Introduction to Dilations
Flags of the World
Image Transformations

Introduction to Dilations

Introduction to Dilations

Students explore dilations and learn a new function that enables them to create enlargements and reductions of images.

Lesson Goals

Students will be able to:

  • Explain 'center' and 'scale factor' as related to dilations

  • Demonstrate understanding that dilations change measurements of a figure proportionally

Student-Facing Lesson Goals

  • I can describe what a dilation is using words or actions.

  • I can determine, given the scale factor, if the dilation will be larger or smaller than the original image.

  • I can figure out the dimensions of a shape after a dilation.

Key Points for the Facilitator

  • Students should discover independently that a scale factor of <1 creates a smaller image (reduction) and a scale factor of >1 creates a larger image (enlargement).

  • Students should connect the scale factor to previous knowledge of percentages.

  • The scale function in WeScheme will not allow for negative scale factors. Negative scale factors are covered in Dilations on the Coordinate Plane.

Prerequisites

  • Students should be familiar with Circles of Evaluation.

Materials

Math Standards (CCSS)

  • CCSS.8.G.A, Understand congruence and similarity using physical models, transparencies, or geometry software.

  • CCSS.MATH.PRACTICE.MP2, Reason abstractly and quantitatively.

CS Standards (CSTA)

  • CS Standards here.
Glossary
accessor functions

functions to extract values from a data structure

axis

a number line on a scatter plot, used to place points that represent pairs of values in data sets

contract

a statement of the name, domain, and range of a function

domain

the type or set of inputs that a function expects

function

a mathematical object that consumes inputs and produces an output

range

the type or set of outputs that a function produces

Get Ready:

Students should have their computer, contracts page, and pencil.

Launch: (10 min)

Which One Doesn’t Belong?

Which One Doesn’t Belong? Which One Doesn’t Belong?🖼Show image

Give students 20-30 seconds to look at the image and decide which one they think does not belong, then move into groups according to the item they chose.

Give students 1-2 minutes to discuss their choice as a group before moving into group discussion and debate.

All the figures are cubes that have had some element of their appearance altered, whether it’s the position on the table, the angle it’s sitting at, its color, or its size. However, they’re all still cubes.

Strategies for English Language Learners

MLR 5 — Co-Craft Questions and Problems: Give students time to think and discuss with a partner or a small group before large group discussion. Encourage students to build off each other’s responses and move towards mathematical language.

Explore: (10 min)

Have students open the Scaling Exploration teachpack and investigate with their partner, use ./lessons/fl-intro-to-dilations/pages/intro-to-dilations-wb1.pdf to guide them.

Discuss: (10 min)

  • What new tools did you discover in this activity? (bitmap/url, scale, image-width)

  • What do you think the contract for bitmap/url is? (bitmap/url: String -> Image)

  • What do the different parts represent? (The String is a URL (an address on the Internet), and the Image is the picture found at that URL, or address)

  • What is the domain for scale? The range? (Domain is Number Image, Range is Image)

  • What does the Number appear to mean? (The scale factor, how much bigger or smaller the new image will be)

  • What do you notice about the scale factor when using the scale function? (We can use either decimals or fractions, a scale factor of less than one makes the image smaller and greater than one makes the image larger, negative numbers don’t work, etc)

  • Why is being able to change the size of an object useful? What are some situations where you’ve needed to use this skill?

Practice: (10 min)

Students practice identifying scale factors and missing lengths. The facilitator may choose to have students work together as a class, in partners, or individually. Some sample problems are included on ./lessons/fl-intro-to-dilations/pages/intro-to-dilations-ex1.pdf.

Create/Apply: (5 min)

Students open the "Define Values" teachpack and search for images on the Internet and bring them into WeScheme using bitmap/url, then scale them to create a scene of their choosing.

If students will be completing the Game Project, this is a good time for students to find player, target, danger, and background images for their game.

Some demo text only

Test of vocab items:

accessor functions

axis

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap:Cosmology by Jack Kepler, Ike Newton, and Al Einstein is licensed under a Creative Commons 4.0 Unported License. Based on a work at www.BootstrapWorld.org. Permissions beyond the scope of this license may be available by contacting schanzer@BootstrapWorld.org.

Flags of the World

Flags of the World

Students demonstrate what they’ve learned about image composition to recreate a nation’s flag with code.

Lesson Goals

Students will be able to:

  • Decompose a composite image into its component parts

  • Create composite images using functions and spatial reasoning

Student-Facing Lesson Goals

  • I can figure out what shapes make up an image.

  • I can create complex images using combinations of smaller images.

Key Points for the Facilitator

  • Samples of Flags - a visual guide to some flags appropriate for this project (require knowledge of overlay, overlay/align, beside, above)

  • Contracts are especially important in this lesson - students should have their contracts page open and be able to figure out why they can’t combine three images at once.

  • While learning, most students will define a new image with every step, which is completely fine and expected at this stage. As students grow more comfortable, they may discover that they can nest functions together without these extra definitions.

Prerequisites

  • Students should be familiar with Circles of Evaluation.

  • Students must be familiar with Image Manipulation functions for this activity.

