Additionally, teachers must consider when and how to utilize occasional whole-group lesson experiences. The frequency of whole-group lessons depends entirely on student readiness and the content being taught. I recommend an approximate ratio of 4:1 (small group : whole group) as a guideline when planning lessons. For example, students might receive 4 days of small group guided math, followed by 1 whole-group lesson. In this model, the teacher uses the small group lessons to scaffold student understanding and teach prerequisite skills so that all students might be able to participate more equally in the whole-group lesson (which could be a low-floor/high-ceiling problem, a 3-act task, or parallel problems).

It is important to keep in mind the purpose of small group guided instruction when deciding when to integrate whole-group lessons. Flexibility and responsiveness to student needs is necessary. There are certain times when whole-group instruction may be appropriate. For example, if you are teaching the Grade 4 expectation: "estimate, measure, and record the mass of objects (e.g., apple, baseball, book), using the standard units of the kilogram and the gram," you could probably do this through whole-class lessons and investigations. Most students, given appropriate tools, differentiation, and pre-teaching, can meet this expectation. Allowing students to measure objects in grams rather than kilograms is a simple way to differentiate for those students who have an IEP which does not yet include rounding or decimals. And measuring the mass of objects less than 100g is a simple way to differentiate for students who have not yet mastered 3-digit numbers. So, for this expectation, I would most likely use a whole-class instructional model.

Deciding whether or not to use a small- or whole-group instructional model for each expectation is an important decision when planning. in almost all cases, however, small group instruction will be advantageous over whole group instruction.

You should consider the curriculum and the needs of your students when deciding how to structure your weekly lessons. For example, if I was teaching the Grade 4 expectation "add and subtract decimal numbers to tenths, using concrete materials (e.g., paper strips divided into tenths, base ten materials) and student-generated algorithms," I would almost certainly decide to utilize small group instruction. This is because, based on a diagnostic assessment, I would likely have students that would need more concretizing of decimal numbers before any addition or subtraction could take place. I might also have a group of students that would already have a concrete understanding of adding and subtracting decimals to tenths, and could move straight to generating their own algorithms.

With small group guided instruction, the ultimate goal is to have all students reach the same grade-level expectation (except, perhaps, in the case of students with IEPs with modified math goals). This means that the students with the highest needs will meet with the teacher the most often. Each small group lesson should be intentional and specific, and designed to help those students ultimately meet the grade-level expectation.

There are endless ways to structure a guided math block. I have chosen to highlight 2 which offer many advantages over other methods that I have seen. The one that you choose should be based on your students' ability to monitor their own learning, their grade level, and your own personal preference and classroom management style.

Note that both methods listed here do not include the teacher table as a station. This is important and intentional. Taking yourself out of the rotation allows students to go to the station activities in heterogeneous groups. The only time students are grouped homogeneously is when they are with you, receiving precise instruction on a specific skill. At all other times, students have the opportunity to collaborate, discuss, play, build, solve, and write within their mixed-ability teams. In deciding how to structure your own guided math block, please ensure students are not placed in like-ability groups more than necessary.

Sample Rotation Template

I chose to create a rotation template in Google Slides because it's easy to edit and can include interactive timers. To access an editable version of the template, simply click on the picture above, or here.

The videos at the top of the slide assist in timing the centres. Two have been included: 18 minutes and 15 minutes. If you would like a different amount of time for each station, simply click “Insert” ---> “Video,” then search for a “timer” video (e.g., “12 minute timer”). It is helpful to designate a student every day to be the “time keeper,” who presses play on the appropriate video at the beginning of each rotation.

The colours of the students’ names indicate their homogeneous group. When you are ready to see a group at the teacher table, simply call their colour (e.g., “I’d like to see the Green Group now, please.”) It is important (before starting guided math) to communicate to students that they will have other opportunities during the week to go to the stations that they miss while they work with you. This will help avoid having students become reluctant to go to the teacher table, for fear of missing out on their favourite station. This is also why it is important to think of guided math in terms of a weekly - rather than daily - plan.

The heterogeneous groups must be chosen carefully. Try to put students together that will work best together. It is somewhat helpful to have at least 2 students of every level (colour) in each group. This way, if you differentiate an activity (e.g. seat work), students will have a partner within their group to collaborate with.

As students’ readiness for various units changes, it is very easy to simply change the colours of the students’ names in order to place them in the correct homogeneous group. For example, a student that was in the Yellow Group for a unit on area and perimeter might get moved into the Blue Group for a unit on probability. This change does not affect the students’ “teams” that rotate through the stations, and makes for easier adjustments based on students’ needs.

