**Learning activities**

Whilst this unit is presented as sequence of five sessions, more sessions than this may be required. It is also expected that any session may extend beyond one teaching period.

**Session 1**

This session is about naming and describing plane shapes, and using these to create a picture. Note: By drawing around the shape the students are creating a two-dimensional shape. Limit the colour selection, as this is relevant to the work in a later lesson.

SLOs:

- Sort attribute blocks and explain their groupings.
- Use geometric language to describe plane shapes.
- Understand the features of a two-dimensional shape.
- Create an artwork using plane shapes.

__Activity 1__

Make attribute blocks available to small groups of students.

Begin by having individual students sort a selection of the attribute blocks into groups, and explain to a partner the groupings they have made. Have them repeat the sorting task, this time categorising them differently.

Encourage and affirm appropriate geometric language, including the correct use of shape names and descriptions of their features.

__Activity 2__

As a class, brainstorm and record on the class chart, all shape and attribute language associated with the task in Activity 1.

__Activity 3__

Make paper, pencils, and pastels or crayons available, *but limit the colour selection.*

*Challenge the students to make a picture of a ***person, object or place** that is important to them. Explain that they are to make their picture using the shape blocks to help them.

Demonstrate to the students how to begin the picture by drawing around several shapes and then colouring in the outline. For example:

Explain why your picture is important to you. (For example: ‘My Dad used to drive an old blue car a bit like this one.’)

__Activity 4__

Have students make and complete their own pictures. When pictures are complete, have each student name their picture, write a short story about it, using words from the brainstorm list in Activity 3. Their story should explain why the subject of the picture is important to them and how they made their picture.

__Activity 5__

Refer to the example picture made in Activity 3 above and to the artworks they have just completed.

Ask: *“Are the shapes two-dimensional shapes or three-dimensional shapes?”* Discuss ideas.

Write the word **‘dimension’ and 2D** below the picture.

Ask for students to discuss in pairs the meaning of what has been written.

Through discussion, develop understanding of the meaning of the word ‘dimension’, of two dimensions and of the abbreviation, 2D.

Highlight the shapes that they have drawn are like (foot) prints only. They are **wide and long, ***but not deep*. Have students explain that two-dimensional shapes have no depth or thickness.

__Activity 6__

- Have students discuss in pairs and decide whether the attribute blocks themselves are two-dimensional or three-dimensional shapes.

- Have them physically take up positions in the classroom to indicate their thinking (for example: 2D on one side of the mat, 3D on the other).

Discuss, conclude and record that the attributes blocks are 3D shapes because they have width, length, and thickness (depth), and we can feel these. Recognise that the attribute block shapes have different thickness or depth.

- Write
*face, edge and vertex* on the class chart. Have students locate and identify each feature on several of the attributes shapes. Write the plurals of each work beside the singular, highlighting the word **vertices**. Make the connection between the 2D language of sides and corners, and the 3D terms edges and vertices.

__Activity 7__

Have students partner share their art works and stories. Conclude by writing on the class chart, **‘We used ***two-dimensional shapes* to make our artworks today.’

**Session 2**

This session is about choosing and responding to a piece of Picasso’s artwork.

SLOs:

- Recognise how shape is an important feature of Picasso’s artworks.

__Activity 1__

Have several students share with the class their art stories from Session 1, Activity 3.

Acknowledge students as artists.

__Activity 2__

Explain that you have a true story to tell about another artist. Read Attachment 1: Picasso. (Omit the quote in the box).

Ask students what they found most interesting in the story.

Record their ideas on the class chart, summarising their learning about Picasso.

__Activity 3__

Write on the class chart: **“Art is a lie that makes us realise the truth.”** Explain this is something Picasso said. Have students discuss what he might mean by this.

Elicit ideas: for example, art does not always show us how things really are (“they lie”) but we recognise this by comparing art with how things are ("the truth").’

__Activity 4__

- Locate around the classroom, several individual small copies of each Picasso’s pictures from Attachment 2, enough for each student to have a picture of their own choice.

Explain what you have done.

- Have students silently complete an ‘art-walk’ once around the ‘gallery of artworks’. Have them make a second rotation, this time choosing and taking an artwork of their choice and returning to their place.

- Make available paper, pencils and glue sticks.

