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In this lesson, students will design a pixel art image then break down the colours into fractions, discuss number patterns & unit fractions, and build the designs in Minecraft.
Welcome to this Minecraft: Education Edition lesson! Before you begin, take a few moments to let us know your thoughts or feedback on how we can improve this lesson in order to better enhance the learning experience that is delivered in your classroom!
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Click and watch this teacher preparation video to help you understand how to teach this lesson. Here is a YouTube link of the teacher video for your reference: https://youtu.be/s6NuaYu4jBA
Start Here: Teacher Preparation Video
Develop understanding of fractions as numbers.
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts
Understand a fraction a/b as the quantity formed by a parts of size 1/b.
Creativity
Critical Thinking
Project Based Learning
Go through the pictures on the Opening Sideshow with your class. The point of the slideshow is to teach how to build and explain the math models.
Once you have figured this out you can build these models and project them on the board, while your students take notes and write the math in their notebooks. The pictures the student will work on will look like this.
Once you feel your students have discovered the concept of parts to a whole unveil the Big Idea: “Fractions are Parts of a Whole.”
To design their prototypes, have students click on the scratch link below to use this pixel art creator. https://scratch.mit.edu/projects/53198188/ Have a quick reminder about arrays and ask the students how many tiles are in the Pixel Art Creator. (Answer: 9x12=108 ) To use, the arrow keys move the cursor around and key on the keyboard stamp in colours. B is blue, Y is yellow, R is Red, Spacebar is black. There are a lot of colours in the program and you can see the full list by looking at the code in the script. Do this by clicking on the “See inside” button on the upper right hand corner of the screen and then the “Scripts” tab just to the right of the stage. Alternatively, students can use Microsoft Excel to create their prototype by filling in the cells with different colours. It should take students about 15 minutes to design their pixel art Find your Color Fractions Students will then find out what each colours fraction is by using the number of units used over the whole pixel art. Open the attached example, Pixel Pumpkin. The pumpkin will be. 1/108 is white 12/108 are grey 4/108 are green 2/108 are red 11/108 are yellow 34/108 are orange 44/108 are black Next they will add their units to check if they are correct 1+2+4+11+12+34+44=108. Then check their work with a calculator. Best practices: If they did not get the correct answer let them keep using the calculator, so they can focus more on finding their mistakes then just crunching number.
Now that they have their math and design they are ready to build their pixel art in Minecraft. To do this it is best to split the screens between Scratch and Minecraft like this so they can look at their prototype and use the cursor on to help count blocks while building in Minecraft. Then document and label.
Take a peer’s fraction colours to make a new pixel art piece.
Code a new colour on the Pixel Art Creator.
What happens when you added all the colours up, was there a pattern with any other numbers?
How did the fractions help explain how much of each colour you needed?
Depth of Knowledge 4 The student did all of the following:
The student was able to design an original piece of pixel art.
The student was able to breakdown their pixel art into colours and write them as fractions.
The student was able to transform a peer’s pixel art by using their same fractions of colours in a new design.
The student was able to document their models with pictures in their portfolios.
The student was able to explain number patterns in fractions, such as “a/a=1, or say “if I add up all the numbers it equals the whole.”
The student was able to organize fractions by size using the same denominators.
Depth of Knowledge 3 The student completed 5 out of the listed above
Depth of Knowledge 2 The student completed 3 out of the 6 listed above
Depth of Knowledge 1 The student completed 2 out of the 6 listed above
Check out the Tips & Tricks video playlist that will help you and your students better use Minecraft: Education Edition in the classroom:
https://youtube.com/playlist?list=PLkh9rrdH-ARER03ojhFYtmoFDVuACYJLa
More videos added periodically so make sure you check often for more content!
Click and watch the student pause and play video with your class, pausing and playing as needed. This will help your students understand how to navigate through this lesson and Minecraft world and complete the activities located within them. Enjoy!
Check out the YouTube link of this video for your reference: https://youtu.be/95UdpxM0u9I
Student 'Pause & Play' Video
Specific Outcome 13: Demonstrate an understanding of fractions by:
explaining that a fraction represents a part of a whole
describing situations in which fractions are used
Specific Outcome 8 : Demonstrate an understanding of fractions less than or equal to one by using concrete, pictorial and symbolic representations to:
name and record fractions for the parts of a whole or a set
model and explain that for different wholes, two identical fractions may not represent the same quantity
provide examples of where fractions are used.
