National Library of Virtual Manipulatives
 geometry
 graphing
 probability
 algebra
 prediction
 thinking critically
 analyzing evidence
 selfreflection
Pros
Simple to use and free of charge, with virtual manipulatives for almost any topic and grade level.Cons
Not so easy on the eyes, and won't play nice with iPads, iPhones, or iPod touches.Bottom Line
Students who struggle with difficult math concepts may like the trialanderror format, but the vintage design and unclear feedback may scare some away.None, although the site claims that new features to allow the customization of manipulatives are on their way.
Kids will like the visual nature of these interactive tools, but the appeal may be limited by their strippeddown, "old school" look.
Kids enter numbers and adjust variables to see the outcome on graphs and visual displays. By experimenting, kids can learn through experience. When paired with reflection, this can become a powerful learning opportunity.
The site doesn't give many descriptions or explanations, but the interactives are designed to be used primarily by teachers or with the guidance of a teacher.
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.
Read More Read LessDating back to 1999, the National Library of Virtual Manipulatives (NVLM) is a collection of Javabased 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 Javacapable 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 PreK through 12^{th} grade.
Read More Read LessThe 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 kidfriendly 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.
Read More Read LessKey Standards Supported
Creating Equations  
HSA.CED: Create Equations That Describe Numbers Or Relationships  
HSA.CED.1  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. 
Geometry  
1.G: Reason With Shapes And Their Attributes.  
1.G.1  Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 
2.G: Reason With Shapes And Their Attributes.  
2.G.1  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. 
3.G: Reason With Shapes And Their Attributes.  
3.G.1  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. 
4.G: Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles.  
4.G.1  Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. 
5.G: Graph Points On The Coordinate Plane To Solve RealWorld And Mathematical Problems.  
5.G.1  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., xaxis and xcoordinate, yaxis and ycoordinate). 
6.G: Solve RealWorld And Mathematical Problems Involving Area, Surface Area, And Volume.  
6.G.2  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 realworld and mathematical problems. 
7.G: Solve RealLife And Mathematical Problems Involving Angle Measure, Area, Surface Area, And Volume.  
7.G.4  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. 
8.G: Understand And Apply The Pythagorean Theorem.  
8.G.6  Explain a proof of the Pythagorean Theorem and its converse. 
K.G: Identify And Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, And Spheres).  
K.G.3  Identify shapes as twodimensional (lying in a plane, “flat”) or three dimensional (“solid”). 
Measurement And Data  
4.MD: Solve Problems Involving Measurement And Conversion Of Measurements From A Larger Unit To A Smaller Unit.  
4.MD.1  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  
1.NBT: Understand Place Value.  
1.NBT.2  Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases: 
2.NBT: Understand Place Value.  
2.NBT.2  Count within 1000; skipcount by 5s, 10s, and 100s. 
3.NBT: Use Place Value Understanding And Properties Of Operations To Perform MultiDigit Arithmetic.4  
3.NBT.1  Use place value understanding to round whole numbers to the nearest 10 or 100. 
5.NBT: Understand The Place Value System.  
5.NBT.3  Read, write, and compare decimals to thousandths. 
K.NBT: Work With Numbers 11–19 To Gain Foundations For Place Value.  
K.NBT.1  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  
1.OA: Understand And Apply Properties Of Operations And The Relationship Between Addition And Subtraction.  
1.OA.3  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.) 
2.OA: Represent And Solve Problems Involving Addition And Subtraction.  
2.OA.1  Use addition and subtraction within 100 to solve one and twostep 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 
3.OA: Represent And Solve Problems Involving Multiplication And Division.  
3.OA.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. 
4.OA: Use The Four Operations With Whole Numbers To Solve Problems.  
4.OA.1  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. 
5.OA: Analyze Patterns And Relationships.  
5.OA.3  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. 
K.OA: Understand Addition As Putting Together And Adding To, And Under Stand Subtraction As Taking Apart And Taking From.  
K.OA.5  Fluently add and subtract within 5. 
The Number System  
6.NS: Apply And Extend Previous Understandings Of Multiplication And Division To Divide Fractions By Fractions.  
6.NS.1  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 3/4cup 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? 
Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.  
6.NS.6  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. 
7.NS: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers.  
7.NS.1  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. 
7.NS.2  Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 
8.NS: Know That There Are Numbers That Are Not Rational, And Approximate Them By Rational Numbers.  
8.NS.1  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. 
8.NS.2  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  
HSS.MD: Use Probability To Evaluate Outcomes Of Decisions  
HSS.MD.5  (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. 
See how teachers are using National Library of Virtual Manipulatives
Teacher Reviews
 Great way to help student visually understand5May 13, 2014
 Helps Build foundational concrete understandings of abstract concepts5November 8, 2013
 Fantastic Online Manipulatives5November 1, 2013
 Great source for math practice at all levels and areas!4October 30, 2013
Lesson Plans
Lesson Plans

Developing Strategies for Addition and Subtraction ComputationMathGrade 22 steps
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Developing Strategies for Addition and Subtracting ComputationadditionGrade 22 steps
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Developing Strategies for Multiplication and Division ComputationMathGrade 42 steps
February 2, 2016