How to check every student's paper work in elementary math

Why this matters

In one 4th grade class, 26 students divide 372 by 6 on paper. One student writes "10" next to a line where she only subtracted 6. Her last line still comes out to 0, so she writes 71 and moves on to the next problem with the same habit. The teacher can walk past five or six desks during practice, and the rest of the work waits in a stack until that night.

Check each line, then let the student find the mistake

Partial quotients is a way to divide in chunks: subtract groups of the divisor you know, like 50 groups of 6, and add up the groups at the end. 4th graders learn it because the Common Core asks them to divide "using strategies based on place value" and to explain the calculation (CCSS 4.NBT.B.6). Students aren't expected to divide fluently with the standard long division method until 6th grade (CCSS 6.NS.B.2).

1. Read every line of the student's work
2. Ask the student to check the answer by multiplying it back
3. Point to the line only if the check doesn't help

A teacher can't read 26 papers line by line while students are still working. Sparky, Flint's AI tutor, reads each photo as soon as a student sends it.

One division problem, from photo to fixed answer

Maya is a 4th grader in the partial quotients activity. She solves the problem on paper and sends a photo with the camera button. Every student in the class has their own chat like this one, and Sparky sets each problem in that student's interest.

Sparky uses the student's interestSparky reads a line of the student's photoSparky asks the student to check, instead of saying what's wrong

M

Maya

Interest: Trading cardsOn her paper: Wrote 10 groups, subtracted 6

Sparky

What's something you really like? It could be a sport, an animal, a game, anything.

Maya

i like trading cards

Sparky

372 trading cards shared equally into 6 binders. How many cards go in each binder? Solve it on paper with partial quotients, then send me a photo.

Maya

here is my work

Sparky

Good effort getting all the way to 0! There's a small mistake hiding in there. Multiply your answer by 6. Does it equal 372?

Maya

71 x 6 is 426. thats bigger than 372

Sparky

Right, 426 is bigger than 372, so something is off. You wrote 10 groups next to −6. 10 groups of 6: how much is that?

Maya

60. oh i took away 6 but i wrote 10 groups. so 72 take away 60 is 12, and 12 is 2 groups of 6. 50 + 10 + 2 = 62

Sparky

You found it and fixed it yourself. Can you multiply 62 × 6 and tell me what you get?

Maya

62 x 6 = 372!

Sparky

That checks out. You used chunks of 50, then 10, then 2. Could a bigger chunk at the start get you there faster?

Found the wrong line herself and fixed her answer to 62

Sparky read every line of the photo, so it knew the mistake was the line with 10 groups beside −6. It didn't say so at first. Multiplying 71 by 6 showed Maya her answer was too big, and when she still needed help, Sparky named the line and asked one question about it. Maya did the fix herself, then checked 62 the same way. The last question pushes her toward bigger chunks: 60 groups of 6 is 360, which leaves only 12.

Maya and her chat are an example we wrote for this page. Sparky's replies are shortened from a test run of the activity with the same photo.

See whose work needs a second look

Sparky grades each chat against the activity's rubric. The activity page shows who needs help right now, what the class does well, and what to practice next.

Set up the activity for free

The partial quotients activity is in Flint's public library, with Sparky's role, guidelines, greeting and a rubric already written. Open it, select Try this activity to copy it into a free Flint account, and move it to a class. Students select the camera button to take a photo of their paper, or the paperclip to upload one. Students without a camera can type their lines. In the activity settings, select Try session myself to test the activity as a student before you assign it.

For 5th grade, where students divide by two-digit numbers, change the problem size in Guidelines for Sparky. For example:

For more math activities, see Flint for math.