Around the Shape

Overview

Students explore that the distance around the boundary of a two-dimensional shape is its perimeter. Building on their understanding of centimetres, straight lines and simple 2D shapes, they identify, measure and calculate perimeter by adding side lengths in practical classroom contexts.

Learning intentions

We are learning to:

• identify the boundary and perimeter of a 2D shape
• measure the sides of simple shapes in centimetres
• calculate perimeter by adding all side lengths
• explain how perimeter is useful in everyday situations

Key vocabulary: boundary, perimeter, side, length, centimetre (cm), measure, add, total, 2D shape.

Success criteria

• I can point to and describe the boundary of a shape.
• I can measure each side accurately in centimetres, starting at zero on the ruler.
• I can add all the side lengths to find the perimeter.
• I can explain what my answer means and include the unit, centimetres.

Curriculum links

• Te Mātaiaho Mathematics and Statistics — Measurement: understanding that the distance around the boundary of a 2D shape gives its perimeter.
• Measurement: using centimetres and appropriate measuring tools to measure length.
• Number: adding whole numbers and recording mathematical thinking clearly.
• Mathematical and statistical practices: representing, reasoning, communicating and checking solutions; working collaboratively and showing manaakitanga.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Teacher opens with the perimeter hook and learning intention and shows a picture of a rectangular garden needing a border, asking, “What would we need to know to put a fence all the way around it?” Students turn and talk, then share ideas about “around”, “inside” and “outside”.

2. 5–13 min · Explicit teaching and modelling. Teacher draws a rectangle and highlights its outside boundary, introducing perimeter as the distance around the boundary; model measuring each side with a ruler from zero, recording 8 cm, 4 cm, 8 cm and 4 cm, then calculating 8 + 4 + 8 + 4 = 24 cm using the boundary, ruler and worked-example slides. Students trace the boundary in the air, identify which measurements count, and repeat the calculation with a partner.

3. 13–22 min · Guided practice. Teacher displays a square, rectangle and irregular rectilinear shape, thinking aloud: “Have I measured every side? Have I added each length once?” Use the guided-practice shape slides and ask: “Where is the boundary?”, “Which side have we not measured?”, “What unit should we use?”, and “How can we check our total?” Students work in pairs to measure prepared shapes, record side lengths and calculate each perimeter. Pause to compare strategies and address errors.

4. 22–34 min · Differentiated measuring task. Teacher distributes the perimeter measuring and calculating worksheet and organises pairs, reminding students to measure carefully rather than estimate. Students complete tasks at an appropriate level:

• Support: measure clearly drawn squares and rectangles with whole-number sides, using a ruler guide and a four-box “measure, record, add, label” scaffold.
• Core: measure rectangles and simple irregular shapes, then calculate and explain one answer.
• Challenge: compare two shapes with the same perimeter or design a shape with a perimeter of 20 cm, recording and checking all sides. Teacher conferences with groups and asks, “How do you know you have included every side?”

5. 34–41 min · Real-world perimeter investigation. Teacher gives each pair a classroom object or marked floor/table space and the line and shape prompt cards to support prompts such as identify, describe and real world. Students choose a safe rectangular object or space, predict whether its perimeter will be greater or less than 50 cm, measure its sides in centimetres and calculate the distance around it. Pairs share one result, explaining what could usefully be measured around that object, such as ribbon, tape or a border. Ensure objects remain still and students measure cooperatively.

6. 41–45 min · Plenary and exit ticket. Teacher returns to the final discussion and exit-ticket prompt and asks students to explain the difference between length across a shape and distance around it. Students complete an exit ticket: “A rectangle has sides 6 cm, 3 cm, 6 cm and 3 cm. What is its perimeter? Show the addition and write the unit.” They add one sentence: “Perimeter means…”.

Resources

• the perimeter introduction, modelling, practice and plenary deck
• the perimeter measuring and calculating worksheet
• Rulers marked in centimetres
• Prepared paper shapes, including rectangles, squares and simple irregular rectilinear shapes
• Pencils, erasers and coloured pencils
• Classroom objects or marked spaces suitable for measuring
• Mini-whiteboards and pens
• the line and shape prompt cards

Assessment

• Observe whether students identify the outside boundary rather than the inside area, begin rulers at zero and measure every side.
• Use questioning during modelling and guided practice: “What does perimeter tell us?”, “Why do we measure all the sides?”, “What unit belongs in the answer?”, and “How could you check it?”
• Review the worksheet and exit ticket for accurate measurements, addition, units and explanations. Note students who add only two sides, confuse perimeter with area, or write a number without centimetres.

Differentiation

• Provide pre-drawn shapes with bold boundaries, ruler-placement modelling, a number line for addition and a partner who can explain thinking without completing the task.
• Support learners with visual vocabulary cards, gestures for “around” and “inside”, repeated sentence starters such as “The perimeter is ___ cm because…”, and opportunities to discuss in their strongest language before sharing.
• For students needing additional support, use shorter sides and measure one side at a time with an adult or peer; accept oral explanations alongside written recording.
• Extend confident mathematicians by asking them to find different shapes with the same perimeter, explain whether equal side lengths are necessary, or design a shape for a real-world border and justify the total.