# Virtual Manipulatives

*Note: *For a Virtual Manipulative to be listed on this website

It must have a hands on equivalent that could be present in the classroom.

It cannot use Flash or Java to run.

It must be free for teacher/classroom use.

All teacher resources listed are publically available websites and subject to change.

**Grades: **Grade 6 to 9, Foundations of Mathematics 10 and 20.

**Strands: **Numbers, Patterns and Relations

**Tool Description: **Algebra Tiles allow for learning basic numeracy, counting, calculation and algebraic equations. The tiles represent 1, -1, x, -x, and x-squared. Arrangement of the tiles helps students to see patterns and solve algebraic problems visually.

**Teacher Resources:**

**Grades: **Grade 3 to 8

**Strands: **Shape and Space

**Tool Description: **AngLegs is a hands-on manipulative for discovering angles and angle relationships.

**Teacher Resources: **

**Sample Lessons:**

**Grades: **Pre-K to Grade 5

**Strands: **Shapes and Space, Patterns and Relations

**Tool Description:** Attribute blocks are different coloured blocks of similar shapes. They are designed to be sorted and used to link common attributes.

**Teacher Resources:**

**Grades: **Kindergarten to Grade 6

**Strands: **Number, Patterns and Relations

**Tool Description:** Base 10 blocks come in singles representing ones (1x1), rods representing tens (1x10), squares (also called flats) representing 100 (10x10), and cubes representing 1000 (10x10x10). These are also referred to as *Dienes Blocks. *Each block has indents, unlike Cuisenaire rods, so students may quickly compare them. Some base 10 block sets come with two colours of each block type, allowing students to represent positive and negative numbers. These manipulatives come in handy with place value, counting, basic addition, subtraction, multiplication, and division.

**Teacher Resources:**

**Grades: **Grade 3 to 8

**Strands: **Patterns and Relations

**Tool Description:** Balances and scales are useful to show the balance and equality of equations. These manipulatives can be used to analyze what happens when we alter one side of an equation. They can also be used to solve for unknowns in any given equation when modelled.

**Teacher Resources:**

**Grades: **Kindergarten to Grade 4

**Strands: **Numbers, Shape and Space

**Tool Description:** The manipulatives in this category can be used for introduction to scales and measurement devices, most notably in the use of time. They may also be used in developing an understanding of fractions.

**Teacher Resources:**

**Grades: **Kindergarten to Grade 5

**Strands: **Patterns and Relations, Numbers, Shape and Space

**Tool Description: **These different coloured squares can be used for pattern recognition, area, perimeter, counting, sorting, and pentominoes tasks. They are a low abstraction tool.

**Teacher Resources:**

**Grades: **Kindergarten to Grade 6

**Strands: **Numbers, Patterns and Relations

**Tool Description:** Counters are various tokens, squares, or cubes, that are used for counting activities. They are often useful for beginner addition, subtraction, multiplication, and division. As most counters come in at least two colours, they are also useful for sorting and patterning activities. Square and cube counters have the added benefit of being useful for area, perimeter, and volume expansions.

**Teacher Resources:**

**Grades: **Grade 2 to 9

**Strands: **Numbers, Shape and Space, Patterns and Relations, Statistics and Probability

**Tool Description:** Cuisenaire rods are rods of different lengths based on centimetre measurements. Each colour of rod corresponds to a specific length, making them easy to identify by students. They are considered to have a higher level of abstraction than other manipulatives, this means they can up used for counting, basic algebraic functions, area, perimeter, volume, and geometry.

**Teacher Resources:**

**Grades: **Kindergarten to Grade 11

**Strands: **Numbers, Statistics and Probability, Patterns and Relations

**Tool Description: **Dice and spinners are often used in the teaching of probability. They can also be used for practice by random number operations. The type of die you want to use can vary from a standard 6-sided die to a fraction die to a 16 sided die.

**Teacher Resources:**

**Grades: **Grade 3 to 8

**Strands: **Numbers, Shape and Space

**Tool Description: **Fraction circles are a pre-made set of equally divided circles into their fractional parts. All of the parts add to the same size whole. Depending on the application, circle pieces can be made as small as 1/32.

**Teacher Resources:**

**Grades: **Grade 3 to 8

**Strands: **Numbers, Shape and Space

**Tool Description: **Similar to fraction circles, fraction tiles take one whole bar and split it into equal parts to show equivalency. Fraction tiles have the added bonus of being able to examine area as well. These manipulatives may also be known as *fraction strips.*

**Teacher Resources:**

**Grades: **Grade 1 to 8

**Strands: **Shape and Space

**Tool Description: **Most pegboards come with an arrangement of pegs in rows and columns. However, some pegboards also come with pegs in a circular arrangement. They can be used to explore geometric shapes, perimeter, area, and how the three concepts relate. They may also be used for learning fractions or working with a cartesian grid. This could be done by placing four geoboards together to make a four-quadrant cartesian plane.

