In this unit students develop number, measurement, and shape understandings, skills and language, through making and working with play dough in a technology context.

- Sort shapes by their appearance.
- Justify the classification of shapes using geometric language
- Identify the differences between 2D and 3D shapes.
- Recognise that two-dimensional shapes are flat and have no ‘thickness’.
- Use non-standard units to measure capacity.
- Recognise that shapes with three dimensions have ‘thickness’ or depth, as well as width and length.
- Make and describe three-dimensional shapes.
- Create fair-shares by dividing a length into fractions of equal size.
- Explain how to share a length into equal parts.
- Describe conservation of quantity using familiar vocabulary.
- Use the names and symbols for common fractions.

Several key number understandings are developed through this unit: Students will apply their knowledge of whole numbers to 20 throughout these lessons, they will make and describe fair shares, and will learn to use ‘one third, one quarter and one fifth’ to name the equal parts that they have made. Introducing the students to the fraction symbol, name and word is very important, as students are coming to understand the concept of finding equal parts of one whole. As students work with making equal parts, they begin to understand that the more equal parts one whole is cut into, the smaller each of those parts is.

As students use the same size portions (fractions) of play dough to make different shapes, they encounter the concept of **conservation** of quantity, meaning the understanding that something stays the same in quantity even though its appearance changes. More technically, conservation is the ability to understand that redistributing material does not affect its mass, number or volume.

As student explore two-dimensional and three-dimensional shapes, they need to understand that there are shapes that are flat and without ‘thickness’ (2D) and that these have different properties from shapes that we can hold easily and which are wide, long *and thick* (3D). Note: attribute blocks, paper, and cardboard are all three-dimensional. As they sort and describes shapes, justify and explain their groupings, they develop important attribute language that is essential to their ongoing work and conceptual understanding in geometry. In making, mouldings, and explaining their own shapes, students combine their developing understanding of dimension with their growing geometric vocabulary. This will include reference to sides, corners, edges and ‘roundness’ (absence of corners).

In measuring with non-standard units students learn key ideas that are fundamental to measuring accurately, and to measuring with standard units of measure. Students should understand that the measuring device (spoon or cup) must be full to the top and include no overflows, that the same units are used, that these need to be counted as they are used, and that they should be chosen because they are appropriate for the task. Working with length develops students' understanding of the following:

- measurement units must be the same size
- measurement units must not change
- there should be no gaps or overlaps in the measurement of length units.

#### Cross-curricular links (Technology)

These mathematical ideas are embedded within the practical task of making and sharing play dough, and are explored through the technology process of planning, ‘manufacturing’, and packaging a product.

**Associated Achievement Objectives**

Technological Practice, level 1

- AO 1: Outline a general plan to support the development of an outcome, identifying appropriate steps and resources.
- AO 2: Describe the outcome they are developing and identify the attributes it should have, taking account of the need or opportunity, and the resources available.

Technological Knowledge, level 1

- AO 2: Understand that technological products are made from materials that have performance properties.
- AO 3: Understand that technological systems have inputs, controlled transformations, and outputs.

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:

- adjusting expectations for sophistication of language used and shapes made by individual students
- having students work in pairs or small groups for some activities
- strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
- 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 make them more interesting to your students. For example allowing your students to choose the colour of play dough they make and use. If appropriate you could time this unit with a school fair and students could make and sell their play dough as a stall at the fair.

Te reo Māori kupu such as ine (measure), āhua (shape), and tatau (count) 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 measurement that they use at home.

- A copy of
*Perfect Square*, by Michael Hill (available online) - Copymaster 1, Copymaster 2
- Flat cardboard or paper shapes
- Pattern mosaic blocks (foam and of the same size)
- 3D shapes
- A collection of plastic washable shapes
- Paint
- A sorting box
- A selection of cups and spoons of different sizes
- Flour
- Salt
- Cooking oil
- Cream of tartar
- An electric kettle and water
- Food colouring
- Plastic knives
- Cuisenaire rods
- Small plastic bags of different sizes
- Paper
- Glue
- Coloured pencils/crayons
- Pencils and erasers
- A set of balance scales
- A selection of products with simple clear labels (showing ingredients and suggested use)
- Camera

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

**Session 1**

SLOs:

- Sort shapes by their appearance.
- Justify the classification of shapes using geometric language.
- Identify the differences between 2D and 3D shapes.
- Recognise that two-dimensional shapes are flat and don’t have “thickness”.
- Begin to understand technological practice and describe a desired outcome.