Have students glue their chosen picture onto their paper, leaving sufficient space to write about it.

Remind the students that in Session 1 they wrote about their own artworks.

Explain that each student is to write about the Picasso picture they have chosen.

Their writing should:
- explain their feelings about the picture
- explain how they think Picasso made the picture
- include a short story about why the picture might be important to Picasso.

Clarify the task with the students, list on the class chart any special words that they might need and set a time limit.

- Extend the task for those who finish quickly, by having them explain how their picture fits with Picasso’s statement in Step 3 above.

__Activity 5__

- When the task is complete, have students who chose the same picture, form a group. Have the students share their responses in their groups, comparing their ideas.

- Ask, “Who wrote something about “shapes” in their writing?”

Have several students take turns to talk about the way Picasso uses shapes in his pictures, including identifying the features of those shapes. For example: In *Picture 1*, triangles with lots of corners (angles) have been used.

__Activity 6__

Conclude the session by having several students share their writing about Picasso’s artwork.

**Session 3 and 4**

This session is about exploring the features of a three-dimensional shape, recognising that it is comprised of plane shapes, and representing 3D shapes in an artwork.

SLOs:

- Understand and describe the features of a cube.
- Create an artwork, developing a practical understanding of the relationship between 2D and 3D shapes.

__Activity 1__

Begin by having several more students read their Picasso artwork stories.

__Activity 2__

- Make paper and pencils available.

Have students form pairs with their Picasso artworks. Partners should have different pictures.

Write on the class chart the headings: *Colour Shape Other*

Have students write these headings on one shared piece of paper. Set a time limit.

Have students look at both Picasso pictures and record on the chart under the three headings *the things they notice about both art works*.

- Have student partners share their findings with another pair.

Discuss as a class, highlighting (in most instances) the narrow range of colours, light/dark contrasts, different angles of geometric shapes.

__Activity 3__

- Show the class a wooden cube.

On the class chart, write *cube* and list its features, including the number of faces, edges and vertices. Highlight that we can view a cube from different angles.

- Write
*cubism* on the class chart. Explain that it is a name for an art style that Picasso is famous for. Have students suggest what this might be and record their ideas/definitions on the class chart.

If required, complement the student’s ideas with these points:

Cubism:
- uses simple geometric shapes
- shows things from different viewpoints in any one artwork
- sometimes breaks up (or fragments) 3D shapes into parts
- shows the plane (2D) shapes that make up 3D shapes.

Talk about each of these, having students find and discuss examples in their artworks in front of them.

__Activity 4__

- Explain that the students will make their own
*cubist* artwork about one thing that is important to themselves. Refer to Picasso’s use of music/musical instruments or parts of these.

Make available at least one copy of Attachment 3 per student, scissors, glue, A4 paper, pencils, crayons/pastels.

Explain that their completed artwork should:
- Include parts of something that are important to them personally
- Fill the A4 page
- Use the shapes or parts of shapes from Attachment 3
- Show the shapes connected or touching in some way
- Include lines they have drawn
- Include their own (limited) choice of colour in empty spaces.

- Model the beginning of this process.

Cut out one cube shape from Attachment 3. Discuss this with reference to the wooden cube, highlighting that this is a way of capturing a 3D shape in art.

Cut the cube (or cuboid) picture into its component parts.

Recognise and discuss the **squares (and rectangles)** that result. These are the 2D shapes that make up the 3D shape.

Look at the **parallelogram** shapes. Discuss that this is what happens to the square and rectangular faces when they are shown in 2 dimensions.

- Show the developing process.

For example: a plant (leaf) may be something important to the artist.

This can be cut and arranged alongside some shapes to produce the artwork.

- Refer to the features noted in the headings: colour, shape and other, in Activity 2, Step 1 above. Are these Picasso style features reflected here?

- Refer to the cubism features list in Activity 3, Step 2 above. Are these features evident here?

- Identify next steps to complete the artwork. (Fill the page, include more cube shapes of parts of these, fill in any white paper spaces remaining with appropriate colours.)

__Activity 5__

Have students begin their artworks. Have them stop and review progress throughout, reflecting on their own work and giving feedback to others.

__Activity 6__

Finish artworks with a title.

