3-5
In this lesson, students apply their knowledge of addition equations to create number sentences using an electronic balance tool.
6-8
Students typically learn about the concepts of identity, inverse,
commutativity, and associativity by exploring the four basic operations
(+, –, ×, and ÷) with integers. In this lesson, students investigate
these concepts using a geometric model. Moves are performed with a
rectangle, and the results of an operation that combines two moves are
analyzed. Students determine if the operation is commutative or
associative; if an identity element exists; or if there are inverses
for any of the moves.
6-8
Using a scheme similar to the one in the Rectangle
lesson of this unit, students will further explore the concepts of
identity, inverse, and commutative and associative properties. Students
investigate and analyze moves performed with a plus sign, and an online
activity is available to help students with this investigation.
6-8
In this lesson, students will compare the price of a toll to the distance traveled. Students will investigate data numerically and graphically to determine the per-mile charge, and they will predict the cost if a new tollbooth were added along the route.
6-8
Students will measure the length and width of a rectangle using both standard and non-standard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. For many middle school students, this discovery is surprising.
3-5
A puzzle involving five dice and a non-standard pattern is used to promote problem-solving skills.
6-8
In the following lessons of this unit, students will have an opportunity to fully explore the patterns that result from the Paper Pool game. In this lesson, however, students will only spend time learning the rules, playing the game, and collecting data.
6-8
Students will continue their investigation of the Paper Pool game by exploring more tables and organizing the results. Using the data that they collect, they will attempt to find a relationship between the size of the table, the number of hits that occur, and the pocket in which the ball lands.
6-8
In the first four lessons of this unit, students investigated the Paper Pool game, collected data, identified patterns, and made predictions about the number of hits, the pocket in which the ball lands, and the path of travel. In this lesson, students finalize their work and write a report that summarizes all of their findings.
6-8
In this lesson, students continue their investigation by discovering a rule to predict the pocket in which the ball will land. As an extension, students can also consider the number of squares that a ball crosses while traversing its path.
