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Purpose

This unit draws on students' knowledge of local buildings and asks them to construct buildings. In turn, teachers are provided with opportunities to observe and listen to students' use of topic-specific language. Using blocks is a powerful medium for improving students' perception of objects and encourages creativity.

Achievement Objectives
GM1-2: Sort objects by their appearance.
Specific Learning Outcomes
• Classify shapes into categories.
• Discuss differences and likenesses of the shapes.
• Explore, experiment and talk about the form and function of the shapes in their own language.
Description of Mathematics

Spatial understandings are necessary for interpreting and understanding our geometric environment. In the early years of schooling, emphasis should focus on the recognition, sorting and exploration of shapes, and on the investigation of the properties of shapes. In the van Hiele model of geometric thinking, it is asserted that students move through five levels of understanding. The first of these levels is emergent, in which students recognise shapes by their appearance rather than their characteristics.

This unit focuses on the second level of van Hiele's model, in which students differentiate between specific properties of figures. This might include identifying the number of sides a triangle has or the number of corners in a square. In turn, students recognise the specific properties that make one shape different from another.

Ideas about form and function can best be developed through actions (manipulating materials). This unit gives students opportunities to develop their powers of observation, intuition, and imagination by exploration, experimentation, and discussion, mainly through the use of large blocks.

Within their 'real world' environment children meet both flat and solid shapes. There is much discussion about which is easier to consider first in learning. The students probably find exploring solid shapes more exciting. Moreover, their earliest experiences will probably be with 3-dimensional shapes. However, some educators feel that work with flat shapes should be done first. Both should be explored extensively and should provide opportunities for students to communicate their findings about shapes. This unit links the two through the use of photographs, pictures, and flat and solid shapes.

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

• restricting or extending your expectations of the criteria students use to categorise shapes. For some students, "it has straight sides" may be sufficient, while others may identify more specific features (e.g. number of sides)
• providing an amount and range of shapes of blocks that you think will challenge your students
• challenging students to make more complex buildings
• exploring digital shape models
• providing opportunities for students to work in pairs and small groups in order to encourage peer learning, scaffolding, extension, and the sharing and questioning of ideas
• working alongside individual students (or groups of students) who require further support with specific area of knowledge or activities.

The activities in this unit can be adapted to increase the relevance of this unit to your students. Consider how you might make connections to students' interests, cultures, and learning from other curriculum areas. For example, you may like to consider a field trip to a different location with particularly interesting shaped buildings, such as a local marae, shopping centre, or particularly interesting shaped house.

Te reo Māori kupu such as āhua (shape), tapa (side), mata (face), kokonga (corner), and the names for specific shapes could be introduced in this unit and used throughout other mathematical learning. You could also encourage students, who speak a language other than English at home, to share the words related to shapes that they use at home.

Required Resource Materials
• Large number of blocks (e.g. wood off-cuts) of differing shapes and sizes
• Photos of a variety of local buildings (enough for 2 pictures between a pair of students)
• Books and photos showing buildings and bridges in progress
• Camera
• Resources to create a class book (e.g. page templates, a digital tool).
Activity

Session 1

In this session students explore and describe the properties of 3-dimensional objects, and use these properties to classify given shapes.

1. Give each child a solid shape and ask them to think of a statement they could make about it. Model this for the class (e.g. my shape has straight sides, my shape has four corners). You might write the sentence starter "my shape" on the board for students to use. Emphasise that it does not matter if students make the same/similar statements as their peers. Have students share their statements with a partner, and then with the whole class.
Statements might include: My shape is round. My shape has straight sides. My shape is flat. My shape is big.
2. As students share their statements with the whole class, write the descriptive words used onto the board. Emphasise that these are words that describe the shapes.

flat   round   straight

1. Ask the students to work with a partner to to sort an assortment of blocks according to their mathematical properties (colour is not a mathematical property). You might model this with a few shapes. E.g. "these shapes are alike because they both have 4 sides. These shapes are different because one is round and one has 3 sides".
2. Ask the students to come up with their own classification or criteria for sorting (e.g. number of sides, 3D or 2D, long, big, flat, round etc. Have pairs share their classification and how it has been used to sort their shapes.
How did you sort your shapes?
Can you/anyone think of another way we could sort these shapes?

