Following a reading of Jeannie Baker’s ‘Belonging’, in this lesson plan, students are given the task of designing a community space with the perimeter of 240 metres. Prior to developing their plans students estimate the sizes of their features by conducting a hands on investigation of their estimates using tools, supporting them to develop a concrete awareness of the size of their areas and a deeper understanding of the size of a metre square Students use Geometer’s Sketchpad to create their designs and must show all measurements including lengths, widths and areas.

• Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)
• Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

Year 6 Measurement and Geometry:

• Convert between common metric units of length, mass and capacity (ACMMG136)

Students have a solid understanding of the attributes of length, perimeter and area and also a clear understanding of the distinction between each. They are familiar with the formal measurement unit of square metres and have hands on experience with estimating, measuring and comparing areas. Students have an understanding of conservation, in that different shapes with the same perimeter may have the same area. Students have also had experience with reading and interpreting a small scale.

Once students are able to measure and record using formal units they should be provided with tasks which investigate the relationships between formal measurement unit. This experience provides the opportunity for students to explore the connections amongst the units of length, perimeter and area, and an opportunity to apply their understandings using a simple formula: Length x Width = Area. This experience also provides an authentic task which requires problem solving skills and integrates learning across the KLAs while also demonstrating how measurements skills are applied in everyday contexts. Geometer’s Sketchpad is used as a tool as it has been found to enhance teaching and learning across all mathematical areas.

During the experience students estimate the sizes of their features before a hands on investigation of their estimates using tools, supporting them to develop a concrete awareness of the size of their areas and a deeper understanding of the size of a metre square. Students are also provided with the perimeter rather than area size so they can continue to explore conservation. Lastly, research shows that measurement and geometry concepts should be introduced and explored in connected ways in order to foster higher levels of thinking. This experience clearly shows the connections between measurement and geometry.

For students to:

• Understand different shapes can have the same perimeter;
• Make reasonable estimates for areas of their designs ie. The barbeque area;
• Choose the most appropriate tool to investigate their estimates;
• Calculate the area of various rectangular and square shapes in their designs using formal units and a basic formula;
• Develop and use a simple scale to calculate areas.

Lesson:

Following a reading of ‘Belonging’ and taking inspiration from concepts in the book, students are given the task of designing a community space. For example, a garden space where families can come and share a barbeque etc. Students are told the area has a perimeter of 240 metres. They will use Geometer’s Sketchpad to investigate the shape of their area and design their chosen features. They are given a scale to use of 1 cm2 = 10 m2. Students must include the measurements for all areas of their designs and may use a calculator to calculate the formula required to produce the varying measurements. Items students could possibly include: playground, sports area, sand pit, community vegetable garden, water feature, toilets, barbeque, grassed picnic area, bike riding track, gardens.

Students begin by estimating the measurements of their designs. On the oval, they are the given the choice of tools (ruler, tape measure and trundle wheel) to test out their estimated measurements to ensure they are reasonable. Students then continue to use the Sketchpad to record their designs including measurements. They record their problem solving strategies for measuring the varying areas. One completed students save their file to a class folder. During reflection time students share their plans on the
IWB and as a group are able to discuss differences and share ideas.

• How come the shape of your area is different to Joe’s? How can they both have the same perimeter? (Problem Solving);
• Why is important to draw your design to scale? (Communicating);  How did you work out the area of the path around the outside of the park? (Problem Solving);
• Is there something else you can think of that has a similar area to your park? (Problem Solving)

The use of Geometer’s Sketchpad provides an interactive and engaging way to enhance learning and student motivation. The use of calculators may also assist in students accuracy and efficient and calculating he area formula. Lastly the IWB provides an  interactive tool to support reflective thinking and promote a community of learners .

Students are given the task to design a park area. They use grid paper to design their spaces and calculate the perimeters and areas using the scale 1 cm = 1 m.

• MA2-9MG: Measures, records, compares and estimates lengths, distances and perimeters in metres, centimetres and millimetres, and measures, compares and records temperatures;
• MA2-10MG: Measures, records, compares and estimates areas using square centimetres and square metres

Assessment:

Through questioning and students ability to share their problem solving strategies and reasoning, as well as mathematical language used; Through observation of student estimations and choices of measuring tool; Analysis of work sample.

Resources:

• ‘Belonging’ by Jeannie Baker
• Rulers, tape measure, trundle wheel
• Access to computers and ipads with Geometer’s Sketchpad Program

 

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