__Activity 1__

- Read the book
*Perfect Square*by Michael Hall. - Discuss and talk about shapes that children know.

__Activity 2__

- Make available to each student a selection of shapes including flat cardboard or paper shapes, pattern mosaic blocks and a selection of 3D shapes (marbles, small balls, dice).

Have them sort their shapes into groups, show a partner, and justify their categories.

As they do so, listen and highlight key attribute language that is used. Say things such as:*Tell me about your groups. What were you thinking when you made your groups?**Can you see these shapes around our classroom or school? Where else have you seen them recently?*

You could provide images of different community buildings and have students identify the shapes, from their collection, that have been used in the building's design.

Record the language on a class chart. For example: round, square, triangle, rectangle, corners, sides, edges, like a box, like a ball etc. - Repeat this several times, challenging the students each time to group them in different ways. Observe and share interesting examples with the class.
- Read together some of the words and phrases recorded on the chart.
- Ask students to make a group of flat shapes and a group of not-flat shapes. Provide time for students to work on this and share their work with a partner.
- As a class, discuss which shapes are 'flat' and which are 'not-flat'. Use a class chart to display (i.e. glue, attach) one of each kind of shape (2D and 3D). Together, list the features of each shape. Develop the understanding that shapes can be flat and without ‘thickness’ (2D) and like a print only. Shapes can also be wide, long
*and thick*(3D) and can be easily held and felt on all sides.

__Activity 3__

- Make a selection of washable plastic (3D) shapes available.
- Have each student make a composite print picture of a person, by dipping the face of a shape into paint and pressing it onto paper, and then repeating this process with different shapes. Model this process for students. You might have them use paper shapes or plastic tiles to experiment, prior to using paint.
- Have students describe their prints and name the shapes that they have used to compose their person. They can name their “flat” person.
- Highlight that the shape person is wide and tall but does not have thickness or fatness. Introduce and explain the term two-dimensional.
- Have students write a descriptive caption below their shape print (this could be done in writing time).

__Activity 4__

- Explain that the class is going to make their own wide, long
*and thick*(3D) shapes. - Have the students suggest what could be used. Guide the conversation to play dough.
- Have children suggest what might be needed to make play dough, including ingredients and utensils. Accept and record all of their suggestions. Read them together.

__Activity 5__

- Display and read a large copy of the recipe (Copymaster 1). Draw attention to any items that were suggested in the discussion prior. Discuss additional items that have not been suggested (e.g.
*why do you think we need to add...?)*. Encourage students to consider the nature of the ingredients (e.g. binding, dry, wet). Discuss that effect of adding the boiling water to flour and salt (they change their consistency). Explain that cream of tartar helps to make the play dough last longer (it is a preservative). - Talk about what the play dough should be like when it is made. List the qualities that the students suggest. For example: ‘not too soft so that when a shape is made it stays in that shape’, ‘not runny’, ‘smooth and not all lumpy’.

**Session 2**

SLOs:

- Use non-standard units to measure capacity.
- Make and describe three-dimensional shapes.
- Recognise that shapes with three dimensions have ‘thickness’ or depth, as well as width and length.

__Activity 1__

- Display the ingredients and equipment for making the play dough, including a selection of cups and spoons of different sizes.
- Display the play dough recipe and read it together again.

Have students check off on the recipe each of the ingredients, and the utensils. - As a class, make the play dough together.

