Purpose

In this unit students learn to find areas of rectangles, to recognise and describe rotation and reflection in conventional designs, and to apply precise measurement skills and enlargement techniques to create a functional geometric design for a quilt.

Achievement Objectives

Specific Learning Outcomes

- Recognise that patchwork is a functional and creative art form..
- Identify and describe rotation and reflection within simple designs.
- Calculate areas of rectangles.
- Accurately measure to create a pattern template, and cut pieces.
- Calculate the amount of required materials.
- Identify key stages in a design process and make a plan.
- Assemble pieces, giving attention to accuracy and precision.
- Critique and evaluate measurement and transformation elements in a product.
- Describe a design process, including giving the measurements and calculations.

Description of Mathematics

Patchwork quilting provides a rich context for developing the understanding of key and measurement and geometric concepts and skills.

At this level students are refining their ability to accurately use linear scales. As they measure length dimensions in a practical context that demands precision, they refine their understanding of the accuracy that is possible when they use a combination of centimetres and millimetres, and they explore the relationships between the different length units of measure. Students are also given practical opportunities to consolidate their knowledge and understanding of area and to use their multiplicative strategies with whole numbers.

The patchwork-quilting context is one of tessellating shapes. As students work with these, they become aware of angles. The explicit understanding that there are four 90degree angles tessellating at point, is not developed within this series of lessons. However, the opportunity is there to do so, particularly as student reflect upon the mathematics in the quilt making process and critique the success of their handiwork.

The way in which the component shapes within a patchwork square transform is fundamental to their design success. Students come to understand that a rotation is a shape *turned* about a point, that a reflection is achieved when the shape is *flipped* over creating a ‘mirror image’ of the shape, and that a translation is a shape *slid* along a line. Whilst students are required in this unit of work to enlarge a design, the geometric nature of that design is such that the application of a scale factor is not essential to achieving success.

**Associated Achievement Objectives**

Technology*Technological practice*

- Undertake planning to identify the key stages and resources required to develop an outcome. Revisit planning and include reviews of progress and identify implications for subsequent decision-making.

*Technological knowledge*

- Understand the relationship between the materials used and their performance properties in technological properties.

*Nature of Technology*

- Understand how society and environments impact on and are influenced by technology in historical and contemporary contexts and that technological knowledge is validated by successful function.

Required Resource Materials

A cloak for a dreamer, by Aileen Friedman

A patchwork quilt (or photographs of patchwork quilts)

A selection of small pieces of left-over fabric

Quilting batting

Fabric to back each quilt (for example, an old bed sheet)

Thick paper

Rulers

Pencils

Erasers

Scissors

Needles

Sewing pins

Cotton thread

Activity

**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 recognising the rotational design elements in conventional patchwork patterns.

SLOs:

- Recognise that patchwork is a functional and creative art form.
- Understand historical and contemporary contexts for patchwork quilts.
- Identify and describe rotation and reflection within simple designs.
- Calculate areas of rectangles.

__Activity 1__

Begin by placing in front of the students a selection of fabric scraps.

Pose the question: *“What can we do with these left over pieces of fabric?”*

Discuss and record the students’ ideas on the class chart.

Acknowledge all ideas, and explain that the class will be making their own patchwork quilt(s).

__Activity 2__

Read: *A cloak for a dreamer*, by Aileen Friedman.

Write * tessellation* on the class chart. Discuss, highlighting the feature of no gaps.

Guide the discussion from the example of cloaks (in the book) to other uses of patchwork, and to quilts in particular.

__Activity 3__

- Brainstorm and record student knowledge of patchwork quilts.

- Together, research patchwork quilts, recording in particular the social contexts of their origins.

Alternatively, read and discuss Attachment 1, recognising that historically, patchwork quilts were an economically and practical way to use left over fabric pieces. Patchwork quilts are both cultural art forms and functional items. This combination of utility and beauty is the reason that they continue to be popular.

- Display a quilt.

Ask for and record student initial responses to the quilt. Note in particular,*the geometric language of shape and transformation.*

- Write
*‘reflection’*and*‘rotation’*on the class chart.

Together, as a class, identify the reflection and rotation evident in the patchwork panels and precisely describe these transformations.

Record at least one example on the class chart,.*using a diagram and words*

- Make available coloured pencils.

Distribute a copy of Attachment 2 to each student.

Have them write a description of the transformation (using a diagram and words) beside each of the designs, explaining the*transformation*process used to create the design.

In the 6th empty panel have them create their own design, and beside it describe the transformation.

- Have students share and discuss their descriptions with a partner, identifying their favourite design.

- Students should file theis completed work safely for use in Session 2.

