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

Five days of lessons for Year 4 Measurement. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus cut-out shape cards and a leaf on squared paper, 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 shape cards once; they are reused across the week. Print the leaf sheet for Day 5.
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. Area is how much surface a shape covers, measured in squares; perimeter is the distance around its edge, measured in lengths. Children mix them up because the same shape has both. The week keeps the two apart and ends with estimating, because most real shapes do not fit a grid neatly.

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.

Informal and formal units

Children start with informal units, such as sticky notes for area and hand spans for perimeter, and see why everyone needs the same unit. Then they use formal ones: unit squares and square centimetres for area, centimetres and metres for perimeter. Area answers say square units; perimeter answers say units.

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 build each measurement on its own: area by covering, perimeter by going round. Day 3 puts them side by side on the same shapes and in real jobs. Day 4 shows they are truly different, because equal areas can have different perimeters. Day 5 takes area to a shape with curved edges, where the answer is an estimate. It builds on reading scaled instruments (AC9M4M01) and on arrays from the times tables (AC9M4A02).

Materials for the week (one trip)

• From the classroom: rulers, pencils, coloured pencils, string or wool, and a pad of sticky notes.
• Optional: square tiles or 1 cm grid paper for building shapes, and a few leaves from the playground for Day 5.
• Cut out once, use all week: the shape cards in this pack. Print one leaf sheet per child for Day 5.

Words for the word wall

area, perimeter, square unit, unit, cover, boundary, edge, length, width, rectangle, square centimetre, estimate, about

Dear families

This week in maths, Year 4 measures area (how much surface a shape covers) and perimeter (the distance around its edge), and learns that the same shape has both.

Try this at home

• Cover a placemat or a book with playing cards or sticky notes. How many does it take? That is its area in cards.
• Walk heel to toe around a rug. How many of your feet? That is its perimeter in feet.
• Ask: would we need the area or the perimeter to buy a fence? A rug? A picture frame?
• Trace your hand on squared paper and estimate its area by counting squares.

My measuring this week

Fill one row a day. Write what you measured, whether it was area or perimeter, and what you found.

Printed from the free seegongsik Area and Perimeter teaching pack · seegongsik.com/au/y4/measurement/AC9M4M02/pack

Cover it with squares

Area is how much surface a shape covers. Children first cover a book with sticky notes and then with their hands, and see that the count depends on the unit, so everyone needs the same one. On a grid the unit is a square: a 4 by 2 rectangle has an area of 8 square units, and rows times columns is a quick way to count it.

We are learning to

• measure area by covering with equal units, with no gaps and no overlaps,
• count unit squares, using rows and columns for a rectangle,
• give the unit with every area.

Success criteria

• I can find the area of a shape on a grid, in square units.
• I can explain why the units must all be the same size.

You need

A pad of sticky notes and a few books. The shape cards (cut-out sheet 1), one set per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Leaving gaps or overlapping the sticky notes, so the count is too small or too big.
• Counting the dots where grid lines cross instead of the squares.
• Writing 8 instead of 8 square units. The unit says what was counted.

Answers

• Part A: 1: 8, 2: 9, 3: 8, 4: 5, 5: 5, 6: 10 square units.
• Part B: any two shapes made of 6 squares, such as 3 by 2 and 6 by 1. Shape cards: A 6, B 5, C 10, D 5, E 8, F 16, G 5, H 6 square units.

Cover it with squares

A. Find the area of each shape

B. Draw two different shapes, each with an area of 6 square units

Around the edge

Perimeter is the distance all the way around a shape. On a grid children walk the boundary one unit edge at a time and count; for a rectangle the four sides add up, 4 + 3 + 4 + 3 = 14 units. Off the grid they measure each side of a book with a ruler and add, and see why a hand span is not a fair unit.

We are learning to

• find a perimeter by counting the unit edges around the boundary,
• add the side lengths of a rectangle,
• measure a real perimeter in centimetres with a ruler.