At each step, ask questions to encourage thinking about accurate and purposeful measurement:*Which cup should we use? Why?*(The same sized cup should be used each time a cup measurement is required).*Which large spoon should we use? Why?*(The same large spoon should be used each time a large spoon measurement is required. This also applies to the small spoon.).*Do we fill this (the cup or spoon) to the top? Why?**If we spill some, is this okay? Why? Why not?**Do we need to count as we measure? Why?* - At each step, model situations of
*inappropriate*measurement techniques and have the students critique these.

For example:*Partially fill a cup/spoon*(the concepts of ‘full’ and ‘empty’ must be understood)*Heap the flour/salt so that it extends above the top of the cup*(the concepts of ‘full’ and ‘empty’ must be understood)*Use different sized cups/spoons*(the same unit should be used)*Spill liquid*(there should be no spills or overflows)*Add more cups than required*(units should be counted)

Note: You might need to make another batch of dough. Ensure that there is enough for all students. You could have students make this second batch with less guidance.

Have individual students measure the ingredients.

__Activity 2__

- Have students work with the dough, challenging them to make shapes with corners and shapes without corners.
- Have students describe what they have made and record the language, including the names of shapes (if known), and geometric vocabulary, that includes reference to sides, corners, edges and ‘roundness’. For example,
*“My shape is round like a ball and has no corners,” “This shape is a bit like a dice or a little box and it’s got lots of corners,”*.

- Have students make a shape person, as they did with paint. Emphasise that, this time, their shape will be three-dimensional. Have them recognise that this person is wide, tall and
*thick or fat*.

- Together evaluate the success of the play dough product. Refer to the list of properties students thought the play dough should have (generated at the end of session 1) and, together, confirm whether the ‘product’ meets the desirable qualities. (For example, does the dough hold its shape?)

__Activity 3__

- Make available pencils, erasers, coloured pencils and paper, or use either the 4-step or 8-step template from Copymaster 2.
- Have students record the process of making play dough by constructing a diagram. They should draw and write an important step in each of the boxes. They should describe each step using brief captions. Explain that their pictures/diagrams should show how to measure the ingredients correctly. This could be done as part of an instructional writing unit.

**Session 3**

SLOs:

- Use non-standard units to measure capacity.
- Create fair-shares by dividing a length into fractions of equal size.
- Use the names and symbols of some common fractions.

__Activity 1__

- Begin by having students share the diagrams they generated at the end of session 2. Note any differences or misconceptions and provide time for students to revise these.
- Review the measurement skills learned in Session 2.
- Tell the students that they will now work in pairs to make some dough for other students in the school or for sale at the school fair.

Together, brainstorm what they will need. Guide the conversation to an agreement that, once the dough is made, it will be packaged in small plastic bags for easy distribution.

Agree that bags of three different sizes and prices can be made. - Make the ingredients and equipment available to student pairs.
- Have them together make a batch of dough. Ensure that you supervise the addition of the boiling water.

__Activity 2__

- Make available sets of plastic knives, and a range of small plastic bags.

Pose this problem for the students to discuss and solve.*You can package your dough into 3 bags, 4 bags or 5 bags.**Decide how many bags you will need and how you will make a fair share for each bag.* - Give the students time to explore the problem and reach solutions for sharing the dough equally.
- Have students demonstrate their methods to the class. Record the key fractional language that the students use in their explanations: fair shares, same size, three parts, four parts, five parts, one third, one quarter and one fifth. As appropriate, write the fraction symbols beside the fraction words and correctly read the symbols together.
- Discuss whether the amount in a bag with one fifth will be more or less than the amount in a bag with one third. Develop the understanding that the more parts the dough is cut into the smaller the parts will be. ie: the greater number of bags they are sharing between the smaller the amount in each bag.

__Activity 3__

- Make Cuisenaire rods available.

Ask,*Can we use these to help us measure a length of dough and make shares fair?*

Accept suggestions from the students. - Roll a sausage shaped length of dough. Use Cuisenaire rods to measure its length by placing them on or alongside the play dough length.

