Calculators

11. Use calculators strategically.

You might be thinking, "Can students really use calculators on the SOL test? That doesn't sound right." The answer is a definite yes.

So, let's understand what's happening here. All of the links below come directly from the VDOE's Mathematics page.

The best place to look to find out whether or not a standard is assessed with or without a calculator is the test blueprint. This document tells you how many questions to expect in each strand and how many field test items there will be. Additionally, each standard that is assessed without the use of a calculator is marked with an asterisk. Since 5.4 does not have an asterisk, this means a calculator is available on all 5.4 questions.

If you have been teaching fifth grade for a while, you might be thinking, "I know I've seen word problems on the test without a calculator. This isn't right."

It's important to know that you're right! You have seen word problems presented without a calculator. However, it's also important to know that the standards have been updated in the last few years. We are now working under the 2016 Math Standards of Learning, and this is one of the changes from the 2009 to 2016 version. This change is confirmed in the 2009 to 2016 Crosswalk (Summary of Revisions) document. Below is a snip of the relevant section. You can see that it had an asterisk in 2009 (left) and now does not in 2016 (right).

So what?

So what does that mean for our classroom practice in this standard? Should we allow students to use the calculator throughout the unit, knowing that they will likely never master multiplication or division of larger numbers this way? Should we ignore the specifics of the standard and never use a calculator?

I think we should fall somewhere in the middle between these two extremes, with strategic use of calculators to support the development of problem solving skills. Here are a some considerations for the 5.4 unit.:

  1. Students will have to solve "naked" decimal multiplication and division problems. When you get to standard 5.5 Decimal Computation, they will need to know how to multiply and divide without a calculator. For this reason, I suggest using some of your time in the 5.4 unit to develop students' comfort with the multiplication and division whole number algorithms. This will make for a smoother transition when you get to decimal computation.

  2. Students will not have to solve "naked" addition and subtraction decimal problems. Addition and subtraction of decimals, outside of practical problems, is assessed in fourth grade. This means that in fifth grade, all whole number and decimal addition and subtraction is assessed with a calculator, inside of practical problems. So what does this have to do with 5.4? If I feel stretched for time and need to cut something out of the practical problems unit, mastering the subtraction algorithm could be the place to minimize my time. Do we want kids to be able to subtract? Of course! But we know how much time multiplication and division will take, and I think our extended time is better spent there.

3. Problem solving is the ultimate goal. Imagine one of your fifth grader grows up and gets a job at Lowe's. They're trying to help a customer determine how many 2x4 boards they will need for a renovation project. What's going to happen? Are they going to whip out a paper and pencil and start working out the long division algorithm? Of course not. Even you and I wouldn't do that. Instead, your student would pull out the calculator on their phone and crunch the numbers. At that point it's most important that your student knows which operation to use, and also how to use estimation to check for reasonableness. On the flip-side, if they mastered the algorithms but can't figure out if they need to multiply or divide, they won't be very helpful. Developing problem solvers is the ultimate goal of this standard.

4. Calculators can be a tool for increasing equity and access to high quality math tasks. We want to avoid denying students' engagement with quality problem solving tasks just because they haven't mastered algorithms yet. For example, imagine that the goal of a lesson is furthering students' understanding of the operation of division and the structure of division practical problems, but you have a student who is struggling to accurately divide with the traditional algorithm. Allowing them to use a calculator in this instance provides access to the learning goal. If computation is not the expressed focus of this lesson, you can make a note to return to this with this particular student at a later time.

5. Introduce students to the Desmos Virginia 4 function calculator. This is the calculator that will be used on SOL tests, so it's a good idea to introduce it now. There are a whole collection of resources available on the VDOE Desmos calculator page, but I found this video to be especially helpful. When I have introduced the calculator to students in the past, I gave them free time to play, then showed the video, then gave them more time to play with the new things they just learned.

If you'd like to learn more, check out the National Council of Teachers' of Mathematics position on calculator use in elementary grades.