Specific Outcome 7: Demonstrate an understanding of fractions by using concrete, pictorial and symbolic representations to:
compare fractions with like and unlike denominators
Specific Outcome 2: Solve problems involving whole numbers and decimal numbers
Identify needs and opportunities for designing, through exploration
Generate ideas from their experiences and interests
Add to others’ ideas
Choose an idea to pursue.
Making
Choose tools and materials
Make a product using known procedures or through modelling of others
Use trial and error to make changes, solve problems, or incorporate new ideas from self or others
Sharing
Decide on how and with whom to share their product
Demonstrate their product, tell the story of designing and making their product, and explain how their product contributes to the individual, family, community, and/or environment
Use personal preferences to evaluate the success of their design solutions
Reflect on their ability to work effectively both as individuals and collaboratively in a group
Use materials, tools, and technologies in a safe manner in both physical and digital environments
Develop their skills and add new ones through play and collaborative work
Explore the use of simple, available tools and technologies to extend their capabilities
Curricular Competencies
Develop mental math strategies and abilities to make sense of quantities
Use technology to explore mathematics
Understanding and solving
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Content
Students are expected to know the following:
- Fraction concepts: Fractions can represent parts of a region, set, or linear model.
- Ordering and comparing fractions: Using concrete and visual models.
- Fractions: Two equivalent fractions are two ways to represent the same amount. Comparing and ordering of fractions and decimals. Equal partitioning.
Improper fractions
Using benchmarks, number line, and common denominators to compare and order, including whole numbers.
Using pattern blocks, Cuisenaire Rods, fraction strips, fraction circles, grids
Identify needs and opportunities for designing, through exploration
Generate ideas from their experiences and interests
Add to others’ ideas
Choose an idea to pursue.
Making
Choose tools and materials
Make a product using known procedures or through modelling of others
Use trial and error to make changes, solve problems, or incorporate new ideas from self or others
Sharing
Decide on how and with whom to share their product
Demonstrate their product, tell the story of designing and making their product, and explain how their product contributes to the individual, family, community, and/or environment
Use personal preferences to evaluate the success of their design solutions
Reflect on their ability to work effectively both as individuals and collaboratively in a group
Use materials, tools, and technologies in a safe manner in both physical and digital environments
Develop their skills and add new ones through play and collaborative work
Explore the use of simple, available tools and technologies to extend their capabilities
Curricular Competencies
Develop mental math strategies and abilities to make sense of quantities
Use technology to explore mathematics
Understanding and solving
Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving
Content
Students are expected to know the following:
- Fraction concepts: Fractions can represent parts of a region, set, or linear model.
- Ordering and comparing fractions: Using concrete and visual models.
- Fractions: Two equivalent fractions are two ways to represent the same amount. Comparing and ordering of fractions and decimals. Equal partitioning.
Improper fractions
Using benchmarks, number line, and common denominators to compare and order, including whole numbers.
Using pattern blocks, Cuisenaire Rods, fraction strips, fraction circles, grids
Numbers
B1.6 Fractions use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts.
Algebra
C3.1 solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves sequential, concurrent, and repeating events
C3.2 read and alter existing code, including code that involves sequential, concurrent, and repeating events, and describe how changes to the code affect the outcomes
Numbers
B1.4 Represent fractions from halves to tenths using drawings, tools, and standard fractional notation, and explain the meanings of the denominator and the numerator.
Algebra
C3.1 solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves sequential, concurrent, and repeating events
C3.2 read and alter existing code, including code that involves sequential, concurrent, and repeating events, and describe how changes to the code affect the outcomes
Numbers
B1.3 Fractions, Decimals, and Percents represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts.
B1.5 Fractions, Decimals, and Percents read, represent, compare, and order decimal numbers up to hundredths, in various contexts
B1.7 Describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings, in various contexts.
Algebra
C3.1 solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves sequential, concurrent, and repeating events
C3.2 read and alter existing code, including code that involves sequential, concurrent, and repeating events, and describe how changes to the code affect the outcomes
Numbers
B1.3 Rational Numbers compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts.
B1.4 Fractions, Decimals, and Percents read, represent, compare, and order decimal numbers up to thousandths, in various contexts.
B1.6 Fractions, Decimals, and Percents describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts
Algebra
C3.1 solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves sequential, concurrent, and repeating events
C3.2 read and alter existing code, including code that involves sequential, concurrent, and repeating events, and describe how changes to the code affect the outcomes
N3.4 Demonstrate understanding of fractions concretely, pictorially, physically, and orally including: • representing • observing and describing situations • comparing • relating to quantity.
