In this unit ākonga describe and classify 2D and 3D shapes. They will use their own language in their descriptions, will explore similarities and differences, and will informally consider sides, corners, curved and straight lines.

- Sort, compare and classify 2D and 3D objects such as triangle, square, oblong, circle, box, cylinder and sphere.
- Describe shape attributes in their own language.

Spatial understandings are necessary for interpreting and understanding our geometric environment. The emphasis in the early years of school should include: recognition and sorting of shapes, exploration of shapes, and investigation of the properties of shapes.

In the van Hiele model of geometric thinking there are five levels. The first (Visualisation) is emergent. At this stage, ākonga recognise shapes by their appearance rather than their characteristics or properties. The second level (Analysis) is where ākonga differentiate specific properties of shapes, for example, the number of sides a triangle has or the number of corners in a square. Ākonga recognise certain properties that make one shape different from others. This unit is focused on this second level of the van Hiele model.

Ākonga discover 2D and 3D shapes within their environment (for example, square, cube, poi, desk, bed, starfish) and there is much discussion about which is easier to consider first. Both need to be explored extensively. Sufficient opportunities need to be given for ākonga to communicate their findings about 2D and 3D shapes.

This unit could be followed by the unit Shape explorers.

The learning opportunities in this unit can be differentiated by providing or removing support to ākonga and by varying the task requirements. Ways to support ākonga include:

- reducing the number of shapes that are sorted and the number of categories that they are sorted into
- limiting or increasing the feely bag to either 2D or 3D shapes, or reduce or increase the number of shapes
- providing or co-creating a reference poster to display in the classroom of the different shapes you discover. This could include images, words (including in te reo Māori) and symbols (this may help beginner readers)
- introduce more or less types of 2D and 3D shapes according to the needs of ākonga.

The context for this unit can be adapted to suit the interests and experiences of your ākonga. For example:

- use objects from the local environment to place in the feely bag (for example, stones, cones, leaves, seed pods, shells, buds)
- make reference to 2D and 3D shapes in your local community (for example, circle, sphere, marae, community garden, playground or public transport).

Te reo Māori vocabulary terms such as āhua (shape), tapawha rite (square), porowhita (circle), and torotika** **(straight) could be introduced in this unit and used throughout other mathematical learning.

- Mosaic tiles
- Shape attribute blocks
- Small blocks
- String
- Geoboards and rubber bands

#### Session 1: Loopy Shapes

In this activity we sort shapes according to attributes. Working with blocks in this exploration gives ākonga a chance to construct their own understandings about shapes and how they are related.

- Gather ākonga around a supply of shape blocks, mosaic tiles and attribute blocks.
*Do you see any ways that these blocks are alike? How are they alike?**Can you see any blocks that are different? How are they different?* - Use one of the categories suggested by the ākonga to sort the blocks.
*Let’s sort the shapes by size and see how many we have.* - Put three loops of string or make chalk circles or set rings/hula-hoops out for ākonga to sort the blocks in.
- Begin by putting a small shape in one of the loops.
- Distribute the shapes and have ākonga sort them into the three loops.
- Look at and discuss the shapes in the loops.
*Which loop has the most? Check by counting.**Do the shapes in this loop have other things in common?* - Sort the blocks using another attribute. Some possibilities are:
- colour
- shapes with 3, 4, 5 or 6 sides
- shapes that are round and shapes that aren’t

Let ākonga work in small groups to sort sets of shapes in a number of different ways. Circulate among the groups encouraging ākonga to describe the classification used. Tuakana/teina groupings could work well here.

#### Session 2: I spy a shape

In this session we play a version of ‘I spy’ ( or 'Kei te kite ahau') that helps ākonga focus on the shapes around them and the number of sides the shapes have.

*I spy a shape with four sides. You walk through it when you come into the classroom. What is the object?*- Have the ākonga who guesses correctly go to the door and count the number of sides. Record this on a chart.
*I spy another object with four sides. This one we look out of. What is the object?*- Once more get the guesser to count and check the number of sides.
- Let ākonga take turns giving clues about a shape in the class for others to guess. Each time get the guesser to check the number of sides.
- Encourage ākonga to give information about the relative length of the sides of the shape. For example, all sides are the same length; this side is longer.