**Session 5**

This session is about reflecting upon and consolidating the key learning about 2D and 3D shapes and about one artist.

SLOs:

- Identify and articulate key learning about geometric shapes.

__Activity 1__

Have students display on desks, their cubism art with titles. Explain that the students will undertake a slow and silent art-walk in which they are to notice works they particularly like. They should look closely at these and decide what it is that makes them appealing to them personally.

__Activity 2__

Have several students share their ideas and feedback on the artwork they have noticed, explaining what they like about it. Have them refer to the artwork criteria.

__Activity 3__

Make available poster paper large enough to accommodate the student artworks from Session 1 and Session 4, Activity 5.

Have each student place (and glue) both artworks onto the poster paper, leaving sufficient space to attach a reflective comment.

__Activity 4__

On writing paper, have students:

a. Write which of their own artworks they prefer, writing at least three reasons for their preference.

b. Explain what they have learned about geometric shapes through their exploration of Picasso’s art and of cubism.

c. Attach their reflections to their poster paper beneath their artworks.

__Activity 5__

- Have student share and display their reflections. Discuss.

- Reflect on Picasso’s statement:
**“Art is a lie that makes us realise the truth.”**

Recognise that the artworks do not show things as they are, but they helped us to see some things that are true.

On the class chart list the ‘true’ things (truth) that students have learned about art and about mathematics (geometry).

__Activity 6__

Conclude the session by sharing some of your own favourite Picasso artworks. Discuss the fact that shape is a feature of much of his work.

## Mathematical magic

This unit provides you with a range of opportunities to assess the entry level of achievement of your students.

This unit can be differentiated by altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

Some of the activities in this unit can be adapted to use contexts and materials that are familiar to students. For example:

## Prior Experience

It is expected that students will present a range of prior experience of working with numbers, geometric shapes, measurement, and data. Students are expected to be able to use simple addition and subtraction in situations where sets are joined, separated, and compared.

## Session One

Talk to your students about the purpose of the unit which is to find out some information about them, so you can help them with their mathematics. In the first session students explore a ‘magic trick’ about dice and extend what they find to develop their own magic trick. Look for your students to generalise, that is, explain why the method works every time.

Dice FacesCard Sums(Acknowledgement to Jill Brown, ACU Melbourne, for the idea)In this example below only 5 is odd so the total is 20 + 1 = 21.

Note that students may find variations on a general rule:

The highest sum possible is 25, if all the odd numbers show up. Each time an odd card is turned over one is lost from the sum. The even number is always one less than the odd number. If you see how many even numbers there are you take that number from 25. For example, below there are three even cards, 0, 2, and 8, so the sum is 25 – 3 = 22.

Possible extension:

Suppose you wanted to make the trick look even more impressive by making 10 cards; 0-1, 2-3, 4-5, …,16-17, 18-19.

How could you work out the total without adding all the numbers then?## Session Two

In this session the theme of mathematical magic is continued as students look for patterns in the place value structure of 100. Begin with a Slavonic Abacus and a Hundreds Board.

Slavonic abacusDoes the student use the tens and ones structure of the abacus or attempt to count in ones?

How many beads are on the whole abacus? How do you know?If 45 beads are on the left side, how many beads are on the right side?You might revisit the fact that five tens are fifty. Fifty mean five-ty or five tens.

Do you know the nursery rhyme about Bo Peep?Read or play a YouTube clip of the Rhyme to your students if needed.

(Student A), please move some of my sheep to the left side and cover up the rest so I cannot see them (using an A4 sheet of paper).Can you work out how Bo Peep did it. How could she know 72 sheep were missing so quickly?Crosses PatternIn this task students apply place value to explain why a pattern on the hundreds board works every time.

2 + 22 = 24 (top and bottom numbers) and 11 + 13 = 24 (left and right numbers).

Possible extension:

Any square on the hundreds board is magic. The numbers along each axis have the same sum. Why?

Below 12 + 23 + 34 = 69, 13 + 23 + 33 = 69, 14 + 23 + 32 = 69, 22 + 23 + 24 = 69.

Hopefully more able students can see that this works for the same reason that the crosses pattern works. The for each line, the sum is three times the centre number, with one of the end numbers the same amount more than that number as the the other is less.

