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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Topic A. Patterns and Functions

Indicator 1. Identify, describe, extend, and create numeric patterns and functions

Objective c. Complete a function table using a one operation (+, -, ×, ÷ with no remainders) rule

Clarification

Previously, students have been asked to extend patterns by making a generalization that moves them from the results at each level to the results at the next level. The only way that they can find the results at the 100th level using this method is to complete each level through the 99th level. A rule that relates the level number with the results at that level can be used to find the results at any level. A function table is a set of ordered pairs that matches each input value (level number) with an output value (level results). For every input there is only one output. There is a relationship between input and output. This relationship is called a function. Each function has a rule.

Classroom Example 1
InputOutput
26
39
4?
824

Class discussion:

  • What is the relationship between input and output?
    2 + 4 = 6 but 3 + 4 does not equal 9
    2 × 3 = 6 and 3 × 3 = 9
    Check: Does 8 × 3 = 24? Yes!
    So the rule is to multiply the input by 3 to get the output.
    (Rule: Input × 3 = output )
     
  • Now to find the missing function value, apply the rule. 4 × 3 = 12. If the input is 4, the output is 12.
     
  • If the input is 50, what is the output? 3 × 50=150. If the input is 50, the output is 150.
     
  • What if the output is 21? What is the input?
    The inverse operation needs to be applied.
    21 ÷ 3 = 7. If the output is 21, the input is 7.
/instruction/clarification/mathematics/grade4/xml/1A1c.xml