This page is for reflection on the activities I did in my class on diagnosing and directing learning in math

The first activity we did in class was making patterns using toothpicks. This ties into one of the most fundamental math skills, which is working with patterns. It is a good example of a low floor high ceiling task. This means that it is accessible to those struggling with this area of math but also to those who are advanced in it. In this case, those struggling are able to make something while those more advanced in this area are able to challenge themselves to make more complicated patterns. It is also open to interpretation regarding whether to make patterned designs or simply a line of symbols like square, triangle, square repeated.

Another activity we did in class was building 2D and 3D shapes using a variety of materials. This ties into learning geometry by reinforcing what features each shape has. It can be cross-curricular by teaching about structures for science. It is accessible to diverse students because we were given multiple materials to choose from; toothpicks, marshmallows, clay, and pipe cleaners. It is low floor high ceiling because students are free to keep it simple, build the most complex shape they can think of, or do anything in between.

Another activity involved using snap cubes to build rectangular prisms. This also ties into geometry by reinforcing what makes a rectangular prism. The instructions gave the definition in case anyone forgot. The size of the prism is for the individual to decide. It is low floor high ceiling because it can be done many different ways. One can make a solid block or a frame of a prism.

An activity we did on the first day of class was with snap cubes. We had to randomly break a stick of ten into two pieces, show one piece to a partner and have them guess how many are in the other piece. This ties into learning subtraction, because you have to subtract the number shown from ten to determine the other number. I am not sure if I would consider it low floor high ceiling. The skill set required is pretty uniform and there is not a wide range of difficulty levels. Students simply have to know how to subtract from ten.

One activity we did in class was called Snowman Dice. We were given a sheet with all possible numbers you can get from rolling two standard six-sided dice. The task was to roll until every number had come up at least once. It had the option of competing with another person to see who gets all the numbers first. This ties into addition because it requires adding two numbers together on each roll. It is low floor high ceiling if students are given options for the type of dice. Some may prefer numbers while others may prefer counting dots or a combination of the two. Click here for more in depth analysis

Two activities we did in class involved guessing numbers. First, we were asked to choose a number and have the other person ask questions to guess it. A few classes later, we each had a number clipped to our backs and asked other people questions in order to guess it. This can tie into many different aspects of the curriculum. The questions can be about what it is greater than or less than, what factors the number has, tens place and one's place, and other trivia about numbers. This makes it good for every grade level. It is low floor high ceiling because struggling students can stick to what they know while more advanced students can use complex concepts to make it more interesting to them. Click here for more in depth analysis

One activity we did in class was estimating the length of things and then measuring to see how close we were. It ties into the curriculum because it is about measurement and estimation. It can be considered low floor high ceiling because students can measure things that are small and easy for them, or challenge themselves with harder things to estimate.

Another estimation activity we did was estimating the time it would take to perform certain tasks and then timing ourselves to see how close we were in estimating. Once again, estimation and a form of measurement. It is also low floor high ceiling because students can make it simple or complex with the tasks they choose.