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Will This Be on the Test? (August 2026)

by Aren Lew

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Welcome to the latest installment of our series, 鈥淲ill This Be on the Test?鈥� 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.

Download the packet.

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One type of question students may encounter is a straightforward calculation. It may be straightforward because students do not have to figure out what operation to do, but that doesn鈥檛 mean the question is easy. If we teach students to memorize steps for calculation procedures, they end up having to do a lot of memorizing. We have addition, subtraction, multiplication, and division (and more), and we could potentially teach a different procedure for each of these operations with whole numbers, decimals, fractions, and negative numbers. We can only hope that they know which procedure to apply and get all the steps right.

Or we could take a different approach. The first Standard for Mathematical Practice (Make sense of problems and persevere in solving them) applies to calculation as much as it applies to tasks in context.

Here is a calculation question. Your challenge is not to use a memorized procedure. Think about what you know about the numbers involved and the meaning of the operation. Make sense before you persevere. Ask yourself what the question means. What creative strategies can you come up with?

Here are some possible approaches:

1. Estimate by truncating. The thing that makes this question challenging is the decimals, so what if we ignore them? That does change the question, but it might still get us close enough in a multiple-choice setting. In this case, 4锝�7 = 28, so we can be sure the answer is more than 28. We have two answer choices that are more than 28 but close to it. Do you think we鈥檝e cut off a lot or a little in truncating the numbers? Is the answer just a tiny bit more than 28 or a bit bigger than that?

In the real world, it can be useful to truncate numbers (i.e., ignore the decimals) in certain contexts. Suppose I earn $4.80 per hour and I work 7.2 hours. Knowing that I鈥檓 earning more than $4 per hour and that I鈥檓 working more than 7 hours, means I know for sure that I will make more than $28. ($4.80 per hour may seem like a low wage, but tipped workers may make less than minimum wage as a base pay rate.) Truncating numbers for the purpose of estimating may make more sense than rounding to the nearest whole if it is important that your estimate not be too big. (If I round my hourly wage up to $5, I risk thinking I鈥檓 making more money than I am.)

2. Estimate with nearby whole numbers. One way of understanding this question is that we need to find a little more than 7 groups of a number that is almost 5. 7 groups of 5 is 35. Is our answer bigger or smaller than 35? That鈥檚 hard to tell from this approach. 5 is a little bigger than 4.8, but 7 is a little smaller than 7.2, so it鈥檚 not obvious whether we鈥檇 end up with a number a little bigger or a little smaller than 35, but knowing the answer is close to 35 seems to be good enough here.

3. Draw an area model. An area model is a great way to get a handle on a multiplication that seems complicated or overwhelming. To find the answer to a multiplication of two numbers, you can draw a rectangle whose dimensions are those two numbers. The area of the rectangle will be the answer to the multiplication (product). This is an example of an area model sketch a student could draw in a test situation to make sense of the multiplication.

The answer to the multiplication is the sum of the areas of all four regions. Here is one way those might be arrived at or estimated:

7 x 4 = 28 (I remember that one)

7 x .8 is almost 7 x 1, so that is almost 7.

.2 x 4 = .2 + .2 + .2 + .2 = .8. That is almost 1.

.2 x .8 is almost .2 x 1 so that is a little less than .2.

All together that is almost 28 + 7 + 1 + a little bit more, so about 36.

The big benefit to this kind of area model is that it makes clear the parts of the product. Even if a student is not sure how to multiply the decimal parts, the area model can still get them close to an answer. There is an answer choice in the question that seems reasonable but doesn鈥檛 include all the regions in the area model. Can you spot it?

One way to get exact answers from area models is to draw them with grids. Drawing an area model with a grid can make all the pieces clearer, but it may be impractical in a test situation. However, it is a great tool for building conceptual understanding of multiplication with all kinds of numbers (wholes, fractions, decimals, signed numbers) and even algebraic expressions. For example, this area model shows a multiplication where wholes, tenths, and hundredths can be seen in the product. Can you see them? Can you figure out the product from this picture?

This area model was generated using a . Play around with it yourself and consider how having used this in class could prepare students for encountering other decimal multiplications in test situations.

None of the strategies here have gotten us to an exact answer. In the case of a multiple-choice test question, that is often not a problem. An estimate is often good enough in the real world as well. When an exact answer is required in the real world, we have several options. We can use a visual tool like an area model to make the task visible and find the area of each region. We can use a procedure, especially if it is one we have learned conceptually, starting with concrete and visual tools like area models and then moving to more abstract ways of representing quantities. Or we could use a calculator 鈥� that is allowed in most real-world situations, although it is still helpful to estimate to avoid and error from pressing the wrong button. Regardless of which approach we take in the real world, it is important that we make sense of the problem before we start down any solution path.

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