Session 2

In this session students look at shapes used in buildings.

1. Take the students for a walk around the school (or local community) to familiarise them with basic shapes seen in relevant buildings. Focus particularly on their form and function. You might visit a building that is related to learning from another curriculum area (e.g. the marae, the swimming pool, the museum). You could also ask students to bring in a photo of their favourite building.
2. Display pictures of the buildings, or, if students have brought in a picture of a building, get them to share their picture with a partner or the whole class.
3. Describe the buildings together.
What do they look like? Can you describe them? Can you use some of the describing words we used to describe the shape blocks? Refer back to the list created in the last session.
What are the shapes used for in this building?
Why do you think that shape has been used?
Descriptions might include: “The side of the building is like a square with a triangle on top”.
4. Have students work in pairs to describe what is the same and different about the buildings presented. Have students share their ideas back to the class.
5. Show the students photographs of buildings around the school and ask if they can recognise them, eg. the ramp outside Room 4, the door into the staffroom, triangular eaves on the school hall, the back of the bike shed, etc.
6. Through a chosen writing approach, create a class story (and/or an independent piece of writing) about the shapes students have seen in the buildings. Use the photographs as illustrations. Compile these into a class book (this could be done digitally - note that it will be added to later on).

Session 3

In this session students discuss features of solid shapes needed for buildings.

1. Read some of the class stories from the day before.
2. Present the blocks again. Ask students to imagine they are making a building. Discuss the features needed for those constructions (form and function - e.g. walls, a roof, windows, stairs etc.) This could be linked to specific buildings in your area (e.g. "a new sports centre is being built in our neighbourhood. Let's imagine we are building it with these blocks".) As part of this, you might invite a city planner, builder, or architect in to talk to your class about the construction of local buildings.
3. Discuss which shapes would stack together, which would be good to make a bridge, a wall, a tower (and any other local features or features students identify).
4. In groups let the students construct their building. Have them show it to the class and talk about its construction.
Which part do you think is strong and why? Are there some parts that you need to fix up so that it won’t fall down if I jump up and down near it?
What could your building be used for?
5. Photograph their buildings and record some of their ideas about their construction. This could be done in a writing lesson.

Session 4

In this session students look at books and photographs of buildings and construct their own building. The students will photograph their own construction from different views.

1. Put the students in groups and let them share books or photographs which focus on buildings – frames for houses, triangular shapes for bridges, rectangular shapes for windows and doors.
2. Allow the students time to read or look at the books and photographs. Encourage them to talk about the shapes they see in the books and see if they can find similar shapes in the classroom blocks.
3. Let the students construct another building, using the blocks, for a purpose they have seen demonstrated in the photos/books (e.g. a bridge a truck could go over, a tower that won't fall over, a ramp that a toy car could go right down). Provide opportunities for them to talk with another group, and to the whole class, about the reasons for their use of particular shapes.
4. Tell students that their buildings need to be built so that they won’t collapse when put to a test. Decide on a test as a class (e.g. 5 big jumps). Have students test out their building, one group at a time, and see if it passes the test. If the buildings do not pass the test, discuss why this could be, and provide time for students to re-construct their buildings. Encourage students to test, revise, and re-test their buildings to ensure they pass the test. Roam and provide support. After an appropriate amount of time, have students share their revised buildings with the class, and have them demonstrate whether it passes the test or not.
5. Photograph the models from top, front and back.

Session 5

In this session students make and complete their group books for presentation to the class.

1. Distribute the pictures you took in the last session to the groups of students. Have each group draw and name different shapes they have used for their building and glue onto a new page.
2. Have each student write a statement (helped by teacher or aide) of how they used that shaped block. This could be done in a writing lesson.
3. Compile the pages into a group book (this could be done digitally).