Wyoming Math F.LE.1a
The Standard
Distinguish between situations that can be modeled with linear functions and with exponential functions. Verify that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
2023 Wyoming Mathematics Content and Performance Standards · Construct and compare linear, quadratic, and exponential models and solve problems.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare outputs at equal input intervals. They decide whether the outputs change by a fixed amount or a fixed factor, then use that pattern to classify a table or story.
What Mastery Looks Like
- A student can show that 20, 15, 10, 5 drops by 5 each step, while 20, 10, 5, 2.5 halves each step. They name the first pattern linear and the second exponential, even though both decrease.
Common Misconceptions
- Students may call any growing pattern exponential. They may check for a common factor across unequal input intervals or mistake a fixed percent change for a fixed amount.
How to Assess It
- Give students two tables with inputs 0, 1, 2, 3: A has outputs 4, 7, 10, 13, and B has outputs 4, 8, 16, 32. Ask them to label each pattern and show the differences or factors that prove it.
Lesson moves
Ways to Teach It
Start with two tiles, then add three tiles each round for one set and double the tiles for another; record both counts.
Ask students to explain why 5, 10, 15, 20 and 5, 10, 20, 40 need different models.
Give pairs six output cards to sort into linear, exponential, or neither, then have them check differences and factors.
Compare a savings account receiving $20 each month with one earning 2% interest each month; calculate three months of balances.
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Printable F.LE.1a Worksheet
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