Check out the video here. In case you can’t watch the video, here are some tips on how to implement small group instruction. 

In case you can’t watch the video, here are some tips on how to implement small group instruction.  The video goes into much more detail, though.

1. MAKE MATERIAL READILY ACCESSIBLE

When you watch a cooking show, all the ingredients have been cut, prepped, and measured ahead of time to keep the viewer engaged. The same is true with students. You will make the most of your limited small group time by having all supplies and materials readily accessible or easy to obtain. This is a routine and procedure to practice with students: What will they need to bring to the small group every time they participate? 

On the small group supplies note, I highly recommend going beyond paper and pencil.  This could mean students work on dry erase pockets or use manipulatives.  You can find my favorite small group manipulatives here, but common workroom supplies like sticky notes or dot stickers can also do the trick.

2. TAKE IT ONE SKILL AT A TIME

The Texas standard 7.3B states, “The student is expected to apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.”

Do not plan small group instruction for the entire standard. It is too much. Small groups should focus on a very specific skill. For this standard, you might want to just focus on multiplying fractions. We want to go as bite-sized as possible. This way you can hone in on the misconception and scaffold accordingly, and students can leave a small group feeling successful and not overwhelmed.

3. ASSESS FOR THE PURPOSE OF DIFFERENTIATING

In order to see which students need some math small group intervention, rely on formative assessments: exit tickets, homework questions, or even just circulating and checking a specific problem during group practice. 

I don’t recommend using state assessments to make groups because the data is not as specific (or timely) as it can be. Also, keep in mind that small groups are flexible. Not all students will struggle with the exact same skills, so you don’t always have to pull the same students together. 

Lastly, use your small group time to also assess their mastery of that skill. Either keep notes by hand or, better yet, use a Google Form to enter anecdotal notes so the data can later be sorted. You can find a Google Form template here. 

4. KEEP THE MINI-LESSON MINI

This tip goes hand in hand with tip #2. When teachers focus on one skill at a time, this allows for the mini-lesson to stay mini. If you spend too much time with one group, then other students are at risk for getting off-task, less time is spent with other small groups (or no time), and this can impact your next day math small group rotations. 

What should be happening during small group?

You can do anything! There are no wrong answers here. You are giving real-time feedback to students, which is so valuable. You might be asking questions, eliciting responses, addressing misconceptions, and/or praising your students. You can do this through task cards, working with manipulatives, or showing the math in a different way.   

5. HOLD ALL STUDENTS ACCOUNTABLE

The most common question I hear in regard to small group instruction is, “How do I hold all students accountable?” Great question! Keep it as familiar as possible. It should be something they have done before, something that self-checks, and something that will prevent you from being interrupted. This can be scavenger hunts, stations, independent work, or digital activities. Remember to hold students accountable by using timers, recording sheets that will be turned in, and occasionally circulating. 

6. MAINTAIN CONSISTENCY

If you haven’t used small groups before, it is going to be a challenge. But, like anything that is challenging, it gets easier the more often you do it. Remember:

“Success is neither magical nor mysterious. Success is the natural consequence of consistently applying basic fundamentals.” – Jim Rohn

Maneuvering the Middle has been publishing blog posts for nearly a decade. This post was originally published in 2019. It has been edited for relevance and clarity.

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Fortunately, while that is the only way I ever learned division, there are now numerous other options for division, so students can feel successful. And though I believe the standard division algorithm is a necessity for math, it doesn’t have to be the only way students learn and internalize division.  

Before we jump into division, a quick reminder of the types of division we have. We have partitive division and measurement division.

In a Partitive division problem, the number of groups is known, and you are solving for the number in each group. Think of it like this – I have 12 cookies and want to divide them evenly by 4 children. How many cookies does each child receive?

In a measurement division problem, the number in each group is known, and you are solving for the number of groups. For example, I have 12 cookies and want to give each child 4 cookies. How many children can receive 4 cookies?

Now that we’ve reviewed the two types of division, here are 4 division strategies to try!

1. Partial Quotient Division

Partial quotient division does exactly what it sounds like – you work to find parts of the quotient (answer) and then add them together to find the overall quotient. 

Let’s take 432/18…

Here is a takeaway that will make teaching partial quotient division more accessible for your students; don’t try to have students do all of their multiples of 18 (which is normal when teaching the standard algorithm). It isn’t necessary. Instead, have students do friendly numbers. Depending on your dividend and divisor, this could be 10 or 100. In our case, 10 makes more sense, so 18×10=180.  Also, if I go ahead and find 18×2=36, it is painless to find 18×20=360. 

