problem solving practice scale drawings

Scale Drawings - Grade 7

Suggested learning targets.

• I can solve problems involving scale drawings, when given scale.
• I can compute lengths and area from a scale drawing.
• I can reproduce the drawing of a different scale using a given scale drawing.

The following diagram shows an example of scale drawing. Scroll down the page for more examples and solutions on how to use scale drawings.

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How to Solve Scale Drawings Word Problems

Scale drawings word problems involve the application of proportion and scale in real-life scenarios. These problems require a solid understanding of how to interpret and work with scale drawings, as well as the ability to set up and solve equations. In this article, we will guide you through the step-by-step process of solving scale drawings word problems. Whether you are a student studying for a math exam or an individual looking to enhance your problem-solving skills, this article will help you master the art of solving scale drawings word problems.

A Step-by-step Guide to Solving Scale Drawings Word Problems

Let’s break it down step by step:

Step 1: Understand the Problem

The first step is to carefully read the problem and make sure you understand what you’re being asked to find. You need to identify the actual size of the object or distance and the scale used in the drawing. This is typically represented as a ratio.

Step 2: Identify the Scale

The scale should be given in the problem. It might be something like \(1:100\), which means that \(1\) unit on the drawing corresponds to \(100\) of the same units in real life. If the scale isn’t given directly, you may have to calculate it from information in the problem.

Step 3: Set Up a Proportion

Once you’ve identified the scale, you can set up a proportion to solve for the unknown. A proportion is an equation that shows that two ratios are equivalent.

For example, if a \(1\)-inch drawing represents \(4\) feet of a building, and you have a \(3\)-inch drawing, your proportion might look like this:

\( \frac{1 in}{4 ft}=\frac{3 in}{X ft} \)

Step 4: Solve for the Unknown

Next, you solve the proportion for the unknown variable. To do this, you can cross-multiply and solve for the variable.

Using the above example:

\(1 in \times X ft = 3 in \times 4 ft\)

\( X = \frac{(3 in \times 4 ft)}{1 in}= 12 ft \)

So, a \(3\)-inch drawing of the building would represent a \(12\)-foot actual height.

Step 5: Check Your Answer

Finally, always check your answer to make sure it makes sense in the context of the problem.

In our example, does it make sense that the building is \(12\) feet tall if the \(3\)-inch drawing is scaled up? Since our scale was \(1\) inch for every \(4\) feet, and we had a \(3\)-inch drawing, it indeed makes sense that the actual height is \(3\) times the \(4\) feet, which is \(12\) feet.

Remember, practice makes perfect. The more problems you work through, the better you’ll get at solving these types of problems.

by: Effortless Math Team about 10 months ago (category: Articles )

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5 Fun Scale Drawings and Scale Factors Activities

I love teaching scale drawing and scale factors in 7th grade math!

Picture this: a group of your 7th graders gathered around a table, their eyes sparkling with curiosity. As you dive into creating characters from their favorite video game using scale drawings, their excitement reaches new heights!

Knowing that they could bring one of their favorite games to life at the end of the lesson, they start to pay attention to the instructions and even ask clarifying questions.

Your job is halfway done at that point.

In this blog post, I will share the best 5 fun activities to teach scale drawing and scale factors…yes, including a project themed after Minecraft, a video game popular with my 7th graders! They all cover the CCSS standards 7.G.A.1.

Let's jump right in, shall we?

On this page

1. scale drawings & scale factors guided notes, 2. scale factors & map scales digital pixel art for google sheets, 3. scale drawings unofficial minecraft project, 4. scale drawings & similar figures pdf worksheets, 5. scale drawings blooket, save money on scale drawings activities, want free resources.

Get my free resource library with digital & print activities—plus tips over email.

What is it?

If you’re looking for a no prep, print-and-go resource to teach students to find scale factors, set up proportions in scale drawings, and map scales, these guided notes are perfect!

This all-inclusive lesson includes guided notes with visuals, step-by-step instructions, practice activities, and real-life applications. This 10-page resource provides sketch notes on scale drawings of geometry figures (similar triangles and polygons, anyone?), practice sheets to compute lengths of scale drawings, color by number activities, a thrilling maze, and a section dedicated to real-life math applications of scale factors and map scales in GPS systems.

And best of all I have a lesson plan that you can use to teach this, with ideas on how to use it in your classroom.

Why do I love this?

I love these notes because they are visual, filled with doodles and colors that make note-taking fun! I love their sections for introducing the lesson, practice, and real-life applications.

They work well as graphic organizers, scaffolded notes, and interactive notebooks. And it's artsy—if your students love color by number, color by code, or sketch notes, they'll love these lessons.

