Area of a Rectangle: a week of ready-to-teach maths
Five days of lessons for Year 6 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus a Cover up game board, area bingo boards with call cards, a mini-check and every answer.
Start here: five minutes to Monday
- Skim the week at a glance on the next page.
- Print the five days. Each day is two A4 sheets: a plan and a worksheet.
- Print a Cover up board for each pair, and cut out the bingo boards and call cards once for the class.
- Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
- Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.
No maths background needed
This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: area counts the unit squares that cover a surface. In a rectangle the squares sit in rows and columns, so the length says how many squares make a row and the width says how many rows there are, and area = length × width. The formula still works when a side is not a whole number, and it runs backwards too: divide the area by one side to find the other.
One day, one lesson
The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.
Words to watch
Area is the surface a shape covers; perimeter is the distance around it. A square centimetre (cm²) is a square 1 cm by 1 cm, and the small raised 2 shows that two lengths were multiplied. A hectare (ha) is a square 100 m by 100 m, used for land. Length and width are just the two sides of a rectangle; the board calls them width and height, and which is which does not change the area.
The week at a glance
One lesson a day for a week. Each day stands on the day before, so run them in order.
| Day | Lesson | Children learn and do | On screen |
|---|---|---|---|
| 1 | Cover with squares | See area as the unit squares that cover a rectangle, count them in rows and columns, and find hidden and half squares | Area is covering with squares; Rows times columns |
| 2 | The formula | Measure real rectangles, use area = length × width, and write areas in square units | Using the formula |
| 3 | Square units | Build a square metre, choose square centimetres, square metres or hectares, and solve covering problems | Choosing square units |
| 4 | Split and add | Find the missing sides of L-shapes, then their areas two ways: split and add, or the whole take away the corner | Splitting a composite shape |
| 5 | Work backwards | Find a missing side from the area and one side, and solve practical problems with turf, tiles and paint | Finding a missing side |
How the week builds
Day 1 covers rectangles with squares and counts them in rows and columns; Day 2 turns that into the formula; Day 3 chooses the square unit; Day 4 splits composite shapes into rectangles; and Day 5 runs the formula backwards to solve practical problems. It builds on the Year 5 work of counting squares and finding perimeters (AC9M5M02) and on converting metric units (AC9M6M01). It leads to the Year 7 areas of triangles and parallelograms (AC9M7M01), each found by relating the shape to a rectangle.
Materials for the week (one trip)
- From the classroom: rulers, metre rulers or tape measures, two dice per pair, coloured pencils, scissors and this pack printed.
- For Day 3: old newspapers, sticky tape and a metre ruler for each group of four, and a few sheets of A4 paper.
- Print once: a Cover up board for each pair, and the bingo boards and call cards for the class.
Words for the word wall
area, surface, unit square, square centimetre (cm²), square metre (m²), hectare (ha), length, width, row, column, formula, composite shape, split, perimeter
Dear families
This week in maths, Year 6 works out why the area of a rectangle is length × width, and uses it to solve practical problems, such as how much turf a lawn needs or how many tiles cover a floor.
Try this at home
- Measure a table, a rug or a bed and work out its area in square centimetres or square metres.
- Count the tiles on a floor or a wall in rows and columns, and find the total without counting each one.
- Look for things priced per square metre, such as carpet, turf or paving, and estimate a cost for one room.
- Pace out a rectangle at the park and estimate its area in square metres.
Areas this week
Fill one row a day. Write something you found the area of, its length and width, and its area.
| Day | What we measured | Length and width | Area |
|---|---|---|---|
| Monday | |||
| Tuesday | |||
| Wednesday | |||
| Thursday | |||
| Friday |
Printed from the free seegongsik Area of a Rectangle teaching pack · seegongsik.com/au/y6/measurement/AC9M6M02/pack
Cover with squares
Area is the amount of surface a shape covers, found by counting the unit squares that fit inside with no gaps and no overlaps. In a rectangle the squares fall into rows and columns, so children can multiply instead of counting one by one, even when most squares are hidden or some are halves.
We are learning to
- explain area as the number of unit squares that cover a shape,
- find the number of squares in a rectangle from its rows and columns,
- count half squares as part of an area.
Success criteria
- I can say why a rectangle 4 squares long and 3 squares wide covers 12 squares.
- I can find the area of a rectangle when only its first row and column are drawn.
You need
The worksheet, one per child, and a Cover up board (cut-outs) with two dice for each pair.
