Assessing Addition & Subtracting for Middle Grade Students

Now that my class has wrapped up numeration, it's time to move on to computation. The first order of business is adding and subtracting. Since I teach fourth grade, our guiding standard is 4.NBT.B.4: "Fluently add and subtract multi-digit whole numbers using the standard algorithm."

Neither adding nor subtracting whole numbers appears in the fifth grade standards, so you know what they say: The buck stops here. I am responsible for mastery of addition and subtraction of any number with and without regrouping. 

Even though I feel that my students should have a good grasp of this concept already, I must pretest to make sure. (And fifth grade teachers should probably do this as well.)

This simple test would show if my students could (1) add without regrouping, (2) add with regrouping, (3) subtract without regrouping, (4) subtract with regrouping, (5) subtract across zeros, and (6) appropriately use estimation as a tool for checking accuracy.

My results? All of my students showed mastery of addition (with and without regrouping) and subtraction without regrouping. About half of the class needs remediation on subtraction with regrouping and/or across zeros. More than three-fourths could not estimate (or estimated in an inappropriate manner). The most common error students made was rounding the answer to their problems in an attempt to estimate.

I've decided to place them in two groups. Those who mastered addition and subtraction (even if they're not too hot on estimation yet) and those who mastered everything will have a quick lesson on the purpose of estimation then move on to adding, subtracting, and estimating decimals. (We reviewed tenths and hundredths last week, so it will segue well.) Students who need help with subtracting with regrouping will get it - - - as well as a lot of practice with estimation.

If you think I'm a bit obsessed with estimation, you are correct. Even though it isn't in the standard, I believe a good mathematician uses estimation to judge an answer's reasonableness all the time. While my fourth graders will be writing their estimates, the ultimate goal is rapid mental calculation. Therefore, except in rare cases, students should round each number to the largest place value when estimating.

Those who peek in my classroom this week will see kids subtracting with regrouping, asking themselves, "Is my answer reasonable?" and estimating like crazy!

P.S. If you're creating computation worksheets for your students, try the font called Courier. All letters, numbers, and spaces are equally justified; therefore, everything stays lined up from row to row.