Turns (nzmaths activity) – curriculum level 1
Shapes with sticks (nzmaths activity) – curriculum level 3
Origami box – from curriculum level 3
Changing shape – curriculum level 2
Tetrahedron – curriculum level 3
Equilateral triangle – curriculum level 3
Creating nets – curriculum level 3-4
Turns from nzmaths
Purpose
In this unit we look at the beginning of the concept of angle. As students come to understand quarter and half turns, they also begin to see that ‘angle’ is something involving ‘an amount of turn’. These ideas are explored by using students’ bodies, toys, games and art.
Achievement Objectives
GM1-1: Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units.
GM1-3: Give and follow instructions for movement that involve distances, directions, and half or quarter turns.
WARC session resources used
WARC materials * card * paper * fabric * string or wool
Other * paint *crayons * scissors * drawing pins
TURNS ACTIVITY 1
Demonstrate full, half and quarter turns.
- Use a big circular piece of paper or fabric, or alternatively a chalk circle drawn on carpet or concrete.
- Have a student come to the centre of the circle and put their arm straight out in front.
- Get someone else to place a marker on the edge of the circle showing where the person is facing and their arm is pointing.
- Demonstrate the full turn as the person slowly turns all the way around and ends up back at their beginning point. Have everyone trace the full turn on the ground with their finger.
- Choose another person to come to the centre of the circle, face the same starting point and demonstrate a half turn. How far will they need to go? Where should they stop? Stress the idea of ending up facing the opposite direction.
- Repeat for quarter turn if the group is ready otherwise wait until they have had some practice doing full and half turns.
Resources for the activity
- Large fabric circle
- Markers e.g. pieces of wood, card, pegs
TURNS ACTIVITY 2
Prior to this session tie pieces of string to enough crayons for each child to have one, with a few spares to avoid arguments about colours.
- Provide each student with a crayon with string attached. Show them how to fix one end of the string by using a drawing pin or the finger of one hand. Then show how they can make a quarter turn arc by sweeping the crayon through a quarter turn. You will need to draw their attention to the importance of keeping the end of the string still and maintaining tension on the string.
- Ask students to make several ‘quarter turns’ in the same colour. Check that their turns are approximately correct.
- Having done quarter turns , students choose a new colour and create half turn arcs. Draw their attention to the relationship between quarter and half turns.
- Have each child choose a third colour and create some full turns. Draw their attention to the relationship between full, quarter and half turns.
Resources for the activity
- Crayons with string tied to them
- Drawing pins
- Card to put the paper on and then stick the drawing pins into
- Paper to make the turns on
TURNS ACTIVITY 3
This session is similar to that of the session with crayons and string except that here the quarter turns are made using ‘combs’ the students make for themselves. As an alternative, you may prefer to have students use crayons lying flat to create the same effect.
- To produce combs, give the students cardboard rectangles and get them to cut out ‘teeth’ to make ‘comb’ shapes similar to the diagram below.
- By holding one end fixed, students should be able to rotate their ‘combs’ through quarter and half turns after dipping their combs in different coloured paint.
- Give students the opportunity to make patterns with their ‘combs’ based on quarter and half turns.
- Students could be encouraged to produce several pages of patterns. Let them choose the one that they like best for their Turns Book.
- While they are involved in this activity check that their ‘comb’ shapes do represent quarter and half turns. There is no need to measure their work precisely but their turns should be close to the right magnitude.
Resources for the activity
- Cardboard rectangles – about 10cm in length
- Scissors
- Paper
- Three colours of paint prepared in containers that will take the 10cm lengths of card
Shapes with sticks from nzmaths
Purpose
In this unit students make and investigate a variety of three dimensional shapes. By examining a wide range of shapes and looking at the relationship between the numbers of faces, edges and vertices they see whether they can “discover” Euler’s famous formula.
Achievement Objectives
GM3-3: Classify plane shapes and prisms by their spatial features.
WARC session resources used
WARC materials * “toothpicks” – paper rods
Other * blu tac
- Look at one of the dice or other cube models that you have available.
Can you make a model of this shape using these straws (or toothpicks) and blu tac? - Make models of cubes.
- Make some more shapes with the materials available, you can cut the straws to make polyhedra with shorter edges. Some of the simpler examples are shown below.
- The activity on nzmaths has extensive coverage of the teaching and learning ideas for this unit of work, the notes here are to support exploring the materials needed.
Resources for the activity
- “toothpicks” – paper rods
- blu tac
Origami box
http://www.origami-instructions.com/origami-box.html
WARC session resources used
WARC materials * paper – cut to square
Other * scissors
Changing shape from nzmaths
https://nzmaths.co.nz/sites/default/files/ChangingShape.pdf
WARC session resources used
WARC materials * card
Other * scissors *ruler *pencil
Making a tetrahedron from an envelope
Instructions for making a tetrahedron from an envelope
WARC session resources used
WARC materials * envelopes
Other * scissors
Equilateral triangle folding from nrich
WARC session resources used
WARC materials * paper
Creating nets
Take one of the nets available in the pile.
- Visualise what you think the net will make.
- Fold the net into a 3D shape.
- Identify the shape that it makes.
- Unfold to get back to the net.
- Create a smaller (or larger) net that has the same basic properties.
- Cut out and fold to make the 3D shape – check against the original net and shape.
WARC session resources used
WARC materials * carboard nets *card (or paper) to create own nets
Other materials *ruler *scissors *pen/pencil