## All Lessons

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### Extending to Symbols

6-8

In Parts I and II of this investigation, students learn about the notion of equivalence in concrete and numerical settings. As students begin to use symbolic representations they use variables as place holders or unknowns. This part of the i-Math investigation illustrates the continued transition from the concrete balance view of equivalence to a more abstract view.### Hospital Locator

9-12

Students begin with a problem in a real-world context to motivate the need to construct circumcenters and then incenters of triangles and to make sense of these constructions in terms of bisecting sides and angles.### Exploring Diagonals and the Pythagorean Theorem

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.### Discovering the Area Formula for Triangles

6-8

In this lesson, students develop the area formula for a triangle. Students find the area of rectangles and squares, and compare them to the areas of triangles derived from the original shape.### Fair and Square: Using Concrete-Pictorial-Abstract Activities to Maximize Area

3-5, 6-8

Students discover the
relationships between area and perimeter as they prep for playing Square Off, a
wonderful Calculation Nation^{®}game. This lesson helps students understand the math of area and perimeter, which will help to maximize their scores when playing the game. Creating human-sized rectangles and working with geoboards provide concrete experiences before moving on to pictorial and abstract work with area and perimeter of rectangles.

### Deep Sea Duel

3-5, 6-8

Using the online game Deep Sea Duel, students play a card game against Okta. The objective is to choose cards so that some subset of three cards within their hand has a particular sum. Students will play several variations of the game, attempt to identify a winning strategy, and compare the game to other games that they know. ### Cutting Conics

9-12

Students explore and discover conic sections by cutting a cone with a plane. Circles, ellipses, parabolas, and hyperbolas are examined using the Conic Section Explorer tool. Physical manipulatives such as dough can optionally be used as well.### Big Math and Fries

6-8

We are lucky to live in an age where there is a lot of nutrition information available for the food we eat. The problem is that much of the data is expressed in percents and some of those percents can be misleading. This lesson is designed to enlighten students about how to calculate percent of calories from fat, carbohydrates, and protein. The calculations are made to determine if a person can follow the Zone Diet with only McDonald's food items.### Balancing Shapes

6-8

Students will balance shapes on the pan balance applet to study equality, essential to understanding algebra. Equivalent relationships will be recognized when the pans balance, demonstrating the properties of equality.### Barbie Bungee

6-8, 9-12

The consideration of cord length is very important in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and *ouch*! In this lesson, students model a bungee jump using a Barbie

^{®}doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

### Frogs on a Log

Pre-K-2

Students learn their first basic addition facts as they make the
connection between counting and finding one more than a number.
Students will manipulate frogs on a number line to represent adding 1
to a number.### 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.