Asking students to explore new concepts with these virtual manipulatives can be great when combined with a lecture or reading activity. Afterwards, it can be powerful to bring the class together, look at the virtual manipulative again, and have them reflect on what they've learned. Also, these manipulatives could be assigned as homework, or as a supplement to traditional practice problems. Parents may find it helpful to be able to "play" with these tools alongside their child. While the site doesn’t give many specifics to teachers, there are lots of potential uses here. Teaching algebraic thinking to elementary school students? Just display one of the interactive games or demonstrations on the board, or let students explore it on a laptop with just some simple instructions. Even in small groups, these tools are engaging and effective.Continue reading Show less
Dating back to 1999, the National Library of Virtual Manipulatives (NVLM) is a collection of Java-based interactive tools that teach math concepts. While some of the concepts can be quite complex, most of the tools have a very simple (and dated) appearance. However, they'll run on any Java-capable browser (not on Apple's mobile devices). On the site's home page, users find a Virtual Library containing tools under the following categories: Numbers and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability. Each category is divided into resources for different grade levels, from Pre-K through 12th grade.
The idea alone of a library of manipulatives like this is a novel concept; after almost 15 years in the making, the site still has a lot of potential. However, an update –- not only to design but usability –- would be a great way to make this site accessible to more kids. That said, given the tools' exploratory nature, the site can be great for allowing students to discover math concepts on their own. By experimenting, students are often more successful in building deeper understanding, and even though the site gives little in the way of direction, it can be great when used in this way.
If using these tools to support specific parts of your curriculum, you'd be wise to help students along; either direct them toward areas of focus, or give them some context by showing them examples beforehand. Because not all the manipulatives give kid-friendly feedback, the site would do well to build in some better interactivity. Also, for your visual learners, the NVLM can be great for helping kids see and understand abstract concepts like variables and statistical probability.
Key Standards Supported
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Explain a proof of the Pythagorean Theorem and its converse.
Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”).
Measurement And Data
Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
Number And Operations In Base Ten
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
Count within 1000; skip-count by 5s, 10s, and 100s.
Use place value understanding to round whole numbers to the nearest 10 or 100.
Read, write, and compare decimals to thousandths.
Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
Operations And Algebraic Thinking
Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Fluently add and subtract within 5.
The Number System
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
Using Probability To Make Decisions
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.