With "Must do/May Do" menus, students have certain tasks they must complete that day, along with other choices once they have finished their required tasks. The order in which the students complete the tasks is up to them.

The advantage of choice menus is that you have more flexibility than the traditional rotation model. For example, your stations don't need to fit into tidy 15-minute boxes. If your students have a particularly complex problem to solve, for example, they may take longer to complete it. And you would only need to assign that problem (and maybe one other task) under the "must do" column. The manner in which you would take groups for small group instruction would be the same as in the rotation model; you would simply call a homogeneous "colour" group and work with them. Due to the less structured nature of the choice menus, you would also have more flexibility with the timing of your small group. You are free to take more or less time with certain groups, depending on their grasp of the skill you are teaching. (Keeping in mind that you would still ideally be seeing 3 groups/day).

I recommend having a weekly STEAM challenge that may take several days for students to complete (given about 15-20 minutes each day to work on it). The Arts Now website has lots of ideas for integrating art; engineering ideas can be inspired by the resources in your classroom. For example, if you have access to Legos or K'Nex, you can simply have students build structures that: span a width of 50 cm (bridge); are between 30-40 cm tall; resemble a miniature version the CN Tower and use exactly 1/4 blue bricks (Lego); are nets of specific 3D shapes, etc. Try to be creative and let students have time to have a little fun with their math during the STEAM activities.

Technology should be used creatively more often than for practise. For example, have students create a collage in Google Slides of triangles around the classroom. Each triangle can be labeled with its category and/or measures of interior angles. Students in upper elementary can also make videos teaching others about specific math procedures/concepts (this is a fantastic way for them to solidify their own understanding!). Occasionally, having students practise their skills using mPower, Knowledgehook, Prodigy, and other online games is also appropriate.

Be wary of teaching too many games. This can be a major time-waster. Look for "evergreen" games that can be used for multiple skills. Dominoes, for example, are great: there are dominoes for place value, telling time, geometric shapes, etc. The game of "Bump," is another great example. Do a simple search on Teachers Pay Teachers for Bump Math, and you'll see versions for multiplication, finding greatest common factors, etc. (there are many free bump games available online, but you'll see that it is also easy to make your own). One game, many ways.

No matter what stations you decide to create for your students, ensure that they are able to do them independently. Spend time upfront showing students where to access materials/manipulatives, and how to indicate to you that they need assistance (I have them write their name on a certain area of the whiteboard). You will also need to spend a lot of time modeling appropriate behaviours for station activities. Then, let the students practise going through 1 or 2 stations every day for a week, during which time your main role is to encourage and support appropriate behaviours. Spend time modeling, practising, and reflecting (and more time modeling, practising, and reflecting!) until you're satisfied that students will know how to manage themselves while you take small groups.

Another component in an effective math program is still whole-group problem solving. This type of lesson should occur much less often than small-group instruction, with an approximate ratio of 4 days of small group instruction to 1 day of whole group. This ratio is subject to change based on grade level (with primary students receiving more days of small group instruction, and intermediate students receiving fewer), content being covered (certain units lend themselves to almost exclusive small group instruction), and student readiness.

I like to think of math in terms of reading; just as students must first "learn to read" before they can "read to learn," students must "learn to math" before they can "math to learn." I think of the small group instruction as time to teach students how to math, and large- and whole-group problem solving as "mathing to learn."

For whole-group lessons, choose a task that most students would find engaging, and that has an entry point for all students. This can be in the form of a 3-Act Task (such as those found on www.gfletchy.com), an open problem (such as those created by Marian Small - examples can be found here), or a 3-part problem (such as the Unit Problems which can be found in Math Makes Sense textbooks).

To set up an effective small group guided math program, teachers should:

• Assess students on a small group of specific expectations to determine homogeneous groups.

• Decide whether to utilize a rotation model or choice menu model.

• Co-create behaviour expectations and model appropriate behaviours for station activities. Spend time practising, then reflect and repeat.

• Plan a week's worth of math, using 1 or 2 curriculum expectations as a guide. Set narrow and focused goals for each small group lesson. Each lesson should be accompanied by an "I can" statement.

• Plan station activities for students to complete while they are not meeting with the teacher. Stations should be simple to set up and explain, and students should be able to work on them independently.

• Depending on student readiness, plan a whole-group problem solving experience.

• Continue to assess through formative and diagnostic assessments in order to move students to the appropriate groups.

• Have fun with it! Students should see the "teacher table" as their favourite station. Use manipulatives, targeted instruction, and lots of positive reinforcement to ensure student engagement and success.