Lesson flow (about 50 minutes)
| 10 min | Cover it Show the two pictures (see the box). Children say each count before you press. Ask: “Why must the squares leave no gaps and not overlap?” |
| 25 min | Rows and columns Children count by rows in Part A, then find the hidden squares in Part B. Ask: “Only the top row and the left column are drawn. How do you know how many squares are hiding?” |
| 15 min | Halves, then Cover up Children count the half squares in Part C, then pairs play Cover up (cut-outs). Ask: “Two half squares make one whole. Does length × width still give the right count?” |
Two half-sessions instead? Split after Part A; start Session B with the hidden squares in Part B.
Watch for these ideas
- Counting a corner square twice, or missing one, when counting around the edge.
- Adding the sides (4 + 3) instead of multiplying them.
- Counting a half square as a whole one.
Answers
- Part A: 3 rows of 6 = 18; 5 rows of 4 = 20; 2 rows of 8 = 16 squares.
- Part B: 7 × 4 = 28; 9 × 3 = 27; 6 × 6 = 36 squares.
- Part C: 6 whole squares and 2 halves make 7, and 3.5 × 2 = 7; 16 whole squares and 4 halves make 18, and 4.5 × 4 = 18. Length × width still works.
Cover with squares
A. Count by rows
____ rows of ____ = ____ squares
____ rows of ____ = ____ squares
____ rows of ____ = ____ squares
B. Hidden squares
Only the first row and the first column are drawn. How many squares cover each rectangle?
____ × ____ = ____ squares
____ × ____ = ____ squares
____ × ____ = ____ squares
C. Half squares
The yellow squares are halves. Count the whole squares and the halves, then check with length × width.
Whole squares ____ Halves ____ Area ____
Length × width = 3.5 × 2 = ______
Whole squares ____ Halves ____ Area ____
Length × width = 4.5 × 4 = ______
The formula
Because the squares sit in rows and columns, the area of a rectangle is its length times its width: area = length × width. The squares need not be drawn, since two measured sides are enough, and the answer is in square units because two lengths were multiplied. Children measure real rectangles, use the formula, and find that the longer rectangle is not always the bigger one.
We are learning to
- state the formula for the area of a rectangle and say why it works,
- measure two sides and use the formula,
- write areas in square units.
Success criteria
- I can explain why 8 cm × 5 cm gives 40 cm².
- I can measure a book cover and find its area.
You need
The worksheet, one per child, a ruler each, a tape measure for each pair, and the area bingo boards and call cards.
Lesson flow (about 50 minutes)
| 10 min | Use the formula Show the board (see the box). Children work out each area before you press. Ask: “Why is the answer in square centimetres, not centimetres?” |
| 25 min | Measure and multiply Pairs measure in Part A, then children use the formula in Part B. Ask: “A sheet of A4 is 21 cm by 29.7 cm. What would you round it to, and why?” |
| 15 min | Bigger or not? Children compare in Part C, then the class plays Area bingo (cut-outs). Ask: “The 12 m × 5 m garden is longer. Why does the 8 m × 8 m garden cover more?” |
Two half-sessions instead? Split after Part A; start Session B with the rectangles in Part B.
Watch for these ideas
- Writing an area in cm instead of cm².
- Adding the sides, or finding the perimeter, when the question asks for the area.
- Thinking the longer rectangle must have the larger area.
Answers
- Part A: measurements vary. An A4 sheet is about 21 × 30 = 630 cm² (623.7 cm² exactly).
- Part B: 54 cm², 96 m², 60 cm², 10 m², 500 m², 49 cm².
- Part C, the one that covers more: 8 m × 8 m (64 m² beats 60 m²); 7 cm × 9 cm (63 cm² beats 60 cm²); 4 m × 4 m (16 m² beats 15 m²); the same (30 cm² each).
The formula
Area of a rectangle = length × width. Write the answer in square units: cm² or m².
A. Measure and multiply
| Thing | Length | Width | Area |
|---|---|---|---|
| your exercise book cover | ________ cm | ________ cm | ________ cm² |
| a sticky note | ________ cm | ________ cm | ________ cm² |
| a sheet of A4 paper | ________ cm | ________ cm | ________ cm² |
| the top of your desk | ________ cm | ________ cm | ________ cm² |
| the classroom floor (to the nearest metre) | ________ m | ________ m | ________ m² |
B. Find the area
Area = ____________
Area = ____________
Area = ____________
Area = ____________
Area = ____________
Area = ____________
C. Which covers more?
Find both areas, then circle the rectangle that covers more. If they are the same, write “same”.
