9-12
Static Nim is a one-pile game between two players. In this game, the maximum number of tokens that can be removed on each turn remains constant throughout the game. In this lesson, students will learn to represent the positions as the vertices of a directed graph and the moves as the edges of the graph. Also, they will learn that solving a game means finding a partition of the vertices into two sets such that three important properties are satisfied.
9-12
In static nim, the set of possible move sizes remains the same during the play of the game. In various versions of dynamic nim, the rules are such that the maximum number of counters that can be removed on each turn changes as the game is played. This maximum can depend on the current size of the pile, the number of counters removed on the previous play, or the move number of the game. In this lesson, students will explore the second type, where each move determines the maximum move size of the next move.
9-12
In this lesson, students consider the costs of owning a car and ways to lessen those costs. In particular, highway and city mileage are considered, and optimal mileage is calculated using fuel consumption versus speed data.
6-8, 9-12
In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of “tagged” items to the number of items in a sample is the same as the ratio of tagged items to the total population.
6-8, 9-12
By using sampling from a large collection of beans, students get a
sense of equivalent fractions, which leads to a better understanding of
proportions. Equivalent fractions are used to develop an understanding
of proportions.
This lesson can be adapted for lower-skilled students by using a
more common fraction, such as 2/3. It can be adapted for upper grades
or higher-skilled students by using ratios that are less instinctual,
such as 12/42 (which reduces to 2/7).
Scaffold the level of difficulty in this lesson by going from a simple
ratio such as 2/3 to more complicated ratios such as 2/7 or 5/9.
9-12
This lesson plan for grades 9‑12 is adapted from an article in the January 2000 edition of Mathematics Teacher.
The following activities allow students to explore alternative voting
methods. Students discover what advantages and disadvantages each
method offers and also see that each fails, in some way, to satisfy
some desirable properties.
6-8, 9-12
In this lesson, students purchase the common items used in their mathematics classroom such as desks, chairs, calculators, manipulatives, etc. They are given a budget that they must work within plus coupons that they must use when making their purchases. The lesson lets students have fun while applying the concepts of discount and percent. Since students use a purchase register to track their purchases, it also serves as a review of integer operations.
9-12
In this lesson, students learn Polya's four-step problem solving heuristic and how to use metacognition. They practice these on simple word problems and equations, then apply the techniques to games and more complex problems. The problem solving heuristic can be applied to problems outside of mathematics and used for cross-curricular activities.
9-12
Before there were electronic calculators, there were logarithm tables and slide rules. In this lesson, students make and use slide rules to discover the properties of logarithms. The technique, analogous to number-line addition, reinforces the hierarchy among the operations of addition, multiplication, and exponentiation.
9-12
This lesson allows students to extend their idea of sequences beyond a list of numbers to mathematical objects like intervals by asking them to examine the infinite intersection of these sequences. This lesson works especially well just after students have worked with infinite geometric series. It even contains an unexpected application of geometric sequences and series.