**Teacher Resources:**

**Grades: **Grade 6 to 12

**Strands: **Shape and Space

**Tool Description:** Geometry tools encompass a number of tools from a standard geometry kit (rulers, protractors, compasses, and squares). These tools enable students to explore angle and geometric relations.

**Teacher Resources:**

*As each tool in this category is specialized and contains resource links, none are listed here.*

**Grades: **Grade 8 to 12

**Strands:** Patterns and Relations, Shape and Space, Numbers, Statistics and Probability

**Tool Description: **Graphing calculators quickly graph multiple mathematical expressions on a cartesian plane. They are useful for analyzing patterns within similar expressions.

**Teacher Resources:**

**Grades: **Grade 1 to 5

**Strands: **Numbers

**Tool Description: **Number charts are useful for analyzing patterns and repetitions that occur within whole numbers. They may be used for basic addition, subtraction, multiplication, division, and recognizing patterns.

**Teacher Resources:**

**Grades:** Kindergarten to Grade 10

**Strands: **Number

**Tool Description: **Number lines allow students to conceptualize concepts such as addition and subtraction of positive and negative numbers, repeated addition (multiplication), groupings (division), fractions, decimals, and multiple representations of the same number. They may also be used in pairs to approximate the roots of numbers.

**Teacher Resources:**

**Grades: **Grade** **3 to 9, Workplace and Apprenticeship 10 and 20, Foundations 10 and 20.

**Strands: **Shape and Space, Number

**Tool Description: **This category outlines several measurement tools that replace their real-world counterparts. In here are callipers, micrometres, rulers, and thermometers. These virtual manipulatives are best for learning how to use measurement tools.

**Teacher Resources:**

*As each measurement device is unique, activities and links are left to the independent tools in this section.*

**Grades: **Grade 1 to 7

**Strands: **Shape and Space

**Tool Description: **Miras and Georeflectors allow students to conceptualize mirror images, reflections, congruences, and symmetry. Virtual georeflectors have an advantage over concrete ones as they work better for students with visual impairments.

**Teacher Resources:**

**Grades: **Grade 1 to 5

**Strands: **Shape and Space, Numbers

**Tool Description: **Pattern blocks are a set of basic shapes; hexagon, trapezoid, parallelogram, triangles, square, and rhombus. They are useful for examining geometric properties. They may be useful with demonstrating symmetry, counting, geometry, angles, fractions, and non-base 10 activities.

**Teacher Resources:**

**Grades: **Grade 1 to 7

**Strands: **Numbers

**Tool Description: **Place value manipulatives allow students to conceptualize the relevance of a place value to the size of the number. Teachers may expand these to include repeated addition.

**Teacher Resources:**

**Grades: **All

**Strands: **All

**Tool Description: **Random number generators can be used by students or teachers, especially in the older grades, for determining randomized numbers within a specific interval or type. Some random number generators may also be used to find number sets, such as a set of numbers that will fit a specific normal curve.

**Teacher Resources:**

*No resources have been added to this category. It is notable that there are many different types of random number generators, including ones that can do sets of data to reflect or normal curve or a specific type of data set.*

**Grades: **Grade 3 to 9, Foundations 10, Workplace and Apprenticeship 10 and 20.

**Strands: **Shapes and Space

**Tool Description: **Geosolids, or geoblocks, allow students to conceptualize various objects and the shapes that construct the object. Geosolids are useful in making comparisons between geometric solids and when working with area, surface area, nets of an object, and volume.

**Grades: **Grade 3 to 9, Workplace and Apprenticeship 10 and 20.

**Strands: **Shape and Space, Number, Patterns and Relations, Statistics and Probability

**Tool Description: **Snap cubes are cubes that link together to either make patterns or objects. They can be used for patterning, demonstrating symmetry, addition, subtraction, multiplication, and division. They are useful for helping students to conceptualize the faces of an object. These may also be called *connecting* or *linking* cubes.

**Teacher Resources:**

**Grades: **Grade 1 to 8

**Strands: **Shape and Space, Number

**Tool Description:** Tangrams are geometrically created and related shapes. All 7 shapes can be put together to make a square. Tangrams are typically considered puzzle pieces as they can be used to make a number of different shapes by how they are arranged. Tangrams might be used with fractions, area, perimeter, or angles.

**Teacher Resources:**