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.
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
Nature of Technology
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
Fabric to back each quilt (for example, an old bed sheet)
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.
This session is about recognising the rotational design elements in conventional patchwork patterns.
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).
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.
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.
Conclude the session by sharing problem solving strategies and agreeing, as a class on optimum dimensions for the patchwork squares and border strips.
This session is about selecting a design, fabrics, and understanding the practical skills and process required to create a patchwork square.
Begin by reviewing the dimensions of a patchwork square agreed upon in Session 1, Activity 4 (For example: 20cm x 20cm).
Model and complete the following:
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.)
Make calculators available (optional);
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:
Ensure that the process is well modeled and understood.
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.
Make available needles, cotton thread and scissors.
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.
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.
This session is about describing and critiquing the design and production process, and recognising the application of mathematics within patchwork quit design.
Provide sufficient time for students to complete tasks in Session 3 and 4.
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.
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.
Have students form small groups (four people) and share their flow diagrams.
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.
Have student share their statement from Activity 2 above, recognising and discussing the geometry and measurement skills involved in the quilt-making process.