Illuminations

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Cubed Cans

6-8

In this lesson, students will use formulas they have explored for the volume of a cylinder and convert them into the same volume for rectangular prisms while trying to minimize the surface area. Various real world cylindrical objects will be measured and converted into a prism to hold the same volume. As an extension, students may design and create a rectangular prism container according to their dimensions to compare and contrast with the cylinder.

Hitting Your Mark

6-8

Darts is a popular game in which players throw 3 darts, one at a time, aiming for a target. Different regions of the board give different points. In this lesson, students learn how to change the scale of an object, and how to measure and draw angles using a protractor. By the end of the lesson, students have created their own dartboard. The dartboard can later serve to emphasize properties of angles and angle pairs. This activity is a good one to do prior to a lesson in which students construct circle graphs. The practice they will get in this lesson drawing circles and measuring angles will help them in their quest to more accurately create circle graphs.

Geology Rocks Equations

6-8

In this lesson, students explore linear equations with manipulatives and discover various steps used in solving equation problems. Students use blocks and counters as tactile representations to help them solve for unknown values of x.

Graphs from the Unit Circle

9-12

In this lesson, students use uncooked spaghetti to transfer lengths from the unit circle to a function graph on large butcher paper. In the process, they discover the key features of sine and cosine graphs. The activity is presented for students working in degrees, but another version of the handouts is provided for students working in radians.

Fractional Clothesline

6-8

In this lesson, a string will be stretched across the classroom and various points will be marked for 0, 1, 2, 3, and 4. This classroom number line will be used to show that all proper fractions are grouped between 0 and 1, and that improper fractions or mixed numbers are all grouped above 1. Students clip index cards with various proper fractions, improper fractions, and mixed numbers on the clothesline to visually see groupings. Students then play an estimation game with groups using the same principle. Encouraging students to look at fractions in various ways will help foster their conceptual fraction sense.

Feeding Frenzy

6-8

In this activity, students will multiply and divide a recipe to feed groups of various sizes. Students will use unit rates or proportions and think critically about real world applications of a baking problem.

Hay Bale Farmer

6-8

In this lesson, students will use dimensions of round and square hay bales to calculate and compare volumes. They also calculate unit prices to determine which hay bale is the better value. Finally, students explore how to fit round and square bales into a barn to maximize volume, and decide which type of hale bale is the best choice.

Equations of Attack

6-8

Students will plot points on a coordinate grid to represent ships before playing a graphing equations game with a partner. Points along the y-axis represent cannons and slopes are chosen randomly to determine the line and equation of attacks. Students will use their math skills and strategy to sink their opponent's ships and win the game. After the game, an algebraic approach to the game is investigated.

Describe the Graph

3-5, 6-8

In this lesson students will review plotting points and labeling axis. Students generate a set of random points all located within the first quadrant. Students will plot and connect the points and then create a short story that could describe the graph. Students must ensure that the graph is labeled correctly and that someone could recreate their graph from their story.

A Swath of Red

6-8

A political map of the United States after the 2000 election is largely red, representing the Republican candidate, George W. Bush. However, the presidential race was nearly tied. Using a grid overlay, students estimate the area of the country that voted for the Republican candidate and the area that voted for the Democratic candidate. Students then compare the areas to the electoral and popular vote election results. Ratios of electoral votes to area are used to make generalizations about the population distribution of the United States.

Adding It All Up

6-8

In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an interactive tool and paper and pencil to foster an understanding of how different patterns can lead to the same solution. After comparing results with a partner, students develop a formula showing the relationship between the number of sides of a polygon and the sum of the interior angles.

Building Height

6-8

Students will use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building. The class will compare measurements, talk about the variation in their results, and select the best measure of central tendency to report the most accurate height.

Area Contractor

6-8

This lesson gives students the opportunity to explore surface area in the same way that a contractor might when providing an estimate to a potential customer. Once the customer accepts the estimate, a more detailed measurement is taken and a quote prepared. In this lesson, students use estimation to determine the surface area of the walls and floor of their classroom. They check the reasonableness of their estimates, and then measure the classroom for accuracy.

Extending to Symbols

6-8

In 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 investigation illustrates the continued transition from the concrete balance view of equivalence to a more abstract view.

Alike and Different

Pre-K-2

This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Students compare objects to identify similarities and differences. In addition, students are introduced to Venn Diagrams.

Grandma's Button Box

Pre-K-2

In this lesson, students have opportunities to identify properties and to sort, classify, organize, and display data. They solve problems and make, explain, and defend conjectures. They extend their knowledge by making generalizations and consolidating their thinking.

Exploring Equations

9-12

In this lesson, students use their knowledge of weights and balance, symbolic expressions, and representations of functions to link all three concepts.

Dividing a Town into Pizza Delivery Regions

9-12

Students will construct perpendicular bisectors, find circumcenters, calculate area, and use proportions to explore the following problem:

You are the owner of five pizzerias in the town of Squaresville. To ensure minimal delivery times, you devise a system in which customers call a central phone number and get transferred to the pizzeria that is closest to them. How should you divide the town into five regions so that every house receives delivery from the closest pizzeria? Also, how many people should staff each location based on coverage area?

From Fish Food to Pictures to Symbols

Pre-K-2

Students build upon their understanding of greater than, less than, and equal to by observing quantities and making comparisons using various instructional materials. The fish cut-out, with its mouth open, represents the greater than or less than symbol; the clam cut-out represents the equal to symbol. Using fish lips as a transition point, students will apply their understanding of greater, less, and equal to the standard symbols (>, <, =) as you introduce symbolic notation at a developmentally appropriate level.

Fish Food, More or Less

Pre-K-2

Students are introduced to the concepts of greater than, less than and equal to by observing quantities and making comparisons. Using various instructional materials such as modeling clay, buttons, beans, and cotton balls, students create amounts to compare using the open-mouthed fish. Depending which fish is chosen, the fish cut-out (with its mouth open) represents either greater than or less than. For equivalent amounts, a clam cut-out represents equal to.

This introductory lesson can be assessed through visual observation and verbal questioning. A group size of 3 – 6 students per group is optimal.

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