Measurement - Area
Outcome: MS3.2
Selects and uses the appropriate unit to calculate area, including the area of squares, rectangles and triangles. /Key Ideas
Select and use the appropriate unit to calculate area.Recognise the need for square kilometres and hectares.
Develop formulae in words for finding area of squares, rectangles and triangles.
WORKING MATHEMATICALLY OUTCOME/S
Questioning
Asks questions that could be explored using mathematics in relation to Stage 3 content.
Applying Strategies
Selects and uses appropriate mental or written strategies, or technology to solve a given problem.Communicating
Uses some mathematical terminology to describe or represent mathematical ideas.
Reasoning
Checks the accuracy of a statement and explains the reasoning used.
Reflecting
Links mathematical ideas and makes connections with existing knowledge and understanding in relation to Stage 3 content.
Knowledge and Skills
Students learn about
· recognising the need for a unit larger than the square metre
· identifying situations where square kilometres are used for measuring area, eg a suburb
· recognising and explaining the need for a more convenient unit than the square kilometre
· measuring an area in hectares eg the local park
· using the abbreviations for square kilometre (km2) and hectare (ha)
· recognising that one hectare is equal to 10 000 square metres
· selecting the appropriate unit to calculate area
· finding the relationship between the length, breadth and area of squares and rectangles
· finding the relationship between the base, perpendicular height and area of triangles
· reading and interpreting scales on maps and simple scale drawings to calculate an area
· finding the surface area of rectangular prisms by using a square centimetre grid overlay or by counting unit squares / Working Mathematically
Students learn to
· apply measurement skills to everyday situations
eg determining the area of the basketball court
(Applying Strategies)
· use the terms ‘length’, ‘breadth’, ‘width’ and ‘depth’ appropriately (Communicating, Reflecting)
· extend mathematical tasks by asking questions
eg ‘If I change the dimensions of a rectangle but keep the perimeter the same, will the area change?’ (Questioning)
· interpret measurements on simple plans (Communicating)
· investigate the areas of rectangles that have the same perimeter (Applying Strategies)
· explain that the area of rectangles can be found by multiplying the length by the breadth
(Communicating, Reasoning)
· explain that the area of squares can be found by squaring the side length (Communicating, Reasoning)
· equate 1 hectare to the area of a square with side 100 m (Reflecting)
LEARNING ACTIVITIES (Area 7)
INTRODUCING THE NEED FOR A LARGESTANDARD UNIT
Discuss with the students units, which would be suitable for measuring large areas. What shape would they be? What size would they be? Why are square units best for measuring area?
Link this activity with the next activity in which a square metre is constructed.
THE SQUARE METRE
In pairs, students use newspaper and glue or tape to construct a square metre. Why do we call it a square metre? (It would be useful for each student to have a representation of a square metre, especially when a group needs to measure a large floor area).
COVERING A SQUARE METRE
How many students fit onto a square metre? Try it with the students sitting down, standing, lying down, etc. Why might there be a variety of results? Repeat the investigations with Year 6 students, adults, kindergarten students, etc.
ESTIMATION
Estimate first and then use the square metre(s) to measure a variety of floor areas. Allow students to consider the problem of covering the whole area where an uncovered portion is less than a square metre. Discuss the problems of overlapping and gaps.
CONSERVATION
Make some extra square metres that can be cut up and made into different shapes such as rectangles. Is this still a square metre? Does it cover the same amount of space? How do we know?
In pairs students change a square metre into another shape.
Decorate it and clearly label it “one square metre”. Display these in the classroom, hallway or library.
DIRECT COMPARISON
Find things that are:
- smaller than a square metre
- larger than a square metre
- equal to (or almost equal to) a square metre.
Students record findings by drawing or listing areas measured on a chart.
LARGE BOXES
About how many square metres of cardboard would it take to make a box for a refrigerator, deep freeze, washing machine, television set, etc? Open out a large cardboard box to determine its surface area. Students and their parents could investigate the surface area of large cartons that would be needed to package some of their household appliances. / LEARNING ACTIVITIES (Area 8)
SURFACE AREAS
Show students a collection of objects, eg a card, a small book, a matchbox, a ticket, a stone and ask
- “How can we measure the total surface area of these objects?”
- “Can square metres be used?”
- “What sort of unit would be best?”
- “Which object will have the most surface area?”
Have the group agree on a unit and use it to measure the surface area of each of the objects. If the students do not agree to use the square centimetre it may be necessary to repeat activities from Area 7. List some objects in the classroom or the school that could be measured in square centimetres. Estimate, then measure them using square centimetres. Use various counting strategies where larger items are measured, eg sheets of paper, book covers. Order the objects in terms of their areas.
BLOBS
Make hand or foot prints using pencils or paints on art paper and measure using 1 cm grid transparency overlays. Students have to practise strategies for dealing with parts of a square centimetre.
