By Jen Hawkins, IM Facilitator and IM K-5 Product Specialist
Illustrative Mathematics believes that students can achieve success as mathematical thinkers by working through problems and consolidating their learning through classroom discussions and anchoring activities. The IM K–5 Math curriculum was designed to deliver high-quality grade-level content in this manner. How can a teacher in a multi-grade classroom provide this experience to more than one grade in the same room?
Teachers aren’t just essential workers; they are also frequently miracle workers. All teachers encounter students on varying levels in their classrooms and they work to meet their needs, but being charged with delivering content on two, or at times even three, different grade levels in math within the same classroom is an entirely stepped-up sort of challenge! During the alpha and beta pilots of IM K–5 Math we included schools with multi-grade classrooms and we know even more schools with multi-grade classes will be using IM K–5 Math in the 2021–22 school year. This blog is intended to share some of the strategies employed and difficulties experienced in the pilot years, and to also suggest some ideas for the multi-grade teacher to use in the year ahead.
Beliefs and Values
The vision of Illustrative Mathematics is a world where all learners know, use, and enjoy mathematics. Our curriculum supports problem-based instruction and is aligned to the Common Core content and practice standards. With IM, students become confident mathematicians through solving problems and participating in productive discussions led by teachers skilled in orchestrating those discussions. Whether the teacher leading the learning is teaching in a conventional single-grade classroom or in a multi-grade classroom, the elements that distinguish our curriculum are the same: inviting students to the math, promoting deep study of concepts and procedures through solving problems and productive struggle, and consolidating understanding of mathematical ideas with teacher-led discussion. We believe students in any classroom, whether it contains a single grade or more than one, learn during their discussions with one another and in the whole-group discussions orchestrated by the teacher to summarize the content learning. The following quotes are from multi-grade pilot teachers.
“We established early on that students learn just as much from each other as they do from me. I spent a lot of time encouraging students to listen and respond to each other during math discussions.”
The multi-age classroom presents the challenge of how to provide the experience of rich classroom discourse to more than one grade at a time. The teacher will need to have classroom management structures in place that allow them to discuss with students at one grade level while other students are engaged in math activities that they can do independently or in partnership with a peer.
IM K–5 Math resources can support effective multi-grade learning environments. Teachers in multi-grade classrooms employ flexible instruction structures and will need enriching options, hands-on resources, and engaging activities to continue and support the learning when students are not in discussions with their teacher. An important component of IM K–12 Math is responding to student thinking, and we encourage teachers to keep that focus in a multi-grade-level group, even as we acknowledge that the lesson structure may be more fluid. Teachers may have to reorganize components, things will be different, but the success that can be experienced from facilitating effective student discourse can be experienced.
“IM centers and activities, plus games [from other resources]…were a regular part of our math time. All of these games promoted and supported number talks and conversations, and the discussion of strategy and problem-solving skills….”
Structuring the Multi-grade Classroom
“The structure of our math time varied. On a ‘typical’ day, our math time would start out with some warm-ups, mental math, or group problem-solving/math challenges, then a brief lesson using some of the lesson activities, partner and individual work-time, and ending with a group share and discussion.”
There are many resources within IM K–5 Math to support high-quality instruction within different instructional formats. Typically, a multi-grade teacher organizes their classroom with the following structures:
- whole-group time
- all students learning content or being introduced to content at the same time
- small-group Instruction
- teacher-led groups, sometimes based on grade level
- partner activities
- students working and problem solving with a partner while the teacher may be holding small-group instruction, and other students might be working independently
- independent work
- students working, exploring, and problem-solving on their own while the teacher may be holding small-group instruction, and other students may be engaged in working with a partner
Whenever possible, whole-group time should be planned deliberately. It is through discussions that teachers move students’ thinking further. To provide these opportunities, the multi-grade teacher might pull from the instructional routines connected to topics being studied. Every IM K–5 Math lesson “invites students to the math” with one of 10 different instructional routines used as lesson warm-ups. These routines include Number Talks, Which One Doesn’t Belong, Choral Counting, How Many Do You See, and others. Whenever students can talk together and learn from one another, everyone is enriched by the questions asked and the ideas shared.
