6-8, 9-12
This lesson invites students to investigate the patterns when a "plus sign" (a cross-shaped arrangement of five squares) is placed on the board in various locations. Students will conjecture about the pattern of the five displayed numbers, the sum of the five numbers, and any other patterns that they notice. Students may also explore similar patterns when other shapes, such as a 2 × 1 rectangle, are placed on the hundreds board.
9-12
In this lesson, students will learn to read an antifreeze chart to determine the necessary mix of antifreeze and water for protection against various temperatures. Students will then numerically analyze a particular cooling system to determine how much fluid to drain in order to get the desired percent concentration of antifreeze. Finally, students will set up a system of equations to solve the same system.
6-8, 9-12
Students will use vertical movement of an elevator to evaluate signed number expressions.
The idea behind the method of adding and subtracting signed integers offered in this lesson and the next is that the number of rules that students have to memorize and the amount of understanding are minimal, while the underlying concepts are not trivialized.
6-8
The interactive paper pool game in this i-Math investigation provides an opportunity for students to further develop their understanding of ratio, proportion, and least common multiple.
6-8
Students further explore square roots using the diagonals of rectangles. Using measurement, students will discover a method for finding the diagonal of any rectangle when the length and width are known, which leads to the Pythagorean Theorem.
9-12
Starting from the concrete notion of weights and balance and moving to symbolic expressions and representations of functions, this i-Math investigation has focused on some of the issues that arise along the way. In this part, this connection is extended to functions. More sophisticated tools allow for a greater diversity of investigations.
6-8, 9-12
In this lesson, students will adapt expressions that add or subtract two signed integers.
9-12
This interactive demonstrates why (
a +
b)
2 = a
2 +2ab + b
2.
3-5
Use this applet to determine the volume of a box by filling it with cubes, rows of cubes, or layers of cubes. Determine the surface area as well by using the box's net.
6-8
In this lesson, students construct the 12 pentomino figures then utilize them to explore area and perimeter. By the end of the lesson students will be able to identify those constructions that are pentominoes and those that aren't. Students will also be able to calculate area and perimeter of pentomino combinations.