Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

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Algebra

Finding the Balance

Pre-K-2, 6-8
This lesson encourages students to explore another model of subtraction, the balance. Students will use real and virtual balances. Students also explore recording the modeled subtraction facts in equation form.
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Algebra

Magic Squares

6-8
This lesson explores magic squares from both a historical and mathematical perspective. The mathematical analysis leads into symbolic algebraic representation of the patterns. This lesson is based upon an article from the April 2001 edition of Mathematics Teaching in the Middle School. 
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Geometry

Polygon Capture

6-8
In this lesson, students classify polygons according to more than one property at a time. In the context of a game, students move from a simple description of shapes to an analysis of how properties are related. This lesson was adapted from an article which appeared in the October, 1998 edition of Mathematics Teaching in the Middle School.
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Data Analysis and Probability

Skin Weight

6-8
In this lesson, students complete a chart by multiplying or dividing a given value, compare two categories in a line graph, and identify number patterns.
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Measurement

Whale Weight

6-8
In this lesson, students investigate relationships between numbers, identify number patterns,
represent the information in graphic chart form, and generalize the results of an investigation. Specifically, students explore the relationship between a whale's length and its weight.
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Data Analysis and Probability

Heartifacts

6-8
This lesson emphasizes the connections between science and mathematics by using a performance, or authentic, assessment format. Students explore applications involving their own heart. This activity involves students in interpreting factual information in a variety of problem-solving situations. Students also create and solve an original problem.
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Measurement

Finding the Balance

6-8
In this lesson for grades 6‑8, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum. The focus of this lesson is the relationship between the length of the arm and the mass of the objects.
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Data Analysis and Probability

The Celebrated Jumping Frog

6-8
Using the story "The Celebrated Jumping Frog of Calveras County" by Mark Twain, students simulate a jumping-frog contest and determine the distances "jumped." The students record the distance of individual jumps in centimeters and determine the total distance jumped (the sum of the three separate jumps) and the official distance (the straight-line distance from the starting line to the end of the frog's third jump). The students compare the range and median of the total distances with those of the official distances of the group.
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Data Analysis and Probability

Spinning Tops

6-8
Students measure distances using standard and nonstandard units and record their measurement in various tables. Then they are asked to use descriptive statistics to report the results. During a top-spinning contest, students measure the distance along a curve using indirect measurement. They record the data for their group in a chart, and compute their individual median and the group median.
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Number and Operations

A Lunch-In Affair

6-8
Students organize and prepare a luncheon for the entire class. Working in committees, each group of students is responsible for a different aspect of the event.