Success criteria

• I can find the perimeter of a shape on a grid, in units.
• I can measure the sides of an object and add them to find its perimeter in centimetres.

You need

Rulers and a book per pair. The shape cards (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with measuring a book.

Watch for these ideas

• Counting the squares along the edge instead of the edges: a corner square has two outside edges.
• Missing the edges that go into an inside corner of an L shape.
• Giving the number of squares, the area, as the perimeter.

Answers

• Part A: 1: 14, 2: 10, 3: 12, 4: 12 units. Part B: depends on the book; a book 30 cm by 21 cm has a perimeter of 30 + 21 + 30 + 21 = 102 cm.
• Part C: 6 is the number of squares, the area. The perimeter counts edges round the outside: 10 units. Shape cards: A 10, B 10, C 14, D 12, E 14, F 16, G 12, H 14 units.

Around the edge

A. Find the perimeter of each shape. Put a dot where you start counting.

B. Measure the perimeter of a book with a ruler

C. Ali says the perimeter of shape 2 is 6 units because it has 6 squares. What would you tell Ali?

Area or perimeter?

The same shape has both an area and a perimeter, and a real job needs one or the other. Carpet covers a floor, so it needs the area; a fence goes round a garden, so it needs the perimeter. Children sort jobs, find both measurements for the same shapes, and build rectangles on the board to watch both change.

We are learning to

• decide whether a job needs the area or the perimeter,
• find both measurements for the same shape,
• explain the difference: squares inside, lengths around.

Success criteria

• I can say whether a job needs area or perimeter, and why.
• I can find the area and the perimeter of the same shape, with the right units.

You need

The shape cards (cut-out sheet 1). The worksheet, one per child.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Choosing by the bigger number. The job decides, not the size of the number.
• Using one unit for both: area in square units, perimeter in units.
• Thinking area and perimeter always change together by the same amount.

Answers

• Part A: a fence around a garden, perimeter; carpet for a bedroom floor, area; a frame around a painting, perimeter; paint to cover a wall, area; ribbon around the edge of a cake, perimeter; tiles for a bathroom floor, area; grass seed for a new lawn, area; a border around a noticeboard, perimeter.
• Part B: 1: area 15 square units, perimeter 16 units; 2: area 7 square units, perimeter 12 units; 3: area 6 square units, perimeter 12 units. Part C: 4 by 3 has area 12 and perimeter 14; 5 by 3 has area 15 (up 3) and perimeter 16 (up 2).

Area or perimeter?

A. Does each job need the area or the perimeter?

B. Find the area and the perimeter of each shape

C. Draw a 4 by 3 rectangle and find both. Then draw it 1 unit wider. What changed, and by how much?

Same area, different perimeter

Area and perimeter really are different, and today proves it. Twelve squares make three rectangles, 12 by 1, 6 by 2 and 4 by 3, all with area 12 but with perimeters of 26, 16 and 14. The long thin one has the most edge; the squarest has the least. The other way round, rectangles with a perimeter of 12 have areas of 5, 8 and 9.

We are learning to

• make every rectangle with a given area,
• compare the perimeters of rectangles with the same area,
• find rectangles with the same perimeter but different areas.

Success criteria

• I can draw rectangles with the same area and find each perimeter.
• I can explain why the same area can have different perimeters.

You need

Square tiles, 16 per pair, or grid paper. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with area 16.

Watch for these ideas

• Expecting the same area to give the same perimeter.
• Counting 2 by 6 and 6 by 2 as two rectangles. Turned round, it is the same one.
• Thinking a bigger area always has a bigger perimeter: 4 by 4 has more area than 12 by 1 but less edge.

Answers

• Part A: 12 by 1: area 12, perimeter 26; 6 by 2: area 12, perimeter 16; 4 by 3: area 12, perimeter 14. Part B: 16 by 1: area 16, perimeter 34; 8 by 2: area 16, perimeter 20; 4 by 4: area 16, perimeter 16.
• Part C: 5 by 1: area 5, perimeter 12; 4 by 2: area 8, perimeter 12; 3 by 3: area 9, perimeter 12. The squarest rectangle has the least edge for its area (4 by 3) and the most area for its edge (3 by 3).

