What does a mathematician do?

We live in a world filled with mathematics. You measure and count from the moment you wake up. A measuring and counting device, called a clock, probably wakes you. There is a lot of mathematics behind the design of clocks.

Barkley and Ted realize that mathematics is not just numbers and number facts. Mathematicians look for and describe patterns. Applied mathematicians may use what they’ve learned to draw conclusions about the world, or they may look for these patterns simply because it’s fun.

Mathematicians begin with a set of basic assumptions that seem reasonable. From these ideas they develop systems of thinking that are useful in solving problems and working in the real world. Euclid’s geometry is one example of a system of thinking that is used by builders and physicists the world over.

Mathematicians use a common vocabulary, conventions, and similar experiences to share what they learn with other mathematicians. In many ways, we are all mathematicians as we recognize patterns and apply abstract concepts.

The National Council of Teachers of Mathematics (NCTM) has identified several topics or strands of mathematics important for all learners. These include:

* Number and Operations – the ability to understand numbers and the meanings of operations and how they relate to one another

* Algebra – the ability to understand patterns and relationships

* Geometry – the ability to analyze characteristics and properties of geometric shapes and locations

* Measurement – the ability to apply techniques, tools, and formulas to understand an object’s attributes that can be measured

* Data Analysis and Probability – the ability to select and use appropriate statistical methods to analyze data

* Problem Solving – the ability to solve problems and build new mathematical knowledge through problem solving

* Reasoning and Proof – the ability to recognize and use various types of reasoning and methods of proof

* Communication – the ability to communicate mathematical thinking to others

* Connections – the ability to recognize and understand how mathematical ideas interconnect and build on one another

* Representation – the ability to create and use representations to model and interpret mathematical ideas

NCTM would agree with Barkley’s computer that there’s much more than numbers and number facts to mathematics and what mathematicians do.

**What does a mathematician do?**

**National Council of Teachers of Mathematics Standards:**

Geometry: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

This activity helps students learn to graph ordered pairs.

**(BACKGROUND INFORMATION)**

This is what we already know about mathematicians:

- Mathematicians look for and describe patterns.
- Applied mathematicians may use what they’ve learned to draw conclusions about the world, or they may look for these patterns simply because it’s fun.
- Mathematicians begin with a set of basic assumptions that seem reasonable.
- Mathematicians use a common vocabulary, conventions, and similar experiences to share what they learn with other mathematicians.

**Activity – Navigating Through Coordinates**

graph paper (with added drawings)

**Pre-Lesson Instructions:**

- Prior to the lesson, transfer the animal drawings on the graphs at the end of the directions to graph paper for each student. You may choose to create overhead transparencies of each graph instead of giving each student their own copies of each graph.

- Review some of the traits of mathematicians with your students by watching the video newsbreak “What does a mathematician do?” Discuss that one thing mathematicians do is look for patterns and ways to describe patterns and location. Discuss with your students the importance of using mathematics to identify specific locations.
- In this lesson, students will use ordered pairs to identify a specific location. Remind students that the first number in an ordered pair is found on the horizontal line, and the second number is found on the vertical line. Draw a sample graph on the board and practice these concepts. Draw a straight line on the graph paper that goes through specific points. Ask students to name the points using ordered pair.
- Give each student graph paper with the added drawings OR instruct students using overhead transparencies of the graphs.
- Ask students to describe the location of the animals (crab, sheep, bird, guinea pig, rabbit) on the graph paper. For the first graph, ask these questions:
- What animal is found at (1,1)?
- Where is the guinea pig?
- The bird is at ______?
- What animal is at (2,5)?
- Where is the rabbit?

- Ask students to describe the location of the animals on the second graph. Use these questions:
- What animal is found at (2,2)?
- Where is the guinea pig?
- The bird is at ____?
- What animal is at (3,9)?
- Where is the rabbit??

- Discuss whether this is an easy or hard task. What would make this task easier?

First Graph:Second Graph:

**Extension:**

Give students blank graph paper with labeled axes. Ask students to place their own drawings on the graph and write questions about the location of the drawings. Allow students time to switch graphs and questions to practice the use of coordinate pairs.