__Activity 4__

Explain that in the next session, each person will choose fabric and sew a patchwork square of their favourite design.

Explain:* “Our problem is to decide how big our patchwork square should be?” *

For practical purposes, set quilt size guidelines, such as:

The quilt should: be a square with a side measurement no shorter than 80cm and no longer than 1m 40cm. be 3 patchwork squares x 3 patchwork squares, or 4 x 4.include fabric panels separating each of the squares. |

*NB. It is suggested that each square has side measurements no shorter than 20cm and no longer than 26 cm and should be an even number. Many traditional quilts use 9 inch x 9 inch squares (22.86cm x 22.86cm).A suggested size for the width of the borders between and around squares, is 5cm.*

- Discuss and identify a useful problem-solving strategy. For example, the students could draw a diagram and try different measurements.

- Give the students the remainder of the session to design a solution to the problem.

- Have students use the measurements of the component parts to calculate the area of each patchwork square, and of the whole quilt, including borders.

__Activity 5__

Conclude the session by sharing problem solving strategies and agreeing, as a class on optimum dimensions for the patchwork squares and border strips.

**Session 2**

This session is about selecting a design, fabrics, and understanding the practical skills and process required to create a patchwork square.

SLOs:

- Accurately measure to create a pattern template.
- Calculate the amount of required materials.
- Select appropriate materials for their purpose.
- Accurately measure and cut fabric pieces.

__Activity 1__

Begin by reviewing the dimensions of a patchwork square agreed upon in Session 1, Activity 4 (For example: 20cm x 20cm).

__Activity 2__

* Model* and complete the following:

- Have each student identify their favourite design from Attachment 2, and number each shape within the design.
- Make available to each student a sheet of thick paper at least as large as the identified size of the patchwork square, a pencil and scissors. Have each student enlarge their design to make a practical template pattern that they will use with their fabric.

To make the pattern template, have each student * accurately* draw a square of the identified size (eg. 20cm x 20cm) and enlarge the chosen design from Attachment 2, to the required size. This will involve making quarters, then dividing each of these into triangles or rectangles according to the selected design. Emphasise and model precision in measuring. (Ensure that a teacher example template is created for use in 4, below.)

__Activity 3__

Make calculators available (optional);

- Have each student:
- identify the number of different (coloured) fabrics they will need. (This will be 2 different fabrics for designs A and B, 3 for designs C and D, or 4 for design E.)
- calculate how many square centimetres of fabric of each kind they will need.
- write their calculation beside the design on Attachment 2.

Discuss and model these calculations as required.

- Have students form pairs and check each other’s calculations.

__Activity 4__

Make sewing pins and scissors available.**Now explain that about double the amount they have calculated for each fabric will actually be required.**

Demonstrate the reason for this by doing the following:

- Using the (teacher) template created in 2 above, carefully cut out each component
*paper shape*.

- Pin one shape onto the
*wrong side*of a piece of selected fabric, ensuring that there is anof extra fabric around all sides.*additional 1 cm* - Cut out the fabric shape
**1 cm larger than the paper template shape, on all sides**.

- Leave the pin in the paper shape template. Fold the spare fabric over onto the paper template and pin down each folded over piece on all three sides (a smaller part of the paper template will be visible and this will be edged with 1 cm right side folded over fabric).

- Use a needle and thread. Secure the folded-over edges in place by sewing them down using a rough running stitch. This should pass through three layers: the folded edge of the fabric, the paper template beneath it, and the right side of the fabric beneath that.

It can be helpful to cut off part of the corner fabric to make neater corners.

(When the triangle is turned to the right side, the fabric triangle will be the same size as the paper template with the spare edge pieces tucked underneath, out of sight and stitched in place.)

- Explain that we do this for each piece of the patchwork square design template.

- Explain that when all pieces are prepared in this way, the students will use small neat stitches along the edges to hand sew the pieces together to complete their patchwork square.

Ensure that the process is well modeled and understood.

__Activity 5__

- Have student pairs discuss the fabrics that are available. Have the students identify the fabrics that would
(for example, thick woollen fabrics, netting, fabric with very open weave), and have the students explain their reasons.**not be suited for the purpose**

- Give each student the opportunity to select their fabric, ensuring that they have approximately double the amount double calculated in Activity 4 above, because they are cutting each piece of fabric bigger than the paper template to allow for folded piece and the seams.

- Have students cut their paper templates into pieces.

Have them place their paper template pieces onto theof the appropriate fabric, pinning them on one at a time.**wrong side****Emphasise the need for economy and very careful placement of each template piece on the fabric, allowing for the 1cm extra on all sides and making best use of the available fabric.**

- Have students cut out each of the individual (oversize) fabric pieces, leaving the pinned paper template attached to each as they do so.

