet and associated web page that demonstrate a sector - a pie shaped part of a circle. The applet shows a sector against the background of the circle of which it is part. The endpoints of the arc defining it can be dragged and the calculation of the area of the sector is updated continuously. The web page has links to related definitions, and a formula for the area of the sector given its central angle. 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 a segment of a circle - a part of a circle cut off by a chord. The applet shows a circle and a segment of that circle, the ends of which can be dragged to resize the segment. You can create the situation where the chord is a diameter and so no segments are created. 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 semi-major and semi-minor axes of an ellipse. The applet has an ellipse whose major and minor axis endpoints can be dragged. As they are dragged the semi-major and semi-minor axes change length and may swap places. The applet also shows the location of the foci, which are always on the major axis, and shows how they move with variation of the semi-axis lengths. 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.

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

This task provides a concrete geometric setting in which to study rigid transformations of the plane. It is important for students to be able to visualize and execute these transformations and for this purpose it would be beneficial to have manipulatives and it will important that the students be able to label the vertices of the hexagon with which they are working.

In this scavenger hunt games students are given the task of finding and identifying real-world shapes in their environment.

In this "word search" style puzzle students practice identifying sequences of shapes.

Small group or partner activities.  Students can use white-board covers to play Guess Who.  Small groups could also play bingo.  

Students are introduced to brainstorming and the design process in problem solving as it relates to engineering. They perform an activity to develop and understand problem solving with an emphasis on learning from history. Using only paper, straws, tape and paper clips, they create structures that can support the weight of at least one textbook. In their first attempts to build the structures, they build whatever comes to mind. For the second trial, they examine examples of successful buildings from history and try again.

Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result is a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.

This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.

An interactive applet and associated web page that demonstrate congruent line segments (segments that are the same length). The applet shows three line segments that are the same length. They all have draggable endpoints. As you drag any endpoint the other lines change to remain congruent with the one you are changing. 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.