Another math tidbit I love is that instead of trying to multiply by 4, it is easier (to me) to multiply by 2 twice. 

You can see in the example above, that I was able to find that 18 went into 432 twenty times and then 18 went into 72 four times. I simply add the partial quotients of 20 and 4 to find the quotient of 24.

Lastly, partial quotients are a great tool because students can find the answer in a variety of ways. Take a look below for another way to solve 432/18.

2. Equivalent Ratios

This is a great strategy for division that reinforces ratios! This may not work for every division problem, but it is similar to partial quotients in that you can work in baby steps to get your quotient. Familiarize your students with these division rules:

• Numbers that end in an even number are divisible by 2.
• Numbers that end in a 0 and 5 are divisible by 5.
• Numbers that end in a 0 are divisible by 10.

Once your students have mastered those rules, you can introduce:

• Numbers with the last 2 digits divisible by 4 are divisible by 4 (ex: 1016, 3412, 1004)
• If the sum of the digits is divisible by 3, then the number is divisible by 3 (ex: 342. 3+4+2 = 9. 9 is divisible by 3, therefore, 342 is divisible by 3.) 

Even if your student cannot get all the way down to 1, they can still divide smaller and more manageable numbers by simplifying. In this example, you can think of it as partitive division, 25 represents the number in 1 group.

3. Multiplying Up

To use the method of Multiplying Up, rewrite the division problem as a multiplication problem. Let’s take the example of 1665/15 =111. Multiplying up asks “15 x ___ = 1655?”

We know that 15×100 = 1500 gets us close to 1665. We can work from there by adding 150 (10 groups of 15) and then again 15 (1 group of 15). 100 + 10 + 1 = 111. Therefore, 1500 + 150 +15 = 1665.

4. Repeated Subtraction

Repeated subtraction is similar to multiplying up (and partial quotient) but backwards. Obviously, these are all related! I think it works best when you are working with dividing numbers with unfriendly divisors (think 3 digit). 

Which division strategy will you try with your 5th grade or upper elementary students?

Related content: Check out this post on Dividing Fractions.

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1. Open Area Model

The area model demonstrates that when multiplying two numbers, you can find partial products and add them together to find the overall product. The open area model is my favorite alternative multiplication strategy and where I would start. After your students understand the basics of an array, the open area model is the next best model for students to fully see what is happening conceptually when multiplying (especially when multiplying 2 digits times 2+ digits). 

The steps are already built in. They know that each box needs to be filled in. This keeps students organized and (hopefully) more accurate. 

Additional benefits: this format will help students in high school Algebra multiplying and dividing polynomials.

2. Partial Product Multiplication

Partial product multiplication is the open area model without the boxes. Essentially, students are completing the exact same steps in the same order, but without the array format. While I wouldn’t start here, I think reinforcing the open area model with a partial product number sentence is the perfect progression. 

3. Distributive Property

Using the distributive property is a multiplication strategy that will later reinforce another important math skill. Have students break down one of the factors into its expanded form and then multiply. 

4. Chunking Using a Ratio Table

You can use a ratio table to split a factor into chunks (in this case 24 was broken down into 4 and 20) to find partial products that are then added together to find the final product. Have students take advantage of friendly math like doubling and multiplying by 10. 

5. Over and Under

In order to use friendly numbers, multiply by more (or less) groups than necessary. Then, subtract the extra groups, or add the missing groups. 

In this example, I traded 18 for 20. After finding the product of 31 and 20, I found the product of 31 and 2 (since 20 – 18 = 2). I subtracted this product of 62 from 620 to find the answer to our original problem 18 x 31.

In this case, I shot under by trading 31 for 30. I knew I would be missing one group of 18 so I added that to the product of 30 and 18.

What multiplication strategy is your favorite? Interested in more multiplication posts, check out our posts on Multiplication Facts and the Distributive Property.

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Pros of a 100 Minute Class Period

• More time
• More instruction
• More support
• More practice
• At the end of the year a student has had double the amount of time in that class than a traditional schedule
• You should definitely be able to get through your scope and sequence with 100 minute class periods
• If you had 100 minute classes, you probably have less students over all

Cons of a 100 Minute Class Period

• 100 minutes is a loooooong time
• Students get distracted
• Classroom management is tough for that long of a time period

Things to Consider

• Students are with you for double the amount of time, but that does not mean that you simply extend a 50 minute lesson. How can you be efficient and productive with the time?
• Students need structure. How can you develop a routine that breaks up the 100 minutes but still provides structure?
• Students (and adults) have a short attention span. A good rule of thumb is that new learning should not take longer than 1 plus your students’ age, so if you teach 12 year olds, your notes should last no longer than 13 minutes (12+1). 

