I teach 4th grade. I never had to take "Math for Teachers" in college because I tested out. Big mistake. I am a boring math teacher. I struggle to use manipulatives and I end up teaching the old-fashioned way. That's been working ok, but I want to be more engaging! I am getting observed on Tuesday and I want to have an engaging lesson.

We are working on division one-digit into 2 or 3 digit with and without remainders. Is there a hands-on way to do this? They kind of understand the "standard algorithm" but not really. Thanks for any and all help!!!

Would using base 10 blocks help? I haven't taught fourth, but it seems like base 10 blocks are used in every grade level for various concepts. If they know the algorithm, have them do it with the base 10 blocks. Are you making up good story problems to go with your lesson, like using their names in the stories? Word of caution: if you haven't been using base 10 blocks, starting with your observation would not be a good idea. They like to play with them and build. Or give them 2-3 minutes to play before using them in lesson.

Try a simple game. I like to do "games" with dice that take little or no prep. You can have them roll the dice 3 or 4 times, record the numbers. Then create the division problem and solve. Its a good way to check if the students are setting up the problem correctly, solving correctly, and checking their work.

To up the rigor, you can have them talk to each other about the problem and solution. Why did you choose to create that problem? How did you solve it? What strategy did you use?

In the groups, you can assign jobs - everyone solves but one person is the checker, one person rolls the dice, one person facilitates the discussion and change after each roll. Whatever works.

They record on white boards if we are just practicing and maybe one on an exit slip if I want to check for understanding. It kind of depends on what I am looking for.

Look at the site www.youcubed.org for other ideas and problems that you can use to increase engagement. I took this class and read Mathematical Mindsets to help me. Hope this helps.

Division is answers the question "How many groups of # can be formed from #?" For example, how many groups of 2 can be formed from 12?

Or--if you have 12 cookies (or pencils or books or …) and every child takes 2, how many children get cookies? 6 children

Or--if you have 13 cookies and every child takes 2, how many children get cookies? 6 and there is 1 cookie left

To use manipulatives for this, start with 12 (pennies, tokens, buttons, whatever you've got) and make groups of 2. Count the number of groups to find the answer.

Is this what you mean? Or are you past that?

Actually, although people tend to have automatic negative reactions to the concept of word problems, they actually tend to understand better when the problem includes things like money or cookies that they care about. The understanding of what division really means is enormously more important than being able to use an algorithm. Using an algorithm by rote isn't ultimately useful because the student has no idea which algorithm to use in a particular situation.

Have you tried other strategies for division than the standard algorithm?

You might look into a partial quotient strategy or an area model strategy as another way for students to understand division. There are a lot of videos online that explain these strategies.

There is a lot of value in students being able to show multiple representations of how to solve problems.

I start "long division" by doing problems as repeated subtraction. Lots of little cubes. Start out by counting the number of cubes for the dividend. Then use language like "How many groups of ___ can we get out of this pile of ____?"
Have students physically sort out the groups and count the groups.

Start with small amounts, then use bigger dividends. It becomes very laborious (on purpose).

Then show the repeated subtraction on a reasonable set of numbers. Once again, start using bigger numbers. This becomes laborious also.

Put on a little show by being whiny about "all this work." Since you've taught the algorithm, ask them if someone knows a faster way. They will likely tell you that you should use long division. (Dead monkeys smell bad; Dracula's mother sucks blood daily; or some other mnemonic device.)

End the lesson by reinforcing that genius mathematicians in the past came up with the standard algorithm so that you could use place value to make long division faster.

Don’t worry too much about being “boring”. If they’re too “entertained”, they might not be focused on the work. I’m what you would maybe call “boring” as well, but most kids actually like it, because they have enough time and repeated practice to actually learn what we’re doing. Sometimes, we switch it up by rotating around the room working on task cards individually, with partners, etc. They get so excited, and I’m like, you’re literally doing the exact same work as before lol.

Aims has a trucking activity to teach long division. It is pretty good - I usually use it every year. I think it is called pack 10 and it uses base 10 blocks. Also, can you add any online division games? The kids love to play them if you have enough devices. Also, iPad can use qr code task cards if you can get enough iPads. Good luck on your observation.

I used to use a lot of literature in my math classes. A fun one for division is The Doorbell Rang. It is about kids and a plate of cookies and they have to figure out how to divide them every time a new person rings the doorbell. Have students use white boards to show their work as you go through the story. Literature adds some interest and is cross curricular.

My students always tend to be more excited when food is involved. Depending on student allergies, you have lots of options for what to use. For instance, give each a fun size bag of M&Ms. Have them count how many of each color they have. Ask them to get with a partner and combine their candies. Then you just need to ask them to group them in various ways and fill in a table with their data (total, # of groups (divisor), # of M&Ms per group (quotient), remainder). Then you could have them group so there is only one green in each group, etc. Have them discuss and show what happens. Sounds like yummy fun.