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.
6-8
In this lesson, students develop a deep conceptual understanding between remainders and the decimal part of quotients. They learn how remainders and group size work together to influence the results that are displayed on a calculator. Students use beans to physically represent quotients that have remainders, and they compare remainders written as fractions of whole groups to the results obtained with a calculator.
6-8
Positive and negative numbers become more than marks on paper when students play this variation of the card game, Rummy. Engaged in a game involving both strategy and luck, students build understanding of additive inverses, adding integers, and absolute value.
6-8
What's at the end of the rainbow or, in this case, the ruler? In this
lesson, students find a treasure using directions involving bearing
(angles) and range (length). In the process, they measure angles
from 0° to 360°, use map scales, and measure lengths.
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.
9-12
In the same way that supporting statements are used to reach a
conclusion in a paragraph-style proof, students modify a cliché or
common phrase to use as a punch line to a humorous story. This lesson
works well in aiding in the transition from two-column proofs to
paragraph-style proofs.
9-12
Students sometimes have difficulty using the order of operations when
evaluating expressions. By converting these expressions into binary
expression trees before evaluating them, students gain a better
understanding of the order of operations. In addition, students learn
to represent algebraic expressions using prefix notation, which is
often called "Polish Notation," because of the nationality of its
inventor, Polish logician Jan Łukasiewicz.
6-8
In this lesson, students analyze ways for calculating weight loss. Students compare the results and choose the method they consider to be the best and most fair.
9-12
In this lesson, students observe a model of exponential decay, and how kidneys filter their blood. They will calculate the amount of a drug in the body over a period of time. Then, they will make and analyze the graphical representation of this exponential function.
