"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." (from NCTM Illuminations)
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In this lesson, "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." (from NCTM's Illuminations)
This is an online graphing utility that is a great supplement to any lesson on graphing box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots.
This lesson focuses on the observation of properties and the classification of objects to build ideas about variables. Learners compare buttons to identify similarities and differences. In addition, learners are introduced to Venn Diagrams by reading "The Elves and the Shoemaker" and sorting their shoes in a giant diagram.
This unit consists of four lessons in which students explore several meanings and representations of multiplication, including number lines, sets, arrays, and balance beams. They also learn about the commutative property of multiplication, the results of multiplying by 1 and by 0, and the inverse property of multiplication. Students write story problems and create pictographs. The unit includes activity sheets, assessment ideas, links to related applets, reflective questions for students and teachers, extensions and a bibliography of children's literature with a multiplication focus.
Students explore the set model for multiplication. They find products using equal sets and present their results in a table. Next students apply their knowledge about multiplication in the creation of pictographs (from NCTM's Illuminations website).
"Students generate products using the number line model. This model highlights the measurement aspect of multiplication and is a distinctly different representation of the operation. The order (commutative) property of multiplication is also introduced. Students are encouraged to predict products and to answer puzzles involving multiplication." from NCTM Illuminations.
"This lesson encourages students to explore the array model of multiplication. The lesson focuses on the factors 4 and 6. Students will also explore products with 0 or 1 as a factors. First students make arrays with counters, and then they create a second concrete example of the array model using toothpicks. They also write problems which involve multiplication." (from NCTM's Illuminations) This is lesson 3 in a 4-lesson unit.
This lesson from Illuminations asks students to use a geometry applet to analyze the characteristics of a square. Graphs are created to show relationships between characteristics (side length, diagonal length, perimeter, area). The lesson involves both algebra and geometry, is appropriate for grades 9-12 and should take one class period to complete.
In this data analysis activity students investigate data in connection with recyclable materials and develop plans to help the environment. Students collect data about aluminum can usage and graph that data in a line plot. The lesson includes student worksheet and extension suggestions.
In this 5-lesson unit primary students identify attributes of buttons and other objects in their classrooms. Throughout the unit students learn to collect data about objects, display the data (Venn diagrams, pictographs, and bar graphs), and analyze the data to determine what this tells us about buttons and/or other objects. Each of the five lesson plans includes necessary student/class worksheets, questions for students, extension ideas, and assessment ideas. Lessons 2 and 3 reference stories that are an important part of the skill development: "The Button Box" by Margarette Reid and "The Elves and the Shoemaker" story.
"Examine the angles in a triangle, quadrilateral, pentagon, hexagon, heptagon or octagon and find a relationship between the number of sides and the sum of the interior angles." (Source: 2000-2012 National Council of Teachers of Mathematics)
In this two-lesson unit, students will "use estimation and measurement skills to determine the ratio of circumference to diameter and explore the meaning of pi. Students will discover the circumference and area formulas based on their investigations." (from NCTM's Illuminations)
In this math activity, learners explore the history of the Stomachion (an ancient tangram-type puzzle), use the pieces to create other figures, learn about symmetry and transformations, and investigate the areas of the pieces. The Stomachion, believed to have been created by Archimedes, consists of 14 pieces cut from a square, which can be rearranged to form other interesting shapes.
"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." (from Illuminations, NCTM)
This two-lesson unit from Illuminations, exposes students to algebra, measurement, and data analysis concepts and the major theme of analyzing change. In the first lesson, students measure the heights of classmates and older students and construct a table of height and age data to compare them. The second lesson's instructional goal is to understand how change in one variable, age, can relate to change in a second variable, height. Instructional plan, questions for the students, assessment options, extensions, and teacher reflections are given.
This worksheet uses The Phantom Tollbooth as a literature basis for problem-solving tasks that challenge students to explore the concept of averages.
In this lesson students use a rule of thumb about the weight of babies to practice doubling and halving numbers. They complete an organized table and compare data using vertical and horizontal double bar graphs. The lesson includes a student activity sheet and extension ideas.
"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." (from NCTM's Illuminations)
"Using a balance in the classroom is a first step to algebraic understanding. Use this pan balance (numbers) applet to practice the order of operations in simplifying numerical expressions and to demonstrate the conventions of using algebraic logic in simplifying expressions" (from NCTM's Illuminations). Lesson 2 of a three lesson unit.