Other units that will support the development of Place Value at level 2 include:

## Session Three

In this session students explore simple two-dimensional dissections in which a shape is cut up into smaller pieces and those pieces are put together to form a different shape. They will need square shaped pieces of paper or card.

Magicians can change objects in to different shapes. We are going to see if you can be a magician.There are four challenges for you to start. You need to use all the pieces of the square and change it into each of these shapes.Copymaster 1 contains the target shapes. Either provide students copies of the Copymaster or display it on screen. Ask the students to work out how to form each shape using all the pieces from the square. Look for your students to:

Copymaster 2 has some target shapes that can be made by connecting all four pieces. Challenge your students to make each target, record the solution, and make up their own target for someone else in the class. Be aware of the need to check for uniqueness. Is the target really the same as another? This brings in ideas about reflection and rotation.

Can you use these four pieces to create a hexagon?## Session Four

In this session students consider the likelihood of magic happening. Students will consider whether the trick is really magic or if something else is involved.

I am closing my eyes now and you can move the cups around while I cannot see. Then I will guess which cup the treat is under.Am I magic or is something else going on?Their beliefs might be deterministic: "You are a teacher, so you are clever."

Some beliefs might acknowledge chance: "There are only two cups. You have a good chance of being right each time."

A student might spot that the cups are marked. If not reveal the trick to them.

What would happen if the cups were not marked?Am I magical or is it just luck?Magicians like to disguise their tricks so the two cups might be a bit simple. Let’s try the same idea but have three cups and one treat. Can you figure out a way to get a treat each time?Being magical in this situation seems bit hard. Let’s keep the three cups but add another treat.S: I always choose the position where a treat didn’t go at first.

T: Did that always work? Did anyone else try that idea? What happened? Why do you think that happened?

Other students might always choose a position where a treat was first located, or randomly select a position.

Extend the activity:

You might extend the task by varying the number of cups and treats, e.g. four cups and one, two, or three treats.

## Session Five

In this session students look for repeating patterns and connect elements in the pattern with ordinal numbers.

Mathematical magicians can think ahead. They can predict the future. Can you?Provide students with a range of materials to form sequential patterns with. The items might include bottletops, corks, blocks, toy plastic animals, pens and pencils, geometric shapes, etc. Give them a copy of the strip that can be made from Copymaster 3 after it is enlarged onto A3 size (x 1.41).

Let students create their own patterns. Look for students to:

^{th}object.Take digital photographs of the patterns to create a book, and ask students to pose problems about their patterns. Students can record the answers to their problem on the back of the page.

Discuss as a class how to predict further members of a pattern. Strategies might include:

Extend the activity:

There are many ways to increase the difficulty of repeating pattern prediction:

Dear parents and caregivers,

For the first week of school our mathematics unit is about mathematical magic. We will investigate number tricks, magical change a square into other shapes, predict the future of a pattern, explain and justify why things work.

## Pirate plays

In this unit we explore the size of a metre and develop our own ways to estimate a metre length.

When students can measure lengths effectively using non-standard units, they are ready to move to the use of standard units. The motivation for moving to this stage, often follows from experiences where the students have used different non-standard units for the same length. They can then appreciate that consistency in the units used would allow for the easier and more accurate communication of length measures.

Students measurement experiences must enable them to:

The usual sequence used in primary school is to introduce the centimetre first, then the metre, followed later by the kilometre and the millimetre.

The centimetre is often introduced first because it is small enough to measure common objects. The size of the centimetre unit can be established by constructing it, for example by cutting 1-centimetre pieces of paper or straws. Most primary classrooms also have a supply of 1-cm cubes that can be used to measure objects. An appreciation of the size of the unit can be built up through lots of experience in measuring everyday objects. The students should be encouraged to develop their own reference for a centimetre, for example, a fingertip.

As the students become familiar with the size of the centimetre they should be given many opportunities to estimate before measuring. After using centimetre units to measure objects the students can be introduced to the centimetre ruler. It is a good idea to let the students develop their own ruler to begin with. For example, some classrooms have linked cubes which can be joined to form 10 cm rulers. Alternatively pieces of drinking straw could be threaded together.

The correct use of a ruler to measure objects requires specific instruction. The correct alignment of the zero on the ruler with one end of the object needs to be clarified.