Materials

Math Standards (CCSS)

CS Standards (CSTA)

  • CS Standards here.
Glossary
accessor functions

functions to extract values from a data structure

axis

a number line on a scatter plot, used to place points that represent pairs of values in data sets

Get Ready:

Students should have their computer, contracts page, and pencil.

Launch: (10 min)

On the board, give students a prompt to think on while they view the video.

What role do flags play in events such as the Olympics?

[2012 Olympic Parade of Nations, window="_blank"]

The video has been cued up to midway through the 2012 Olympic Parade of Nations in London. Watch 45-60 seconds before moving on.

Explore: (10 min)

Have students use the web to investigate flags that are relevant to them or that they have an interest in. Ask students to choose 2 or 3 interesting flags

Discuss: (10 min)

  • What are some recurring themes we see in the flags of different nations?

  • Why do you think some of those themes exist?

  • What do the different colors make you think of?

  • How do you think the colors and shapes of the flag were chosen?

  • Why isn’t there a standard size or shape for a flag? Do you think there should be?

Strategies for English Language Learners

MLR 5 — Co-Craft Questions and Problems: Give students time to think and discuss with a partner or a small group before large group discussion. Encourage students to build off each other’s responses and listen to different cultural perspectives. Some students may be eager to discuss the flag of their family’s home country or lineage, and others may not feel comfortable.

Practice: (10 min)

As a class, practice by recreating the flag of Cameroon together.

Create/Apply: (5 min)

Students create another flag or flags of their choosing.

Synthesizeion Activities:

  • Collaborate with Social Studies or Language teachers to create deeper cross-curricular connections.

  • Print off student-created flags and make a mural in the room or for display in the school.

Some demo text only

Test of vocab items:

accessor functions

axis

Design recipe

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap:Cosmology by Jack Kepler, Ike Newton, and Al Einstein is licensed under a Creative Commons 4.0 Unported License. Based on a work at www.BootstrapWorld.org. Permissions beyond the scope of this license may be available by contacting schanzer@BootstrapWorld.org.

Image Transformations

Image Transformations

Students will learn new functions that mimic the geometric transformations of rotation and reflection.

Lesson Goals

Students will be able to:

  • Demonstrate understanding of rotations

  • Demonstrate understanding of reflections over the x- and y- axis

Student-Facing Lesson Goals

  • I can transform images using rotations.

  • I can transform images using reflections.

Key Points for the Facilitator

  • It’s important that students use non-symmetrical images so that they can see the transformations. Text images work well for this!

  • Students should notice that rotations are counterclockwise unless the rotation angle is negative.

Prerequisites

  • Students should be familiar with Circles of Evaluation.

Materials

Connection Activities

Math Standards (CCSS)

CS Standards (CSTA)

  • CS Standards here.
Glossary
accessor functions

functions to extract values from a data structure

axis

a number line on a scatter plot, used to place points that represent pairs of values in data sets

contract

a statement of the name, domain, and range of a function

function

a mathematical object that consumes inputs and produces an output

Get Ready:

Before the lesson, the facilitator should use the text function to create an image of their name in large letters. Have the image (but not the code) visible to students as they enter. (Use the slider between the Definitions and Interactions windows to hide the code.)

For example: (text "Ms. Frizzle" 100 "orange")

Students should have their computer, contracts page, and pencil.

Launch: (5 min)

As students enter, ask them if they remember the function used to create the name on display. Ask students to create a similar text image for themselves, referring to their contracts page if necessary.

Explore: (10 min)

Inform students that there are three new functions to investigate today, and it’s their job to explore and learn all they can about these new functions and their contracts.

Students try out reflect-x, reflect-y, and rotate on the image of their name, writing down their observations.

Discuss: (10 min)

  • What is the contract for rotate? rotate: Number Image -> Image

  • What is the contract for reflect-x? reflect-x: Image -> Image, same for reflect-y

  • How do reflections and rotations have in common? They are both functions, they both transform, or change, images, they both preserve congruence (isometry)

  • How is a reflection different from a rotation? A reflection produces a mirror image, a rotation is like a turn while a reflection is like a flip

  • How do we measure rotations? Rotations can be measured in degrees or radians, measured counterclockwise

  • Is there a way to use reflections to get the same result as a rotation? A reflection over both the x- and y- axes produces an image that is the same as if we had rotated the image 180 degrees

Practice: (10 min)

“Match My Moves” activity - students get a pre-image and image and figure out the transformations needed to get from the pre-image to the image.

Create/Apply: (5 min)

Create/Apply task

Some demo text only

Test of vocab items:

accessor functions

axis

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap:Cosmology by Jack Kepler, Ike Newton, and Al Einstein is licensed under a Creative Commons 4.0 Unported License. Based on a work at www.BootstrapWorld.org. Permissions beyond the scope of this license may be available by contacting schanzer@BootstrapWorld.org.

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). CCbadge Bootstrap:Cosmology by Jack Kepler, Ike Newton, and Al Einstein is licensed under a Creative Commons 4.0 Unported License. Based on a work at www.BootstrapWorld.org. Permissions beyond the scope of this license may be available by contacting schanzer@BootstrapWorld.org.