This online manipulative features a virtual balance scale. It offers students an experimental way to learn about solving linear equations involving negative or positive numbers. The applet presents an equation for the student to illustrate by balancing the scale using blue blocks for positive units and variables and red balloons for negative units and variables. The student then works with the arithmetic operations to solve the equation. A record of the steps taken by the student is shown on the screen and on the scale. The applet reinforces the idea that what is done to one side of an equation must be done to the other side to maintain balance. Instructions for using the applet, background information about solving equations, and teaching suggestions are included.
This printable sheet is an excellent reference tool for geometry students. It details the formulae for finding the area, volume, and surface area for a variety of two- and three-dimensional shapes and includes an illustration of each that shows which measurements are important to the calculation. Presented are: areas of polygons (square, rectangle, parallelogram, trapezoid, circle, ellipse, triangles); volumes of polyhedra (cube, rectangular prism, irregular prism, cylinder, pyramid, cone, sphere, ellipsoid); and surface area (cube, prism, sphere).
For the learner just being introduced to fractions, this site is an excellent resource. It contain a very basic explanation of what a fraction is and a game for students to practice naming the fraction presented. The game can also be manipulated to have a time limit, to award time for each correct answer, and to time how fast students can get 20 more answers right than wrong.
In this activity, students "demonstrate the ability to represent numbers in scientific notation and use geometry to solve problems about planets in the solar system." This is the third in a series of activities called Math Space Odyssey from PBS's Mathline, and it asks students to calculate the capacity and area of the planets in the Milky Way. In addition, students convert numbers to scientific notation, calculate the distance between planets, and are asked to create and solve their own problem dealing with distance or capacity in the solar system. All relevant data needed is provided on a chart on this site, and the activity and answers can be downloaded as PDFs and printed, ready for classroom use.
This interactive lesson introduces students to the circle, its attributes, and the formulae for finding its circumference and its area. Students then perform a few calculations to practice find the area and circumference of circles, given the diameter.
This ready-to-print work sheet presents students with three problems, and in order to solve them, students must convert between smaller and larger units and use all four mathematical operations. There are a total of seven questions involving these three problems, and the conversions which students must undertake involve dollars and cents, pounds and ounces, grams and kilograms, and centimeters and meters.
This interactive applet allows students to explore cut-outs of polyhedra, including a tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The applet begins with each shape "unfolded" to its two-dimensional form. The slider bar allows students to fold the shape into its three-dimensional form. Students can experiment by folding the sides independently and rotating the shape. This applet can help students understand concepts of surface area and decomposing 3D shapes into 2D elements.
In this lesson, students will examine cylinders and prisms, define them, and measure their surface areas and volumes. The site has clear illustrations, translating the shapes to 2-dimensional figures, and practice problems for educators to solve with the students. There are two example problems at the end that students may tackle alone to solidify their understanding.
This site gives a description of how to divide fractions and gives a sample problem in which the denominator fraction is inverted, the numerators and denominators are multiplied, and the resulting fraction is simplified. It also includes the same problem solved by 'canceling' the fractions to simplify, and completing the process. There is also a game for students to practice their new skill of dividing and simplifying fractions.
This activity challenges students to use proportions to estimate how many 30-minute television shows can be recorded on a VCR tape using the SP (standard play) and the EP (extended play) modes. The activity begins with the observation that fractions, ratios, and proportions are used in comparison shopping, making scale models, and describing population densities. The Hint suggests that students begin by calculating how many half-hour shows could be recorded on the SP setting. Related questions ask students to use data tables to estimate the viewing preferences of different demographic groups. Answers to all questions are provided, as are links to additional resources.
This interactive game asks students to estimate an answer to various problems. While the site does not teach students individual strategies for estimating, it allows them to practice and come up with their own. Answers are considered correct when they are within 10% of the actual answer.
This interactive site demonstrates to students how to estimate and measure using nonstandard units. In this case, Chef Pierre explains how to estimate the length of his baking pans using cinnamon rolls. First, Chef Pierre explains the differences between estimating and measuring and the benefits of estimation in baking. Students are then allowed to explore the lengths of four different pans by placing cinnamon rolls next to them. Students are then asked to estimate the length of pans and test their estimate by measuring.
This applied mathematics lesson features hands-on activities supporting the NCTM Measurement Standard, and can be used to introduce middle school students to a bit of real-world measurement, trigonometry, and geometry through mechanical drafting. All that is needed are measurement tools ŰÓ carpenterŰŞs square, a piece of string, and a protractor. In it, students read an introduction about the importance and various uses of applied trigonometry and practice by examining the classroom and identifying which objects would have been designed by a mechanical drafter. They then discuss which aspects of the object would need to be measured and how those measurements would influence the design. Students practice by placing a string across the carpenter's square and use the Pythagorean Theorem to perform calculations on the right triangles produced. There are a series of extra activities in which students measure classroom objects to solve practical problems.
In this activity, students explore area and perimeter, the difference between them, and how to calculate them. As an introductory activity, students are given 12 tiles and asked to design a rectangle from them and uncover the definitions of area and perimeter. Then, students are given 36 tiles and asked to create as many rectangles as possible, observing the dimensions, area, and perimeter of each. A worksheet is provided, along with centimeter and half-centimeter grid paper.
This resource guides the learner, step-by-step, in creating a scale floor plan of a classroom. The instructions include sample drawings of student work. The activity includes: sketching a map of the classroom; measuring the room and calculating the area and perimeter; creating a scale drawing; and drafting a CAD (computer-aided design) floor plan. The lesson provides students with hands-on, real world practice solving problems of measurement, ratio, and scale.
This site provides an introduction to fractions, including the concept of equivalency, and shows how to reduce, decompose, multiply, divide, add, and subtract them. Illustrations cover all these concepts, beginning with the idea of fractions as parts of a whole, continuing through equivalency, addition and subtraction with like denominators, and finishing with multiplication of mixed numbers. Practice exercises are offered at all levels.
This site presents students with five word problems in which students apply their knowledge of calculating perimeter and area. Students type in and check their answers, or if they are stumped, they can get the answer by pressing "Show Answer."
From Elizabeth Stapel at Purplemath, this module helps students understand how to graph linear equations by making a neat T-chart, finding plot points, plotting points, and drawing the line. There are four pages in this module with clear, systematically presented, step-by-step instructions and plenty of examples and illustrations to help students along.
This game presents students with a number and asks them to find all the factors (divisors) of it between 1-10. There are two modes: the first uses numbers 1-100 and the second uses 101-999. Students then select which numbers are factors and try to open the safe. If they are correct, the safe will open. If they are incorrect, the simulation gives a hint as to how many they have correct and two more tries. There is a calculator built in to the site for students to use to help solve each problem.
This applet allows students to freely build shapes by stacking cubes and "explore the relation between a building (house) consisting of cubes and the height numbers representing the height of the different parts of the building." This exercise helps students visualize and understand the concepts of volume and three-dimensional, measurable space.