Summary
In this activity, students will apply formulas common in secondary and early college-level mathematics in the context of a descriptive scenario. They will apply what they learned during "Power Up: Math ACT Prep, Week 8" to solve story problems that require formulas that are not given. Students will review common formulas used to solve ACT-style questions and apply that learning to practice questions in the style of ACT math problems. This is the ninth activity in a 10-week "Power Up" series for ACT prep.
Essential Question
How can I increase my ACT score?
Learning Objectives
Identify and algebraically represent critical information from a story problem.
Apply formulas and problem-solving skills to story problems.
Materials List
Activity Slides (attached)
Formulas and Stories cards (attached; one set per pair; printed front only)
Formulas handout (attached; one per student; printed front/back)
Exit Ticket handout (attached; one per student; printed front only)
Pencil
Paper
Highlighters
Calculators
Introduction
10 Minute(s)
Introduce the activity using the attached Activity Slides. Use the Bell Ringer strategy to begin class. Have students get their calculators; follow regular classroom procedures for this.
Once students have their calculators, display slide 3 and have students independently answer the question on a piece of notebook paper or elsewhere if you have a classroom norm for bellwork. After a minute, ask for a volunteer to share how they answered the question. Share that the answer is A. Use slide 4 if you need to review a sample response.
Show slide 5 and facilitate a brief discussion over the steps for solving a story problem from “Power Up: Math ACT Prep, Week 8”: (1) drawing a quick sketch, (2) labeling the known, (3) labeling the unknown, and (4) writing an equation. Then ask the class what they think would be helpful for that last step of writing equations. If the response of “knowing formulas” is not quickly shared, ask the class what they needed to know to complete the Bell Ringer (that the problem did not give them). They needed to know the formula for slope.
Share the essential question on slide 6 and the learning objectives on slide 7.
Activity
15 Minute(s)
Have students find a partner or assign partners, then display slide 8. Let students know that there are a lot of formulas that they will need to know for the ACT. It is impossible to give students a complete list of formulas that will be needed for the ACT, as the ACT has a variety of questions. Often a formula needed on the last exam is not needed for the following exam. Explain that the formulas on the cards they are about to see are some of the most common formulas on the ACT that are not otherwise part of this activity series.
Remind students that they already know many formulas that they will likely need for the ACT. For example, they know how to find the perimeter and area of a rectangle; they know the quadratic formula (from Algebra 2); they used the formula for slope to answer the Bell Ringer. Again, be encouraging—it may feel like they need to know so much, but they already do! Their confidence and attitude towards the ACT plays a key role in their performance.
Let them know that today, they will see some formulas that they may remember and some that might be new to them. Give each pair a set of the attached Formulas and Stories cards and introduce them to the Card Matching strategy. Direct students to match each story card with the formula card they think is the best match.
After 2-3 minutes, depending on how quickly the class is completing the card matching, tell students that they have one more minute to finalize their card matching. Give each student a copy of the attached Formulas handout and a highlighter. Then transition to slide 9. Direct students to check their card matches with their handout. Have students use a highlighter to highlight on their handout (not on the cards) what part of the story problem prompted them to match it with that formula. Ask for different volunteers to share how they knew which formula to match with each story problem. Ask the class which formulas they remembered, had forgotten or had not seen in a while, or if any were new. Let students know that the ACT assesses a lot of secondary mathematics content, so it is likely that they will not know all of the formulas needed to answer every question. For example, students in Algebra 2 may not be familiar with the Law of Sines since that is traditionally taught during a Precalculus course, but there may be a question on the ACT asking students to use that formula. For new or forgotten formulas, spend time explaining to the class more details about that formula.
D = R·T is distance = rate · time. Let students know rate is also referred to as average speed because it is the “rate” at which one travels a certain distance during a certain time.
Remind students of the difference between the circumference and area of a circle. Also let students know that they do not need to memorize the formula for the area of a triangle, because a triangle is just half of a rectangle; they already know the formula for the area of a rectangle.
The “formulas” for measures of central tendency are sometimes considered more “math facts” than “formulas,” but remind students of the difference between mean, median, and mode.
Combinations and permutations are likely new formulas for students. However, let them know that they do not need to memorize the formulas; instead, show them how to use their calculator for this. If students can pick between combinations and permutations, then their calculator can help them with the calculations.
Lastly, remind students how to find the volume of any prism: the area of the base times the height of the prism.
Encourage students to make notes on their handout as the class reviews each new formula. There is extra space at the bottom of the back of their handout for them to write any formulas they personally struggle to remember that are not already listed; they will return to this during the Wrap-Up.
