Introducing Powerful Math Routines during the First Weeks of School

The beginning of the school year is a time for many introductions, especially during math class. It’s a time when we build a foundation that supports sense making, independence, and engagement. It’s also a time when we have an opportunity to introduce our students to  math routines that they’ll be engaged in for the rest of the year. 

What are Math Routines? 

Math Routines are 5-15 minute activities that can be used to launch a lesson or keep alive a math skill or concept across the year. For example, if a fifth grade teacher wants to use a math routine to launch a lesson on volume, they might begin by showing students the following picture and asking them how many cubes are in the structure and explain how they know. 

The teacher might continue to use this math routine called  Cube Conversations by Steve Wyborney to begin her lessons during the volume unit. She might also use the slide deck of 3-D structures as a routine throughout the year, re-visiting the concept of volume to ‘keep it alive’ for students so they have ongoing opportunities to practice. 

There are many different types of math routines. Some focus students on solving computation problems, some present visual images for students to think about, some involve choral counting, and others engage students in exploring data. These routines offer powerful opportunities for skill and concept practice and are perfect warm ups for math lessons.  But the key to math routines is engaging students in math discourse with the goal of deepening their understanding of numbers, shapes, and data. 

What Does a Math Routine Look and Sound Like?

Imagine this scenario: A fourth-grade teacher is beginning a unit on fractions. She starts with a math routine called Tell Me All You Can, showing her students the following visual image from Math Transformations’ visual image slide deck. 

“What do you notice and wonder about this picture,” she begins. The teacher gives her students time to think, then asks them to turn to a partner and tell them all they can about the image. When they finish, she calls them back and begins a math discussion, eliciting ideas from students.

“I see ten wholes,” Jasper offers. 

“Agree or disagree?” the teacher asks the class. She calls on Amy who says she agrees with Jasper. “Why do you agree?” the teacher probes. 

After Amy’s explanation, the teacher fields another observation, this time from Tony. He sees sixths, thirds, halves, and wholes. Lots of students nod in agreement. The teacher notices and asks someone to rephrase  Tony’s idea in their own words. After that, the teacher pauses the discussion for a few seconds before asking if anyone would like to explain where they see the fractions in the pattern blocks. Before calling on someone, the teacher waits about eight seconds before choosing a student to respond. This wait time results in many more raised hands. 

Tina jumps in and states, “I notice that a blue block is the same size as two green blocks.” The teacher responds by asking who can add on to Tina’s comment. Jake adds that the blue block is a rhombus and the green one is a triangle. He adds on further, saying that “one-third is equal to two-sixths.”

The teacher continues the math routine for a few more minutes, rephrasing ideas, asking students to add on to comments, before ending the rich discussion after about ten minutes. 

What Makes a Math Routine Successful?

The math routine described in the fourth grade class above seemed to run smoothly. Students’ partner talks were productive and focused, and the discussion that followed surfaced some key ideas about fractions. But successful math routines don’t magically happen. The fourth grade teacher in the scenario used specific strategies called Talk Moves to facilitate the discussions during the math routines she had introduced during the first weeks of school. 

Talk Moves are strategies teachers can use to facilitate and encourage talk in math class. These strategies need to be modeled and practiced regularly during the first weeks of school. Following are examples of each move the fourth grade teacher used during the math routine.

Turn and Talk (Partner Talk): “Turn to a partner and take turns sharing how you solved the problem.”

Using Think Time: “Take your time…” After asking a question, wait several seconds before calling on a student. 

Adding On: “Who would like to add onto what was just said?”

Revoicing: “So you’re saying that….”

Repeating: “Who can repeat, in your own words, what was just said?”

Reasoning: “Do you agree or disagree and why?”

Aside from using Talk Moves, there are several keys to making a successful math routine. The routine…

• should be accessible to a range of learners,
• be interesting and pique students’ interest,
• last only 5-15 minutes (depending on the grade level),
• must engage students in math discourse, and 
• should be modeled and practiced in the first weeks of school.

