Fold and Cut
In this unit students explore line symmetry and the names and attributes of two-dimensional mathematical shapes. The context of this unit is students folding and cutting out shapes to make a series of mathematical shapes.
explain in their own language what line symmetry is
describe the process of making shapes with line symmetry.
name common two-dimensional mathematical shapes
describe the differences between common two-dimensional mathematical shapes in relation to number of sides
This unit has the students using line symmetry in a practical activity. At Level 2 the concept of symmetry is starting to be developed. This lead onto a greater understanding of symmetry at higher levels of the curriculum, e.g. the order of reflective symmetry and rotational symetry. In this unit we look at shapes with reflective symmetry, i.e. objects that have one or more lines of symmetry. The goal at this level is to have the students being about to describe reflective symmetry in their own language and understand this concept.
Learning the names of common two-dimensional mathematical shapes is important and necessary as students develop. Knowing their attributes is very important, with this understanding starting at this level.
Following are common two-dimensional mathematical shapes and their attributes that could be introduced in this unit. Not all these shapes need to be presented to all students in the class. Teachers need to select the ones appropriate, based on the readiness of the students. Less able students may work with triangles, squares, and rectangles, while more able students work on all in the list.
Polygon - a shape with straight line sides
Triangle - a shape with 3 straight sides
Equilateral triangle - all sides the same length and all angles 60°
Right angle triangle - one inside angle is a right angle, 90°
Isosceles triangle - two sides are the same length and two angles are the same
Scalene triangle - all sides are different lengths, all angles are different
Quadrilateral - a shape with 4 straight sides
Square - all sides are the same length, all angles 90°
Rectangle - 2 pairs of parallel sides, all angles 90°
Trapezium - 1 pair of parallel sides,
Rhombus - all sides are the same length, angles between 1° and 179°
Parallelogram - 2 pairs of parallel sides, angles between 1° and 179°
Pentagon - a shape with 5 straight sides
Hexagon - a shape with 6 straight sides
Octagon - a shape with 8 straight sides
Note that pentagons, hexagons and octagons are any shapes with 5, 6 or 8 straight sides. The length of sides do not need to be the same nor do the angles need to be the same.
Pentagons, hexagons and octagons with sides the same length and angles the same are called regular pentagons, hexagons and octagons. A square is a regular quadrilateral and an equilateral triangle is a regular triangle.
Getting Started
- Take a square piece of paper and fold it in half in front of the class.
Using scissors cut out the shape as shown below. Before opening the paper ask the class, “When I open this piece of paper, what shape will the hole in the middle be?”
After the students have had a chance to express their opinions, open the paper and talk about the shape.
Repeat this process cutting out the following shapes.
Discuss the shapes when the paper was folded in half and when it was unfolded. The aim of this discussion is to find out what the students know and notice.
Questions like the following could be used:
“Why did it work like that?”,
“How many sides and how many angles?”
“What do you notice about the length of the sides?”,
“Are any angles the same?”,
“Does anyone know the name of this shape?”
- Challenge the students, “What other shapes could be made by folding a square piece of paper in half and cutting?” and “What shapes do you think are impossible to make?”
- Hand out square pieces of paper and get the class to experiment and try to make some new shapes.
Exploring
Over the next 2 or 3 days the students need to work through the following three tasks. At appropriate times the teacher needs to bring the class together to discuss and teach, making sure the Specific Learning Outcomes of the unit are learnt.
Task 1 - Straight Line Shapes
“How many different straight line shapes can be made by folding a square piece of paper in half and cutting?”
Working in small groups, the students are to make as many of the following as they can.
Make . . .
- 4 different looking shapes with 3 straight sides
- 4 different looking shapes with 4 straight sides
- 4 different looking shapes with more than 4 straight sides
Place these shapes into three piles.
1. Shapes with 3 straight sides
2. Shapes with 4 straight sides
3. Shapes with more than 4 straight sides
For most of this unit the focus is on straight line shapes. Using a ruler to draw the straight lines onto the folded paper, before they cut, is suggested. This way the chances of a straight line are increased and they practice using a ruler and cutting to a marked line.
Once as many different shapes as possible have been made, assign a category of shapes, to pairs of students, e.g. shapes with 3 straight side. The pairs sort their shapes according to the way they look. The students then share with the rest of the class why they sorted their shapes as they did.
Pairs who need help, could be encouraged to look at the length of sides in each shape, e.g. “Are any of the sides the same length?”, or to look at the angles, e.g. “How many angles are larger than a right angle”
Task 2 – Make the Shapes
“How many of the following shapes can you make by folding and cutting?”
Fold a square piece of paper in half, as in Getting Started and Task 1. Cut out some of it and unfold it to make one of the shapes below.
Get the students to predict, before they start on this task, which shapes will be the easiest to make, the hardest to make and whether any will be impossible. Ask why they think they will be easy, hard or impossible.
Make some more challenges like the ones above for others in your class.
Task 3 - Alphabet Shapes
“Make as many letters of the alphabet as you can by folding and cutting.”
Throughout this unit the teacher needs to reinforce the understanding of what reflective symmetry is and the names and attributes of common two-dimensional mathematical shapes. As the class works on the above tasks, small groups could be taken aside to work with the teacher. This would enable the teacher to gauge the understanding of the students and adjust the task to make it ideal for them.
A display of the names and attributes of the shapes would be good so the students could refer to it throughout the unit.
Reflecting
Ask the students to think about the things they have learnt this week, the names of shapes and about reflective symmetry.
The class could be given a blank piece of paper and asked to draw the shapes their group have been learning about.
The more able students could be asked to draw and describe in their own words an Equilateral triangle, Right angle triangle, Isosceles triangle, Scalene triangle, Square, Rectangle, Trapezium, Rhombus, Parallelogram, regular and non regular Pentagon, Hexagon and Octagon. They could also indicate which shapes could be made by folding and cutting. Less able students could be asked to complete less shapes.
We have been exploring different shapes in class this week. Take some time with your child to help them look for objects and shapes around their home that have reflective symmetry. They could make a list of the objects and draw a diagram showing the line of reflection. Appliances, furniture, cutlery, electrical and electronic item around the home could have reflective symmetry.
The two-dimensional mathematical shapes the children are learning about could also be looked for around the house and in their neighbourhood, for example, a stop sign or a trampoline frame could include mathmatical shapes they can describe to you.
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