With this digital math activity , students practice solving problems with similar figures, map scales, scale drawings, and models. Contains 2 pixel art Google Sheets with 21 questions total. Level 1 will have them finding missing lengths using scale factors in similar figures, while Level 2 will challenge them to solve scale drawings and models using map scales.

I've always loved digital pixel art in my classroom , and especially can't get enough of these pixel art Google Sheets because they are self checking! It frees me up to move around the classroom helping different students while having the rest engaged. Students are motivated because pixels are unlocked every time they type in a correct answer.

They're visually stunning, engaging, and oh-so-fun! Plus, it's a fantastic way to reinforce key concepts and make math come alive. Get ready for some serious "aha" moments!

In this printable PDF applied math project , students draw out and color in their favorite Minecraft characters while calculating the scale factor of different images. The product includes instructions, images, and grids to draw out three characters from the game, including Steve, Alex, and Creeper.

Not familiar with Minecraft? Check out my post that covers what it is, why it's so exciting for students, and how to teach with it in your classroom.

I love this project because students love this! Minecraft is a very popular video game that automatically puts students into engagement and focus mode . The finished product of the scale drawings is also the perfect bulletin board decorations.

Note: This activity is NOT AN OFFICIAL MINECRAFT PRODUCT. NOT APPROVED BY OR ASSOCIATED WITH MOJANG.

These printable PDF worksheets take scale drawings, map scales, and computing lengths and area to a whole new level of fun!

Each time your students answer a question correctly in this Doodle Math activity , they'll get to unlock a mystery doodle pattern that they can use to complete an image using the colors of their choice. It's a great way to keep your students engaged and motivated, and the finished images make for cool classroom decorations.

They're a fun and unique twist on classic color by number activities.

This activity includes three levels with 18 questions total covering scale drawings & similar figures. Each correct answer unlocks doodle patterns to complete a mystery image (in this case, a hat). It's perfectly themed for winter, or any time of year really.

Doodling + Math = Pure FUN! This activity is a game-changer when it comes to engaging students. Just listen to what one teacher had to say about Doodle Math:

⭐⭐⭐⭐⭐ “This was difficult for my accelerated students! I loved it and so did they! They found trying to doodle the drawing and win ‘the best doodler’ fun. Students were engaged with the math, but also with their creativity.” - Kay Y.

Blooket is a trivia and review game. A teacher, known as the host, picks a question set and a unique game mode. Then, students will answer questions to help them win. Here is a Blooket practice set for scale drawings or you can search or create your own.

I love the variety of game modes. Some periods benefit from playing the game in groups (called Blook Rush ) while other class periods enjoy one of the different independent game modes like Cafe , Factory , etc.

And there you have it, my math-loving friends – the top 5 activities that will blow your students' minds when it comes to scale drawings, scale factors, and similar figures.

I hope you found at least one activity that will rock your math world! Happy teaching!

P.S. For the best deal, grab the top 4 activities together. Click here.

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I spent 7 years in the classroom working to make math fun and relevant in middle school, by integrating math, art, and technology. I started Congruent Math to share this all with you.

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Scale Drawing

Here we will learn about scale drawings, including creating scale drawings, using scale factors, and word problems.

There are also scale diagrams and drawings worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is a scale drawing?

A scale drawing is an enlargement of an object.

An enlargement changes the size of an object by multiplying each of the lengths by a scale factor to make it larger or smaller .

The scale of a drawing is usually stated as a ratio .

This is said as “ 1 centimetres to 5 metres” and means every 1 centimetre on the diagram represents 5 metres in real life.

In order to interpret and produce scale drawings we need to know the scale factor and the actual lengths of the object.

Below is a scale drawing of a pool with a scale of \bf{1cm:2m} or 1:200.

This means that every centimetre on the diagram represents 2 metres in real life. 

So the 6cm width of the diagram represents a 12m width on the real pool.

The real pool has been been enlarged by a scale factor of \frac{1}{200} to give the scale drawing.

The majority of scale drawing questions will involve polygons or 2D drawings such as floor plans or using a map although there is overlap with topics such as enlargement, construction of triangles , and loci . 

How to calculate the actual / real life distance from a scale

In order to calculate the actual/real life distance from a scale:

State the scale of the enlargement as a ratio in the form \bf{1:n} .

Multiply \bf{n} by the length given from the scale drawing.

Write the units.

Explain how to calculate the actual / real life distance from a scale

Scale drawing worksheet

Get your free scale drawing worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Related lessons on scale

Scale drawing is part of our series of lessons to support revision on scale . You may find it helpful to start with the main scale lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Scale maths
• Scale diagram

Scale drawing examples

Example 1: map.

A map has a scale of 1cm:2km. Find the actual distance represented by 5cm on the map.

2 Multiply \bf{n} by the length given from the scale drawing.

3 Write the units.

Example 2: plan of a building

A plan of a block of flats has the scale 2.5cm:800m. What is the real distance represented by 5.7cm on the plan?