__Activity 6__

Conclude the session by having the students store their fabric patches safely for Session 3.

**Sessions 3 and 4**

These sessions are about recording the design process and sewing the fabric patches to complete patchwork squares.

SLOs:

- Identify key stages in a design process and understand a plan.
- Assemble pieces giving attention to accuracy and precision.

__Activity 1__

- Begin this session by listing on the class chart the key stages accomplished so far in the quilt-making process. Discuss and record next steps.

- These should include: sew down the edges of each fabric piece using a running thread, stitch together all of the fabric pieces to complete the patchwork square, remove the running stitch from each piece, remove each paper template piece from the completed patchwork square. When squares are complete, measure and cut border strips.
*Use a sewing machine to stitch together the pieces of the quilt (the squares and border strips), add (a) backing layer(s), edge the quilt neatly, carry out the quilting process itself which stitches together the three layers of the quilt.***Explain that an adult will complete the steps that require the use of a sewing machine.**

- Have students understand that, when their patchwork square is completed, they will use some of the information on the chart to create a flow diagram that explains to another person
*how to make a patchwork square*.

__Activity 2__

Make available needles, cotton thread and scissors.

- Have students pin down onto the paper the edges
*around each separate piece*, and secure these with a hand stitched running thread.

- When students have sewn the edges of all template pieces with running thread, have students lay out all of their prepared pieces to form the patch design.

- Demonstrate how to sew together one edge of two adjacent pieces.

Put right sides together.

Identify which edge is to be joined.

Using*small over-stitching*, sew along the wrong-side edges joining two pieces.*Emphasise the important of using small stitches that will barely show on the right side, and of precision in matching the pieces together, giving particular attention to places where corners meet.* - Have students complete this step, check, and then repeat, systematically joining adjacent pieces to complete their patched piece. Have them take particular care on the corners.

When a student has sewn together all of their pieces to complete their square, have them turn their square over and remove the running thread around each piece, and the paper template pieces, as these are no longer needed.*Provide ample time for patching to be completed successfully and with care.*

__Activity 3__

As some students complete their patches, if appropriate, have them work in pairs to measure and cut strips of border fabric, according to dimensions decided in Session 1, Activity 4, making an allowance of 1cm all round for piecing together.

__Activity 4__

When all student patches are completed, have students lay these out in the quilt design, deciding on the best location of their own square. They should consider the overall aesthetics of the quilt design.

It is recommended that an adult complete the piecing together of the patched squares and border fabric to complete quilt.

**Session 5**

This session is about describing and critiquing the design and production process, and recognising the application of mathematics within patchwork quit design.

SLOs:

- Critique and evaluate measurement and transformation elements in a product.
- Describe a design process, including giving the measurements and calculations.
- Reflect on the mathematics that is involved in making a patchwork quilt.

**Provide sufficient time for students to complete tasks in Session 3 and 4. **

__Activity 1__

Make available paper, pencils, coloured pencils/felt pens.

As students complete their sewing, have them prepare to make an 8 stage flow diagram of the quilting process by folding one piece of paper in half three times to create 8 even sections.

Have them open their folder paper and number each section 1 to 8.

Have them *create a flow diagram* in which key steps are captured with words and diagrams, explaining the process of making ** their own patchwork square**.

__Activity 2__

Write the statement, ** Mathematics and Patchwork go together**, on the class chart.

Have student pairs discuss with each other whether they agree or disagree with the statement and give reasons why.

Set a time limit and have each student record their ideas about patchwork and mathematics, again using words and diagrams.

__Activity 3__

Have students form small groups (four people) and share their flow diagrams.

__Activity 4__

If possible, display the quilt(s).

Discuss the quilting process, which involves stitching together the three layers. Some students may be able to work on this over time, or an adult may complete this/have completed by sewing machine.

Discuss and evaluate the product.

List on the class chart what was done well, and what could be improved.

__Activity 5__

Have student share their statement from Activity 2 above, recognising and discussing the geometry and measurement skills involved in the quilt-making process.

Home Link

Dear Parents and Whānau,

As part of our mathematics learning in geometry and measurement, we have been designing and making patchwork quilts in class. These are on display.

We would like to talk about the mathematics that we have been learning and tell you about how we went about designing and making our quilts.

You are invited to our class at *(time)* on *(date)* for our presentation.

We look forward to seeing you.

Thank you.

Attachments

Quilts_cm1.pdf227.61 KB

Quilts_cm2.pdf194.54 KB