Metres and millimetres are established using a similar sequence of experiences: first construct the unit and then use it to measure appropriate objects.

This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

The context for this unit can be adapted to recognise diversity and student interests to encourage engagement. For example, the unit could be focused around the voyage from Hawaiki to Aotearoa with activities including measurements for a new waka, and challenges between rival navigators.

## Session one

Begin the session by acting out the following scene with the students.

Characters:

Captain Blood - teacher

Crew / cabin boys and girls - students

Props:

Treasure - a small box

Crooked palm tree - desk

Captain Blood, the pirate decided to bury his treasure.

He started from the crooked palm tree and carefully counted 12 steps, (heel, toe) and then stopped and placed the treasure on the ground.

To make sure that he remembered where he left it he wrote down on his map 12 steps.

He wanted to make really sure that he had measured correctly before digging the hole so he asked a cabin boy or girl to check.

Captain Blood was puzzled how could the cabin boy/girl have a different number of steps.

Had he made a mistake?

Can you think of a measure that Captain Blood could use that is the same for everyone?If the students come up with the suggestion of a metre, ask:

How long is it?

When and where is used as a measurement?When students are measuring encourage them to measure height, depth, width and girth.

could be introduced as a means of recording. Suggestions on how to record incomplete metres could also be discussed.m## Session two

Discuss with the students the type of boats that pirates sailed in.

Provide them with chalk and a metre measure and take them outside to draw the boat to Captain Blood’s requirements.

The students might like to add extras like flags, anchor ropes, and cannons and add them to the measurement list. Encourage students to estimate before drawing.

A metre is as high as …………….(my ribs).

How wide is a metre? A metre is from my fingertips to ……………

## Session three

Do they use the measuring unit consistently without gaps or overlapping?The students can show their results by pasting their outlines on to paper and recording the number beside it.

To finish pose this problem for the crew,

Captain Blood has gone to a boat shop to buy some new canvas for sails. He wants two metres. Can you show me using a body measurement how long two metres would be?## Session four

Talk about where you begin measuring from. (Students can have difficulties identifying the starting points on calibrated rulers. They start from the edge rather than the markings.)

How many centimetre cubes might fit along the metre?If 1cm cubes that connect are available join 100 using two different colours to distinguish the decades. Place the line of cubes on top of the metre ruler and count in tens to 100.

Glue their discoveries to cardboard and display the one-metre patterns.

Discuss that different patterns look as though they have different lengths.

## Session five

Captain Blood has decided to have a sports day for the pirate crew. The events for the day are:

Family and whānau,

We have been busy this week doing lots of measuring using metres. We have found out how many of our handspans equal a metre so that we can estimate lengths. We have also used our metre measuring strings to measure distances around the classroom.

Measuring StringsUse your measuring strings to measure these distances in metres:

If you walked 10 metres from your letterbox where could you end up? Draw a map showing this.

## Figure It Out Links

Some links from the Figure It Out series which you may find useful are:

## Picasso

This unit uses the context of Picasso's art to explore two and three-dimensional shapes, to recognise their features, and to develop in the students appropriate language to discuss Picasso's and their own artworks.

In level one, students have been learning to name some common shapes, becoming familiar with their features. As students are given opportunities, they find their own systems for sorting shapes, justifying their categories and developing the important geometric language of attributes.

Initially, students come to understand two-dimensional shapes as flat or plane shapes that have two dimensions. They have length and width but no depth, and therefore, technically, cannot be ‘held’. As they work with three-dimensional shapes, they come to understand the way in which two-dimensional plane shapes build three-dimensional shapes. Students need to have a clear understanding of the meaning and concept of ‘dimensions’ and should be able to explain in their own words what the abbreviations 2D and 3D mean. The change in language from ‘sides and corners’ for two-dimensional shapes, to ‘faces, edges and vertex/vertices’ is not an insignificant one. The language itself conveys the shape category and should be emphasised and well understood.

As students work with physical shapes they have opportunities to come to understand their defining characteristics. Having them talk about and explain these within a particular learning context, consolidates conceptual understanding. The representation of three-dimensional shapes in the two-dimensional medium that a painted artwork is, creates its own challenge and interest. It should involve deconstructing 3D shapes, recognising that they are comprised of 2D plane shapes. This is a key understanding to be developed at this level.

