## All Lessons

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### Balancing Act

Pre-K-2

Problems such as those in this activity help develop what students already know in preparation for writing equations and learning ways to solve for variables. Students use mathematical models to explore quantitative relationships. When presented with pictures of pan balances with one or more objects in each pan, they communicate relationships between the weights of the objects by comparing the balanced and unbalanced pans. ### Golden Ratio

6-8

Students explore the Fibonacci sequence, examine how the ratio of two consecutive Fibonacci numbers creates the Golden Ratio, and identify real-life examples of the Golden Ratio.### Diagonals to Quadrilaterals

9-12

Instead of considering the diagonals within a quadrilateral, this lesson provides a unique opportunity: students start with the diagonals and deduce the type of quadrilateral that surrounds them. Using an applet, students explore certain characteristics of diagonals and the quadrilaterals that are associated with them.### Caesar Cipher

9-12

In this lesson, students will investigate the Caesar substitution cipher. Text will be encoded and decoded using inverse operations. ### Distributing and Factoring Using Area

6-8

In this lesson, expressions representing area of a rectangle are used to enhance understanding of the distributive property. The concept of area of a rectangle can provide a visual tool for students to factor monomials from expressions.### Flipping for Integers

6-8, 9-12

In this lesson, students will adapt expressions that add or subtract two signed integers.### Elevator Arithmetic

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.

### Counting Embedded Figures

6-8, 9-12

This grades 7-12 activity allows students to look for patterns within the given data. After looking at the pattern, the student should be able to form generalizations for the problem. Furthermore, this activity sharpens the algebraic skills of the students. The problem sharpens visualization skills.### Can You KenKen?

3-5, 6-8

The objective of this lesson is to use combinations to solve KenKen puzzles. An early solution strategy is for students to guess and check and use logic-based elimination. This lesson builds on those strategies by having students systematically list all possible combinations within each cage, the darkly outlined sections of the puzzle. ### Hotel Snap: Building for Profit

3-5, 6-8

Students will be required to build a high-profit yielding hotel using snap cubes. Building costs, rules and regulations, taxes, and income are all variables that students will be required to take into consideration.

### Geometry in Computer Games? An Exploration of Tessellations Used in neXtu

3-5

In this
lesson students will develop a definition for tessellations. They will
also analyze the importance of the tessellated game board in playing and
winning the game NeXtu on the Calculation Nation website.### Digging Up Improper Fractions: Converting Improper Fractions to Mixed Numbers for “Dig It” Game

3-5

This lesson provides a hands-on approach to converting
improper fractions to mixed numbers. In
addition, students locate improper fractions on a number line. Students use
number cards and counters as manipulatives while exploring the relationship
between improper fractions and mixed numbers. Students reinforce their skills
while playing a modified version of Calculation Nation’s “Dig It.”### Desafío en las Profundidades del Mar

3-5, 6-8

Utilizando el juego en linea Deep Sea Duel, los estudiantes participan en un juego de tarjetas contra Okta. El objetivo es elegir tarjetas de modo que algún subconjunto de tres tarjetas den una cantidad determinada. Los estudiantes jugaran variaciones del juego, intentando identificar una estrategia ganadora, y harán comparacion de este juego con otros juegos que ellos conocen.### Conduct an Experiment

9-12

Sea gulls and crows feed on various types of mollusks by lifting them into the air and dropping them onto a rock to break open their shells. Biologists have observed that northwestern crows consistently drop a type of mollusk called a whelk from a mean height of about 5 meters. The crows appear to be selective; they pick up only large-sized whelks. They are also persistent. For instance, one crow was observed to drop a single whelk 20 times. Scientists have suggested that this behavior is an example of decision-making in optimal foraging.### Correlation and the Regression Line

9-12

Interactive computer-based tools provide students with the opportunity to easily investigate the relationship between a set of data points and a curve used to fit the data points. As students work with bivariate data in grades 9-12, they will be able to investigate relationships between the variables using linear, exponential, power, logarithmic, and other functions for curve fitting. Using interactive tools like the one below, students can investigate the properties of regression lines and correlation.### Get the Turtle to the Pond

Pre-K-2

This activity provides opportunities for creative problem solving while
encouraging young students to estimate length and angle measure. Using
the Turtle Pond Applet,
students enter a sequence of commands to help the turtle get to the
pond. Children can write their own solutions using LOGO commands and
input them into
the computer. The turtle will then move and leave a trail or path
according to the instructions given.### Axonometry: Applying Complex Numbers to Art

9-12

In this lesson,
students examine and draw representations of cubes and then learn how to analyze
these representations using complex numbers. Students use what they know about
operations on complex numbers to see if a drawing is an accurate representation
of a cube. They also learn how to generate complex numbers that will produce
such representations. ### Exploring Equations Further

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.### Explore More Tables

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.### Don't Freeze the Engine

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.