Below is just one way to structure your 100 minute class period. Sometimes things do not go according to plan, but it is always a good idea to have a structured routine for both yourself and your students, especially if you will be with them for so long.   

Do First/Bell Ringer/Warm Up 5-10 minutes

I used a very straightforward warm-up routine to get students working when they entered the classroom. The goal is that students can get started without needing assistance from me or their peers.

I used this time to:

• Greet students with a warm smile
• Check homework completion (if I assigned it)
• Take attendance

I would start a timer after the bell rang for 5 minutes and project it. When the timer went off, I spent the next 3-5 minutes either going over the warm up, going over last night’s homework, or a combination of both. 

Hook 2-5 minutes

These few minutes are a great time to introduce the objective and make real-world connections. It can also be utilized to review prior content that is connected or to have students review any new vocabulary. Anything that can create a bit of buy-in is beneficial.

Instruction 15-20 minutes 

The goal of instruction is to give students enough information to understand the concept, but not so much that you are doing all of the heavy lifting in class. It is a fine line to walk.

If you need more than that recommended amount of time for direct instruction, that is okay! Give students the opportunity to practice and engage in a meaningful way before returning to direct instruction. Another idea is to assign our student videos, since they adhere to this time recommendation. 

Remember that direct instruction isn’t your only option to teach a lesson. You could:

• Have students explore using manipulatives
• Think aloud or model
• Ask students to build upon previous knowledge
• Use the Building Thinking Classrooms approach

Lastly, I think it is important to note that if you are using our curriculum, you do not need to go over every single problem on a student handout. Work the problems ahead of time, decide which are the most important, and then save the rest for small group work time. 

Class Activity 20 minutes

This is the time period where students are engaging with the work in pairs or groups. In a 100 minute class, I recommend activities with movement, as well as collaboration. Sometimes we would do card sorts, but rather than sit at desks I would let students do the sort on the floor. Other times I would use stations or scavenger hunts to get kids up and moving or use math dates to have them work with various people. I would circulate and answer questions at this time. If you have a simple worksheet, make sure to read how to turn any worksheet into an activity.

Recap 5 minutes

As the activity wraps up, take a few minutes to recap what they have learned by asking students to summarize the lesson. Depending on the activity you could go over various responses or work a few of the difficult problems together.

Skill Practice 5 minutes

Most students have some need for remediation, gaps in their mathematical foundation, or need to expound upon their problem solving skills. Each day I would spend no more than five minutes addressing basic math skills. At the beginning of the year this was multiplication charts with various missing numbers or adding and subtracting decimals. I often spent several weeks on number sense by practicing converting between fractions, decimals, and percents.  

Station Work 30 minutes

I used this time to focus on small groups and remediation. I would work with small groups on their assignment, some students would work independently on a computer, while others would focus on concepts that they needed additional help with. This is also the time that my co-teacher would come into class, which was a life saver. You can read more about this on my math intervention schedule post.

You can read more about planning for and implementing stations here.

Clean Up/Close 5 minutes

By this time we are all wiped! It was time to wrap up, clean up, put away supplies, and get everything back in order.  

One Hundred minute classes never failed to wear me out, but the extra time was a gift! Especially when I think about the whirlwind of a 45 minute class. 

Who else has 100 minutes for math? How do you structure a 100 minute class? I would love to hear how you break it down!

Click to find out more about Maneuvering Math.

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Noelle presented an amazing math training this summer on Practical Problem Solving Strategies. I was truly amazed at just how much I learned. I will be breaking down the training into 3 blog posts over the course of this month, so if you missed the training, be sure to check back here for more updates.

If you want to learn more, check out this book, Mathematize It!, that covers the topic of teaching how to solve word problems in much more detail.

Today we are going to talk about the 3 types or categories of word problems that you teach and your students may face: action, relationship, and comparison. The purpose of identifying word problem types is to force students to slow down and analyze what is happening in the word problem before jumping to computation.

You can also grab our problem solving posters freebie below!

Action Word Problems

Here is an example of an action word problem: 

How do we know that this is an action? Ask yourself:

• Did something occur?
• Was there some kind of change?

If yes, the word problem likely falls into the action category.

Relationship Word Problems

Here is an example of a relationship word problem: 

How do we know this is a relationship? Ask yourself:

• Are parts being described or referred to in relation to a whole? 
• Is a whole being described or referred to in relation to a part?

If yes, the word problem is a relationship. Here we can see the parts of the marching band relate to the total number of marching band members. 

