Ten Plus One
A Tool for Enhancing the Depth and Complexity of Math Tasks
In the U.S., students spend most of their time in math class learning and practicing procedures. Often, they often do not understand why the procedures work or even what they mean. The result is fragile knowledge: students forget quickly; they struggle to apply what they have learned to solve problems or learn new concepts; and they lose interest and confidence.
Ten Plus One is a practical tool designed to help teachers transform traditional math tasks into more challenging tasks that promote conceptual understanding. It consists of ten strategies to make tasks deeper and one strategy to enhance complexity.
Ten strategies to enhance depth
- Write a story.
Create a story for a calculation or a real-world context for a concept.
- Draw a picture.
Draw a picture or diagram that shows the meaning of a concept or calculation.
- Explain why.
Justify a prediction, answer, or claim using logic.
- Find another way.
Find a different strategy or another answer.
- Compare and contrast.
Compare and contrast expressions, shapes, patterns, strategies, relationships, etc.
- Start with the answer.
Begin with the answer and find the "question."
- Remove information.
Remove words, numbers, or other elements of the task.
- Solve to learn.
Perform the task as a problem before receiving instruction.
- Build a pattern.
Make or extend a pattern of numbers, equations, or shapes based on the task.
- Ask "What if...?"
Change one or more elements of the tasks. Observe the effects.
One strategy to enhance complexity
- Use more...
digits, numbers, operations, shapes, data, parts, variety, steps, ideas, information, definitions, categories, or relationships.
You can use the ten depth strategies right out of the gate. As you gain experience, you will become more and more effective in designing excellent tasks. The complexity strategy, while not difficult to use, usually takes longer to understand well and is more easily misused. Read the materials below to get started. Even better, collaborate with other teachers as you learn. Please feel free to contact me to ask questions or to request support with professional development.