Geometry Family Resources - Tacoma Public Schools · Geometry Family Resources April 2020 . ... QT...
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Geometry Family Resources April 2020
Transcript of Geometry Family Resources - Tacoma Public Schools · Geometry Family Resources April 2020 . ... QT...
Geometry
Family Resources
April 2020
Standards for Mathematical Practices
The Common Core’s Standards for Mathematical Practice (SMPs) focus on what it means for students to be
mathematically proficient. These standards describe student behaviors, ensure an understanding of math, and focus on
developing reasoning and building mathematical communication. Each standard has a unique focus, but each also
interweaves with the others as we put them into practice. These practices empower students to use math and to think
mathematically. The included tasks and activities are an opportunity for students and their families to engage in the
Standards for Mathematical Practice. Below is a quick reference to support thinking about that engagement!
1. Make sense of problems and persevere in solving them • When presented with a problem:
o I identify the meaning of the problem and look for ways to begin solving it. o I make a plan, carry out my plan, and evaluate its success. o I persist in trying to solve it (and change course if needed).
2. Reason abstractly and quantitatively • I make sense of numbers and their relationships in problem situations.
• I use reasoning to take numbers out of a problem and work mathematically with them.
• I can take the mathematics I’ve done with the numbers and understand them in the original problem’s situation.
3. Construct viable arguments and critique the reasoning of others • I make statements about a mathematical idea with the wondering whether it is always/sometimes/never
true.
• I can construct and communicate mathematical arguments.
• I can analyze and articulate the mathematical arguments of others.
4. Model with mathematics • I recognize math in everyday life and use math I know to solve real world problems.
• I use words, numbers, pictures and /or objects to represent a mathematical situation.
• I identify the important quantities -and their relationship to each other- in the situation.
• I draw conclusions based on analysis of my model.
5. Use appropriate tools strategically • I know when to use certain tools (such as graphing calculators, graph paper, etc.) to help me solve problems
and explore and deepen my math understanding.
6. Attend to precision • I am precise when solving problems, thinking about my processes, and communicating my ideas.
• I use mathematical vocabulary when sharing my ideas.
7. Look for and make use of structure • I strive to see and understand patterns and relationships.
• I look for parts of expressions that reveal properties of the expression.
8. Look for and express regularity in repeated reasoning • I notice and describe patterns when solving multiple related problems.
• I pause when solving a problem and look for ideas that I can generalize.
• I make conjectures about what I notice.
Topics:Number Sense, Counting, Probability
Grades:3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Ice Cream Scoop
This is a really nice task as it is open to everyone, can be solved in different ways and
can also extend to work in combinatorics – a nice way of organizing counting. Ask
students to work on this task in groups, and to display their results on posters. Often
we name students’ different approaches and strategies.
Task InstructionsIn shops with lots of ice-cream flavors there are many different flavor combinations,
even with only a 2-scoop cone. With 1 ice-cream flavor there is 1 kind of 2-scoop ice
cream, but with 2 flavors there are 3 possible combinations (eg vanilla/vanilla,
chocolate/chocolate, and vanilla/chocolate).
• How many kinds of 2-scoop cones are there with 10 flavors?
• What about “n” flavors?
• Create a poster that represents your group’s thinking.
MaterialsPencils and Paper
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School Fair Necklaces
Have you ever thought about the mathematics of beading? This challenge will have
you thinking about symmetry and all of the ways you can create different necklaces
with the same beads.
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ReferenceThe NRICH website publishes free mathematics resources designed to challenge, engage
and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support
for teachers by publishing Teachers’ Resources for use in the classroom.
This task can be found at https://nrich.maths.org/9692
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This is a task that combines art, mathematics and design. Students are asked to see and design optical illusions, think about the mathematics inside them and pose mathematical questions for their friends.
Task Instructions:• Optical art consists of geometric shapes and patterns, and is often coloured in black and
white. Look at the three examples, do you see anything about the patterns that cause them to create an optical illusion?
• Using the 100-square grid, create your own interesting pattern. Share your designs with a classmate and find out if they see an illusion when looking at your pattern.
• Did you get any more ideas about the ways to create an optical illusion? Describe your mathematical thinking about ways to do that.
• Can you see any patterns, fractions, or decimals in your artwork? Where are they?• Think of a mathematical question that you could ask about your artwork.• If someone else wanted to recreate your artwork, what directions would you give them?
Materials:• One handout per student• Copies of the 100-square grid handout• Ruler• Colored pencils or markers
Extensions:It is interesting to think about what creates an illusion in optical art. Do optical illusions have certain mathematical properties? One idea would be for the whole class to display their designs and look together to see if certain designs create particular visual properties. If you want to extend this task into a bigger project Wikipedia has some interesting information about optical art.
https://en.wikipedia.org/wiki/Mathematics_and_arthttps://en.wikipedia.org/wiki/Op_art
Reference:Jo Boaler, Michael Jarry-Shore & Cathy Williams
Optical Art Task
Copyright © 2018 youcubed. All rights reserved.
