Week 3: Grades 6-8

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 6-8)

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

Download PDF Download Video (Chrome browser)
Download Poster

Day 2
Toothpick Squares (Grades 6-8)

This activity allows students to see a growth pattern in different ways. We use the number talk approach to debrief the way students are ‘seeing’ the toothpicks so others have an opportunity to see different ways of looking at the problem. This helps students realize that there are different strategies for solving problems in maths and that maths is about generalizing how we see patterns. In this problem students will have an opportunity to generalize the number of toothpicks needed to make any size square. Some may choose to take this pattern further by using toothpicks and marshmallows to consider a 3-D pattern.

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

Download PDF Download Video (Chrome browser)

Day 3
One Cut Geometry (Grades 6-8)

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

Download PDF Download Video (Chrome browser)

Day 4
Art of Patterns (Grades 6-8)

We talk about how mathematics is a creative open subject so this activity is an opportunity to connect some artwork with mathematics. Contemporary artist Sol LeWitt used lines, squares, and cubes to create wall drawings and three-dimensional structures.

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

Download PDF Download Video (Chrome browser)

Day 5
Framing Rectangles (Grades 6-8)

In this activity students explore the relationship between the area of a rectangle and the number of squares that make up a border around it. This activity provides students an opportunity to explore the operations of addition and multiplication, and area and perimeter. Students will work to find patterns as they organize data and look for ways to record their observations. This activity makes space for young mathematicians to count, describe shapes, explore ideas, build with square tiles, investigate conjectures, analyze patterns, organize findings, add and takeaway square tiles, and create visuals to explain and justify their thinking.

Content: Counting, making rectangles, making borders, organize findings, making conjectures, exploring

Download PDF Download Video (Chrome browser)

Messing with Pascal (Grades 6-8)

This activity allows students to explore number patterns within Pascal’s Triangle. They will investigate and ask questions about what happens as constraints are changed. This task is an example of ways mathematicians explore and adapt patterns.

Content: Patterns, Pascal's triangle, investigating, organize findings

Download PDF

Computational Thinking by Polyup (Grades 6-8)

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, Numerical Methods, Logical Thinking, Algorithmic Thinking, Intermediate Problem Solving

Visit Polyup Today! Watch Video in New Window