Power Up: Math ACT Prep, Week 8

Display slide 6 and help create a safe space by letting students know that it is common to be intimidated by a problem full of words. Then explain that it is rare to be given an algebraic problem without context and be asked to solve it in the real world. Remind them that in the real world, they are asked to be problem-solvers and to identify the critical information from a situation and use that information to solve problems.

Display slide 7 and give each student a copy of the attached Story Problems handout. Let the class know that the goal today is to make story problems less scary which can be done by following a few steps: (1) drawing a quick sketch, (2) labeling the known, (3) labeling the unknown, and (4) writing an equation. These steps are on the handout and have more details on the following slides.

Show slide 8 and explain step 1: Draw a Quick Sketch? This step has a question mark because it is not always a step you need to successfully solve a problem. However, if it would be helpful to draw a sketch, it is where one should start. Explain to students that the goal is to not need to re-read the problem, so as they read, if they start to construct a mental image, because they are reading about a shape, for example, then they should sketch that mental image. The mental image is likely a geometric shape, but occasionally, it might be an arrow as a reminder of the direction north or to indicate that something is getting bigger or smaller.

Move to slide 9 and explain step 2: Label the known. Students need to underline or label, often by writing that some letter equals some numerical value or expression, the given information from a problem. On a paper-based test, underlining that information is helpful, but often students are taking a digital test, where underlining is a less helpful approach.

Display slide 10 and explain step 3: Label the unknown. The unknown is what the problem is asking the reader to find; it is what the question is asking for. Labeling this, often as a letter or word equals a question mark, helps avoid the need to re-read the problem.

Show slide 11 and explain step 4: Write an equation. The goal is for students to use the known information from step 2 and the unknown question from step 3 together to write an equation that relates those pieces of information. For example, if a problem gives information about an initial value and a rate of change and is asking about the value at a certain time, then one might use the slope-intercept form of a line equation to relate that known and unknown information.

Move to slide 12 and have students read question 1. Ask the class if they think it would be helpful to draw a quick sketch.

Transition to slide 13 and show students that a helpful sketch would be of a rectangle and the diagonal of the rectangle. Let students know that it does not matter which diagonal they draw (top-left to bottom-right or bottom-left to top-right). Introduce students to the Categorical Highlighting strategy. Give each student two different colored highlighters. Explain that they are to use one color to highlight the known (step 2) and another color to highlight the unknown (step 3). Have students try this on their own.

After a minute, show slide 14 and ask students to compare what they highlighted with what is underlined on the slide. Give students time to reflect and ask questions.

Now ask students to read and solve the problem using steps 1-4. After a minute, show slide 15 so that students can check their work. If students have questions, ask them to keep them for just a bit and maybe jot them down, as the following slides will go through the problem in more detail.

Show slide 16 and explain to students that there is a difference between what they should think and what they should write on the ACT. Since it is a timed exam, students should not show as much work as they would for class. Use the following slides to help students compare what they think and what they write.

Display slide 17 and explain that there are two columns. On the left is what the students are reading and on the right is what students should be writing. Help students understand that when they read the first sentence of this problem, they should be prompted by the word “rectangular” to use step 1 to sketch a rectangle. They should be prompted by the word “diagonal” to sketch the diagonal of the rectangle. Then use step 2 to label the diagonal “84.1.”

Move to slide 18 and explain that when they read the first part of the second sentence, they should use step 2 to label the width of the rectangle “74.”

Show slide 19 and explain that they are still using step 2 to label the height of the rectangle “34 feet less than the width.” This might look like an equation with variables: h = w – 34 or a simplified expression with just numbers: 74 – 34 = 40. Both are good approaches.

Transition to slide 20 and explain that students are now using step 3 to label the unknown: area. This can easily be written as “A = ?” or “Area = ?”

Now show slide 21 and explain that at this point students are ready for step 4: finding an equation that relates the known information of the diagonal, width, and height of a rectangle with the area. Let students know that sometimes they are given too much information, like the diagonal length in this problem. Encourage students to not waste time erasing “extra” information. On the ACT, there are sometimes sets of questions that all refer to the same given problem. What is “extra” information on one question may be valuable information on the next question. Help them also notice that the words in the problem were not the traditional “length and width” or “base and height,” which is why it is important to have a flexible understanding of area like they learned during the third week of this activity series. So they now need to write an equation, which may include variables or may not: A = b·h or A = (74)(40). Then they solve for A, which is 2,960 square feet.

Finish this problem by showing slide 22 and letting them know that the correct answer choice is D. At this point, students may feel like this was a lot of work. Remind them that it is a lot of work to explain all of the thinking that goes on, but thinking itself does not take anywhere near as much time.

Show slide 23 and have students independently try question 2. Tell them to not worry about pacing right now and go through the same steps as they did for question 1: use the highlighters to identify their known(s) and unknown(s). Then read the problem again and practice steps 1-4. Remind students to practice doing the steps as they read the problem.

After a couple of minutes, ask students to share with a partner and discuss their work. After pairs have had some time to discuss, display slide 24 so that students can check their work. Have students help identify the steps used in solving this problem. Give students time to reflect and ask questions.

If time allows, ask for volunteers to share with the class what they found helpful and what they still find challenging. Facilitate a discussion so that students can share their approaches and help each other find success.