Comparison Word Problems

And lastly, here is an example of a comparison word problem: 

How do we know this is a comparison?

Ask yourself:

• Is something in the word problem being described in comparison to something else?

In this word problem, we can see that the cost of popcorn is being described by the cost of the candy. 

Why is this helpful to know?

Why do students need to know this? Well, by observing and “making meaning” from the words and scenarios they are processing, students are less likely to rush to determine a path to the solution. 

Does this sound familiar? Students quickly perform some operations with the values given. In this first step of the problem-solving process, we want to take the focus off the values and direct students to notice what is being described in the problem.

The goal is not for them to be able to identify and put the word problem into the correct category. We simply want students to notice what is happening, and over time they will start to recognize patterns in word problems. 

Next week, I will dive deeper into how we take these word problem types and use them to help students with the first part of the problem solving process: restating the problem.

Grab our problem solving posters freebie!

In the meantime, can you identify the category these sample problems belong in?

1. Ricky buys a package of chicken to use throughout the week. On Monday, he uses 28 ounces to make chicken salad for lunch. On Thursday, he grills 53 ounces of chicken for dinner. If Ricky determines he has 37 ounces of chicken remaining to cook, how many ounces of chicken did he buy at the beginning of the week?
2. Gavin has two pet turtles, a red-eared slider and a map turtle. His red-eared slider weighs 2,680 grams and his map turtle weighs 670 grams. How many times bigger is the red-eared slider than the map turtle?
3. Ivory created a paper chain of her school colors, blue, green, and white, as a decoration for a pep rally. The blue section measured 5.5  feet long, the green section measured 4.25  feet long, and the white section measured 3.75  feet long. What is the total length of the paper chain?
4. A king-sized chocolate bar has a mass of 2.6 ounces. A regular-sized chocolate bar has a mass of 1.55 ounces. How many more ounces is the king-sized chocolate bar than the regular-sized chocolate bar?
5. A nature center has a stocked pond with an automatic fish feeder. The fish feeder has 70.5 pounds of fish food and releases food into the pond twice a day. If the feeder releases 2.6 pounds of food in the morning and 1.2 pounds of food in the evening, how many pounds of food are remaining in the feeder at the end of the day? 
6. The San Francisco Bay Area is hosting a triathlon, a race consisting of swimming, biking, and running. The athletes will swim for 0.75  miles and bike for 15.5  miles. If the total distance of the triathlon is 20.5  miles, how many miles is the running portion of the race?

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Let’s talk about 5 ways to use open number lines in middle school math!

1. Fluency

Adding friendly numbers – This method leaves one addend whole and adds the other addend in friendly amounts. 

In this example, 275 was added to 173 in friendly chunks of 200, 50, 20, and 5 to get the final sum of 448.

Adding to friendly numbers – This method adds a small amount first to get a partial sum that is friendly, then adds the remaining amount in friendly chunks.

In this example, 2 was added to 398 to get the friendly number of 400. Then, the remaining 112 was added in chunks of 100 and 12 to get the final sum of 512.

Distance (Subtraction) – Because subtraction is the distance between the two values, students can use an open number line to count up to the total distance between the two numbers.  Values closer together are better suited for this method.

Removal (Subtraction) – Removal takes away to find the difference between two values. Values further apart may be easier to subtract using removal.

Constant Difference – Add or subtract the same number from both values to make the numbers easier while keeping a constant difference. 

In this example, 620-370 was adjusted by subtracting 20 from each value (620-20=600 and 370-20=350)  and finding the difference between 600-350. (I could have added 30 to 370 and 620 too!)

2. Ratios and Conversions

Double Number Lines – Double number lines are useful for ratios and conversions. If you typically use a table for solving ratio problems, then an open number line is not too far off.

3. Ordering Numbers

You can read more about this in our Ordering Rational Numbers post, but ultimately, no problem that involves ordering numbers is complete without a number line. It provides context and is a way to actually show student thinking. 

While starting with a completely blank number line can work for some students, I recommend writing in whole numbers first.

Example: -½, -2.2, -1.5

Before placing a single number from above on an open number line, I would ask students to provide the integer numbers (for simplicity sake, I am referring to -3, -2, -1, and 0) that make sense with the numbers provided in the example.

Once determined, students will have a much easier job placing -1.5 between -2 and -1 than on a blank number line with -½ and -2.2.

Hint: Use a vertical number line when involving negative numbers.

4. Problem Solving

These problem solving strategies are best explained in word problem format. Please read the word problems to fully understand the open number line diagrams.

Active Situations – This method describes a situation in which quantities are joined or removed. There is a start, a change, and a result.

