Planning tool

Students:

• use a formula to find the perimeter and area of a quadrilateral
• solve problems involving the perimeter and area of a plane shape
• recognise and distinguish between the different quadrilaterals in various orientations
• dissect composite shapes into familiar shapes so they can calculate the area
• solve problems involving the perimeter and area of composite shapes.

Students may:

• confuse the length of a side with a diagonal.
• confuse area and perimeter.
• not use the correct units of measurement. Clarify the units of measurement between area and perimeter. When modelling area and perimeter problems, make the correct use of units explicit.
• believe that only regular shapes have a perimeter and area. Giving students opportunities to estimate and find perimeters and areas (using square centimetre paper) of irregular shapes is important to support student understanding.
• confuse the different quadrilaterals. Use concrete pattern blocks and have students rotate, reflect and compare these to deepen their understanding of the properties of the different shapes and to assist in their recognition.
• believe that length × width will find the area of any shape, not just a rectangle. Use square centimetre paper and have students prove different area formulas will support their understanding that different shapes have different area formulas.
• confuse which height to use when calculating the area of a triangle or parallelogram – using the slanted height rather than the perpendicular height.
• misread m² (and similar units squared), not realising it refers to ‘square metre(s)’.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• I am learning to find the perimeter and area of shapes.
• I will solve area problems using the formula.

Why are we learning about this?

If you can develop a conceptual understanding of perimeter and area rather than simply applying a rule, you will be more successful solving problems in your textbook and, more importantly, in real life. Imagine you work in real estate and a customer asks you the perimeter of a block of land. These are measurements you need to understand, measure and explain.

What to do

1. View the webpage, Can they be equal?
2. Consider the relationship between the area and perimeter of each rectangle and record your answers.
3. Complete the challenge – find rectangles whose area and perimeter are numerically the same.
4. Gather evidence and record in a table to share solutions with the group when we meet next.

Success criteria

• I can use the formulas to find the perimeter and area of shapes.
• I solve practical problems involving the perimeter and area of a plane shape.
• I recognise and distinguish between the different quadrilaterals in various orientations.