“We often did the warm-ups altogether, grades 4 and 5, and used both grade levels depending on the concept. This was valuable for all of them.”
Another option to promote whole-class mathematical conversation is to use slides from the IM Talking Math series. These slides present a single, compelling image and have mathematical questions that range from grade K through grade 5. The multi-grade teacher could remove the grade-level labels of the questions and choose 2 or 3 questions to invite students into the study of an upcoming topic, whether it be fractions or geometry or addition operations.
“I ended up doing a mix of whole-group teaching, differentiated instruction, centers, and independent and partner work.”
At other times the multi-grade teacher will provide problem-solving opportunities and discourse in a small-group Instructional format targeted at student’s grade levels. Sometimes the instructional routines found in the grade-level lesson warm-ups will be used during this time. Also the teacher will want to work through many of the activities and syntheses found in all IM K–5 Math lessons in small-groups to provide problem-solving opportunities and discourse for their students.
“Initially I split our math time between the 2 grade levels—I would teach a lesson to one grade while the other grade did individual and partner work. When there was overlap in the units, I would teach a whole-class lesson and differentiate [as] one of my 4th graders was working at a 5th grade level.”
While the teacher is working with a small group for instruction, other students in the multi-grade classroom may be engaged in partner activities or independent work. In the younger grades paraprofessional staff or a parent volunteer is typically needed to support a multi-grade classroom. Activities labeled as partner or independent in grades K and 1 will most likely need the support of an adult at times.
“I was fortunate to have a…teacher assistant in the room during math time, so she was able to help those in need during the math game/independent work time. Students were instructed to do their own work, and to share any issues or questions they had with the rest of the class.”
In IM K–5 Math there are many lesson activities that, after the initial launch, students could work through with a partner. Another option for partner learning would be the use of the centers in IM K–5 Math. Centers will be a critical element of the multi-grade classroom because of the many center options and different stages. Centers provide the teacher with the appropriate choice of activity to promote fluency and the selection of the right stage based on needs. They are the perfect choice for students to turn to with a partner when the teacher is engaged in grade-level instruction with another group.
“For most of the year, I would have one grade level in the back of the room playing a math game while the other grade level sat on the rug for a lesson with me. Halfway through our math period, the two groups would switch activities.”
When looking for independent work options for students, the multi-grade teacher can start with selecting practice problems for students to do on their own. Or, for the more curious math minds, explorations might provide the best challenge for some students to work on by themselves.
Assessment and Learning about Student Thinking
Another critical component of multi-grade classrooms is formative assessments. Multiple, succinct assessment options are needed for teachers to make informed decisions about needs and groups. IM K–5 Math offers the following assessments options to provide insight into student thinking:
- pre-unit practice problems (in grades 1–5)
- cool-downs for lessons (in grades 1–5)
- checklists to collect observational data (in grades K–1)
- section checkpoints (in grades 2–5)
As in any classroom, the teacher in a multi-grade classroom will want to use formative assessments to make decisions about which partner and independent activities would best suit students. Teachers will want to know which students would benefit from additional support and who would best be suited for a challenge. Groups in a multi-grade classroom may be fluid: perhaps with some content not exclusively based on grade assignments but at times arranged based on determinations of student needs gleaned from formative assessments. For this reason it can be prudent in a multi-grade classroom to remove grade label indications on resources used.
“Cool-downs helped me decide which games and other activities to use to give kids additional practice where they needed it most.”
Formative assessments can also help a teacher decide when further or different support is needed through small-group instruction.
“I used the assessments to evaluate the students’ understanding of the material, and to examine where my teaching had been effective or fallen short. If and when necessary, we would review or re-approach a mathematical concept in a different way. The assessments also allowed me to identify the gaps in their numeracy skills.”
“I often used the cool-downs as morning work to start the day. If I noticed that particular students were struggling with certain concepts, I would individualize their morning work and provide more practice problems.”
Compacting Content to Accommodate Multi-grade Classrooms
A major consideration in the multi-grade classroom is the need to compact or streamline content.
“A lot of preparation is required for each IM lesson, which doubles when you are teaching two grades. Since the [content of the] units …is not aligned between grades (e.g. Grade 4 starts with Factors and Multiples, and Grade 5 starts with Volume), it made it impossible to teach the full lessons every day to each grade.”