Dividing both sides by 2.5, we get 1cm:320m

Example 3: atlas

A world atlas has a scale of 2cm:5 \ 000km. Calculate the real world distance that is represented by 23mm on the atlas.

As the length required is in millimetres, we first need to change the 2cm to millimetres.

2cm:5 \ 000km = 20mm:5 \ 000km

The we can reduce the ratio so we have 1 \ mm:n \ km. Dividing both sides by 20, we get:

How to calculate the scale drawing distance from a scale

In order to calculate the scale drawing distance from a scale:

Divide the real life distance by the scale ratio.

Calculate scale drawing distance examples

Example 4: model object.

A model car is made using the model to an actual distance of 1cm:40cm. The height of the car is 170cm. Calculate the height of the model car.

The ratio given is 1:40

Example 5: floor plan

A plan of a kitchen uses the scale 1cm:0.2m. Calculate the distance on the plan for the actual distance of 5.62m.

The ratio is already in the form 1:n .

Example 6: map of the UK

A map of the UK is drawn using the scale 50cm:1400km. Calculate how far 86.8km would be on the map.

Let’s convert the ratio to the form 1 \ cm:n \ km by dividing both sides of the ratio by 50.

50cm:1400km=1cm:28km

Now we can calculate the length on the map

86.8 \div 28=3.1

Common misconceptions

• Multiplying the real life distance by the ratio scale

The real life distance is multiplied by the ratio scale, giving an incorrect distance on the plan.

• Dividing the model / plan / map distance by the ratio scale

The distance on the model / plan / map is divided by the ratio scale meaning that the real life distance is incorrect.

• Ratio scale not simplified

If given the ratio 2cm:5km, it is easier to calculate when the ratio is in the form 1:n and so we must find an equivalent ratio before using the scale.

Here the ratio would be 1cm:2.5km so 1cm on the map would be equal to 2.5km in real life.

• Incorrect units in the solution

The units for the model are mixed up with the units for the real life distance. For example if we were calculating the distance of 10cm on a map with the scale ratio of 1cm:5km, \ 10 \times 5=50cm is stated whereas the correct solution would be 10 \times 5=50km.

• Converting units

Sometimes the units need to be converted so that you are working with the same units, making calculations much easier to comprehend. Make sure you know how to convert between different metric units. For example, the map scale is given as 1:25 \ 000 which means that 1cm on the map is equivalent to 25 \ 000cm in real life. If the answer is asked to be written in kilometres, the real life value in centimetres must be divided by 100 \ 000 to get the same measurement in kilometres. 1:25 \ 000 = 1cm:0.25km

Practice scale drawing questions

1. A map has a scale of 1cm:3km. How far is the actual distance of 3.5cm on the map?

2. An atlas has the scale 2cm:500km. Calculate the real distance for a length of 15cm on the map.

3. A plan of a bridge uses the scale 10cm:18.2m. The height of the bridge on the plan is 5.9cm. Calculate the real life height of the bridge.

4. A model elephant is created using a scale of 10cm:2.8m. A distance of 138.8cm is taken from the real life elephant. How long is this length on the model?

5. A map of the UK uses the scale 8m:1400km. Calculate the distance on the map that represents the actual length of 132km.

6. The plan of a garage is drawn using the drawing to actual scale of 0.9cm:20cm. What is the length of the garage on the plan, if it is 5.6m in real life?

Model to actual ratio is therefore 1cm:22.\dot{2}cm

Scale drawing GCSE questions

1. A map has a scale of 1cm:0.5km. A dog walker walks around 18km per day. Calculate how far they will have walked on a map.

2. (a) The distance between two cities in an American State is 146.8km. The distance between the two cities on a map is 29.36cm. Calculate the scale ratio of the map to the actual distance in the form 1cm:nkm.

(b) The river that travels through the state is measured on the plan to be 45cm. Calculate the actual length of the river. State the units in your solution.

3. Below is the map of a desert island.

Using the scale provided, calculate the distance between the Palm Trees and the Waterfall.

Distance [6.3-6.7cm]

Their 6.5 \times 50

Learning checklist

You have now learned how to:

• Multiplying and dividing by powers of 10 in scale drawings or by multiplying and dividing by powers of a 1,000 in converting between units such as kilometres and metres
• Solve problems involving similar shapes where the scale factor is known or can be found

The next lessons are

• Units of measurement
• Best buy maths

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Course: 7th grade   >   Unit 8

• Scale drawings
• Scale drawing: centimeters to kilometers
• Interpreting a scale drawing
• Scale drawing word problems
• Creating scale drawings
• Making a scale drawing
• Construct scale drawings
• Scale factors and area

Solving a scale drawing word problem

• Relate scale drawings to area

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