After the game has been played several times get ākonga to draw pictures of 3- or 4-sided shapes in the room. Alternatively you could go for a walk outside to look for shapes and then get ākonga to draw these. Some ākonga may draw irregular 3- or 4- sided shapes such as a trapezium or isosceles triangle, this could be used as a teachable moment to extend some ākonga. Glue the drawings onto charts according to the way that ākonga classify them.

Discuss the charts.*What are some of the things you notice about the shapes you found?**Which did you find more of? Why do you think this is?**Do you know what we call these shapes?*

#### Session 3: In the bag

Which shape is in the bag? Today we reach into feely bags to see if we can work out the shape by touch alone.

- Gather ākonga together in a circle on the mat (mahi tahi model). Show them 5 shapes on the floor including 2D and 3D shapes. These could be small blocks, mosaic tiles or attribute blocks.
- Show ākonga the feely bag.
*One of these shapes is in the bag. I wonder if you can tell me which one just by feeling it?* - Pass the bag around the circle so that each ākonga can feel the shape. Encourage them to think about the shape. Remind them that they shouldn’t point or call out which shape they think it is so that everyone gets a chance.
- As each ākonga feels the shape in the bag, get them to say one thing they notice about it.
*Tell me something you notice about the shape in the bag.* - Once each ākonga has had a turn to feel in the bag, ask them to say which shape they thought it was. Then reveal the hidden shape.
*Is this the shape you were expecting?* - Secretly change the shape in the bag and play again as a whole class.
- In small groups or pairs, ākonga play the game again as the teacher circulates and questions. Change the types of shapes according to the needs of your ākonga.
*Can you describe what you can feel?**Which shape do you think it is? Why?*

#### Session 4: Dominoes

In this session we use the mosaic shapes as dominoes for ākonga to explore shapes and match side lengths as they form a trail of shapes.

- Gather ākonga in a circle on the mat. Tip the mosaic tiles onto the mat in the middle of the circle.
- Tell them they are going to play a game of shape dominoes. They are going to match shape sides that are the same length to make a trail around the mat.
- Let ākonga informally explore sides of the same length by fitting two or more shapes together.
- Place a tile on the floor and get ākonga next to you to choose a shape that could go next.
*Are there other ways that you could place that shape tile?**Are there any ways that shape tiles wouldn’t work?* - Continue around the circle until each ākonga has had a turn.
- Ākonga can continue playing the game in small groups (a tuakana/teina model could work well), with the teacher circulating and questioning.
*What can you tell me about the shape tile you have chosen to go next?**Why did you choose that shape tile?*

#### Session 5: Shape makers

In this session we use loops of string or wool to form shapes using ourselves as the corners. We extend the idea using geoboards and rubber bands.

- Gather ākonga on the mat.
- Have a long piece of thick string or wool and talk about the shape of the string.
*Who can tell me about this piece of string? (Long, curly, wiggly, etc.)* - Hold the string in a long straight line and then let it fall onto the floor in a muddle and get ākonga to describe how the shape has changed.
*What was the string like when we held it tight?**What was it like on the floor?**How else could we hold the string or put it on the floor to change its shape?* - Encourage ākonga to make suggestions about the form of the string and to use their own language to describe it.
- Get each ākonga to hold part of the string and get them to move backwards to form a circle using the whole class and again encourage them to describe the shape in their own language.
- Using a shorter length of string. Get small groups of ākonga to hold the string and to explore the shapes that can be made.
*What sort of shapes can you make with three people? (or 4 or 5 people etc.)**How many sides will the shape have?**Do all the sides have to be the same length?* - Get ākonga to continue exploring string shapes in small groups as the teacher circulates and questions.
- Using rubber bands and geoboards, ākonga can to explore the same ideas.
- The geoboard shapes can be sorted into several sets (as with Loopy Shapes, Session 1) and ākonga can talk about the similarities and differences between the shapes they have made including, number of sides and lengths of sides.
- This can be used to make a chart for display. Photos could be taken of the geoboard shape creations.

Dear family and whānau,

This week we are looking at objects that have the same shapes. For instance doors and windows both have four sides. We found out the names for a number of these shapes, including oblongs (rectangles), triangles and circles.

We would like you and your child to make a list of all things that you commonly use around home that are oblongs (rectangles), triangles or circles. Aim for five things on each list. Your tamariki could draw the object and you could help them write the name of it.