In this unit students develop number, measurement and shape understanding, skills and language, through making and working with play dough.

- Sort shapes by their appearance.
- Justify classifications with explanations that use early geometric language
- Recognise that two-dimensional shapes are flat and have no ‘thickness’.
- Understand how to accurately use non-standard units to measure capacity.
- Recognise that shapes with three dimensions have ‘thickness’ or depth, as well as width and length.
- Independently apply measuring skills using non-standard units of capacity measure.
- Recognise and begin to use the names and symbols of some common fractions.
- Use the principles of non-standard length measurement to divide a length into fractions of equal size.
- Describe the principle of conservation of quantity in their words.
- Explain and draw a technological process that has an outcome, including describing applied measurement and fraction learning.

Key number, measurement and geometry understandings are developed within these lessons that have a technology context.

Students will use whole numbers less than 20 throughout these lessons. They will also make and describe fair shares, learning 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 ofconservation of quantity. This is the ability to understand that something stays the same in quantity even though its appearance changes or, 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: all attribute blocks are three-dimensional, as are paper, and cardboard technically. As they sort and describes shapes, justify and explain their groupings, they are developing important attribute language that is essential to their ongoing work and conceptual understanding in geometry. In having students make, mold and explain their own shapes, they are being given the opportunity to combine their developing understanding of dimension with their growing geometric vocabulary, which will include reference to sides, corners, edges and ‘roundness’ (absence of corners).

In measuring, using non-standard units, students learn key ideas that are fundamental to achieving accuracy, and to measurement that they will undertake in subsequent years, using standard units of measure. As they measure quantities of ingredients, 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. As students work with length, the understanding is being developed that the measurement units must be the same (size) and must not change, that there should be no gaps or overlaps 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.

- 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)
- Perfect Square, by Michael Hill

**Learning activities **

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**

This session is about sorting shapes, including identifying that there is a difference between 2D and 3D shapes, identifying construction materials that could be used to make their own 3D shapes, and considering what will be needed.

SLOs:

- Sort shapes by their appearance.
- Justify classifications with explanations that use early geometric language.
- Recognise that there is a difference 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__

Begin by reading:

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?”*

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.

__Activity 3__

If students have not already done so, pose the task to all children:*‘Make a group flat shapes and another group of shapes that are not flat.’ *

On the class chart draw one of each kind of shape (2D and 3D) and list their features. 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 4__

Make available a selection of washable plastic (3D) shapes.

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 repeat this process with different shapes.

Have them describe their *prints*, where possible naming the shapes that they have used to compose their person and naming the “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 them write a descriptive caption below their shape print.

__Activity 5__

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 6__

Display and read together, a large copy of the recipe (Attachment 1) and tick on the list the items that the children suggested in 5 (above). Discuss additional items that have not been suggested. Have students explain their purpose and describe in pairs the process that they think will be used to make the play dough.

__Activity 7__

- 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’.

- Have students consider and discuss and the nature of the ingredients including what make them stick together to make the dough. 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).

**Session 2**

This session is about developing measurement skills and key understandings as they participate as a class in making play dough.

SLOs:

- Understand how to accurately 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.
- Explain with words and pictures how to accurately measure using non-standard units of measure.

__Activity 1__

- Place in front of the students 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 these questions:*Which cup should we use? Why?*(Elicit an explanation that the same sized cup should be used each time a cup measurement is required).*Which large spoon should we use? Why?*(Elicit an explanation that 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)

__Activity 2__

- Make another batch of dough together to ensure that there is sufficient for all students.

Have individual students measure the ingredients.

Make the warm dough available for students to use.

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,” etc.

- Have students make a shape person as in Session 1, Activity 4, this time in three dimensions. Have them recognise that this person is wide, tall and
*thick or fat*.

__Activity 3__

Together evaluate the success of the play dough product. Refer to the list made in Session 1, Activity 7, Step 1, and together confirm whether the ‘product’ meets the desirable qualities. (For example, does the dough hold its shape?)

__Activity 4__

Make available pencils, erasers, coloured pencils and paper, or alternatively use either the 4-step or 8-step template from Attachment 2.

Have students record the process of making play dough by drawing and writing an important step in each of the boxes, and describe these in brief captions. Explain that their pictures/diagrams should show how to measure the ingredients correctly.

**Session 3**

This session is about student pairs independently making play dough, applying the measurement skills learned in Session 2, sharing the dough into equal parts and understanding the more equal parts there are, the smaller those parts are.

SLOs:

- Independently apply measuring skills using non-standard units of capacity measure.
- Suggest strategies for making fair shares.
- Recognise and begin to use the names and symbols of some common fractions.
- Use the principles of non-standard length measurement to divide a length into fractions of equal size.

__Activity 1__

- Begin by having students share their flow diagrams from Session 2, Activity 4.

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.

__Activity 2__

Make the ingredients and equipment available to student pairs.

Have them together make a batch of dough, supervising the addition of the boiling water.

__Activity 3__

- 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 4__

- 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 modeled, ask the following questions.*Which rods should we use? Why?*

(Elicit an explanation that the rods should be the same size/colour)*How do we place the rods along the length of dough?*

(Elicit an explanation that 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?

(Elicit an explanation that 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 modeled, and make their dough sausage this length.

Model this process, emphasising accuracy, and how to mark and cut the dough into equal parts.

__Activity 5__

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 6__

Go on a fraction walk and look at each other’s fair shares.

As a class talk about and record what they 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**

This session is about applying the measurement and fraction learning from Session 3 and reflecting of geometric shapes.

SLOs:

- Explain with words and pictures how to share a length into equal parts.
- Make and describe three-dimensional shapes.
- Describe the principle of conservation of quantity in their own words.

__Activity 1__

Make available to each student, a photograph taken in Session 3, paper and pencils.

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 there explanation should include measurement and fraction words from the chart.

__Activity 2__

Make available Cuisenaire rods, plastic knives and the class play dough from Session 1.

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.

__Activity 3__

Give time for exploration and review of shape, measurement and fraction skills learned.

__Activity 4__

Have several students explain what they did. Elicit measurement and fraction language, reviewing key learning.

Look at the different geometric/interesting shapes created by one student.

Ask if the same amount of dough is used to make the different shapes.

Through discussion, develop the understanding of conservation: that something stays the same in quantity even though its appearance changes.

__Activity 5__

Using a set of balance scales, as a class investigate the equal mass of two different shapes made with equal portions. Together agree on and record on the class chart, learning from this task.

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**

This session is about having students complete the technology process by designing a label for their packages of play dough, and reviewing learning from Sessions 1–4.

SLO:

- 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 available several labels from different products. 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 possible label content:

For example: a product name, 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.

Highlight the qualities (of the product) listed in Session 1, Activity 6, Step 2.

Agree on the format and content for their labels/packaging information and if appropriate model this.

__Activity 2__

Have students design and complete their ‘label’, then share this with a partner and then with the class.

__Activity 3__

If appropriate, together decide on fair prices for the different sized bags of dough and have students participate in selling their product

__Activity 4__

Review the production process for making and packaging the play dough.

Make copies of Attachment 2 available to each student. Have students draw and write about each stage of the production process.

__Activity 5__

Conclude the session by reviewing key measurement, fraction and geometry learning from these sessions.

Dear Parents and Whānau,

In maths we have made play dough and have made three-dimensional shapes. Please find attached the play dough recipe that we used. Encourage your child to help you make dough at home, and give them an opportunity to explain how to measure the ingredients correctly. Have them enjoy talking about shapes they make. Encourage and praise them when they use simple and appropriate shape and measurement language.