C1.3 · Create nets, plans, and patterns with metric and imperial units

Ontario Grade 11 Mathematics

Geometry and Trigonometry

Grade 11 MBF3C | Study topic C1.3

What you will learn

• Explain the difference between a net, a plan, and a pattern.
• Create a labelled net for a simple three-dimensional object using metric or imperial measurements.
• Create a simple plan or pattern that communicates measurements clearly.
• Check that measurements and units are consistent across a drawing.

1. Measurement bridge: choose and record units

• Write a unit beside every measurement.
• Use a scale when the object is too large or too small to draw at full size.
• Keep related measurements in the same unit system.

2. Nets: unfold faces onto a flat surface

• A net shows the faces laid flat before folding.
• Edges that meet when folded must have equal lengths.
• Label face dimensions and units; include tabs only when useful for joining.

3. Plans and patterns: show layout and construction

• A plan communicates position from a chosen view.
• A pattern communicates the shapes and sizes needed to make or cut pieces.
• Apply one stated scale consistently and label measurements clearly.

4. Check the drawing before using it

• Check completeness, matching edges, units, and scale.
• Use a fold check for a net and a scale check for a plan.
• Make the drawing understandable to someone who did not create it.

Worked example

Example 1: Make a metric net for a small box

1. Identify the face pairs
   A rectangular box has three pairs of opposite faces. The top and bottom use the length and width. The two long side faces use the length and height. The two end faces use the width and height.
   $$2(8\text{ cm}\times5\text{ cm}), 2(8\text{ cm}\times3\text{ cm}), 2(5\text{ cm}\times3\text{ cm})$$
2. Arrange the side faces
   Draw four rectangles in a row, alternating the side dimensions so their vertical edges can join around the box. Use faces measuring 8 cm by 3 cm, 5 cm by 3 cm, 8 cm by 3 cm, and 5 cm by 3 cm. Their heights match, and the widths wrap around the box.
   $$8\text{ cm}+5\text{ cm}+8\text{ cm}+5\text{ cm}$$
3. Attach the top and bottom
   Attach one 8 cm by 5 cm rectangle to an 8 cm edge in the row, and attach the other to the opposite 8 cm edge. Each attached face then meets the correct box edges when folded. The exact position can vary as long as the faces do not overlap when folded.
   $$2(8\text{ cm}\times5\text{ cm})$$

Worked example

Example 2: Draw an imperial plan to scale

1. Apply the scale to the length
   The scale represents 2 ft with each 1 in on the drawing. Divide the real length by 2 ft for each drawing inch. The 12 ft side therefore measures 6 in on the plan. 12$\text{ ft}$\div2 ft/in=6 in
2. Apply the same scale to the width
   Use the same scale for the other side so the proportions stay correct. The 8 ft side becomes 4 in on the drawing. 8$\text{ ft}$\div2 ft/in=4 in
3. Label the plan
   Draw a rectangle 6 in by 4 in. Add a title, write the real dimensions as 12 ft by 8 ft, and include the scale. If the plan includes equipment or a doorway, draw and label those features using the same scale. 1 in:2$\text{ ft}$

Common mistakes and how to avoid them

Lesson summary

• A net lays out the faces of a solid so they can be folded together.
• A plan shows an object or space from a selected view; a pattern lays out pieces to make or cut.
• Use clear labels, units, and one consistent scale when drawing to scale.
• Check matching edges, completeness, and dimensions before using the drawing.

Check your understanding

Key terms

Face

A flat surface of a three-dimensional object.

Net

A flat arrangement of faces that can be folded to form a three-dimensional object.

Plan

A drawing of an object or space from a chosen view.

Pattern

A measured layout of shapes or pieces used to cut or make an object.

Scale

A stated relationship between lengths on a drawing and lengths in real life.

Tab

An extra strip of material that can help join pieces when assembling an object.

Continue through MBF3C

View the complete MBF3C Ontario Grade 11 Mathematics curriculum and lessons

• C1.2 · Represent three-dimensional objects in multiple ways
• C1.4 · Solve design problems under constraints and state assumptions
• C1.1 · Recognize geometric shapes in practical design
• C2.1 · Solve applied right-triangle problems
• C2.2 · Verify the sine law and cosine law using technology
• C2.3 · Choose and apply the sine law or cosine law in acute triangles

Tutor support for C1.3 · Create nets, plans, and patterns with metric and imperial units

Working on C1.3 · Create nets, plans, and patterns with metric and imperial units in MBF3C? Bring the question and your own attempt. In a live session, you can show each step of your attempt and compare it with a worked example. Ask about the first step that does not make sense, then try a similar question yourself.

Explore math tutoring · Request an eligible free 30-minute introduction. Your request is matched by subject and language; a tutor must accept before a time is confirmed.

برای مبحث C1.3 · ساخت گسترده، نقشه و الگو با واحدهای متریک و امپریال در درس MBF3C، سؤال و تلاش خود را همراه بیاورید. در جلسه می‌توانید گام‌های تلاش خود را نشان دهید و آن را با یک نمونهٔ حل‌شده مقایسه کنید. راهنمای معلم ریاضی را ببینید یا جلسهٔ معارفهٔ رایگان ۳۰ دقیقه‌ای درخواست کنید. زمان جلسه پس از پذیرش معلم قطعی می‌شود.

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Mathematics (MBF3C), expectation C1.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

Report a correction or ask a question