In levels 3 and 4 students are challenged to explore and represent objects from different viewpoints and perspectives. The work in this unit of work is a useful precursor to developing these concepts.

Picasso’s art provides a useful context for the exploration of two and three dimensions as well as developing recognition in the students of the importance of shape as fundamental structure of art itself.

Associated Achievement ObjectivesArt

Visual ArtsThis unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

The contexts in this unit can be adapted to recognise cultural diversity and encourage engagement. For example, in addition to the works of Picasso students could respond to cubist works from New Zealand artists. Charles Tole, John Weeks, and Colin McCahon all include elements of cubism in some of their work.

Learning activitiesWhilst this unit is presented as sequence of five sessions, more sessions than this may be required. It is also expected that any session may extend beyond one teaching period.

Session 1This session is about naming and describing plane shapes, and using these to create a picture. Note: By drawing around the shape the students are creating a two-dimensional shape. Limit the colour selection, as this is relevant to the work in a later lesson.

SLOs:

Activity 1Make attribute blocks available to small groups of students.

Begin by having individual students sort a selection of the attribute blocks into groups, and explain to a partner the groupings they have made. Have them repeat the sorting task, this time categorising them differently.

Encourage and affirm appropriate geometric language, including the correct use of shape names and descriptions of their features.

Activity 2As a class, brainstorm and record on the class chart, all shape and attribute language associated with the task in Activity 1.

Activity 3Make paper, pencils, and pastels or crayons available,

but limit the colour selection.Challenge the students to make a picture of aperson, object or placethat is important to them. Explain that they are to make their picture using the shape blocks to help them.Demonstrate to the students how to begin the picture by drawing around several shapes and then colouring in the outline. For example:

Explain why your picture is important to you. (For example: ‘My Dad used to drive an old blue car a bit like this one.’)

Activity 4Have students make and complete their own pictures. When pictures are complete, have each student name their picture, write a short story about it, using words from the brainstorm list in Activity 3. Their story should explain why the subject of the picture is important to them and how they made their picture.

Activity 5Refer to the example picture made in Activity 3 above and to the artworks they have just completed.

Ask:

“Are the shapes two-dimensional shapes or three-dimensional shapes?”Discuss ideas.Write the word

‘dimension’ and 2Dbelow the picture.Ask for students to discuss in pairs the meaning of what has been written.

Through discussion, develop understanding of the meaning of the word ‘dimension’, of two dimensions and of the abbreviation, 2D.

Highlight the shapes that they have drawn are like (foot) prints only. They are

wide and long,Have students explain that two-dimensional shapes have no depth or thickness.but not deep.Activity 6Discuss, conclude and record that the attributes blocks are 3D shapes because they have width, length, and thickness (depth), and we can feel these. Recognise that the attribute block shapes have different thickness or depth.

on the class chart. Have students locate and identify each feature on several of the attributes shapes. Write the plurals of each work beside the singular, highlighting the wordface, edge and vertex. Make the connection between the 2D language of sides and corners, and the 3D terms edges and vertices.verticesActivity 7Have students partner share their art works and stories. Conclude by writing on the class chart,

‘We usedtwo-dimensional shapesto make our artworks today.’Session 2This session is about choosing and responding to a piece of Picasso’s artwork.

SLOs:

Activity 1Have several students share with the class their art stories from Session 1, Activity 3.

Acknowledge students as artists.

Activity 2Explain that you have a true story to tell about another artist. Read Attachment 1: Picasso. (Omit the quote in the box).

Ask students what they found most interesting in the story.

Record their ideas on the class chart, summarising their learning about Picasso.

Activity 3Write on the class chart:

“Art is a lie that makes us realise the truth.”Explain this is something Picasso said. Have students discuss what he might mean by this.Elicit ideas: for example, art does not always show us how things really are (“they lie”) but we recognise this by comparing art with how things are ("the truth").’

Activity 4Explain what you have done.

Have students glue their chosen picture onto their paper, leaving sufficient space to write about it.

Remind the students that in Session 1 they wrote about their own artworks.

Explain that each student is to write about the Picasso picture they have chosen.

