The Montessori Geometry Stick Box contains wooden sticks of different lengths and colors with holes at each end allowing them to be connected to create any shape or angle needed in geometry investigation. This math material makes geometry concepts beautifully visual and entices children to investigate parts and types of shapes, lines, planes, and angles further. It should be used in conjunction with puzzles, cards, or workbooks. It is one of my Top Ten Math Materials for Elementary.
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Preceding Material
Children should be introduced to basic shapes before using the Montessori Geometry Stick Box.
Basic Shapes
Triangles
Sides
Show children a chart of triangles or puzzle pieces that show triangles with the 3 types of sides. Have the child build the triangle with the Montessori Geometry Stick Box and sort them by sides.
- Equilateral– all 3 sides are equal in length
- Isosceles– two sides are equal in length
- Scalene– no sides of equal length.
The child can trace the triangles in a notebook and label them, make a chart or booklet, and play games with building and naming the shapes.
Angles
Show children a chart of triangles or triangles puzzle that show different angles. Show them that in addition to looking at and naming triangles by sides, we can also look at and name them by angles (corners). Triangles have three angles. Have the child build triangles with the 3 different angle types using the Montessori Geometry Stick Box.
- Right angle– has one angle like the angle of a square. Show the child the plastic measuring angle from the stick box. It is a yellow triangle with a corner marked in red. We can also draw a perfect square in the corner of a right-angled triangle.
- Obtuse angle– has one angle that is larger than a right angle.
- Acute angle-has an angle smaller than a right angle.
The child can trace the triangles in a notebook and label them, make a chart or booklet, and play games with building and naming the shapes.
The 7 Triangles by Sides and Angles
Once the child can name and build triangles by sides and angles, he can classify triangles by both their sides and angles. It is helpful to use a matrix to organize the work. He will end up with seven triangles:
- Acute equilateral
- Acute isosceles
- Acute scalene
- Right isosceles
- Right scalene
- Obtuse isosceles
- Obtuse scalene
Quadrilaterals
Quadrilaterals are shapes with four sides. Use a quadrilateral chart or puzzle to introduce the quadrilateral shapes. Allow the child to build each quadrilateral with the Montessori Geometry Stick Box.
- Square– a square is a special rectangle that has four sides of equal length.
- Rectangle– a rectangle has two sets of parallel sides.
- Rhombus- a parallelogram that has all sides of equal length. Also called a diamond.
- Parallelogram– has opposite sides that are parallel. It looks like a slanted rectangle.
- Trapezoid– a quadrilateral with one set of parallel sides. It looks like a table.
- Common quadrilateral (a right-angled trapezoid)- a trapezoid that has a pair of right angles.
The child can trace the quadrilaterals in a notebook and label them, make a chart or booklet, and play games with building and naming the shapes.
Regular Polygons
Polygons are shapes with many angles (or corners). Use a polygon chart or shape puzzle to show the child regular polygons. Allow the child to build each polygon with sticks from the Montessori Geometry Stick Box.
- Pentagon– 5 corners/sides
- Hexagon– 6 corners/sides
- Heptagon– 7 corners/sides
- Octagon– 8 corners/sides
- Nonagon– 9 corners/sides
- Decagon– 10 corners/sides
The child can trace the polygons in a notebook and label them, make a chart or booklet, and play games with building and naming the shapes.
Lines
Parts of a Line
Ray and Origin:
- Take a long piece of string balled at both ends. Unroll it in both directions to demonstrate that a line goes on forever and ever in both directions.
- Take a red pen and mark a point on the string to stop the line. Cut the string at the point. The cut piece of string is now a ray that goes on forever in only one direction.
- The point where you cut is the origin of the ray.
- Label the line by writing the words “origin” and “ray” on two strips of paper and placing them appropriately on the string.
- Children can choose sticks in the Montessori Geometry Stick Box to label with Ray and Origen.
Segment and Endpoints:
- Lay out a string and remind the child that a line goes on forever in both directions.
- Take a red pen and make two points some distance apart to stop the line.
- Take two pair of scissors and cut both points simultaneously. You now have two rays continuing in either direction and a middle piece.
- The middle piece is called a line segment with two endpoints, the two points you cut.
- Label the segment and both endpoints.
- Choose a stick from the Montessori Geometry Stick Box and relate it to the string segment. Each stick in the box is a line segment. The two holes on either end of each stick are the endpoints.
Positions of a Line
Horizontal, Vertical, Oblique (diagonal):
- Show the child a corkboard. It is a plane (a flat surface).
- Demonstrate different lines in space by changing the position of a stick from the Montessori Geometry Stick Box.
- Allow the child to practice moving the stick and naming these three types of lines. They can draw the lines and label them in a math notebook.
Intersecting, Convergent, and Divergent
Intersecting:
- Choose two sticks of equal length from the Montessori Geometry Stick Box. Place one stick horizontally on the work surface. Place the other stick at an angle on top of the first stick so that it crosses the first stick.
- There is a point where the two sticks meet. This point is called the intersection. The two lines are intersecting.
- The child can draw and label the intersection in his notebook.
Convergent:
- Choose two long sticks and create an intersection. Place two happy-faced children on each stick facing the point of the intersection. These children are happy because they will meet each other if they keep walking on the lines.
- Substitute two arrows in place of the children.
- These lines are called convergent. They get closer and closer to each other until they intersect.
- The child can draw and label convergent lines in his notebook.
Divergent:
- Choose two long sticks and create an intersection. Place two sad-faced children on each stick walking away from each other after the intersection. They are sad because they will never meet again.
- Substitute two arrows in place of the children.
- These lines are called divergent. They get farther and farther away from each other.
- The child can draw and label divergent lines in his notebook.
Parallel
- Place one stick horizontally on the corkboard. Place another stick vertically so that it meets and touches the horizontal stick.
- Use the measuring angle in the box to show that a right angle is created where the two lines meet. This is a perpendicular line.
- The child can draw and label perpendicular lines in a notebook.
Perpendicular
- Choose any stick from the Montessori Geometry Stick Box and pin it horizontally on the corkboard.
- Choose another stick and pin it parallel to the first one.
- The child can draw and label parallel lines in a notebook.
Angles
Parts
- Have the child choose two sticks of the same length from the Montessori Geometry Stick Box. Attach the sticks together on the corkboard by putting a pin through the same origin points (holes).
- Remind the child that each line is called a ray. Label the rays.
- The two rays share the same origin point. We call this the vertex. Label the vertex.
- The space between the sides is called the size of the angle. Label the size.
Types
- Take a long and short stick from the box. Place the two sticks together horizontally on the corkboard with the longer stick on top of the shorter stick. Attach them together with a pin at the origin points. Pin the opposite hole on the shorter stick, firmly fixing it to the corkboard while leaving the longer stick free to rotate.
- Rotate the longer stick upward at a diagonal angle to illustrate an acute angle. Continue rotating the stick to illustrate right, obtuse, straight, reflex, and whole angles.
- Using the yellow measuring angle from the box, demonstrate: The straight angle is two measuring angles. The whole angle is four measuring angles.