Perimeter and Area: a week of ready-to-teach maths

Five days of lessons for Year 5 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus twelve rectangle cards, two job mats with twelve job cards, a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Cut out the rectangle cards and the job cards once, and keep each set in an envelope.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. 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: perimeter is the distance around a shape, a length in centimetres or metres, and area is the surface it covers, counted in square units such as square centimetres (cm²) or square metres (m²). A rectangle’s area is its rows times its columns, and an irregular shape is split into rectangles. Every practical problem starts with one question: does the job go around the shape, or cover it?

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.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Days 1 and 2 separate the distance around from the space inside; Day 3 shows that the two can change independently; and Days 4 and 5 take both to irregular shapes and real jobs. It builds on Year 4’s measuring and approximating perimeter and area with formal and informal units (AC9M4M02) and on choosing metric units (AC9M5M01), and it leads to Year 6, where the area of a rectangle becomes a formula (AC9M6M02).

Materials for the week (one trip)

• From the classroom: rulers, a trundle wheel or tape measure, a ball of string, scissors, envelopes, this pack printed.
• Cut out once: the twelve rectangle cards (Day 3) and the twelve job cards (Day 5); keep the two job mats whole.

Words for the word wall

perimeter, area, side, length, width, square centimetre, square metre, rectangle, irregular, split

Dear families

This week in maths, Year 5 works with perimeter, the distance around a shape, and area, the surface it covers. A rug 3 m long and 2 m wide has a perimeter of 3 + 2 + 3 + 2 = 10 m and an area of 3 × 2 = 6 square metres.

Try this at home

• Pace out the edge of a room or a yard together. Is that the perimeter or the area?
• Count the tiles on a floor or a splashback, then check by multiplying rows by columns.
• Ask: to paint a door, do you need its perimeter or its area? To put tape around it?
• Measure a placemat or a book and find its perimeter and its area.

Perimeters and areas I found this week

Fill one row a day. Write what you measured and its perimeter or area, with the unit.

Printed from the free seegongsik Perimeter and Area teaching pack · seegongsik.com/au/y5/measurement/AC9M5M02/pack

The distance around

Perimeter is the distance all the way around a shape, so it is a length, in centimetres or metres. Children add every side, and with rectangles they meet the shortcut: the two different sides added, then doubled. A garden bed 3 m by 2 m takes 3 + 2 + 3 + 2 = 10 m of edging, or (3 + 2) × 2.

We are learning to

• find the perimeter of a shape by adding every side,
• use the rectangle shortcut: length plus width, doubled,
• solve problems about going around a shape.

Success criteria

• I can find the perimeter of a rectangle two ways.
• I can say why a perimeter is in centimetres or metres, not square units.

You need

String, rulers and a tape measure. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the string; start Session B with Part A.

Watch for these ideas

• Adding only the two labelled sides, as in 6 + 4 = 10 for the board rectangle. Every side counts.
• Counting the squares along the edge instead of their outside edges. A corner square has two outside edges.
• Writing a perimeter in square units. It is a length.

Answers

• Part A: 7 + 3 + 7 + 3 = 20 cm; 9 + 2 + 9 + 2 = 22 cm; 6 + 6 + 6 + 6 = 24 cm; 10 + 4 + 10 + 4 = 28 cm. Part B: 14 cm, 18 cm, 16 cm.
• Part C: 34 m; 360 cm; 320 m.

The distance around

A. Find the perimeter of each rectangle

B. Count the edges: each side of a square is 1 cm

C. Fences and edges

The space inside

Area is the surface a shape covers, counted in unit squares. A square 1 cm on each side covers 1 square centimetre, written 1 cm². A rectangle 4 cm by 3 cm holds 3 rows of 4 squares, so its area is 4 × 3 = 12 cm²: multiplying counts the squares without counting each one.

We are learning to

• find an area by counting unit squares,
• find the area of a rectangle by multiplying rows by columns,
• write an area in square units.

