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Illumination Activities from NCTM
Illuminations is designed to:
· Provide Standards-based resources that improve the teaching and learning of mathematics for all students.
· Provide materials that illuminate the vision for school mathematics set forth in Principles and Standards for School Mathematics.
Illuminations is designed to provide preK-12 teachers and math educators online interactive Standards-based resources that improve the teaching and learning of mathematics for all students; and to provide materials that illuminate the vision for school mathematics set forth in Principles and Standards for School Mathematics.
1) (6-8) Data Analysis
A) http://illuminations.nctm.org/LessonDetail.aspx?ID=L585 - Students will play Sticks and Stones, a game based on the Apache game "Throw Sticks," which was played at multi-nation celebrations. Students will collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game.
B) http://illuminations.nctm.org/LessonDetail.aspx?id=U171 – In this two-lesson unit, students compare the heights of friends and classmates at different ages. Through the course of the lessons, students are exposed to algebra, measurement, and data analysis concepts. A major theme of the unit is analyzing change.
C) http://illuminations.nctm.org/LessonDetail.aspx?id=L579 – Using multiple representations, students analyze the frequency of letters that occur in the names of all 50 states.
2) Statistics
A) 600.40.30, 700.40.10, 700.40.25, 800.40.10, 800.40.40 - http://illuminations.nctm.org/LessonDetail.aspx?ID=L239 – In this activity, students examine the United States Census Bureau Web site to investigate projections of the total population of states from 1995-2025. Using the provided data, students will analyze statistics from five states of their choice, develop specific research questions using the data, and create three graphs to compare and contrast the information
B) 800.40.25, 800.40.30 - http://illuminations.nctm.org/ActivityDetail.aspx?ID=77 – Box and whisker plot applet http://illuminations.nctm.org/LessonDetail.aspx?ID=L231 – In this activity students collect height data and then construct a boxandwhisker plot to display the results. The activity sheet presents a sequence for setting up a boxandwhisker plot.
C) 600.40.35, 700.40.25 - http://illuminations.nctm.org/LessonDetail.aspx?ID=L522 - Students choose meals from a menu and then construct a box plot. They use the plot to identify the mean, mode, median and range of the data set.
i) http://illuminations.nctm.org/LessonDetail.aspx?ID=L523 - Students will construct box plots independently. Students identify the mean, median, mode, and range of a set of data.
ii) http://illuminations.nctm.org/LessonDetail.aspx?ID=L537 - Students create a box and whisker plot and compare the mean, median, and mode of a set of data.
iii) http://illuminations.nctm.org/LessonDetail.aspx?ID=L538 - Students create glyphs based on the characteristics of their names. They also enter data into a spreadsheet and sort it in several ways.
iv) http://illuminations.nctm.org/LessonDetail.aspx?ID=L737 - In this lesson, students use information from NBA statistics to make and compare box and whisker plots. The data provided in the lesson come from the NBA, but you could apply the lesson to data from the WNBA or any other sports teams or leagues for which player statistics are available.
v) http://illuminations.nctm.org/ActivityDetail.aspx?ID=160 - This applet allows the user to investigate the mean, median, and box-and-whisker plot for a set of data that they create. The data set may contain up to 15integers, each with a value from0 to100.
D) 600.40.30, 700.40.15, 800.40.10, 800.40.15
i) http://illuminations.nctm.org/LessonDetail.aspx?ID=L535 - Students create bar graphs and circle graphs and find the range and mode of two data sets.
ii) http://illuminations.nctm.org/ActivityDetail.aspx?ID=60 - Use this tool to graph data sets in a circle graph. You can input your own data or alter a premade data set.
E) 600.40.05, 700.40.20 – Statistics and Fractions - http://illuminations.nctm.org/LessonDetail.aspx?ID=L341 - During this lesson, students create their own classroom survey or use previously generated questions to study the class and describe the set [class] in fractional parts. This lesson requires that students identify fractions in real-world contexts from a set of items that are not identical. This lesson is integrated with other areas of the math curriculum, including data analysis and statistics.
3) Probability (800.50.30, 800.50.35, 800.50.40, 700.50.25, 700.50.30, 600.50.25, 600.50.30)
A) http://illuminations.nctm.org/ActivityDetail.aspx?ID=79 - Adjustable spinner
B) http://illuminations.nctm.org/LessonDetail.aspx?ID=L248 – The game of SKUNK - In this lesson, students practice decision-making skills leading to a better understanding of choice versus chance and building the foundation of mathematical probability.