Label “blobs” with their area measurements.
TRIANGLES
Cut a square with 4 cm sides from centimetre grid paper. Find and record the area of this square. Draw in the diagonals and cut along them to form four triangles. Re-arrange the four triangles to make a rectangle. Find and record the area of the rectangle. Comment on the results.
WRAPPING AND MEASURING
Students find surface areas of solids, eg tennis balls, stone, matchbox. Possible strategies include the following.
- Wrap the object in one-centimetre grid paper and mark visible squares and colour in pieces of squares. Then flatten grid paper and think of a way to count crosses and group pieces.
- Flatten a box and measure it with a transparent grid.
- Peel an apple or an orange, finding the area of the skin.
CIRCLES
Approximate the area of a circle to the nearest centimetre. Cover it with one-centimetre squares. Cover the edges of the circle by cutting a minimum number of squares into triangles or other shapes. Records the numbers of squares used and then record the approximate area of the circle.
LEARNING ACTIVITIES (Area 9)
MEASURING LARGE AREASHow is it possible to measure very large areas such as a large park, botanical gardens, farms, suburbs, a city block, a beach or the whole of NSW? How could such measurements be expressed?
Students may suggest square kilometres or hectares or explain how large the area of their farm is. Read out advertisements for homes, land or farms that are expressed in hectares. Find information about Australian states and territories, which is expressed, in square kilometres.
HOW BIG IS ONE HECTARE?
Make a pictorial representation of one hectare and ask:
“How many square metres is that?”
“Could we make one hectare with newspaper metre squares?”
“What other shaped rectangles have an area of 1 ha?”
Ask students to name local places of “about one hectare”, eg car park, football field, playground, paddock. Take students to a large flat area, eg paddock, oval. Using cricket stumps or witches’ hats and trundle wheels, mark out 100 m x 100 m, if possible; otherwise try an area of half a hectare, eg 50 m x 100 m.
How many paces does it take to walk one side of the hectare or half hectare? Use a tallying strategy to assist in counting.
REAL LIFE APPLICATIONS
Students contact the local council, inviting a representative to address them on issues, which relate directly to the local land area and the regulations for its use. Large local area maps may be studied in conjunction with such talks in order for students to identify specific areas, which may be referred to. The following topics may be discussed in relation to hectares, square kilometers and area in general:
- population density
- land usage (industrial, commercial, residential)
- planning regulations (open space, recreational areas).
SCHOOL PLANS
A copy of the plans of the school may provide information about the area of the school site. This work could be integrated with Social Studies activities and may provide interesting historical data where measurements are in Imperial Units. /
LEARNING ACTIVITIES (Area 10)
CALCULATING AREASFind the areas of a variety of shapes drawn on grid paper.
Give about five or six examples. Record findings in a table.
What patterns can students see in the findings? Ask students to explain how they arrived at their result. They should verify their result with further examples.
RECTANGLES
Use tiles that are 1 cm2 in area to make three different rectangles that have areas of 24 cm2.
Draw the on grid paper and label both lengths and breadths.
Students tabulate results, including areas and describe the number patterns, which appear. Repeat the activity with other areas and record findings.
BASE 10 AND CALCULATORS
Ask students to find the length and breadth of a desktop, tabletop, floor space, etc, using Base 10 “flats” and “shorts”. Use calculators to check findings about each area.
DRAW AND CALCULATE
Students are asked to draw a number of rectangles on cm grid paper. They are asked to provide specific details about each rectangle, eg length, breadth, area.
MAKING PLANS OF AREAS
Calculate the areas of floors, play areas, basketball courts, etc. If necessary, break areas into rectangular or square parts, to enable easy measurement using trundle wheels, metre squares, metre rules or tape measures. Calculate the area of a region by forming rectangles. Write a number sentence to illustrate the method of calculation. Area = (6x3) + (4x1) cm2
Resources
1 cm grid paper, trundle wheels, calculators, tape measures, metre squares, metre rulers, notepaper, worksheet activities. / Links
Technology / Language
Larger than, smaller than, area, hectare, perimeter, boundary, square metres. “The sports oval is about one hectare but the playground is smaller.” “The size of our property is measured in hectares.” “This atlas lists the areas of the world’s deserts in square kilometres.” The abbreviation for square kilometre is km2, ie seven square kilometres is written as 7 km2. The abbreviation for hectare is ha, ie, seven hectares is written as 7 ha.
Assessment
Ask students to:• state what can be measured in hectares and why these areas would not be measured in square metres.
• draw or find pictures of things whose area is measured in square metres, hectares or square kilometres, eg building sites, national parks, states. Students collect eight such pictures and order them in terms of area. Students give reasons for ordering the pictures in a specific way. This may require them to use an encyclopedia, geographical records or local government data. / Evaluation
• Were school and local libraries used?
• Which audiovisual and print materials were used?