NY Next Generation Math AI-F.LE.1

AI-F.LE.1 is a cluster heading. These are the individual standards under it.

• AI-F.LE.1.a

  Justify that a function is linear because it grows by equal differences over equal intervals, and that a function is exponential because it grows by equal facto...

• AI-F.LE.1.b

  Recognize situations in which one quantity changes at a constant rate per unit interval relative to another, and therefore can be modeled linearly.

01

What Students Need to Do

Students distinguish Algebra I situations with additive change from those with multiplicative change. Equal differences signal linear models, while equal factors or constant percent change signal exponential models.

02

What Mastery Looks Like

The student uses a table, graph, equation, or context to classify the model and justify the choice. The explanation identifies a constant difference, factor, rate, or percent over equal intervals.

03

Common Misconceptions

Students may classify every increasing pattern as exponential or rely only on a graph's appearance. They may confuse adding a fixed amount with increasing by a fixed percent.

04

How to Assess It

Give one savings account adding $20 monthly and another increasing 4 percent monthly. Ask students to classify each and justify using equal intervals.

1. 01

   Build tables with equal-interval cards and mark successive differences or ratios.

2. 02

   Ask students why adding 10 each period differs from growing 10 percent each period.

3. 03

   Play model sort with linear and exponential tables, graphs, equations, and situations.

4. 04

   Compare a fixed-pay raise with a percentage raise over several years.

• AII-F.LE.5

  Interpret the parameters in a linear or exponential function in terms of a context.

• NY-8.F.3

  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear.