This post explores some ideas for reviewing concepts for TEKS A.9C.
write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay
Staar Performance
On recent STAAR tests, here is how students across the state of Texas have performed.
2023 #14 - 37% correct
2023 #36 - 50% correct
Active, Playful Learning
The activities shared in this post are designed to follow the six principles of Active, Playful Learning:
Active
Engaging
Meaningful
Social
Iterative
Joyful
These six principles, together with a clear learning goal, help students learn.
Students learn through active, engaged, meaningful, socially interactive, iterative and joyful experiences in the classroom and out. When we add a learning goal or engage in guided play we achieve Active Playful Learning.
In other words, math review doesn't have to be boring STAAR prep or mindless worksheets. Instead, students' learning is enhanced when playing with numeracy and algebraic concepts in a guided context. Who says math can't be fun? You can watch a video to learn more about Active, Playful learning here.
Activities
Here's a walkthrough of all the activities on this blog post.
Exponential Growth and Decay Scavenger Hunt
Learning objective: Students will find real-world examples of exponential growth and decay.
Pair students together or put them in groups of three.
Give students a digital recording sheet to document their findings.
Students should search for articles or news stories that explain real-world examples of exponential growth and decay.
Simply typing in those terms into a search engine will most likely result in worksheets and practice math sites. Those should be excluded.
On the digital recording sheet, students will copy and paste the URL of the article/news story, explain the real-world context, and write out the exponential function.
Variations
If students struggle with finding real-world examples, provide sample topics (pictured above and on page 2 of the digital recording sheet).
In addition to writing out the equation, have students note the initial amount (a) and the scale factor (b) in the equation.
Have students create a table with the equation, plotting out how the function changes over various time periods (e.g., 1 year, 2 years, 3 years).
Ask students to graph the equation using a graphing calculator or Desmos.
Exponential Card Sort
Learning objective: Students will classify problems involving exponential growth and decay.
Pair students up and provide each pair a set of cards that have word problems involving exponential growth and decay.
Have students sort the cards into categories, one for exponential growth and the other for exponential decay.
Ask students to discuss how they knew which cards went into the exponential growth category and how they knew which cards went into the exponential decay category.
As a class, create an anchor chart of all the key words found in each category that explicitly describe exponential growth and decay (e.g., increase, decline).
Variations
After students sort the cards, have them write an equation for each of the cards.
Ask students to solve one card from each category.
Ask students to rewrite one card in each category, using key words from the class anchor chart, so that the exponential function changes from growth to decay or vice versa.
Allow students to create their own problems and swap them with another group to sort.
Exponential Matching
Learning objective: Students will match verbal descriptions of exponential situations with their corresponding functions.
Students play in pairs or groups of fours.
Give each group a shuffled set of matching cards.
Play follows the rule of memory match (i.e., students flip two cards over at a time and keep them if they match), where the match is between a verbal description and an exponential function.
Play continues until all the cards have been matched.
Variations
Students can play alone for individual review.
Make two groups of face-down cards, one for the functions and one for the verbal descriptions.
If using the two groups of face-down cards, have students pick one from the verbal description group first. Before picking a face-down card from the function group, students should say or write the exponential function they are looking for.
After play has ended, have students take two of their matches and find the value of the problem situation after 5 time units (e.g., days, hours, weeks, months) and a standard initial amount (e.g., 30).
Exponential Story Problems
Learning objective: Students will create story problems to fit the context of an exponential growth/decay scenario.
Give students example real-world contexts for exponential growth and decay.
Have students generate values for the initial amount (a), growth/decay factor (b), and the time unit (x).
With the values and context now decided upon, have students write a story problem to fit the scenario.
The problem should give the initial amount/y-intercept (a), the growth/decay factor (b), and the time unit (x). It should ask the person solving the problem to write an equation representing the function.
Have students switch their problems with a partner and ask each partner to write an equation to match the new story problem.
Variations
Give students limitation for the values to use (e.g., make the rate a growth factor with a shallow curve, make the y-intercept greater than 10).
Have students solving their partner's problem not only write an equation but also sketch a graph to match. They should then check their graph with a graphing calculator.
Allow students to partner up and provide editing feedback for the story problems, ensuring clarity of the problem and proper conventions.
Instead of writing a matching equation from the story problem, have students give the equation and omit another component (e.g., initial amount, growth factor). Allow partners to identify the missing amount in the context from the given equation.
Take some of the best story problems and create a short extra credit assessment for the class.
Exponential Variants
Learning objective: Students will create variants for a given exponential function.
Give students an exponential function to work with [e.g., f(x)=300(2)^x].
Provide students with common situations for growth and decay contexts in exponential function word problems.
Ask students to write a word problem for that exponential function using three different contexts (see example).
Have students swap their three examples with a partner to solve.
Variations
Pair students up or even put them in a small group to provide extra support for writing the story problems.
Model how to write one story problem for the class and ask them to write the other two.
After writing the scenarios, have students use different colored highlighters or markers to note the following in the function and the story problems: the initial amount, the growth/decay rate, the time period (see page 2 of the example).
After students solve their partner's problem, have them create a table of values and a graph for the function.
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