Part Part Whole – This describes a relationship that includes two or more parts that relate to a whole.

Additive Comparisons – These are situations that describe how two quantities compare to each other. They include a smaller quantity, a larger quantity, and the difference between the two quantities.

I had no idea there are so many ways to use number lines to solve so many different types of middle school math problems. Do you use open number lines?

If you are interested in learning more about open number lines, our Maneuvering Math Intervention Program will be adding a new module called Jump Start in time for Back to School Season! Jump Start is an introductory component to equip students with tools and strategies for number operations and problem solving.

It will help students reason with numbers, recognize and effectively represent problem-solving situations and approach math with increased confidence and tools to use throughout challenging concepts.

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If you are a classroom teacher, then you are probably very familiar with documenting student data and progress. Documenting the differentiation you are providing for every single student while also teaching said students can feel impossible. Hopefully, these tips for organizing your math intervention documentation will make it all more manageable. Plus, there are a few freebies to get you started, so keep reading!

TRACKING PROGRESS

Once I became more skilled at pulling a small group while managing a classroom full of other students, I was ready to level up and track data. What was the point of pulling a small group if I couldn’t see if it was making a difference? I created this Small Group Progress Monitoring Printable to document how my small group of students were progressing. 

I made a ton of blank copies, put them inside a binder, and filled them out whenever I pulled a small group.

If you want a copy for your classroom, you can grab it (along with a few others) here.

KEEP IT SIMPLE

Keep it simple is pretty much my moto!  State testing is right around the corner, and this idea worked really well for my smaller intervention class. This requires some work upfront, but makes the day-to-day, in-class mental load lighter. Here is a solution that worked for me:

1. Create one page with all of the standards listed in kid-friendly language. This is your cover sheet.
2. Create a packet of material that students need the most help with. I would use material from our State Testing Units – the 10 question assessments were perfect. Make the exact same packet for all of your intervention students. 
3. Staple the cover sheet to the packet. The cover sheet is where I differentiated! I highlighted the skills that the individual student needed to work on based on what I saw from their benchmark. For example, Student A might have dividing decimals highlighted amongst other highlighted skills while Student B might have integer operations and creating equivalent fractions highlighted.  Student A could find the section titled dividing decimals and start there.  The next day, they would go to the next highlighted skill.  The cover sheet included a space for me to check off when they mastered the skill.  

Students were practicing exactly what they needed to work on, and I didn’t have to make 15 different worksheets to hand out to 15 different students and try and keep up with who got what.  

Note: Since I took the picture above, Maneuvering the Middle has created an Intervention Binder for both TEKS and CCSS that has a more comprehensive overview of all of the standards. The Student Data Sheet would be perfect to use as a cover sheet. 

MAKE IT VISUAL

After completing a unit, I passed back their unit tests along with a unit test reflection.  The unit test reflection broke down the test into the 3-5 skills that were tested.  Next to the skills, were boxes with the question numbers that aligned to those skills.  Students would go through their test and color in green for questions they got correct and red for problems they got wrong.   This created a great visual for students to see what skills they still needed to develop. 

Students were then able to reflect more effectively on their strengths and their areas needing growth.  I had students keep these reflections in their notebook, so on days when we used Khan Academy or IXL, they could refer to this page and work on the skills they had not mastered yet.  If students hit below a certain threshold, you could assign a video reteaching the topic – a perfect use of our Maneuvering the Middle Student Video Library. Click here to grab your Test Analysis printable!

This reflection never quite took an entire class period, so I paired it with test corrections.

USING EXIT TICKETS

Exit tickets are another way to decide who needs to go into a small group and what you should reteach or practice in the small group.

When I am looking through the exit tickets, I would sort the exit tickets, not according to their grade, but by what the misconception is.  Let’s say the exit ticket is over adding fractions. 

• I might have one stack of exit tickets where students did not find a common denominator and just added the numerator and denominator together (conceptual understanding).  
• Another stack would be for students who made a computation error (procedural fluency).
• Lastly, I might have a stack of students who couldn’t decode the word problem (application). 

Of course, some exit tickets might fall into all three categories, but these different stacks allowed me to prioritize what students to pull in my small group, who just needs more practice, and who needs to be completely retaught.

I hope that this post provided some easy take-aways on how to organize math intervention in your classroom.  Similar to how we scaffold for students, scaffold some of these organization systems into your daily routine.  Choose the tip that would be the most helpful to you or would be the easiest to implement and give it a try!  

What tips do you have for organizing math intervention?

For more tips on pulling small groups, check out Tips for Small Group Implementation here. Interested in learning more about our Math Intervention Binder? Check out the video below.