Optical Art Submitted by Jo Boaler, Michael
Jarry-Shore & Cathy Williams
Optical art consists of geometric shapes and patterns, and is often coloured in black and white. This type of art creates illusions, leaving the viewer with the impression that objects are moving, vibrating, pulsating, or warping. Some examples of optical art are given below.
Look at the 3 examples, do you see anything about the patterns that cause them to create an optical illusion?
Using the 100-square grid below, create your own interesting pattern. It may help to use a ruler and it is a good idea to experiment with different designs; doing your best to create a piece of optical art that creates an illusion. Share your designs with a classmate and find out if they see an illusion when looking at your pattern. Experiment with breaking the squares in the grid into triangles, rectangles, and other shapes.
Copyright © 2018 youcubed. All rights reserved. 2
Optical Art
Did you get any more ideas about the ways to create an optical illusion? Describe your mathematical thinking about ways to do that.
Can you see any patterns, fractions, or decimals in your art work? Where are they?
Think of a mathematical question that you could ask about your art work, that you can give to a friend. Ask your friend your question, and ask them to justify their answer – giving clear reasons for the methods and solutions they come up with.
If someone else wanted to recreate your art work, what directions would you give them? Give precise mathematical statements so that someone could recreate your art without looking at it.
Copyright © 2018 youcubed. All rights reserved. 3
Optical Art
Copyright © 2018 youcubed. All rights reserved. 4
Optical Art
Teacher NotesIt is interesting to think about what creates an illusion in optical art. Do optical illusions have certain mathematical properties? One idea would be for the whole class to display their designs and look together to see if certain designs create particular visual properties. If you want to extend this task into a bigger project Wikipedia has some interesting information about optical art.https://en.wikipedia.org/wiki/Mathematics_and_arthttps://en.wikipedia.org/wiki/Op_art
Mathematical StandardsThese are possible CCSS Mathematical Standards, depending on the students’ mathematical pathways:
Mathematical PracticesCCSS. MATH. PRACTICE. 1 Make sense of problems and persevere in solving them.Do students make sense of the diagrams given to them? Do they pose a question about the artwork, considering its mathematical properties?
CCSS. MATH. PRACTICE. 2 Reason abstractly and quantitatively.Do students decontextualize from the art work and consider mathematical relations and properties? Do they attend to the mathematical properties of the diagram?
CCSS. MATH. PRACTICE. 3 Construct viable arguments and critique the reasoning of others.Do students reason when they are answering the question posed by the first student? Do they consider each other’s reasons and notice any flaws?
CCSS. MATH. PRACTICE. 4 Model with mathematics.Do students use the art work to describe patterns and relationships?
CCSS. MATH. PRACTICE. 5 Use Appropriate Tools Strategically.Do students use rulers or other math tools to create their optical illusion?
CCSS. MATH. PRACTICE. 6 Attend to precision. Do students describe their own design clearly, so that someone else can draw it without looking at the original drawing?
CCSS. MATH. PRACTICE. 7 Look for and make use of structure.Do students look for patterns in the artwork, do they see structure inside the art?
Content StandardsThere are a lot of content standards that will be met in this task that will vary depending on students’ grade level. For example, content standards involving geometry, shapes, fractions, decimals, & measurement.
Copyright © 2018 youcubed. All rights reserved. 5
Nine Colors
Are you a fan of Rubik’s Cube? Do you like to build something to solve a problem?
Here is one of our favorite puzzles!
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ReferenceThe NRICH website publishes free mathematics resources designed to challenge, engage
and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support
for teachers by publishing Teachers’ Resources for use in the classroom.
This task can be found at: https://nrich.maths.org/768
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Topics:Number Sense, Number & Operation
Grades:3, 4, 5, 6, 7, 8, 9, 10, 11, 12
The Four 4’s
Jo has used this task with a lot of success on the first days of school with very hesitant
students. Soon after setting the challenge the board area becomes full of students
putting up their solutions, then returning to their seat to look for more. For students,
it is a very safe and non threatening activity. It builds number sense and is a fun
challenge. This task is also a really nice way of helping students become comfortable
sharing their work in front of the class.
Task InstructionsCan you find every number between 1 and 20 using only four 4’s and any operation?
or
Can we as a class find every number between 1 and 20 using only four 4’s and any
operation?
Here’s an example √4 + √4 + 4⁄4 =
Give this challenge to students and write all the numbers from 1 to 20 on the board.
Then ask students to come to the board and write a solution any time they have one.
The more solutions you get for each number the better.
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Hex
Here’s one to make into a puzzle. Print, cut and have some fun! Or take the next
challenge and construct (draw) your own!
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ReferenceThe NRICH website publishes free mathematics resources designed to challenge, engage
and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support
for teachers by publishing Teachers’ Resources for use in the classroom.
This task can be found at: https://nrich.maths.org/795
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