C) http://illuminations.nctm.org/LessonDetail.aspx?ID=U190 - Students will explore theoretical and experimental probability and the relationship between them. Students will also graph an experiment to further explore the relationship according to the law of large numbers.
D) http://illuminations.nctm.org/LessonDetail.aspx?ID=L448 - Students explore the relationship between theoretical and experimental probabilities using an interactive tool known as a "box model." A "box model" is a statistical device that can be used to simulate standard probability experiments such as flipping a coin or rolling a die.
E) http://illuminations.nctm.org/LessonDetail.aspx?id=L615 - In this grades 68lesson, students are encouraged to discover all of the combinations for a given situation. They use problem-solving skills (including elimination and collection of organized data) to draw conclusions. The use of higher-level thinking skills (synthesis, analysis, and evaluations) is the overall goal.
F) http://illuminations.nctm.org/ActivityDetail.aspx?ID=67 - This applet simulates drawing tickets from a box, where each ticket has a number written on it. After you decide which tickets to place in the box, the applet chooses tickets at random. The relative frequency of each number is displayed in a frequency distribution at the bottom of the applet.
4) Measurement
A) 600.30.20 - http://illuminations.nctm.org/LessonDetail.aspx?ID=L577 - 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.
B) 700.30.10 - http://illuminations.nctm.org/LessonDetail.aspx?ID=L578 - Students will use their knowledge of rectangles to discover the area formula for parallelograms.
C) 700.30.10 - http://illuminations.nctm.org/LessonDetail.aspx?ID=L580 - Students discover the area formula for trapezoids, as well as explore alternative methods for calculating the area of a trapezoid.
D) http://illuminations.nctm.org/ActivityDetail.aspx?ID=108 - Use this tool to determine how the length of the base and the height of a figure can be used to determine its area. Can you find the similarities and differences between the area formulas for trapezoids, parallelograms, and triangles?
5) Measurement - 600.20.30, 600.20.35, 700.30.35, 800.30.05
A) http://illuminations.nctm.org/LessonDetail.aspx?id=U160 - In this unit, students use the area formula for a rectangle to discover the area formulas for triangles, parallelograms, and trapezoids. Students also consider irregular figures whose areas can be determined by estimation or decomposition.
B) http://illuminations.nctm.org/LessonDetail.aspx?ID=L573 - Students measure the circumference and diameter of circular objects. They calculate the ratio of circumference to diameter for each object in an attempt to identify the value of pi and the circumference formula.
C) http://illuminations.nctm.org/LessonDetail.aspx?ID=L574 - Using a circle that has been divided into congruent sectors, students will discover the area formula by using their knowledge of parallelograms. Students will then calculate the area of various flat circular objects that they have brought to school. Finally, students will investigate various strategies for estimating the area of circles
D) http://illuminations.nctm.org/ActivityDetail.aspx?ID=116 - How do the area and circumference of a circle compare to its radius and diameter? This applet allows you to investigate these relationships in the Intro and Investigation sections and then hone your skills in the Problems section.
E) 600.30.25, 700.30.15, 800.30.25 - http://illuminations.nctm.org/LessonDetail.aspx?ID=L570 - This lesson uses a real-world situation to help develop students' spatial visualization skills and geometric understanding. Emma, a new employee at a box factory, is supposed to make cubeshaped jewelry boxes. Students help Emma determine how many different nets are possible and then analyze the resulting cubes.
F) http://illuminations.nctm.org/LessonDetail.aspx?ID=L793 - In this lesson, students use polydrons to create nets of rectangular prisms. They discover that there are many configurations for rectangular prisms with the same volume, and determine that certain configurations minimize surface area. The lesson continues in a discovery activity related to building the most cost-efficient and appealing fish tank.
G) http://illuminations.nctm.org/LessonDetail.aspx?ID=L410 - Students identify which geometric solids can be made from given nets. Students also create nets for common geometric solids.
H) http://illuminations.nctm.org/ActivityDetail.aspx?ID=70 - This tool allows you to learn about various geometric solids and their properties. You can manipulate and color each shape to explore the number of faces, edges, and vertices, and you can also use this tool to investigate the following question: For any polyhedron, what is the relationship between the number of faces, vertices, and edges?