1. 12 m × 5 m or 8 m × 8 m ______________________________
2. 15 cm × 4 cm or 7 cm × 9 cm ______________________________
3. 2.5 m × 6 m or 4 m × 4 m ______________________________
4. 10 cm × 3 cm or 6 cm × 5 cm ______________________________
Square units
Area is measured in squares of a known size: a square centimetre is 1 cm by 1 cm, a square metre is 1 m by 1 m and a hectare is 100 m by 100 m. A square metre is 100 cm along each side, so it holds 100 × 100 = 10 000 cm². Children build a square metre from newspaper, cover it with A4 sheets, choose square units for real surfaces, and work with hectares.
We are learning to
- describe a square centimetre, a square metre and a hectare by their side lengths,
- choose a sensible square unit for a surface,
- find areas of land in square metres and in hectares.
Success criteria
- I can show a square metre and explain why it holds 10 000 cm².
- I can find the area of a 200 m by 150 m paddock in hectares.
You need
The worksheet, one per child; newspaper, sticky tape, a metre ruler and about twenty sheets of A4 paper for each group of four.
Lesson flow (about 50 minutes)
| 10 min | Which square unit? Show the board (see the box). The class votes A, B or C before each press. Ask: “Why don’t farmers measure a paddock in square centimetres?” |
| 25 min | Build a square metre Groups tape newspaper into a square 1 m by 1 m and cover it with A4 sheets in Part A. Ask: “Each side is 100 cm. How many rows of 100 square centimetres fill the square metre?” |
| 15 min | Choose and go big Children choose units in Part B and work with hectares in Part C. Ask: “A hectare is 100 m by 100 m. How many of our newspaper squares would cover it?” |
Two half-sessions instead? Split after Part A; start Session B with choosing units in Part B.
Watch for these ideas
- Thinking a square metre is 100 cm², because a metre is 100 cm.
- Treating a square metre as a length: it is a surface 1 m by 1 m.
- Forgetting that a hectare is 10 000 m², so 30 000 m² is 3 ha, not 30 ha.
Answers
- Part A: 100 × 100 = 10 000 cm²; about 16 sheets’ worth of A4 (each is 623.7 cm²), or 5 by 4 = 20 whole sheets with some hanging over the edge. How many children fit varies.
- Part B: a playing card, cm²; a bedroom floor, m²; a wheat farm, ha; a phone screen, cm²; a netball court, m²; a pine plantation, ha.
- Part C: 10 000 m²; 30 000 m² = 3 ha; 5000 m², half a hectare; the vineyard is 100 m wide (4 ha = 40 000 m²).
Square units
A. Our square metre
Each side is 1 m = ______ cm. Area = ______ × ______ = ______ cm²
Estimate how many A4 sheets will cover it: ______ Cover it. It took ______ sheets.
Some sheets hang over the edge. Is the real number of A4 sheets’ worth more or less than you used? ______
How many of us can stand on it at once? ______
B. Choose the square unit
Circle the square unit that suits each surface.
| a playing card | cm² | m² | ha |
| a bedroom floor | cm² | m² | ha |
| a wheat farm | cm² | m² | ha |
| a phone screen | cm² | m² | ha |
| a netball court | cm² | m² | ha |
| a pine plantation | cm² | m² | ha |
C. Hectares
A hectare (ha) is the area of a square 100 m by 100 m.
| Question | Answer |
|---|---|
| 1. How many square metres make a hectare? | |
| 2. A paddock is 200 m by 150 m. What is its area in square metres? In hectares? | |
| 3. A school field is 100 m by 50 m. What part of a hectare is it? | |
| 4. A rectangular vineyard of 4 ha is 400 m long. How wide is it? |
Split and add
Many shapes are made of rectangles. An L-shape can be split into two rectangles whose areas are added, or seen as a whole rectangle with a corner cut away, whose area is taken off. Any missing side comes from the sides that are given. Children find the areas of L-shapes both ways, check that the two ways agree, and use an area to cost a carpet.
We are learning to
- find the missing sides of a composite shape from the sides that are given,
- split a composite shape into rectangles and add their areas,
- find the same area by taking a corner away from a whole rectangle.
Success criteria
- I can find the area of an L-shape in two ways and show that they agree.
- I can find a missing side from the sides I am given.
You need
The worksheet, one per child, rulers and two coloured pencils each.
