This problem requires children to think about factors and multiples and, in particular, common factors, but it is not necessary for them to have met this term prior to having a go at the task. It offers opportunities for pupils to ask their own questions, find examples, make conjectures and begin to generalize.

This activity provides students an opportunity to go through the data cycle process focusing on a statistical investigative question based on something students would like to learn about themselves. In our day-to-day experiences we are surrounded by variability and this activity provides students an opportunity to formulate a question that can be answered with data, as they collect, consider, and analyze the data and then interpret and communicate their findings. We are thankful for Giorgia Lupi and Stefanie Posavec who shared their Dear Data journey with the world.

This task is an opportunity for students to think about why the rules of exponents work, so they can use them with that understanding, rather than trying to remember rules. The handout has a table with some sections already completed so students can complete the rest by noticing patterns and discussing them.

Many students in the US think of Pi as a number they should memorize, when the most important idea for students to learn is that Pi is a very cool relationship, that exists inside all circles in the world. In this task students will find that relationship themselves, through cutting and folding, and be asked to reflect on it.

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.

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

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.

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.