As this is being modelled, ask the following questions.*Which rods should we use? Why?*(The rods should be the same size/colour)*How do we place the rods along the length of dough? (*There should be no gaps or overlaps)*Where do I begin to measure? Why?**Where does my measurement end? Why?**Do we need to count as we measure? Why?*(We need to know how many rods/units long it is)

At each step model situations of*inappropriate*measurement techniques and have the students critique these.

For example:*Use different colour rods*(the concept of the same unit must be emphasised)*Leave gaps between the rods*(the concept of no gaps and no overlaps must be emphasised)*Have rods sticking over the ends of the dough length*(the understanding of where to begin measuring and where to end, should be emphasised). - Explain that because they are making fair shares they should first choose the number of same colour rods they need (3, 4 or 5), put them end to end, as has just been modelled, and make their dough sausage this length. Model this process, emphasising accuracy, and how to mark and cut the dough into equal parts.
- Have students select the rods they will use and complete the measurement and fair shares task. They should then place the fair shares in the plastic bags. Have them display their bags.
**Take photographs of this process.**

__Activity 4__

- Go on a fraction walk and look at each other’s fair shares.
- As a class, discuss and record what students notice. Review key fraction ideas developed in the lesson. For example, ‘fractions are fair shares or parts the same size, three equal parts are called thirds’, etc.
- Review how to correctly measure length, ensuring that the units, and thus the fractional parts, are the same size. For example, ‘the same size rods should be laid end to end alongside the dough, with no gaps or overlaps’.

**Session 4**

__Activity 1__

- Make a photograph taken in Session 3, paper, and pencils available to each student (or pairs of students).
- Review the fraction and measurement language and key ideas from Session 3.
- Have students write an explanation of what they are doing in the photograph. Emphasise that their explanation should include measurement and fraction words from the chart.

__Activity 2__

- Make Cuisenaire rods, plastic knives and the class play dough from Session 1 available.
- Have each student divide their own portion of dough into at least 5 equal parts. With each part they are to model an interesting (geometric) shape and describe each of these to a friend.
- Have students share their work with a partner. They should identify what shapes have been used, explain how they made the shape, and should compare their shape with a partner.
- Choose a few students to share with the class. Encourage students to explain what they did, in detail, and with the use of measurement and fraction language. Through discussion, develop understanding of
**conservation**: something stays the same in quantity even though its appearance changes.

__Activity 3__

- As a class, use a set of balance scales, and investigate the equal mass of two different shapes made with equal portions. Record the mass of the different shapes, and any statements from students, on a class chart.

For example,*“when we make different shapes with the same amount of dough, the shape changes but the amount of dough doesn’t.”*

**Session 5**

In this session students complete the technology process by designing a label for their packages of play dough, and reviewing learning from Sessions 1–4. Students will explain and draw a technological process that has an outcome, including describing applied measurement and fraction learning.

__Activity 1__

- Have students display their plastic bags of dough from Session 3. Ask what the bags need if they are to be ‘sold’ to other people. Guide discussion to an agreement that the ‘product for sale’ needs a label.
- Have several labels from different products available. Read these together, and ask students to notice and suggest what should go on the labels/or into the bags with the play dough product. List the different ideas. For example:

- a product name
- a picture of the product
- a list of ingredients
- the weight of the contents
- instructions for use
- the name of the manufacturer
- use-by date
- a barcode.

- Discuss with the students the importance of each of these. Agree on the format and content for their labels/packaging information and if appropriate model this.
- Have students design and complete their ‘label’, then share this with a partner and then with the class.
- If appropriate, together decide on fair prices for the different sized bags of dough and have students participate in selling their product
- Review the production process for making and packaging the play dough.

Make copies of Copymaster 2 available to each student. Have students draw and write about each stage of the production process. - Conclude the session by reviewing key measurement, fraction and geometry learning from these sessions.

Dear families and whānau,

Recently in maths we have made play dough and have used it to make three-dimensional shapes. Please find attached the play dough recipe that we used. Encourage your child to help you make play dough dough at home, and give them an opportunity to explain how to measure the ingredients correctly. Have them show you, and talk about, shapes they can make with the play dough.