Introducing Partner Talks Using Interactive Modeling

Of all the talk moves available to teachers, Partner Talks are probably the most important during a math routine (or during any math lesson). Partner Talks provide a safe space for students to share their ideas, especially those who are learning English as a second language or for students who are shy and hesitant to participate in whole class discussions. Partner Talks are key to successful math routines. Consider the following scenario:

Imagine that you are a second grade teacher, and it’s the first week of school. You want to introduce Number Talks, a powerful math routine, to your students (learn about Number Talks here). You begin this math routine by posing the problem 29+12. You ask your students to turn to a partner and share their answer and strategy. What happens next isn’t what you had envisioned. Students are off task, looking away from their partner. One student sits alone without someone to talk to. Some are chatting about what they had for breakfast. A few have already solved the problem and look bored. Others seem frustrated. What went wrong?

Perhaps the math problem was too difficult for some of the students at the beginning of the year. Maybe the teacher didn’t give students enough time to mentally solve the problem. And maybe the class just didn’t know how to engage in a partner talk. 

Sometimes we assume that an activity like a Partner Talk should be easy, but it’s not. Simply turning to a partner and sharing ideas takes practice. Students need to know how to take turns, listen, explain their math thinking, and try to understand their partner’s thinking. Students need to learn these skills, and one way for teachers to help is to use Interactive Modeling, an activity from the Responsive Classroom.

Interactive modeling starts like a fishbowl, where students sit around and watch as you model what you want them to learn. The process might take time, but it’s time well spent and will save you time moving forward. Following is the sequence of steps for using Interactive Modeling to teach students how to engage in a partner talk (or any procedure or routine you want to teach). 

1. Say what you will model and why. “In a minute I’m going to show you how to engage in a partner talk with a person sitting next to you. Partner talks are important because they give you a chance to explain or share your thinking with one other person and listen to what they have to say.  It’s a safe place to share your ideas.”
2. Model the behavior. To model, have the class sit in a circle or a place in the room where everyone can see. You choose a volunteer to sit next to you and be your partner. You start your partner talk by facing one another, taking turns sharing your answer to the problem posed, explaining the strategy that you used. You might even post the directions or protocol for this activity, referencing them as you model. For example: turn and face your partner, take turns sharing your thinking, maintain eye contact and listen to your partner, stay on topic.  
3. Ask students what they noticed. After the partner talk, you ask the class, “What did you notice us do during our partner talk?” The students name what they saw and heard. You prompt them if they missed anything important.
4. Have all students practice. Next, have the students pair up with the person sitting next to them and take turns sharing.
5. Provide feedback. “I noticed that most of you took turns. I noticed that you shared your answer and how you got your answer. I also noticed that you maintained good eye contact with your partner.” Giving feedback is key because it reinforces the partner talk procedure. 

For the first several partner talks you have students practice, we recommend starting with topics that have a ‘low cognitive demand’. For example, you might want to have students think of their favorite food and then take turns sharing with their partner. Once the class knows the protocol for the activity, then they’re ready to engage in partner talks about more academic content. 

Three Powerful Math Routines to Start the Year

Number Talks

Number Talks are a 10–15-minute math routine focused on developing mental math skills, number sense, procedural fluency, and math discourse skills. Dot Talks use dot arrangements rather than numbers.

How It Works:

1. Present a math problem. 
2. Students solve the problem mentally.
3. Students discuss their answers and strategies with a partner.
4. Students share their strategies publicly while the teacher listens, records their thinking, and facilitates student-to-student interaction. 

Dot Talk Example, Kindergarten/First Grade Video Link

Number Talk Example, Fourth Grade

Dot Talks Slide Deck for Kindergarten from Math for Love. 

In our blog posts, we’ve written extensively about Number Talks. If you haven’t done so already, we invite you to visit the following posts, which you can access here.

• Number Strings: A Different Kind of Number Talk
• How Can We Adapt Number Talks for Distance Learning?  Insights from Richie Moreno

Choral Counting 

Choral Counting is a routine that helps students notice patterns in our number system and develop their math discourse skills. Choral Counting can also support students’ understanding of counting concepts, place value, and the four operations including fractions and decimals (from Choral Counting & Counting Collections, Routledge Publishers, 2018).

