Start the Conversation in Math: Sentence Starters, Stems & Frames

Recently, I was thrilled when I met a group of second graders using phrases like “I think this because . . .” and “I respectfully disagree with ___ because . . .” during a math discussion. I couldn’t help but feel appreciation for their teacher. I just knew that the teacher had used language scaffolds with these little learners, who were now coming to me ready to dive into mathematical discussions and model the language used in mathematical discourse for their peers.

It is essential for educators to provide collaborative experiences that give students opportunities for rich math conversations. Many students, however, haven’t been taught the language skills yet to clearly express their understanding.

In general, students are expected to find math instruction meaningful and connect it to their day-to-day lives. Instead of giving students plug-and-play formulas and algorithms, educators must provide the tools to help them make sense of math, take ownership of their learning, and think like mathematicians. 

Math learners generally learn best through collaboration and mathematical discourse—an approach that lets students rehearse and vocalize their thinking, and then edit it when errors and misconceptions are encountered. When teachers coach students to use sentence starters when explaining mathematical thinking, it can enhance the classroom environment and help students communicate ideas clearly, practice using academic vocabulary, ask and answer questions, and clarify misconceptions.

What are math sentence starters and sentence frames?

Sentence starters and sentence frames are types of language scaffolds that can be used to support student math talk and writing. Sentence frames are also sometimes called sentence stems. When we give students these scaffolds, we are not giving away the answer to a question, as students are still expected to do the mathematical thinking. Rather, these scaffolds provide an entry point to a response. They present a framework that can guide students’ thinking, along with an opportunity to start a discussion or writing activity. Students are still expected to utilize their background knowledge and expressive language skills to verbalize their thinking.

The difference between a sentence starter and a sentence frame (or stem) lies in the amount of language scaffolding that is provided. Sentence frames, or the more heavily scaffolded response frames, provide the most support by giving an overall sentence structure that “frames” the language around student thinking. Sentence frames remove a cognitive barrier for students who struggle to both gather their thoughts and express them using language that may be unfamiliar to them.

On the other hand, a sentence starter, or sentence stem, gives students a jumping-off place to express their thinking. Sentence starters can be useful for learners who already have the academic language skills to express their thinking but need additional support with articulating their thoughts fully. When you give sentence starters to students, you take away one of the biggest hurdles some students face in joining a math discussion: knowing where to begin.

Over the last couple decades, the language demands in the math classroom have grown significantly. This can be attributed to several factors, including the emphasis on real-world problems and math practices in Common Core and different state standards, as well as a changing makeup of math students, notably including a growing population of multilingual learners. To effectively demonstrate understanding in math, there is an expectation that students are able to justify their reasoning, critique the reasoning of others, and use precise language and accurate math vocabulary. With these mathematical practices spanning all of grades K–12, language scaffolds are one useful tool for educators to have.

Language scaffolds can be used to:

• Facilitate whole-group discussions. 
• Provide scaffolding for students to use academic vocabulary during partner and group work. 
• Give students an opportunity to prepare for participating in a later discussion. 
• Jump-start student writing when answering a reflection prompt.

The benefit of language scaffolds to specific learners

While language scaffolds are generally beneficial for all learners, they can be particularly beneficial for multilingual learners and students with special needs such as language-based disabilities, anxiety, or ADHD. Some students may be adept at communicating their mathematical thinking in one language but struggle to communicate in another.

The good news is that communication in mathematics is a skill that can be taught through explicit modeling and language routines. Language scaffolds help in both cases:

• Multilingual learners get support with language structure that is less scaffolded than a response frame.
• Students with expressive language disabilities get language support to help with the process of producing speech or written language.
• Students with anxiety get help planning their response.
• Students with ADHD are given a structured model for answering.

Though language scaffolds can be a beneficial accommodation for specific students, a student does not need to have a diagnosis or classification to benefit from them. Many students struggle to express their thinking in math, possibly due to lack of confidence. By making these scaffolds available to all learners, students who need that language support are getting the tools they need right when they need it.

Mathematical language routines

Let’s take a look at what some language scaffolds look like in practice. HMH’s Into Math includes a variety of language routine activities, along with videos where peer coaches model the activities. One such activity uses Information Gap Cards. A Grade 4 sample is provided below, along with a corresponding video of the cards being used.

Below are another set of sample Information Gap Cards and corresponding peer coaching video, aimed at at a seventh grade math classroom.

Examples of sentence starters for math

Sentence starters are not just for students; sometimes they’re for teachers. We can all use some support when it comes to making mathematical concepts accessible, and sentence starters and frames are a research-based tool to help us teach with fidelity, both to a particular program and to general best math teaching practices.

Here are some questions and sentence starters to encourage classroom participation and elicit deeper thinking during math discussions:

Examples of sentence frames for math

Scaffolds are only useful if they are appropriate for the learner, so it is essential to know where your students’ skills are at that moment. Make sure to gauge through formal and informal assessment what type of language supports your learners might need right now. These needs can be varied, so it is often essential to recognize if your learners need more support than sentence frames can provide. Some learners may need additional grammar and syntax support to help them structure verbal or written responses, which they can receive more readily through response frames.

Here are some reflection questions you might ask with accompanying sentence frames:

Providing language scaffolds throughout a math lesson

In plenty of math lessons and activities, students are practicing speaking and listening to math talk throughout their learning. This creates opportunities to provide sentence starters and response frames which can be used to support learners in these discussions at every phase of the lesson. Below are some ideas for how to use these language scaffolds during your next math lesson.

Sentence starters, math talk, and accountable talk during partner and group work

It is no secret that students learn best through collaboration, but the classroom management aspect of group work can sometimes make planning for it daunting. So, how can you ensure that students are staying accountable during collaborative activities? One strategy is to establish routines for group work and provide sentence frames for accountable talk.

Accountable talk is a type of classroom discussion where learners are specifically held accountable for using academic and domain-specific vocabulary during partner and group discourse in math. In practice, accountable talk discussions can be empowering for students, as it allows them to take more ownership of both their peers’ and their own learning while the teacher facilitates learning experiences. Try out this group work routine while providing language scaffolds to keep students accountable.

Sharing with math sentence stems

By preparing students with open-ended questions related to the lesson’s goals, we can guide their learning and have them articulate their own takeaways at the end of a lesson. Using sentence starters helps students practice their responses before sharing. This can also be done as a writing activity, ensuring everyone is ready to participate by the end of the lesson.

Reflect on learning with sentence frames and starters

After a lesson is over, you can have students complete an exit ticket to assess if they understood the skills and concepts presented in the lesson. Rather than the exit ticket providing a problem for students to complete, consider asking an open-ended question that gets to the heart of the learning. Then, provide sentence frames to students who need support in answering the question in written form.

Try it out

Not only are sentence starters an essential language scaffold for the math classroom, but they are also versatile and can be used during any phase of a lesson in which learners are expected to demonstrate understanding. Sentence starters can be as general or specific as you need them to be without taking any of the mathematical thinking tasks away from your students. 

In general, sentence starters can level the playing field by giving learners who need them a jump-start to responding to a written or verbal prompt. Learners additionally get an access point to participation in mathematical discourse and written activities.

Language scaffolds are about more than supporting multilingual learners. By integrating them into your math lesson, you not only enhance students’ mathematical discourse but also empower all students to articulate their understanding with confidence. This approach fosters a more inclusive and collaborative learning environment, where every student has the tools to succeed and contribute meaningfully.

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