Subject Area
Math

Activity Overview
If you had to count the number of cells there were in a 10 inch by 10 inch flat surface, what would be the best way and or ways to estimate it without counting every cell?

Objective
Students will calculate and estimate the number of cells in a 10 by 10 inch flat surface.

Materials
paper and pencil
ruler
math journal

Estimation

Discuss the concept of rounding and giving an estimation. Have each student estimate how many cells are on the surface of the (represented) box. Break students up into groups of three.
Have students:
1. Estimate of the number of cells.
2. Computing the answers. Write those totals down in the journals.
3. Reflect in their journals the estimates, real answers, and methods that would be the best way to count the cells without counting each one individually.
4. Check with another person and see if the answers are close to one another. Reflect on why or why not.
5. Figure out how people count the number of people in a outdoor concert without every counting each person individually.

Assessment Options
Check for the accuracy of their answers in their journals.

Standards and Benchmarks
Standard 1: Uses a variety of strategies in the problem-solving process
1. Understands how to break a complex problem into simpler parts or use a similar problem type to solve a problem
5. Represents problem situations in and translates among oral, written, concrete, pictorial, and graphical forms
6. Generalizes from a pattern of observations made in particular cases, makes conjectures, and provides supporting arguments for these conjectures (i.e., uses inductive reasoning)
7. Constructs informal logical arguments to justify reasoning processes and methods of solutions to problems (i.e., uses informal deductive methods)

Standard 3: Uses the basic and advanced procedures while performing the processes of computation
3. Selects and uses the appropriate computational methods (e.g., mental, paper and pencil, calculator, computer)
7. Knows when an estimate is more appropriate than an exact answer for a variety of problem situations

Standard 4: Understands and applies basic and advanced properties of the concepts of measurement
6. Selects and uses appropriate units and tools, depending on degree of accuracy required, to find measurements for real-world problems
7. Understands formulas for finding measures (e.g., area, volume, surface area)
8. Selects and uses appropriate estimation techniques (e.g., overestimate, underestimate, range of estimates) to solve real world problems

Standard 7: Understands and applies basic and advanced concepts of probability
3. Understands how predictions are based on data and probabilities (e.g., the difference between predictions based on theoretical probability and experimental probability)

Standard 8: Understands and applies basic and advanced properties of functions and algebra
11. Understand the properties of arithmetic and geometric sequences (i.e., linear and experimental patterns)

Standard 9: Understands the general nature and uses of mathematics
1. Understands that mathematics has been helpful in practical ways for many centuries
2. Understands that mathematics often represent real things using abstract ideas like numbers or lines; they work with these abstractions to learn about the things they represent