Their writing should:

Activity 5Have several students take turns to talk about the way Picasso uses shapes in his pictures, including identifying the features of those shapes. For example: In

Picture 1, triangles with lots of corners (angles) have been used.Activity 6Conclude the session by having several students share their writing about Picasso’s artwork.

Session 3 and 4This session is about exploring the features of a three-dimensional shape, recognising that it is comprised of plane shapes, and representing 3D shapes in an artwork.

SLOs:

Activity 1Begin by having several more students read their Picasso artwork stories.

Activity 2Have students form pairs with their Picasso artworks. Partners should have different pictures.

Write on the class chart the headings:

Colour Shape OtherHave students write these headings on one shared piece of paper. Set a time limit.

Have students look at both Picasso pictures and record on the chart under the three headings

the things they notice about both art works.Discuss as a class, highlighting (in most instances) the narrow range of colours, light/dark contrasts, different angles of geometric shapes.

Activity 3On the class chart, write

and list its features, including the number of faces, edges and vertices. Highlight that we can view a cube from different angles.cubeon the class chart. Explain that it is a name for an art style that Picasso is famous for. Have students suggest what this might be and record their ideas/definitions on the class chart.cubismIf required, complement the student’s ideas with these points:

Cubism:

Activity 4cubistartwork about one thing that is important to themselves. Refer to Picasso’s use of music/musical instruments or parts of these.Make available at least one copy of Attachment 3 per student, scissors, glue, A4 paper, pencils, crayons/pastels.

Explain that their completed artwork should:

Cut out one cube shape from Attachment 3. Discuss this with reference to the wooden cube, highlighting that this is a way of capturing a 3D shape in art.

Cut the cube (or cuboid) picture into its component parts.

Recognise and discuss the

squares (and rectangles)that result. These are the 2D shapes that make up the 3D shape.Look at the

parallelogramshapes. Discuss that this is what happens to the square and rectangular faces when they are shown in 2 dimensions.For example: a plant (leaf) may be something important to the artist.

This can be cut and arranged alongside some shapes to produce the artwork.

Activity 5Have students begin their artworks. Have them stop and review progress throughout, reflecting on their own work and giving feedback to others.

Activity 6Finish artworks with a title.

Session 5This session is about reflecting upon and consolidating the key learning about 2D and 3D shapes and about one artist.

SLOs:

Activity 1Have students display on desks, their cubism art with titles. Explain that the students will undertake a slow and silent art-walk in which they are to notice works they particularly like. They should look closely at these and decide what it is that makes them appealing to them personally.

Activity 2Have several students share their ideas and feedback on the artwork they have noticed, explaining what they like about it. Have them refer to the artwork criteria.

Activity 3Make available poster paper large enough to accommodate the student artworks from Session 1 and Session 4, Activity 5.

Have each student place (and glue) both artworks onto the poster paper, leaving sufficient space to attach a reflective comment.

Activity 4On writing paper, have students:

a. Write which of their own artworks they prefer, writing at least three reasons for their preference.

b. Explain what they have learned about geometric shapes through their exploration of Picasso’s art and of cubism.

c. Attach their reflections to their poster paper beneath their artworks.

Activity 5“Art is a lie that makes us realise the truth.”Recognise that the artworks do not show things as they are, but they helped us to see some things that are true.

On the class chart list the ‘true’ things (truth) that students have learned about art and about mathematics (geometry).

Activity 6Conclude the session by sharing some of your own favourite Picasso artworks. Discuss the fact that shape is a feature of much of his work.

Dear family and whānau,

In maths we have been exploring two-dimensional and three-dimensional geometric shapes. We have also been learning about Picasso and cubism, and have made some artworks of our own.

We would really like you to visit our classroom art gallery. You are invited to write your comments and feedback in our art visitors’ book.

We look forward to seeing you.

Thank you.

## Cuisenaire mats

In this unit students use Cuisenaire rods (or other equivalent material that fits together precisely) to make “number mats” that illustrate a variety of numerical patterns and can be visually appealing. They formally record the number relationships in the mat.

It is important for students to know the meaning of the equality sign. Realising that “=” indicates that the two expressions on either side of it are equal is a key step on the road to algebra. These two expressions have the same status - one does not have to be the “answer” of the other.