Success criteria

• I can find the area of a rectangle by multiplying.
• I can draw two different rectangles with the same area.

You need

Sticky notes or square tiles for modelling. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the sticky notes again.

Watch for these ideas

• Adding the sides for area: 4 + 3 = 7. Area counts the squares inside.
• Writing an area in centimetres instead of square centimetres.
• Losing count in a shape that is not a rectangle. Mark each square as it is counted.

Answers

• Part A: 10 cm², 6 cm², 8 cm². Part B: 8 × 3 = 24 cm²; 6 × 5 = 30 cm²; 9 × 4 = 36 cm²; 7 × 7 = 49 cm².
• Part C: any two of 1 by 18, 2 by 9, 3 by 6 (each 18 cm²).

The space inside

A. Count the squares: each square is 1 cm²

B. Multiply to find the area

C. Draw two different rectangles with an area of 18 cm²

Same area, new perimeter

Area and perimeter can change separately. Rectangles 1 cm by 10 cm and 2 cm by 5 cm both cover 10 cm², but their perimeters are 22 cm and 14 cm. Children sort rectangles of equal area and find that the closer a rectangle is to a square, the shorter its perimeter; and with a fixed length of fence, the squarest rectangle holds the most.

We are learning to

• find the area and the perimeter of the same rectangle,
• show that rectangles with the same area can have different perimeters,
• find the rectangle with the most area for a length of fence.

Success criteria

• I can find two rectangles with the same area and different perimeters.
• I can explain which rectangle needs the least fence for its area.

You need

The rectangle cards (cut-out sheet 1), one set per pair. A 20 cm loop of string per pair, if you have it. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after the sort; start Session B with Part B.

Watch for these ideas

• Thinking equal areas mean equal perimeters, or the other way round.
• Using the perimeter rule for area: 5 + 4 = 9 for a 5 cm by 4 cm rectangle.
• Forgetting that a square is a rectangle too.

Answers

• Part A: 12 cm²: B (26 cm), F (14 cm), K (16 cm); 16 cm²: C (16 cm), H (20 cm), L (34 cm); 18 cm²: D (22 cm), G (38 cm), J (18 cm); 24 cm²: A (22 cm), E (20 cm), I (28 cm).
• Part B: 1 by 9, 9 cm²; 2 by 8, 16 cm²; 3 by 7, 21 cm²; 4 by 6, 24 cm²; 5 by 5, 25 cm²; the square holds the most. Part C: 4 m by 4 m, 16 m² (1 by 7 gives 7 m², 2 by 6 gives 12 m², 3 by 5 gives 15 m²).

Same area, new perimeter

A. Sort the rectangle cards into piles of equal area

B. A loop of string 20 cm long makes these rectangles

Which rectangle covers the most? ________________________

C. The best patch

Jo has 16 m of fence for a rectangular vegetable patch. The sides are whole metres. Which rectangle gives the most room to grow? Show the rectangles you tried.

Irregular perimeters

An irregular shape has no shortcut: its perimeter is every side added. L-shapes often hide a side or two, but opposite sides still match up: the longest side across equals the two shorter sides across from it, added, and the same goes up and down. Children find the missing sides first, then tick each side as they add it.

We are learning to

• add every side of an irregular shape,
• find a missing side from the sides opposite it,
• compare an L-shape with the rectangle that fits around it.

Success criteria

• I can find a missing side of an L-shape.
• I can find the perimeter of an irregular shape and show I used every side once.

You need

Coloured pencils, for ticking each side as it is added. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the room again.

Watch for these ideas

• Missing the inward sides of an L, so only four sides are added.
• Measuring a missing side on the drawing with a ruler. Work it out from the sides opposite.
• Adding a side twice. Tick each side as it is added.