Show slide 10 and give students some advice for the ACT: if you forget a formula, make a guess, make a mark (bookmark) the question to later return to, and then move on to the next question. Consider also sharing that, similarly, if a formula is given, but one is unsure how to solve for the unknown, using guess and check with the answer choices is a good approach.
Wrap-Up
10 Minute(s)
Display slide 11 and use the Exit Ticket strategy to individually assess what students have learned. Explain to students that they will have five minutes to answer five questions. Give each student a copy of the attached Exit Ticket handout and have students keep their paper face down until you start the timer. Once everyone has a copy of the handout, tell them to turn their paper over. Start the 5-minute timer on the slide.
After the time expires, show slide 12 and review the answers with the class. Remind students that the ACT is not designed for everyone to earn a perfect score and that it is okay if they only answered approximately half of the questions correctly on this assessment.
Show slide 13 and direct students’ attention to the bottom of the back of their Formulas handout. Direct students to write down any formulas or math facts that they forgot or did not know or that are not already listed on the handout, as the class reviews the questions from the Exit Ticket handout. Use slides 14-20 as needed to review the work for the given questions.
Before you dismiss, show slide 21: You Powered Up! and remind students to practice the action they selected on their Goal Setting handout from week 1. Encourage them to add an action of “memorizing and applying formulas” if this is an area in which they would like to improve.
Next Step
Complete the following week’s activity, “Power Up: Math ACT Prep, Week 10,” which will focus on right-triangle trigonometry.
Research Rationale
Standardized testing in high schools has long stood as a metric for assessing college readiness and school accountability (McMann, 1994). While there has been debate surrounding the accuracy of such metrics, as well as concerns regarding equity, many institutions of higher education continue to make these scores part of the admissions process (Allensworth & Clark, 2020; Black et al., 2016; Buckley et al., 2020). Aside from admissions, it is also important to keep in mind that standardized test scores can also provide students with scholarship opportunities they wouldn’t otherwise have (Klasik, 2013). Though the topic of standardized testing continues to be debated, effective test prep can ensure that our students are set up for success.
With several benefits to doing well on college admissions tests, it is important to consider how best to prepare students for this type of high stakes test. Those students from groups that may historically struggle to find success, such as those in poverty or first generation college students, especially stand to benefit from effective test preparation (Moore & San Pedro, 2021). The American College Test (ACT) is one option students have for college admissions testing that is provided both at national centers and school sites. Taking time to understand this test including the timing, question types, rigor, and strategies for approaching specific questions can help to prepare students to do their best work on test day and ensure their score is a more accurate representation of what they know (Bishop & Davis-Becker, 2016).
Resources
Allensworth, E. M., & Clark, K. (2020). High school GPAs and ACT scores as predictors of college completion: examining assumptions about consistency across high schools. Educational Researcher, 49(3), 198-211.
Bishop, N.S. & Davis-Becker, S. (2016). Preparing examinees for test taking: guidelines for test developers and test users. 2nd edition. Crocker, L. (Ed). In Handbook of test development (pp. 129-142). Routledge.
Black, S. E., Cortes, K. E., & Lincove, J. A. (2016). Efficacy versus equity: what happens when states tinker with college admissions in a race-blind era? Educational Evaluation and Policy Analysis, 38(2), 336–363. http://www.jstor.org/stable/44984542
Buckley, J., Baker, D., & Rosinger, K. (2020). Should state universities downplay the SAT?. Education Next, 20(3).
K20 Center. (n.d.). Bell ringers and exit tickets. Strategies. https://learn.k20center.ou.edu/strategy/125
K20 Center. (n.d.). Card matching. Strategies. https://learn.k20center.ou.edu/strategy/1837
K20 Center. (2021, September 21). K20 Center 5 minute timer. [Video]. YouTube. https://youtu.be/EVS_yYQoLJg?si=fJvuvFWH3vJ3B0z9
Klasik, D. (2013). The ACT of enrollment: the college enrollment effects of state-required college entrance exam testing. Educational Researcher, 42(3), 151–160. http://www.jstor.org/stable/23462378
McMann, P. K. (1994). The effects of teaching practice review items and test-taking strategies on the ACT mathematics scores of second-year algebra students. Wayne State University. https://www.monroeccc.edu/sites/default/files/upward-bound/McMannP.-the-effects-of-teaching-practice-review-items-ACT-mathematics-second-year-algebra.pdf
Moore, R., & San Pedro, S. Z. (2021). Understanding the test preparation practices of underserved learners. ACT Research & Policy. Issue Brief. ACT, Inc. https://files.eric.ed.gov/fulltext/ED616526.pdf