Lesson flow (about 50 minutes)
| 10 min | Split it Show the board (see the box). Children say each part’s area before you press. Ask: “Is there more than one way to split an L-shape? Do both ways give the same total?” |
| 25 min | Two ways Children find the missing sides in Part A, then the area by splitting and by taking the corner away. Ask: “The bottom is 10 m and the top is 6 m. How long is the step, and how do you know?” |
| 15 min | Carpet the room Children cost the carpet in Part B, then draw their own L-shape in Part C. Ask: “Is it quicker to split this room or to take the corner away? Why?” |
Two half-sessions instead? Split after the first L-shape in Part A; start Session B with the second.
Watch for these ideas
- Guessing an inside side from the picture instead of working it out from the sides given.
- Splitting so that the two parts overlap, and counting the overlap twice.
- Multiplying the outside sides (10 × 8) and forgetting the corner that is cut away.
Answers
- Part A: (1) the inside sides are 4 m and 3 m; split 48 + 20, or 80 − 12, both 68 m²; (2) the inside sides are 5 cm and 4 cm; split 49 + 15, or 84 − 20, both 64 cm²; (3) the inside sides are 3 m and 5 m; split 54 + 12, or 81 − 15, both 66 m².
- Part B: 48 − 6 = 42 m²; 42 × $40 = $1680.
- Part C: shapes vary; check that the two rectangles add to 20 squares.
Split and add
A. Two ways
Find the two missing sides. Then find the area by splitting and adding, and by taking the corner away.
Split and add: ______ + ______ = ______
Whole take away the corner: ______ − ______ = ______
Split and add: ______ + ______ = ______
Whole take away the corner: ______ − ______ = ______
Split and add: ______ + ______ = ______
Whole take away the corner: ______ − ______ = ______
B. Carpet the room
Carpet costs $40 for each square metre.
Cost of the carpet: ______
C. Your own L-shape
Draw an L-shape with an area of 20 squares. Colour the two rectangles you split it into and write their areas.
Work backwards
The formula runs both ways. If you know the area and one side, divide the area by that side to find the other: a 48 m² rectangle 8 m wide is 6 m long. Practical problems need both directions: how much turf, how many tiles, how long a garden bed. Children find missing sides, solve practical problems and check that each answer is a sensible size.
We are learning to
- find a missing side from the area and the other side,
- find the side of a square from its area,
- solve practical problems with area, cost and tiles.
Success criteria
- I can find the other side of a 48 m² rectangle that is 8 m wide.
- I can work out how many 50 cm tiles cover a 3 m by 2 m floor.
You need
The worksheet, one per child.
Lesson flow (about 50 minutes)
| 10 min | Missing side Show the board (see the box). The class votes A, B or C before each press. Ask: “Which multiplication fact helps you find the missing side?” |
| 25 min | Practical problems Children find the missing sides in Part A, then solve the problems in Part B. Ask: “Why is it easier to count the tiles in rows and columns than to divide the two areas?” |
| 15 min | Fit the sandpit Children solve the sandpit puzzle in Part C. Finish with the self-check quiz as a class game. Ask: “Why does no whole-number sandpit of 18 m² fit the corner?” |
Two half-sessions instead? Split after Part A; start Session B with the problems in Part B.
Watch for these ideas
- Multiplying the area by the side instead of dividing.
- Halving the area to find the side of a square: a 64 cm² square has sides of 8 cm, not 32 cm.
- Mixing units, such as a floor in metres and tiles in centimetres, so the numbers do not divide.
Answers
- Part A: 7 m, 8 cm, 12 m, 9 cm, 10 m; the square’s sides are 8 cm.
- Part B: (1) 54 m², 54 × $12 = $648; (2) 6 across and 4 down, 24 tiles; (3) 6 m; (4) 2 coats of 15 m² is 30 m², so 3 tins.
- Part C: 1 × 18, 2 × 9, 3 × 6 each have a side longer than 5 m; 4 m by 4.5 m fits (other sizes with both sides between 3.6 and 5 m work too).
Work backwards
A. Find the missing side
? = ____________
? = ____________
? = ____________
? = ____________
? = ____________
A square has an area of 64 cm². How long is each side?
