Week 3: Grades 9-12

This Week of Inspirational Math is dedicated to Maryam Mirzakhani

It is with both pleasure and sadness that I dedicate this year’s “Week of Inspirational Mathematics” to the life and work of my friend and colleague who tragically died recently – the mathematician Maryam Mirzakhani. A few months ago we held a workshop for middle school girls at Stanford, I discussed the workshop with Maryam before-hand and we agreed that I would share her photos and ideas – many of the girls came up to me afterwards and said that learning about Maryam changed everything for them.


Click here for the full text of Jo Boaler’s dedication, a radio show and video about Maryam, and a topology task honoring her work


Day 1
Building Shapes (Grades 9-12)

This is one of our favorite team building activities. Students work together using a rope to create 3-D shapes. The teacher plays the role of the skeptic and asks students to justify how they know their shape satisfies its defined characteristics. Students will need everyone in their group to successfully build these complex shapes and provide a convincing argument.

Content: Describing and making 2-D and 3-D shapes, making convincing arguments, critiquing other people's arguments, developing proof

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Day 2
Number Visual Pennies (Grades 9-12)

This activity allows students to explore a visual pattern. Students use visuals to think about numbers and find a total. This problem allows students to solve it in a variety of different ways. This activity connects to solving systems of equations. Students can share their different strategies for approaching the problem with each other.

Content: System of equations, making conjectures, investigating, number sense, generalizing

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Day 3
One Cut Geometry (Grades 9-12)

This is a mind-blowing activity! We love it here at youcubed and every time we have used it people walk away celebrating the challenge and their mistakes! The goal is to create 2-D geometrical shapes by cutting them out of a folded piece of paper with just one cut. Are you intrigued? Join us on a wonderful adventure.

Content: Symmetry, shapes, investigating, making conjectures, testing conjectures

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Day 4
Irrational Folding (Grades 9-12)

This activity is designed to give students the opportunity to explore, visualize, and create a representation of the relative lengths of the square roots from 1-10. This is very important as the brain scientists we meet with tell us that we hold numbers in our brains on something like a number line. Do you see irrational numbers on a line when you think of them? Many times we learn about square roots without the context of the magnitude of the value of the number. Students will be challenged to make sense of the length of each of these square roots in relation to each other. Have students work together in groups on this task since they will need each of their experiences and ideas to come up with strategies for showing the different square roots on the origami paper.

Content: Square roots, area, relationship of a square's area and dimensions, coordinate plane, number line, Pythagorean theorm, triangle relationships, rewriting square roots

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Day 5
Square Mania (Grades 9-12)

In this activity students look into a pattern and diagram where their first task is to verify the number of lines and squares. This is often a great discussion between students because some of the objects they need to count are not obvious. This has been a favorite task of our students and some have spent a lot of time working on it beyond class time. That makes it a perfect low-floor high-ceiling task! Doing math doesn’t mean that we must resolve a problem by the end of class time. Mathematical thinking can go on for as much time as students want to commit to the task.

Content: Counting, area, making conjectures, using conjectures, investigating

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World Wealth (Grades 9-12)

In this activity students will experience mathematics as a powerful tool for understanding the world and making sense of data. Students will simulate the distribution of wealth throughout the world by dividing up cookies to model the amount of wealth on each continent. We like to use cookies for this activity. You can substitute some other model for the representation if cookies aren’t your best option.

Content: Proportional reasoning, analyzing and representing data

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Skip Pattern (Grades 9-12)

This activity requires students to work together to make sense of a visual pattern. There is space in this activity for students to experience multiple ways of seeing patterns and working to describe and explain what they see. This pattern is different from other patterns they may have seen because this visual shows every fifth case. This may be confusing to students at first. Give them freedom to explore the patterns in the different ways they choose.

Content: Pattern finding, generalizing, geometric representation, number sense

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Computational Thinking by Polyup (Grades 9-12)

Polyup is a free and open computational thinking playground where students can experiment with numbers and functions. Students will "mod", or modify, a variety of expressions, equations, and algorithms to solve mathematical puzzles and discover the beauty of math in a visual environment. With self-paced activities geared towards 3-5th, 6-8th, and 9-12th grades, Polyup works great as a supplement to any math classroom. It is available on the web and runs on any device, including Chromebooks, phones, and tablets.

Content: Number Sense, Operations, Order of Operations, Functions, Sequences, Series, Numerical Methods, Calculus, Logical Thinking, Algorithmic Thinking, Advanced Problem Solving

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