Lesson Plan –Area, Perimeter and Volume APP

Mental and Oral StarterUse mini white boards to ask pupils to calculate areas and dimensions of different shapes. Slides 6 – 9.

Main Activity Explain to pupils that they work for a Landscape Gardening Company. Explain that their task is to come up with two designs for a raised flower bed which has an area of 24cm2. Refer to the starter activity as a reminder of how to do this. Give pupils the ‘Client’s Stipulations’ sheet with the additional information about the cost of the wall and the soil. Also provide the step by step instructions to break the task down for students. Students should produce two flower bed designs clearly showing all their working out.

PlenaryAsk pupils to complete the pink APP sheets.

Objectives and Habits of Mind•Level 4 / 5 Produced a scale drawing of a Rectangular Design flowerbed, calculated the perimeter and volume. •Level 6c Produced a scale drawing of a Triangular Design flowerbed, calculated the perimeter and volume. •Level 6b/6 Produced a scale drawing of a Kite or Parallelogram Design flowerbed, calculated the perimeter and volume. •Level 7 Produced a scale drawing of a Circular or Trapezium Design flowerbed, calculated the perimeter and volume.

KeywordsCross Section, Dimension, Length, Width, Height, Prism

Probing QuestionsLevel 4

Find areas by counting squares and part squares of shapes drawn on squared paper.

How do you go about finding the perimeter of a shape?How are the perimeter of a shape and the area of a shape different? How do you remember which is which?

Level 5Find any one of the area, width and

length of a rectangle, given the other two.

Find the area and perimeter of simple compound shapes made from rectangles.

For a given area (e.g. 24cm2) find as many possible rectangles with whole number dimensions as you can? How did you do it?Always true, sometimes or never true? ‘If one rectangle has a larger perimeter than another one, then it will also have a larger area.’

Level 6

Calculate the area of triangle and parallelograms

The area of a triangle is 12cm2. What are the possible lengths of the base and height?Why do you have to multiply the base by the perpendicular height to find the area of a parallelogram? You can use a diagram to explain your answer.What other formulae for the area of 2D shapes do you know? Is there a formula for the area of every 2D shape?

Probing Questions

Level 7

The cross section of a skirting board is the shape of a rectangle, with a quadrant (quarter circle) on the top. The skirting board is 1.5cm thick and 6.5cm high. Lengths totalling 120m are ordered. What volume of wood is contained in the order? 

Talk me through the steps you took when finding the surface area of this right prism.  If you know the height and volume of a right prism, what else do you know? What don’t you know? How many different square-based right prisms have a height of 10 cm and a volume of 160 cm3? Why? What do you need to know to be able the find both the volume and surface area of a cylinder?

RAGFormula, volume, area, perimeter, prism

LO To design a feature flower bed and calculate the cost of the build

21 Apr 2023

Starter Activity

Complete the never heard the word grid

Key Words Never heard before?

Heard of but not sure what it means?

Know what it means and can explain it in contextJot down your ideas here...

Polygon

Length

Width

Height

Perimeter

Area

Formula

Circumference

Pi

8cm

4cm

What’s my Area?

80cm2

What are my dimensions?

6cm

5cm

What’s my Area?What are my dimensions?

30cm2

6cm

5cm

What’s my Area?What are my dimensions?

3cm100cm2

What’s my Area?What are my dimensions?

78.5cm2

4cm

RAGFormula, volume, area, perimeter, prism

LO To design a feature flower bed and calculate the cost of the build

21 Apr 2023

Learning Objectives :-

• To produce a scale drawing • To calculate perimeter, area and volume.• To substitute values into a formula.

You will know that you have achieved this when .....

1.You have produced a scale drawing of your flower bed2.You have calculated the length of the wall3.You have calculated the amount of soil needed to fill the flower bed4.You have calculated the total cost.

•Level 4 / 5 A Rectangular Design

•Level 6c A Triangular Design

•Level 6b/6a A Kite or Parallelogram

•Level 7 A Semi Circle or Trapezium

The Task

You work as part of a landscape gardening company. A client has approached you to design and give a quote for a raised flower bed.They have a few stipulations which you need to follow. In your pairs you need to come up with two designs and give a quote for the cost of materials for each one.

The Client’s Stipulations

• The flower bed must have an area of 24m2, but it can be any shape.

• The raised bed needs to be surrounded by a brick wall.

• It needs to have a depth of 50cm (0.5m) and be filled with soil.

The Client’s Stipulations:• The flower bed must have an area of 24m2.• The raised bed needs to be surrounded by a brick wall.• It needs to have a depth of 50cm (0.5m) and be filled with soil.

What You Need To Do:1. Come up with two designs for the

raised flower bed that are different shapes. Draw a scale diagram of each design with dimensions shown.

2. Calculate the length of wall that will be required to go around the garden.

3. Using the information on your information sheet calculate the cost of the wall.

4. Calculate the volume of your raised flower beds.

5. Give a quote for the cost of soil.6. Present your two designs with final

quotes for each design on a poster that could be presented to the client. They are picky customers and will want to see the calculations made.

It costs £20 per metre for a 50cm high wall.

Soil costs £40 per cubic metre.

24cm2

Extension task. Use one of these flower bed designs

24cm2

24cm2

Today’s Task

Chose a shape for your flower bed which will have an area of 24m2

Draw a scale drawing of your flowerbed, showing all measurements.

Calculate the length of the wall of your flowerbed by finding the perimeter.

Work out the cost of your wall.

Calculate the amount of soil needed by finding the volume of your flowerbed.

Work out the cost of your soil.

Work out the total cost for the wall and the soil.

Do the same for a different shaped flowerbed..

Your will assess each others work on:

• The presentation of their ideas and designs.

• The presentation of their calculations and results.

• The accuracy of their calculations.

Our Rectangle Design

Steps3 & 4 - The WallThe perimeter of my design:

P = 2 x 3 + 2 x 8= 22m

Cost = 20 x 22= £440

Steps 5 & 6 - The SoilThe volume of our garden:V = area x depth

= 24 x 0.5= 12m3

Cost = 12 x 40= £480

AreaA = 3 x 8 = 24m2

Steps 7 - Total Cost

Wall £440Soil £480TOTAL £920

Our first design is a rectangle shaped raised garden. The final cost will be £920.

Steps1 & 2 – The design

level Shape/Space/Measure

8 I understand the difference between formulae for area, perimeter and volume by considering dimensions.

7 I can calculate volumes and surface area of prisms and cylinders.

6 I can find the area of triangles, kites, parallelograms, trapeziums and circles. I can use formulae for the volume of cuboids. I can find the volume and surface area of cuboids.

5 I can find the area of rectangles, squares and triangles using a formula.

4 I understand the difference between area and perimeter and I can find the area and perimeter of shapes by counting squares.

3 I can find the perimeter of a shape by counting squares.

Tips / Hints

My teachers comment ......

My teachers question is ......

My answer is ......

To be a better learner I could................

Less Helpful More Helpful

Work Faster / do more Stay on task.

Be neater Clearly show my working out.

Try the harder ones Put my hand up to ask a question when I don’t understand.

Talk less Make sure that when I am talking to the people on my table, I am talking about the Maths.

Listen more when the teacher is talking. Contribute answers and questions during the explanation part of the lesson.