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

Learn to create nets, plans, and patterns with metric and imperial units through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Geometry and Trigonometry

Grade 11 MBF3C | Study topic C1.3

A drawing can help someone build, cut, or assemble an object. A net shows the flat faces that fold into a three-dimensional object. A plan shows an object or space from a chosen view, such as looking down from above. A pattern is a measured layout used to cut or make pieces. In this lesson, you will create these drawings with metric and imperial units. You will practise measuring, labelling, and checking that the parts fit together.

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

Before drawing, review length and measurement. Length tells how far it is from one point to another. Common metric units include millimetres (mm), centimetres (cm), and metres (m). Common imperial units include inches (in) and feet (ft).

Choose a unit that suits the object. A small cardboard box may be measured in centimetres or inches. A room plan may use metres or feet. Use one system consistently within a drawing unless you clearly label a conversion. Do not write an unlabelled number: a length of 12 could mean 12 cm, 12 in, or another unit.

A scale drawing uses a fixed relationship between lengths on paper and lengths in real life. For example, a scale of 1 cm to 10 cm means every 1 cm on the drawing represents 10 cm on the object. A scale helps a large object fit on a page while keeping its proportions.

\text{ cm on drawing}

=10 cm in real life

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 face is a flat surface of a solid object. A net is a flat arrangement of faces that can be folded to make a three-dimensional object. A rectangular prism, such as a box, has six rectangular faces. Opposite faces have the same dimensions.

To create a net for a box, identify its length, width, and height. Draw the faces so their shared edges have matching lengths. Arrange the faces so they can fold up without overlapping. Add tabs if the net is intended for construction; tabs are extra strips of material used for joining edges. Tabs do not change the measured size of a face.

A labelled net communicates more than an outline. Include the dimensions, units, and any scale. If the net is not drawn to scale, say so and rely on the labels for exact measurements. A quick paper mock-up can help check whether the faces fold into the intended shape.

face edge lengths match when folded

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 is a drawing that shows an object or space from a selected view. A floor plan, for example, looks down from above and shows the arrangement of walls or objects. A pattern is a measured layout of pieces to cut or make, such as pieces for a simple box or a craft project.

Start by deciding what the drawing needs to communicate. A plan may need the position and size of features. A pattern may need the outline and dimensions of every piece. Use straight edges for straight sides, and mark important corners clearly. Add a title or view label so the reader knows what the drawing represents.

For a scaled plan, apply the same scale to every length. Suppose a wall is 4 m long and the chosen scale is 1 cm to 1 m. The wall is drawn 4 cm long. A doorway that is 1 m wide is drawn 1 cm wide. Using one scale keeps the relative sizes accurate. Include the scale and units with the finished plan.

\text{drawing length}=\frac{\text{real length}}{\text{scale factor}}

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

A useful drawing is clear enough for another person to follow. Check that every needed side or feature is shown, each measurement has a unit, and repeated or joining edges agree. For a net, imagine folding each face. For a plan, compare the drawn lengths using the stated scale. For a pattern, check that each piece has a complete outline and a clear measurement.

When working in imperial units, label inches or feet rather than relying on the reader to guess. When working in metric units, use a suitable unit consistently. If you must convert units, show the conversion and label the resulting measurement. Do not mix units silently, because a correct-looking drawing can then be built at the wrong size.

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

A closed rectangular box is 8 cm long, 5 cm wide, and 3 cm high. Describe a net that could be drawn and label its six faces.

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.
$2(8\text{ cm}\times5\text{ cm}), 2(8\text{ cm}\times3\text{ cm}), 2(5\text{ cm}\times3\text{ cm})$
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.
$8\text{ cm}+5\text{ cm}+8\text{ cm}+5\text{ cm}$
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.
$2(8\text{ cm}\times5\text{ cm})$

Answer: The net has two faces measuring 8 cm by 5 cm, two measuring 8 cm by 3 cm, and two measuring 5 cm by 3 cm. Label all measurements in centimetres.

Check: The four side faces wrap around with total width 26 cm, and their common height is 3 cm. The top and bottom each match the box’s 8 cm by 5 cm opening.

Worked example

Example 2: Draw an imperial plan to scale

A rectangular work area measures 12 ft by 8 ft. Create a plan using a scale of 1 in to 2 ft. State the drawing dimensions and describe how to label the plan.

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
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
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 $\text{ ft}$

Answer: Draw a 6 in by 4 in rectangle and label it as a 12 ft by 8 ft work area, with the scale 1 in to 2 ft.

Check: Each drawing dimension multiplied by 2 ft per inch gives the stated real dimension: 6 in represents 12 ft, and 4 in represents 8 ft.

Common mistakes and how to avoid them

Leaving units off a dimension.

Correction: Write the unit beside every measurement so the size is unambiguous.

Using a different scale for different sides of one plan.

Correction: State one scale and apply it to every measured length in the drawing.

Drawing faces in a net with edges that do not match.

Correction: Check that the lengths of edges joined by folding are equal.

Assuming a net must be drawn at actual size.

Correction: Use a stated scale when needed, or label a drawing as not to scale.

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

Question 1

A net for a closed rectangular box includes two faces measuring 9 cm by 4 cm. What do these faces represent?

The top and bottom
The four side faces
The tabs only
The scale label

Show answer and explanation

The top and bottom

The top and bottom of a rectangular box have the same length and width, so both faces measure 9 cm by 4 cm.

Question 2

A plan uses a scale of 1 in to 3 ft. A wall is 15 ft long. How long should the wall be on the plan?

3 in
5 in
12 in
45 in

Show answer and explanation

5 in

Each drawing inch represents 3 ft, so 15 ft is represented by 15 divided by 3, or 5 in.

Question 3

Which check is most useful for a net before folding?

Confirm that joining edges have matching lengths.
Confirm that all measurements use different units.
Confirm that every face has a different shape.
Confirm that the net includes a floor-plan view.

Show answer and explanation

Confirm that joining edges have matching lengths.

Faces that meet along an edge must have equal edge lengths for the net to fold into the intended object.

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.

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About this lesson

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

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