N4.6 Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to: • name and record fractions for the parts of a whole or a set • compare and order fractions • model and explain that for different wholes, two identical fractions may not represent the same quantity • provide examples of where fractions are used.
N5.5 Demonstrate an understanding of fractions by using concrete and pictorial representations to: • create sets of equivalent fractions • compare fractions with like and unlike denominators.
N6.7 Extend understanding of fractions to improper fractions and mixed numbers.
3.N.13. Demonstrate an understanding of fractions by n explaining that a fraction represents a portion of a whole divided into equal parts in describing situations in which fractions are used n comparing fractions of the same whole with like denominators [C, CN, ME, R, V]
· Identify common characteristics of a set of fractions.
· Describe everyday situations where fractions are used.
· Represent a fraction concretely or pictorially.
4.N.8. Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to n name and record fractions for the parts of a whole or a set n compare and order fractions n model and explain that for different wholes, two identical fractions may not represent the same quantity n provide examples of where fractions are used [C, CN, PS, R, V]
· Represent a fraction using concrete materials.
· Identify a fraction from its concrete representation.
· Name and record the shaded and non-shaded parts of a set.
· Name and record the shaded and non-shaded parts of a whole.
· Represent a fraction pictorially by shading parts of a whole.
· Name fractions between two benchmarks on a number line (horizontal or vertical).
· Order a set of fractions by placing them on a number line (horizontal or vertical) with benchmarks.
5.N.7. Demonstrate an understanding of fractions by using concrete and pictorial representations to n create sets of equivalent fractions n compare fractions with like and unlike denominators [C, CN, PS, R, V]
· Create a set of equivalent fractions and explain why there are many equivalent fractions for any fraction using concrete materials.
· Formulate and verify a rule for developing a set of equivalent fractions.
· Identify equivalent fractions for a fraction.
Fractions:
· Represents a fraction in a variety of ways, based on a whole or a collection of objects.
· Uses objects, diagrams or equations to represent a situation and conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of addition, subtraction and multiplication by a natural number)
· Generates a set of equivalent fractions
· Reduces a fraction to its simplest form (lowest terms)
N13 Demonstrate an understanding of fractions by: • explaining that a fraction represents a part of a whole; • describing situations in which fractions are used; • comparing fractions of the same whole with like denominators.
N8 Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to: name and record fractions for the parts of a whole or a set; compare and order fractions; model and explain that for different wholes, two identical fractions may not represent the same quantity; provide examples of where fractions are used.
N7 Demonstrate an understanding of fractions by using concrete and pictorial representations to: create sets of equivalent fractions; compare fractions with like and unlike denominators.
N4 Relate improper fractions to mixed numbers.
N13: Students will be expected to demonstrate an understanding of fractions by · explaining that a fraction represents a part of a whole · describing situations in which fractions are used · comparing fractions of the same whole with like denominators.
N08: Students will be expected to demonstrate an understanding of fractions less than or equal to 1 by using concrete, pictorial, and symbolic representations to name and record fractions for the parts of one whole or a set compare and order fractions model and explain that for different wholes, two identical fractions may not represent the same quantity provide examples of where fractions are used
N07: Students will be expected to demonstrate an understanding of fractions by using concrete, pictorial, and symbolic representations to create sets of equivalent fractions compare and order fractions with like and unlike denominators.
N04: Students will be expected to relate improper fractions to mixed numbers and mixed numbers to improper fractions.
3N13 Demonstrate an understanding of fractions by: • explaining that a fraction represents a part of a whole • describing situations in which fractions are used • comparing fractions of the same whole that have like denominators.
4N8 Demonstrate an understanding of fractions less than or equal to one by using concrete, pictorial and symbolic representations to: • name and record fractions for the parts of a whole or a set • compare and order fractions • model and explain that for different wholes, two identical fractions may not represent the same quantity • provide examples of where fractions are used.
5N7 Demonstrate an understanding of fractions by using concrete, pictorial and symbolic representations to: • create sets of equivalent fractions • compare fractions with like and unlike denominators.
N13 Demonstrate an understanding of fractions by: • explaining that a fraction represents a part of a whole; • describing situations in which fractions are used; • comparing fractions of the same whole with like denominators.
N8 Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to: name and record fractions for the parts of a whole or a set; compare and order fractions; model and explain that for different wholes, two identical fractions may not represent the same quantity; provide examples of where fractions are used.
N7 Demonstrate an understanding of fractions by using concrete and pictorial representations to: create sets of equivalent fractions; compare fractions with like and unlike denominators.
N4 Relate improper fractions to mixed numbers.