This very important idea is fundamental to a sound platform on which to proceed to algebra proper at a later level. It is introduced here by way of a geometric technique that links numbers via Cuisenaire rods.

This unit could be repeated at a higher level by assigning a value other than 1 to the white rod.

## Links to Numeracy

This unit provides an opportunity to develop students’ number knowledge in the area of Grouping and Place Value. It also provides a way develop early part-whole thinking in the addition and subtraction domain as it allows students to clearly see the different ways a number can be partitioned.

To develop students knowledge of groupings within 5 and ten focus their attention while they are working with the 5-mat and the 10-mat.

Can you find 2 numbers that join together to make 10 on the 10-mat?Can you find two different numbers?How many different combinations can you find?List the combinations as they are identified. Encourage students to see the relationships between the two addends: as one increases, the other decreases. This may also be illustrated using the Cuisenaire mats:

This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

The context in this unit can be adapted to recognise cultural diversity and student interests to encourage engagement. For example, in place of a Cuisenaire mat students could work with images of a waka ama with a defined number of seats, with coloured shirts to represent number patterns. For example in a 5-waka, there can be 3 red and 2 blue shirts (3 + 2), 4 red and 1 blue shirt (4 + 1), or 3 red, 1 blue and 1 green shirt (3 + 1 + 1).

## Getting Started

Here the concept of a 5-mat is introduced. It is constructed from combinations of Cuisenaire rods that all have the same length as the yellow rod. The 5-mat is a device to help students explore equality of combinations of numbers. It also helps them to see that “=” means “is equal to”.

(When Cuisenaire rods are exactly made in units of 1 cm, some students may also be able to check the length by measuring.)

Draw a clearly labelled diagram on the blackboard, for reference.

4 + 1

2 + 3

1 + 1 + 1 + 1 + 1

or 5 x 1

= 5

= 5

= 5

= 5

Note that it is important to keep the numbers in the order that they appear on the mat: 2 + 3 and 3 + 2 would be different rows of the 5-mat. Note also that there are two relationships shown by the row of 5 whites; one is an addition and one a multiplication.

Explain that the 5-mat also shows other relationships that are true. For example, 1 + 3 + 1 = 4 + 1 and 5 x 1 = 2 + 3 etc. This use of equality may seem strange to students because it does not give an answer on the right hand side. Explain that “=” means “is equal to”.

Students write down relationships from the 5-mat and read out their favourites to the class.

## Exploring

Here the concept of equal is explored further using mats of different sizes.

Did anyone else find something like this?Is 4 + 8 = 8 + 4? Why?

Did anyone else find something like this that did NOT work?Did anyone else find something like this?Is 2 x 6 = 6 x 2? Why?

Did anyone else find something like this that did NOT work?

Rows that show a strong visual pattern may also show interesting number patterns.

Make me a mat that shows that 4 + 7 = 2 + 9.What other equalities can a mat like this show?

Make me a mat that shows that 2 x 5 = 3 + 7.

What other equalities can a mat like this show?

Let the students pursue this aspect of the problem in pairs.

## Reflecting

This section brings together all that the students have discovered so far.

Is it true that 2 x any number = that same number x 2? Why? Why not?

Possible extensionsThe ideas above can be extended for more able students and older students. So this unit could be used with students at Levels 3 or even 4.

? + 1 + 5 = 12; and

? + 1 + 5 = 3 x 4.

Answering this could lead to a statement such as 5 x 3 + 1 = 16.

Use a mat to check whether2 x 5 + 4 = 6 + 1 + 7or5 + 3 x 4 = 7 + 9.Dear parents and whānau,

This week in maths we have been using coloured plastic Cuisenaire rods to make " Cuisenaire mats" which help to show that the equal sign “=” says that the numbers on either side of it are the same. Here is an example of a 12 mat. (The white rod = 1, the red = 2, the green = 3, the pink = 4 and so on.) Each line of colours = 12.

Looking at the green and pink rows, this shows 3 + 3 + 3 + 3 = 4 + 4 + 4. This can be read as 3 + 3 + 3 + 3

is the same as4 + 4 + 4. Talk with your child about what other equations can be written using the 12 mat.## Figure it Out Links

A link from the Figure It Out series which you may find useful is: