Planning tool

Students:

• use examples to explain how to measure area and perimeter of rectangular shapes
• use the area formula to calculate the area of rectangular shapes
• explain how to find the area of a figure that is composed of other shapes
• use reasoning strategies to find the area of rectangular shapes.

Some students may:

• be developing their understanding of the conservation of area. They may experience difficulty understanding that if a shape is cut up and reformed it will still have the same area (e.g. a trapezium can be made into a rectangle). Use paper folding, where students divide and cut a rectangle into two identical triangles to form a parallelogram or an isosceles triangle. Through recognising that the area does not change after the shape has been transformed, students may better understand the principle of conservation of area.
• lack the spatial awareness to break a shape into separate parts, determine the area of each, and then put back together to give total area for the original shape. Developing spatial awareness and an understanding of the properties of shapes will also help students comprehend the relationship between area and perimeter.
• not fully understand area and perimeter. Use a variety of activities to demonstrate the lack of relationship between the one-dimensional perimeter and the two-dimensional area. Students may believe that surfaces with the same area must have the same perimeter, and vice versa. Using grid paper or geoboards will help students identify that these attributes are separate. Students can create different rectangles with an area of 16 cm² then calculate the respective perimeters. This can lead students to make conclusions about their findings as they describe the characteristics of the rectangles.
• confuse formulas for area and perimeter and have difficulty determining which formula to use when measuring both attributes. This can happen if the concepts for area and perimeter are introduced simultaneously or by teaching the abstract formulas too quickly without providing students adequate time to comprehend their meanings. Use targeted teaching strategies to enable students to discover the formula themselves through recording dimensions and area in a table and look for patterns.

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

• We are learning how to measure area using formal units.
• We are learning how to decompose and rearrange shapes to find their areas.

Why are we learning about this?

• Area helps you to quantify physical space. In real life, area measurements can help with working out quantities, for example, how much wallpaper is needed to cover a wall.

What to do

1. Find a large box. Estimate how much wrapping paper you would need to wrap the box. Record your estimation.
2. Cover one face of the box with a sheet of wrapping paper. Mark the around edges of the box on the non-coloured side of the wrapping paper. Work out the area of that face. Record your answer.
3. Repeat the steps above for the remaining five faces of the box.
4. Calculate the total area of the wrapping paper needed to cover the box. Draw a diagram to show all your measurements.

Success criteria

I can:

• find the area of a rectangular shape
• combine areas of a shape when working out the area of a box
• estimate and work out how much wrapping paper is required to cover a box.