# “Low Floor, High Ceiling” Problems

“Low Floor, High Ceiling” math problems have multiple entry points so they are accessible to all students, but they can also be solved at higher levels. These rich problems have the following characteristics:

• Require an inquiry approach when solving.
• Do not have a predetermined solution pathway in advance.
• Have many possible representations of solutions and strategies.
• Involve the process of exploring and understanding the deeper nature of mathematical concepts as a by-product of solving the problem.

## Dan’s fourth grade class was asked to come up with their own mathematical questions to investigate after watching this video on an award winning bottling plant in Australia.

Lakota Band leader, Greg Snyder, has a math problem:

How can 272 band members, playing 15 different instruments be placed into arrays that can fit onto a street that’s 57 feet wide?  Continue reading

## Security Camera Equations & Algebra in First Grade

Students in first grade have been working with the equal symbol, and the greater than/less than symbol. They’ve created number stories and equations using the data they collected from counting the number of security cameras the stores in the neighborhood have. Some of these equations are simply true statements, and some have missing addends, or missing sums, depending on the story they created. Continue reading

## Introducing the Equal Symbol as a Relationship Model

Students in first grade are learning that the equal symbol doesn’t necessarily mean to “do” something. It can just mean that a mathematical statement is “true”. Continue reading

## First Grader’s Data Representations of “Safe” and “Unsafe” Lead Them to Social Responsibility.

The students in first grade are learning how to collect data and communicate the results of their data in a representation that makes sense to them.

Both classes spent time outside observing and recording “safe” and “unsafe” events in the neighborhood before each class decided on a topic to collect data on. Safety is also the larger topic they are learning about in social studies. Sarah’s class collected data on bicyclists and whether or not they wore helmets. Ariane’s class collected data on broken benches in the nearby parks. Continue reading

## A rich student-to-student discussion by first graders on the meaning of the equal symbol.

What does: 1 + 7 = ___ + 6

have to do with: 3x + 9 = 5x + 5

…and why are first graders arguing with each other over the meaning of the equal symbol?