Investigating PatternsCornell Notes & Additional Activities

Topic: Investigating Patterns

Tool Box: Numeric and graphic representations of data

Linear vs. non-linear data

Pattern recognition

Predictions based on patterns

How do I look for patterns?

When looking for a pattern compare the numbers in the 1st column to all the other columns. Look for numbers changing using addition, subtraction, multiplication or division.

What is a variable?

A variable is a letter or symbol used to represent one or more numbers.

How is an expression used?

An expression can be used to solve for any given value. Just substitute the given value for the variable.

Topic: Investigating Patterns

How do I graph data?

After deciding what data will be graphed, decide what number scale will be most appropriate. What is the lowest and highest numbers that occur in your data, can I count by 1’s, 2’s etc. Then make sure to label the x and y axis correctly using the titles of the columns. Then plot your points.

What does a Linear Model look like?

A Linear Model is a set of data that has a constant rate of change (slope) and a graph that looks like a line.

What are equivalent expressions?

Equivalent expressions give the same result for any given input, but the expressions look different.

What are multiple representations?

Multiple Representations are used to display data and to find answers and/or predictions. The 4 multiple representations are data table, expressions, graphs, and verbal problems.

Activity 1.1

1 3 3 3

2 6 12 3

3 9 27 3

4 12 48 3

1) Describe any patterns you notice in the table of values

2) Assume the pattern in each column continues. If you were given a random number, how would you determine if the number would appear in one of the columns.

3) Based on your investigation of the table of values, how could you label the columns? Explain your reasoning.

4) Write an expression that represents this relationship between numbers in the same rows in columns 1 and 2. Explain how you could use this expression to determine the value in row 45 of column two.

5) Create a graphical representation of the relationship between two columns in the table.