IM K–5 Math resources include the Section Level Planning Guides (found in the IM Community Hub) that can help teachers make decisions on which lesson to prioritize. These guides identify the following:
- critical lessons (Deep Dive components) for group instruction times
- explorative lessons (Explore, Play & Discuss component) that with modifications can be used as independent activities or at home
- additional lesson components (Synthesize & Apply components) that can be adapted for independent use or with the support of another adult in the classroom
- on-going practice and anytime resources that can be used as partner activities or independent work
The Section Level Planning Guides (SLPG) can help when a teacher is either looking for more time to accommodate unfinished learning needs before beginning new content, or when lessons need to be consolidated to fit into multi-grade learning time. The teacher in a multi-grade classroom can use the SLPG to make decisions about which lessons are critical to include in small-group instruction, which lessons might be used as partner or at-home activities, and by omission, which lessons can be dropped to make time for all the multiple levels of learning being delivered.
Each grade level in IM K–5 Math tells a coherent mathematical story, following an intentionally designed sequence that grows from invitation to deep study and then consolidation. What can the multi-grade teacher do when the two grades they are teaching have stories that don’t “match up” in sequence?
“There was some flexible grouping. Especially toward the end of the year, in the geometry, measurement, and time units, I had the first and second grade groups working together.”
As mentioned previously, the teacher in a multi-grade classroom may at times employ a more fluid structure of lesson components and will need to drop activities, considering what is essential to make learning for more than one grade “fit”. And this sort of flexible thinking will come into play when considering the units and when the story of the mathematics aligns with the different grades in the classroom.
Learning from Experience
As our students learn when we are teaching, so also do we learn about our practice as we teach. We adjust and try new things, and build off our successes. We make changes. We share our success. IM K–5 Math pilot teachers shared the following:
“Most of the students love math! We talked daily about being ‘efficient mathematicians’ and had rich discussions about different learning styles and approaches to solving math problems. The students talked openly about their own strengths and weaknesses, and were very supportive of each other. IM helped the students become better thinkers.”
And the IM K–5 Math pilot experiences gave us information about the challenges:
“It would be helpful if the content of each unit lined up between the grades, so that I could progress through the material sequentially and still have both age groups talking about the same concepts.”
As an educator, you know your students best. Illustrative Mathematics does not have a multi-grade classroom lesson blueprint for you. We have a powerful curriculum that has the elements needed for students to learn and go far: grade-level problem-solving, engaging activities, and the tools for effective discourse.The teacher facilitating the learning in a multi-grade classroom is a mathematical thinker as well, solving problems creatively, using structure to make decisions and learning from experience. We invite you to experiment and trust in the brilliance of your students. We look forward to learning more from you about IM K–5 Math and the multi-grade classroom.
Will you be teaching in a multi-grade classroom this school year?
It will not be easy, but you can succeed. You will learn, reflect, and get better with each lesson and unit.
“We got through a lot of material! And I’m always finding things I can do better next year.”
Reflection as you teach is part of the process, you will find teacher reflection questions with each lesson. Bouncing ideas off colleagues, learning from one another: it’s what we expect from our students and what we encourage among educators. Please consider connecting on the IM Community Hub with others teaching in multi-grade classrooms. We encourage you to share ideas, discuss strategies, and support each other through the challenge of teaching in a multi-grade classroom. Like any community, working together makes everyone stronger!
Jen Hawkins is an IM facilitator and IM K–5 Product Specialist. Jen has a B.A. from the University of the Virgin Islands in elementary education with a concentration in mathematics, and an M.A. from Mount Holyoke College in teaching mathematics. Her first teaching position was in a multi-grade classroom at Peace Corps Elementary school in St. Thomas. Since then she has worked as a teacher and as a math coach in elementary schools and middle schools in both the Caribbean and in Massachusetts. For a number of years she left the classroom to focus on her passion for assessment, working at the Massachusetts DESE on the Mathematics MCAS test, first as a test developer and then as the administrator. She believes mathematics is the language of quantity and shape that everyone, with the right resources and support, can appreciate and enjoy. She loves to travel, collect vintage wares, and dance to great music.