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.

Students build and draw three-dimensional cubes made up of small unit cubes. Student study patterns by analyzing the number of sides painted of each unit cube, which made up the larger painted cube.

This is a youcubed favorite which comes from Mark Driscoll. The activity encourages students and teachers to engage in visual, creative thinking. We have coupled MarkÕs activity with asking students to reason and be convincing, two important mathematical practices.

Students will use technology to explore products and the patterns as they complete charts.

This activity allows students to explore how numbers are composed, by having them look at different ways of grouping them. There are many different strategies and methods students can use to come up with a solution. Students can use actual pennies, draw diagrams, and use charts to keep track of their findings. As students explore they will notice many different patterns in the numbers they are exploring.

This is a fun drawing activity that gives students an opportunity to represent their math facts.

This is a quick game that can be played to practice addition. It provides fun by tempting a player with making that next roll to get a higher score. Soft dice or an app to simulate a dice roll can make this a quiet activity for fun and practice.

HereÕs a game where students can color patterns in a hundred chart showing multiples of a number they have rolled.

This game provides students an opportunity to practice addition, subtraction, multiplication and division as they try to reach 100 on a number chart. The game can be modified by adding more dice or using dice with more than 6 sides. Students will have fun playing as well as making up their own rules for a new game.

This task comes from a book in a series of three books by Math Solutions, called Math for All: Differentiating Instruction. ItÕs a good way for students to experience different patterns on a number line. The focus is on patterns and provides students options for picking their own starting numbers. ItÕs great for building vocabulary and thinking mathematically.

This is a paper and pencil version of an old game. It is fun for young children and anyone can enjoy the game of chance mixed with the fun of finding a strategy. There is even more opportunity for conversation about odds and probability.

We often see growth pattern tasks that focus on numerical questions like ÒHow many squares are in the 100th case?Ó or ÒHow many squares are in the nth case?Ó These are good questions, but we only ask them after we focus on what the shape looks like and how it grows. We start by asking students ÒHow do you see the shapes growing?Ó and we ask that they make their answer entirely visual, that they forget about counting and numbers. Color coding is often a great tool for this.

This task comes from a book in a series of three books by Math Solutions, called Math for All: Differentiating Instruction. This is another investigation where students can practice addition and think about combinatorics Ð a nice way of organizing counting. The task ends with asking students to write about their thinking.

It seems that taxis have been a part of my life for years. When I was a teacher and academic in London I would see the iconic Black cabs zipping around the streets of London, and I would occasionally travel in them. It was years later when these Black cabs became important again, as some of the first evidence on the plasticity of brains Ð even adult brains Ð came from studying the brains of drivers of Black cabs in London (see video link below). Researchers found that after their intensive spatial training the brains of the drivers of Black cabs strengthened and grew. Years later I was teaching my freshman class when I met Tessa, who proposed this taxi activity for youcubed.

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. The first appearance of four 4Õs was in English mathematician: WW Rouse BallÕs Mathematical Recreations and Essays in 1892, and then revisited by Constance Reid in ÔFrom Zero to InfinityÕ in 1955.

Children will develop the concept of inclusion, that larger numbers ÒincludeÓ smaller numbers.

This is a great game with lots of strategy. High school students enjoy playing! The game provides a great way to practice and build fluency in single digit multiplication. If a player needs support, tools like calculators and times tables can be provided. We have also included two versions of the game board, one 6 x 6 grid and the other an 8 x 8 grid. During and/or after playing students can discuss strategies. During play students can justify their product at each turn through words, symbols or pictures. Students will also enjoy making up their own rules for new games.

This game is a great way to practice and build fluency with the addends 0 Ð 12. As students develop new strategies they will begin to use subtraction. Encourage students to discuss, write about or illustrate their strategies after they have played. You can also ask students to explain why they are choosing their addend and to justify the sum of their addends during play.

Students explore the area of trapezoids as they draw different examples of trapezoids.