Same area, different perimeter

A. Draw every rectangle with an area of 12 square units, then find each perimeter

B. Now every rectangle with an area of 16 square units

C. Find three rectangles with a perimeter of 12 units. What is each area?

D. What do you notice about the squarest rectangle each time?

Estimate the area

Most real shapes do not fit a grid, so their area is estimated. Children count a leaf on squared paper three ways: whole squares only (too small), every square the outline touches (too big), and whole squares plus the part squares that are half or more covered. The third way is close, because the parts counted too much and too little roughly cancel out.

We are learning to

• estimate the area of a shape with curved edges on a grid,
• compare three ways of counting and say which is closest,
• estimate a curved perimeter with a piece of string.

Success criteria

• I can estimate an area by counting whole squares and squares half or more covered.
• I can explain why that estimate is close to the real area.

You need

Per child: the leaf sheet (cut-out sheet 2), two coloured pencils and a piece of string.

Lesson flow (about 50 minutes)

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

Watch for these ideas

• Counting every square the outline touches, so the estimate is far too big.
• Counting tiny slivers as whole squares.
• Expecting one exact answer. Estimates a few squares apart are both good.

Answers

• Part A: 24 whole squares and 16 half or more, so about 40 square units (anything from 36 to 44 is a good estimate). Whole squares only give 24, too small; every touched square gives 54, too big. The leaf’s real area is about 40 square units.
• Part B: depends on the hand. Part C: about 24 units. Part D: the bits counted too much and too little roughly cancel out.

Estimate the area

A. The leaf (on the leaf sheet)

Which count is too small? Which is too big? Which is closest?

B. My hand, traced on the grid

C. The edge of the leaf, measured with string

D. Why is whole squares + half-or-more squares a good estimate?

Shape cards

Cut out the eight cards, one set per pair. Partners take turns to find a card’s area (Day 1), its perimeter (Day 2) and both (Day 3), and check each other.

Teacher note: the areas are in the Day 1 answers and the perimeters in the Day 2 answers.

The leaf sheet

One sheet per child for Day 5. Estimate the leaf’s area, then trace your hand on the grid below and estimate that too.

The leaf

Trace your hand here, fingers together

What we know: Area and Perimeter

1. What is the area of the first shape? ______ square units
2. What is its perimeter? ______ units
3. The second shape: area ______ square units, perimeter ______ units
4. Area or perimeter? Fencing a paddock: __________   Covering a table with a cloth: __________
5. A 6 by 2 and a 4 by 3 rectangle both have an area of 12. Are their perimeters the same? ______ Show how you know.
6. Draw, or describe, a rectangle with a perimeter of 12 units and an area of 9 square units. ______________
7. A puddle covers 10 whole squares and 6 part squares. 4 of the part squares are half or more covered. Estimate its area: ______ square units
8. To measure the area of the classroom floor, would you use square centimetres or square metres? Why? ______________

Answers and marking guide

Answers

1. 15 square units (3 rows of 5).
2. 16 units (5 + 3 + 5 + 3).
3. Area 7 square units, perimeter 12 units.
4. Perimeter; area.
5. No: 6 by 2 has perimeter 16 and 4 by 3 has perimeter 14.
6. A 3 by 3 square: 3 + 3 + 3 + 3 = 12 and 3 × 3 = 9.
7. About 14 square units (10 whole + 4 half or more).
8. Square metres: square centimetres are far too small for a floor, so the number would be huge.

A quick three-level guide

Eight questions, three ideas. A child at standard finds area in square units and perimeter in units, keeps them apart, and estimates the area of a curved shape sensibly.

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: covering, edges, area or perimeter, same area, and estimating.