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Will This Be on the Test? (September 2025)

by Aren Lew

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Welcome to the latest installment of our series, “Will This Be on the Test?” Each WTBotT features a new question similar to something adult learners might see on a high school equivalency test and a discussion of how one might go about tackling the problem conceptually.

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Welcome back to our continuing exploration of how to bring real conceptual reasoning to questions students might encounter on a standardized test.

Here’s a question inspired by a situation I encountered this summer. Where do you see math in your life that might lend itself to interesting explorations? See Building Classroom Community in an Online Environment by Jean Oviatt-Rothman for more ideas about how real world math can come into the classroom.

Here is this month’s question:

Here are some approaches:

1. Draw a picture. The numbers in this question aren’t that big, so it doesn’t take long to sketch out the whole group. A student might draw a picture something like this, drawing out the swimmers and assigning lifeguards to each group of six swimmers:

How might this picture help a student answer the question? What ideas do you have about the swimmers who aren’t in a group of six?

2. Make a table. A slightly more abstract way of making sense of the relationships in this scenario is to make a table showing how many swimmers can be protected by a certain number of lifeguards. Each lifeguard can protect 6 swimmers, so a table could look like this:

Lifeguards	Swimmers
1	6
2	12
3	18
4	24

The number 20 doesn’t show up in the “swimmers” column, so how does the table help us answer the question? We can see that 3 lifeguards will only protect 18 swimmers, so that is not enough. What does that mean about the number of lifeguards required? What do we do with the information that 4 lifeguards can protect 24 swimmers when we only need to protect 20?

3. Check the answer choices. An often reliable strategy for approaching a multiple choice question is to consider each answer choice as a separate yes/no question. This can be inefficient, but in this case, it could be a good way in. Because we are looking for the smallest number of lifeguards needed, a student can start with the smallest number and work their way up until they get to a number of lifeguards that is enough. It could look like this:

In the College and Career Readiness Standards for Adult Education, this question falls under standard 6.RP.3: “Use ratio and rate reasoning to solve real-world and mathematical problems…” When we think about questions involving ratios, many of us turn to the cross product. This may feel like the kind of question where setting up and solving a proportion is a quick and efficient way to the answer. In this case, using the cross product will give an answer that 3.333… lifeguards are needed. Not only is this answer not among the answer choices, but it doesn’t make sense because you can’t have a fraction of a lifeguard. I have seen many students pick the answer choice that is closest to their answer when their calculation gives an answer that is not among the answer choices. In this case, that would lead to picking B, an incorrect answer, even though this is a situation involving proportional reasoning and even though 3.333… is a correct answer to a proportion that models the situation.

Questions like this remind us of the importance of Standard for Mathematical Practice 2 (MP.2): “Reason abstractly and quantitatively.” It states that, “Mathematically proficient students bring two complementary abilities to bear on problems involving quantitative relationships: The ability to decontextualize … and the ability to contextualize….” This means that it is important to be able to work abstractly with quantities, for example to set up proportions using the numbers from a scenario, but it is equally important to keep checking in with the context.

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