Answers

• Part A: 3 + 4 + 4 + 2 + 7 + 6 = 26 cm; 8 + 2 + 3 + 4 + 2 + 4 + 3 + 2 = 28 cm; 2 + 4 + 6 + 4 + 2 + 6 + 10 + 6 = 40 cm. Part B: missing 3 and 4 cm, perimeter 32 cm; missing 3 and 3 cm, perimeter 28 cm.
• Part C: the L is 26 cm and the rectangle around it 26 cm, the same; the U is 40 cm against 32 cm, longer by the two sides of its notch.

Irregular perimeters

A. Find each perimeter

B. Find the missing sides first, then the perimeter

C. The rectangle around it

Draw the rectangle that just fits around Shape 1, and the one around Shape 3. Find each rectangle’s perimeter. Which shape has the same perimeter as its rectangle? Why does the other not?

Irregular areas and real jobs

The area of an irregular shape comes from rectangles: split it, find each area, and add. An L can be split across or down, or seen as a big rectangle with a corner taken away, and every way gives the same area. Then children sort real jobs: going around (perimeter, in m or cm) or covering (area, in m² or cm²).

We are learning to

• find the area of an irregular shape by splitting it into rectangles,
• check the area a second way,
• decide whether a job needs perimeter or area, and give the unit.

Success criteria

• I can split an L-shape into rectangles and add their areas.
• I can say whether a job goes around or covers, and answer with a unit.

You need

The job mats and job cards (cut-out sheet 2), one set per group. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the job cards.

Watch for these ideas

• Using a side that belongs to the other rectangle after splitting. Mark each part’s own two sides.
• Adding the sides of each part instead of multiplying them.
• Giving an area in metres, or a perimeter in square metres.

Answers

• Part A, for example: 4 × 6 + 4 × 2 = 32 cm²; 3 × 7 + 3 × 2 = 27 cm²; 10 × 2 + 4 × 5 = 40 cm². Part C: 42 − 15 = 27 cm².
• Part B: A around, 130 m; B cover, 12 m²; C around, 50 cm; D cover, 15 m²; E cover, 6 m²; F around, 16 m; G cover, 600 cm²; H cover, 48 m²; I around, 90 m; J around, 420 cm; K cover, 4 m²; L around, 180 cm.

Irregular areas and real jobs

A. Split each shape into rectangles and find its area

B. Job cards: go around or cover?

C. A second way

Find the area of Shape 2 another way: take the missing corner away from the rectangle that fits around it.

Rectangle cards

Cut out the twelve cards (Day 3), one set per pair. Each small square stands for 1 square centimetre, so each side is counted in centimetres.

Teacher note: four piles of three. The piles and perimeters are on the Day 3 plan.

Job mats and job cards

Keep the two mats whole and cut out the twelve job cards (Day 5), one set per group. Decide whether each job goes around a shape or covers it, then work out how much is needed.

Teacher note: six jobs go around and six cover. The answers are on the Day 5 plan.

What we know: Perimeter and Area

Work on your own. Show your thinking if you can.

1. A rectangle is 9 cm long and 5 cm wide. What is its perimeter?   __________
2. What is the area of the same rectangle?   __________
3. What is the area of this shape? Each square is 1 cm².   __________
4. What is the perimeter of this shape?   __________
5. Find the missing side, then the perimeter.   Missing side: ______   Perimeter: ______
6. Split this shape into rectangles to find its area.   __________
7. Rectangles 2 cm by 10 cm and 4 cm by 5 cm have the same area. Which has the shorter perimeter?   __________
8. A bedroom floor is 5 m long and 4 m wide. How much carpet covers it? Write perimeter or area, and the answer with its unit.

Answers and marking guide

Answers

1. 28 cm
2. 45 cm²
3. 11 cm²
4. 26 cm
5. Missing side 4 cm; perimeter 28 cm
6. 28 cm²
7. 4 cm by 5 cm (24 cm against 18 cm)
8. Area: 20 m² of carpet

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by naming whether the job goes around the shape or covers it.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: finding a perimeter, finding an area, comparing rectangles, irregular perimeters, and irregular areas.