____________
B. Practical problems
1. A backyard 9 m by 6 m is covered with turf at $12 a square metre. What is the area, and what does the turf cost?
______________________________________________________________________________
2. A bathroom floor 3 m by 2 m is covered with square tiles 50 cm by 50 cm. How many tiles are needed?
______________________________________________________________________________
3. A garden bed must cover 12 m² and be 2 m wide. How long must it be?
______________________________________________________________________________
4. A wall 5 m long and 3 m high gets 2 coats of paint. A tin covers 10 m². How many tins are needed?
______________________________________________________________________________
C. Fit the sandpit
The school wants a rectangular sandpit with an area of 18 m². It must fit in a corner 5 m by 5 m.
1. List every whole-number size with an area of 18 m². Do any fit? ______________________________
2. Find a size that fits. Show that its area is 18 m². ______________________________________
Cover up
Print one board for each pair. You need two dice and a coloured pencil each.
Cover up (Day 1)
- Take turns to roll two dice. Draw a rectangle that size anywhere it fits: a 3 and a 5 make a rectangle 3 squares by 5 squares.
- Write its area inside as a multiplication, such as 3 × 5 = 15, and colour it in your colour. Rectangles may not overlap.
- If your rectangle does not fit anywhere, miss that turn. When neither player can fit a rectangle twice in a row, add up your areas. The bigger total wins.
Teacher note: the board is 20 × 14 = 280 squares. A double six covers 36 squares and a double one covers 1. Check each area by multiplying, not by counting.
Area bingo
Cut out the six boards and the sixteen call cards once, one set for the class. Print more boards for a bigger class.
Area bingo (Day 2)
- Give each child or pair a board. Shuffle the call cards face down.
- Turn over a call and read it aloud, such as “a rectangle 6 m by 7 m”. Players work out the area and cover it if it is on their board.
- The first to cover a full row, column or diagonal calls Bingo, and must say the rectangle for each covered area.
Teacher note, every call and its area: 3 by 4, 12 cm²; 2 by 7, 14 m²; 3 by 6, 18 cm²; 4 by 5, 20 m²; 3 by 8, 24 cm²; 4 by 7, 28 m²; 5 by 6, 30 cm²; 4 by 8, 32 m²; 5 by 7, 35 cm²; 6 by 6, 36 m²; 5 by 8, 40 cm²; 6 by 7, 42 m²; 5 by 9, 45 cm²; 6 by 8, 48 m²; 7 by 8, 56 cm²; 8 by 9, 72 m².
What we know: Area of a Rectangle
Work on your own. Show your thinking if you can.
- What is the area of a rectangle 7 cm by 6 cm? ______
- Explain why the area of a rectangle is length × width. ______________________________________________
- What is the area of a square with sides of 9 m? ______
- Circle the best square unit. The area of a tablet screen: cm², m² or ha. The area of a farm: cm², m² or ha.
- A rectangle has an area of 56 m² and one side of 8 m. How long is the other side? ______
- An L-shape is a 10 m by 6 m rectangle with a 4 m by 2 m corner cut away. What is its area? ______
- Turf costs $15 a square metre. What does turf cost for a lawn 8 m by 5 m? ______
- A floor 4 m by 3 m is covered with square tiles 50 cm by 50 cm. How many tiles are needed? ______
How did this week feel? Circle one: I can teach it · I am getting there · I need more help
Answers and marking guide
Answers
- 42 cm².
- The unit squares sit in rows and columns: the length is the number in each row and the width is the number of rows.
- 81 m².
- a tablet screen, cm²; a farm, ha.
- 7 m (56 ÷ 8).
- 60 − 8 = 52 m².
- 40 m², so 40 × $15 = $600.
- 8 × 6 = 48 tiles.
A quick three-level guide
| Idea | Working towards | At standard | Beyond |
|---|---|---|---|
| Area as covering (Q2) | counts squares one by one | explains the formula with rows and columns | explains why the formula works with half squares too |
| Using the formula (Q1, Q3, Q5) | adds the sides or leaves out the square unit | multiplies to find an area and divides to find a side | finds the side of a square from its area |
| Square units (Q4) | mixes up a square metre and a metre | chooses cm², m² or ha to suit the surface | changes square metres to hectares |
| Composite and practical (Q6, Q7, Q8) | multiplies the outside sides of an L-shape | splits or takes away, and solves cost and tile problems | checks each answer is a sensible size |
Eight questions, four ideas. A child at standard answers most questions and can explain the formula with rows and columns of unit squares.
Weekly class record
Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.
| Name | Covering | Formula | Square units | Composite shapes | Working back |
|---|---|---|---|---|---|
The five columns are the five days: covering with squares, the formula, square units, composite shapes, and working backwards.