The Arizona STEM Acceleration Project

GRID SCALE DRAWING

Grid Scale Drawing

A 5th grade STEM lesson

Kasi Johnson

10-13-2023

Notes for teachers

Students should be able to explain the scaling ratio used to create different images. Students should be able to design a scaled drawing by reducing and enlarging the image individually.

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Students will be able to understand proportional relationships with rescaling a drawing. Students will be able to draw a reduced scale drawing and enlarged scale drawing in the end. Students will also be able to identify the ratio/fraction used for the scale change.

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List of Materials

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1. YouTube video for Scale Drawing:

https://www.youtube.com/watch?v=W3nLSeBr7hI&t=107s

1. Grid paper
2. Pencil
3. Ruler
4. Computer
5. Image picture to enlarge and reduce, magazine/cartoon images

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Standards

5.NF.B.5a: Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

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.Arizona - K-12 Academic Standards: 7.G.A.1

Common Core State Standards: Math.7.G.1 or 7.G.A.1

Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

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5.MP.5 Use appropriate tools strategically. Mathematically proficient students consider available tools when solving a mathematical problem. They choose tools that are relevant and useful to the problem at hand. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful; recognizing both the insight to be gained and their limitations. Students deepen their understanding of mathematical concepts when using tools to visualize, explore, compare, communicate, make and test predictions, and understand the thinking of others.

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Standards

5.G.A.2 Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

5.G.B Classify two-dimensional figures into categories based on their properties.

5.G.B.3 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

5.G.B.4 Classify two-dimensional figures in a hierarchy based on properties.

Objectives:

Today, students will be able to show their understanding of scales (resizing) using fractions and drawings.

Today, students should be able to explain the scaling ratio used to create different images.

Today, students should be able to design a scaled drawing by reducing and enlarging the image individually.

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Agenda (120 minutes)

• Step one:
• Introduce scale drawing and how it relates to maps, images, and other areas of math and everyday life.
• Introduce vocabulary for this lesson: scale drawing, reduce, enlarge, ratio
• Have students evaluate two similar images to identify the scale used for the drawing (a map may be useful for this part)
• Students will discuss with a partner the ratio they believe to have been used in the image and justify their reasoning.
• Step two:
• Students will draw a fish going from ½ inch scale to 1 inch scale to see the change.
• Have students determine a scale to use in order to draw the same image (the students need to determine their own scale/ratio to create a reduced or enlarged scale of the same image, may want to use same fish image)
• Students will share with the class their construction of the image and identify what ratio was used to create the scale drawing.

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• Step three:
• Watch Scale Ella video and pause as she solves the scale ratio for each problem. Have students complete the math to solve the unknown.
• Students will use grid paper to create a scale drawing of an image they choose (have a set of pictures that are small for them)
• Create a grid using a ruler on the original image (1 cm scale grid)
• Using that grid, decide a scale to reduce the image (try ½ cm scale)
• Step four:
• Students will draw a cartoon scale drawing. The student will design a reduced scale and an enlarged scale to reproduce the image both ways.
• Follow the same steps above: create a grid on the original image and then create the scale to reduce and enlarge the image (try ½ cm and 3 cm).
• The students will present their two drawings and identify their ratios used for the scales.

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WHAT IS SCALE DRAWING?

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https://www.youtube.com/watch?v=XtkU4VkWh8I

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Scale drawing is when you use a ratio to enlarge or reduce an image.

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What are some occupations that you could use scale drawing for?

*Real World Scenarios

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What is RATIO and why is that important in scale drawing?

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Ratio: actual height/scaled height

Example: You have a picture that is 10 cm in height and want to enlarge the image to a wall that is 3 m in height.

10 cm/3 m or 10 cm/300 cm

1/30 cm: 1 cm of picture equals 30 cm on the wall.

15 cm/4.5 m width: 15 cm/450 cm equals 1/30 cm

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Grid: Area used to measure/draw scale ratio

Example:

1 cm by 1 cm on original image

Enlarge: h x w scale ratio

Reduce: h x w scale ratio

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Enlarge Scale Drawing

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When the ratio of the drawing is larger than the original, making the drawing size increase.

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Reduce Scale Drawing

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When the image is smaller than the original image, making the drawing size decrease.

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What is the ratio of the 2 shapes? Which sides match up? How was it enlarged / reduced in size?

Scale Image

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What scale is being used?

How could we enlarge?

How could we reduce?

Scale Ella

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As you watch the video, solve the scale ratio problems on a separate piece of paper. Discuss and compare answers before resuming the video.

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YOUR TURN:�

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Choose an image from the pile of pictures:

1. Create a grid with ruler for the original image (2 cm x 2 cm).

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1. Enlarge the image using a different scale on grid paper

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1. Share your final drawing to the class.

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Hands-on Activity Instructions

You will choose a cartoon to draw two new images. (Ex. on other page to print out)

1. Choose an enlarged ratio scale for the drawing and using grid paper drawing the image enlarged.

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1. Choose a reduced ratio scale for the same drawing and using grid paper draw the image reduced.

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Assessment

Students creating an enlarged scale image and presenting to the class the image ratio used.

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Students creating a reduced scale image and presenting to the class the image ratio used.

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At the end of lesson, students will choose a cartoon image to reduce and enlarge using their own ratio.

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Students will be able to explain the ratio used in both scales and show the steps taken to create the two images.

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Differentiation

Students may use larger grid blocks to help them map out or design their picture grids.

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Students can try and sketch it out on their own if they are having trouble with ratios.

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Students can work in partners to help each other figure out the ratio for their grid drawings each student needs to design.

Remediation

Extension/Enrichment

On a computer, students can research some artistic portraits that use grid scale drawings that were enlarged in to real world scenarios. (Buildings, Cars, Statues)

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Students can choose more difficult pictures to enlarge or reduce on the grid scale drawing.