I) http://illuminations.nctm.org/LessonDetail.aspx?ID=L408 - Students discover Euler's Formula, a way of calculating the number of faces, edges, and vertices of geometric solids.
J) http://illuminations.nctm.org/LessonDetail.aspx?ID=L409 - Students construct physical models of geometric solids.
K) http://illuminations.nctm.org/LessonDetail.aspx?ID=L672 - Using an area tool on the computer, students will begin to develop an understanding of area. Students will use 12"×12" paper squares to measure the area of a door. They will determine whether area increases or decreases as the length or width of their door changes.
L) http://illuminations.nctm.org/ActivityDetail.aspx?ID=21 - One of the most important measurements in geometry is the measurement of area. The applets in this Interactive Geometry Dictionary(IGD) will show you how to find the area of some common shapes.
M) 700.30.15, 800.30.25 - http://illuminations.nctm.org/LessonDetail.aspx?id=L762 - 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.
N) 800.30.20 - http://illuminations.nctm.org/LessonDetail.aspx?id=L783 - 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.
6) Geometry – 600.20.60, 700.20.70, 800.20.50 – Transformations
A) http://illuminations.nctm.org/LessonDetail.aspx?ID=L731 - This lesson introduces students to the world of symmetry and rotation in figures and patterns. Students learn how to recognize and classify symmetry in decorative figures and frieze patterns, and get the chance to create and classify their own figures and patterns using JavaSketchpad applets.
B) http://illuminations.nctm.org/LessonDetail.aspx?ID=L732 - Students will identify and classify reflections and symmetries in figures and patterns. They will also create frieze patterns from each of the seven classes using the supplemental activity sheets.
C) http://illuminations.nctm.org/ActivityDetail.aspx?ID=168 - Students can experiment with the seven classes of Frieze patterns with this activity. They can explore the transformations that constitute each of the seven categories.
D) http://illuminations.nctm.org/ActivityDetail.aspx?ID=167 - Students will recognize rotation symmetry in figures and examining various rotation symmetries.
E) http://illuminations.nctm.org/ActivityDetail.aspx?ID=169 - Students will recognize dihedral symmetry and reflections in figures and examining various symmetries.
F) Polygons - http://illuminations.nctm.org/LessonDetail.aspx?ID=L277 - Students identify and classify polygons according to various attributes. They then sort the polygons in Venn Diagrams, according to these attributes. Extensions to fundamental ideas about probability and statistics are also included.
G) http://illuminations.nctm.org/ActivityDetail.aspx?ID=34 – Shape sorter activity.
H) http://illuminations.nctm.org/LessonDetail.aspx?id=L765 - In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an applet 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.
7) Number Relationships – The Factor Game
A) http://illuminations.nctm.org/LessonDetail.aspx?ID=L620 - The Factor Game engages students in a friendly contest in which winning strategies involve distinguishing between numbers with many factors and numbers with few factors. Students are then guided through an analysis of game strategies and introduced to the definitions of prime and composite numbers.
B) http://illuminations.nctm.org/ActivityDetail.aspx?ID=12 - The Factor Game is a fun, interactive game that exercises your factoring ability. You can play against the computer or against a friend.
C) http://illuminations.nctm.org/ActivityDetail.aspx?ID=64 - With this activity, you can visually explore the concept of factors by creating rectangular arrays with an area equal to the product of the factors.
8) Rational Numbers
A) Fractions - http://illuminations.nctm.org/LessonDetail.aspx?ID=L784 - 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.
B) http://illuminations.nctm.org/ActivityDetail.aspx?ID=18 - This applet allows students to individually practice working with relationships among fractions and ways of combining fractions.
C) http://illuminations.nctm.org/ActivityDetail.aspx?ID=11 - This tool explores several representations for fractions using adjustable numerators and denominators. You can see decimal and percent equivalents, as well as a model that represents the fraction.
D) http://illuminations.nctm.org/ActivityDetail.aspx?ID=44 - This tool explores several representations for fractions using adjustable numerators and denominators. You can see decimal and percent equivalents, as well as a model that represents the fraction.
E) http://illuminations.nctm.org/ActivityDetail.aspx?ID=45 - This tool explores several representations for fractions using adjustable numerators and denominators. You can see decimal and percent equivalents, as well as a model that represents the fraction.
9) Ratios, Proportions, and Percents