Manipulatives in Mathematics
manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it
The use of manipulatives provides a way for students to learn concepts in a developmentally appropriate, hands-on and an experiencing way
Content (Manipulatives)
Fraction Law of signed number Geoboard (with PPT) Platonic Solids (with PPT) Archimedean Solids Pie Chart Algebra Tiles
Objectives
To help student develop the ability of solving fraction in an easy and interesting way
To motivate students to learn fraction with the use of this manipulative
Pedagogical use: This instructional material is
composed of two manipulatives: (1) board and (2) tiles
Thinking Blocks Fraction Manipulative teaches students how to model and solve word problems involving fractions and whole numbers.
Thinking Blocks Fraction Manipulative is ideal for students who are learning model drawing strategies. Thinking Blocks Fraction manipulative is best suited for students ages 10+.
Procedure:1. Identify the total number of
parts (fraction) then build a model using the same tile color.
Example: The whole is
55
45
35
15
25
55
2. If you are asked to add and then simply put the corresponding number of tile (numerator) on top of the tile you constructed in step 1.
15
25
55
45
35
15
25
15
25
Objectives
To help students master the basic operation
To motivate students learn the law of signed number with the use of this manipulative
To develop speed an accuracy in solving equation with the basic operation
Pedagogical use: Law of signed number flashcards can be use in drills and practices. This can help students develop speed and accuracy in performing the basic operation.
Procedure: Just like the typical flashcards,
the teacher flashes the given equation and the students should immediately answer the equation presented.
The signs and the operation can also be change as well as the given numbers
Objectives
To help students solve the area and perimeter of a given polygon in a fun and interesting way
To aid the teacher in making the students understand the lesson on area and perimeter of a polygon in an easy manner
Pedagogical use: Improvised geoboard is
a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other polygons
It consist of a physical board with a certain number of dots used in finding the area and perimeter of a certain polygon
Procedure: Just like the typical geoboard, the
teacher will create a polygon out of the dots but the only difference is that instead of using a rubber band the teacher will use white board pen to draw a polygon on the improvised geoboard.
A rectangle is any quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (90°).
A Rhombus is a shape with 4 equal straight sides. Opposite sides are parallel, and opposite angles are equal. And the two diagonals of a rhombus bisect each other at right angles.
Parallelogram
𝜃
A B
C
𝑑1 𝑑2
D
Given diagonals and and an included angle : Area=
Given two side a and b and one angle A:Area=ab sin A
A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same.
Triangle
Given base b and height h:Area=
Give three sides: Area = where s= semi perimeter
s=
h
b
ac
𝜃
Circle is a set of all points in a plane that are at a given distance from a given point, the center; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. The distance between any of the points and the centre is called the radius.
Area1.Find the area
of Plane Y, X and Z
2.The sum of the area of plane Y, X and Z is the total area of the Irregular Figure
a e
cb
g
d
f
h ij
Z
Y
X
𝐴𝑋= h𝑎
𝐴𝑍=𝑒𝑓𝐴𝑌=𝑐𝑖
𝐴𝑋𝑌𝑍=𝐴𝑋+𝐴𝑌+ 𝐴𝑍
A geoboard is a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other polygons. It consists of a physical board with a certain number of nails half driven in, around which are wrapped rubber bands.
In finding the perimeter:Count the number of nails surrounding the shape formed by your rubber band and the total number of the nails corresponds the perimeter of the shape
In finding the area:
Every four nails of the shape formed by the rubber band serves as one unit. Count the number of the units inside the shape and the total units corresponds to the area of the shape.
Materials used:
Chipboard Double adhesive tape Colored paper Glue Scissors Poster paint Pattern from
http://www.korthalsaltes.com/
Objectives
To determine the different faces and forms of the platonic and Archimedean solids through this models
To develop students understanding about polyhedra
History of the Platonic Solids
Platonic solids were known to humans much earlier than the time of Plato. There are carved stones (dated approximately 2000 BC) that have been discovered in Scotland. Some of them are carved with lines corresponding to the edges of regular polyhedra.
The name “Platonic solids” for regular polyhedra comes from the Greek philosopher Plato (427 - 347 BC) who associated them with the “elements” and the cosmos in his book Timaeus.
“Elements,” in ancient beliefs, were the four objects that constructed the physical world; these elements are fire, air, earth, and water. Plato suggested that the geometric forms of the smallest particles of these elements are regular polyhedra.
There are five regular polyhedra that were discovered by the ancient Greeks
The Pythagoreans knew of the tetrahedron, the cube, and the dodecahedron; the mathematician Theaetetus added the octahedron and the icosahedron
Symbolism from Plato:› Octahedron =
air› Tetrahedron =
fire› Cube = earth› Icosahedron =
water› Dodecahedron
= the universe
Tetrahedron
The tetrahedron is bounded by four equilateral triangles. It has the smallest volume for its surface and represents the property of dryness. It corresponds to fire.
Number of faces: 4Number of vertices: 4Number of edges: 6
Cube
The cube or hexahedron is bounded by six squares. The hexahedron, standing firmly on its base, corresponds to the stable earth
Number of faces: 6Number of vertices: 8Number of edges: 12
Octahedron
The octahedron is bounded by eight equilateral triangles. It rotates freely when held by two opposite vertices and corresponds to air
Number of faces: 8Number of vertices: 6Number of edges: 12
Dodecahedron
The dodecahedron is bounded by twelve equilateral pentagons. It corresponds to the universe because the zodiac has twelve signs corresponding to the twelve faces of the dodecahedron.
Number of faces: 12Number of vertices: 20Number of edges: 30
Icosahedron
The icosahedron is bounded by twenty equilateral triangles. It has the largest volume for its surface area and represents the property of wetness. The icosahedron corresponds to water.
Number of faces: 20Number of vertices: 12Number of edges: 30
Objective
To show the relationship between the perimeter of the circle and a parallelogram
To develop students ability in analyzing a certain concept
Pedagogical use: This is can be use in fraction and finding the relationship between the circle and parallelogram
Objectives
To help students learn how to represent and solve algebra problem with the use of the algebra tiles
To motivate students in solving algebraic equation in a fun and interesting waY
Pedagogical use:Algebra tiles are known as mathematical manipulatives that allow students to better understand ways of algebraic thinking and the concepts of algebra. These tiles have proven to provide concrete models for elementary school, middle school, high school, and college-level introductory algebra students.
Procedure:Use tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.