Activity: Mystery Functions

Download:	Mystery_Functions.xls - with the answers available (right click to save, left click to open)
	Mystery_Functions_Hidden.xls - with the answer columns hidden (right click to save, left click to open)

Overview: There are 20 different mystery formulas in this spreadsheet. For each one the student enters several numbers for the "Input" and examines what comes out for the "Result", trying to determine each function by looking for patterns.

Instructions:

• Open the spreadsheet to be seen by the entire class, or have individual students open it at their own computers.
• Explain to students that this spreadsheet has 20 different formulas that they need to discover.
• To figure out each formula they are to try several different numbers in the "Input" box for each problem. Then they are to examine what they get in the "Result" box each time. They should look for patterns to determine what the formula is. The may wish to write down the info from their trials.
• When they think they have an answer, they can check it by clicking in the corresponding box under "Formula". The function will be shown in the formula bar above the sheet.
• The 20 functions get harder as they go, starting with one operation, then progressing to two operations, the use of parentheses, and finally exponents.
• This activity is great for investigating patterns, working with variables and algebraic expressions, and order of operations.

Standards (Ohio Academic Content Standards):

• Math - Grade 2 - Patterns, Functions, and Algebra
  • #3 - Create new patterns with consistent rules or plans, and describe the rule or general plan of existing patterns.
• Math - Grade 3 - Patterns, Functions, and Algebra
• #3 - Use patterns to make predictions, identify relationships, and solve problems.
• #7 - Create tables to record, organize and analyze data to discover patterns and rules.
• Math - Grade 4 - Patterns, Functions, and Algebra
  • #1 - Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications.
  • #4 - Use rules and variables to describe patterns and other relationships.
• Math - Grade 5 - Patterns, Functions, and Algebra
  • #1 - Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs.
  • #3 - Use variables as unknown quantities in general rules when describing patterns and other relationships.
• Math - Grade 6 - Patterns, Functions, and Algebra
  • #1 - Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.
  • #2 - Use words and symbols to describe numerical and geometric patterns, rules and functions.
• Math - Grade 7 - Patterns, Functions, and Algebra
  • #1 - Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.
• Math - Grade 8 - Patterns, Functions, and Algebra
  • #8 - Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.