The authors of Choral Counting & Counting Collections offer some wonderful and innovative ways to lead counting exercises, making for a powerful math routine. 

How It Works:

1. The teacher chooses a starting number (starting from 1 or any other number), which number to count by (counting by 1s, 2s, 5s, 20s, 1/4s, 1/2s, and so on), and how she wants to organize the count. 
2. As the teacher and students count together, the teacher records the numbers in organized rows or columns of different quantities.  
3. As the teacher and students count together, the teacher pauses along the way asking students what they notice, to make predictions about an upcoming number, and so on. 
4. When the students have counted together far enough to get a good chunk of numbers on the board, the teacher again asks students what they notice and records their ideas, sometimes highlighting their noticings with a marker so patterns are more visible to the class. The teacher might also ask students follow-up questions such as:

• • “Is what you are noticing happening anywhere else?
  • “What if we keep going? What do you think will happen?”
  • “What number do you predict will be next?”
  • “What is a number we would say in our count if we kept going?
  • “What number would we never say in our count if we kept going?

Choral Counting in K-2 Classrooms

Choral Counting in the primary grades can help students learn number names, the counting sequence, and connect the number words with their written symbols. This routine can also help students learn about the relative size of numbers and identify patterns and structure in our number system. 

In kindergarten for example, a teacher had the class count by 1s starting with one. They organized the count in the following way.

Once the count was done, kindergartners noticed lots of things. They saw repeating numbers in each column. They also noticed that the numbers in the last column all end in zero, which led the class to count by tens together. The teacher used Talk Moves, rephrasing students’ comments to highlight important mathematical ideas.  And the teacher asked questions to push on students’ thinking, questions such as, “What number will go after 30 when we count by ones? What about when we count by tens?”                    

The next day, the teacher organized the count differently so that the class could notice other patterns. For example, this time the numbers in the last column got bigger by four (4, 8, 12…). The teacher modeled curiosity by commenting aloud, “I wonder why that happened?” 

In first grade, a teacher choral counts with the class, starting at 50. 

Once the choral counting stops, the teacher asks students what they notice. She might even ask them to predict what comes next. The noticings that students make can surface important mathematical ideas about our base ten number system. For example, a big idea students may notice when counting by tens is that our number system is based on patterns of 10 that go beyond 100.

During the first weeks of school in the early grades, introducing this routine should include giving students lots of practice choral counting in unison and using Talk Moves to help them communicate their math thinking. In the beginning of the school year, a teacher might start out having the class count by 1s starting from 1, count by 1s starting from a number other than 1, count by 1s backwards starting from different numbers, count by 1s going beyond 100, and count by 2s, 5s, 10s. 

Choral Counting in Grades 3-5

In third grade for example, students can use Choral Counting to explore multiples of different numbers. Below, a third grade teacher counted by 3s with the class and chose to organize it the following way. She then asked students what they noticed. 

The students saw patterns in odd and even numbers. They noticed consistency in the difference between adjacent numbers. For example, the difference between the numbers in the rows is always 3, while the difference between the numbers in the columns is always 12. Choral counting not only supported students’ developing multiplication skills, but also gave them insight into the structure of our number system. 

Fourth and fifth grade teachers can use Choral Counting to help students develop their understanding of fractions and part-to-whole relationships. For example, after counting by fourths, the teacher asks her students what they noticed. As you look at the fractions, what do you notice?

Visual Images

Visual images can prompt students to look at the world through a mathematical lens. Depending on the questions we ask, students can quantify, describe, compare, measure, and wonder when shown a visual image. 

Illustrative Math’s Talking Math is one of my favorites. This is a visual image math routine that focuses on developing math vocabulary, math discourse skills, problem solving and critical thinking. Check out our blog post that provides more detail about what this routine might look like in kindergarten.

How It Works: 

1. Use the slide deck to choose an image to show the class.
2. Show the ‘invitational launch slide’ that includes open-ended questions such as, What do you notice? What do you wonder? What do you see? What patterns do you notice? What questions do you have about the picture? What math words do you think of when you look at this picture?
3. Show the next slide and pose the questions that are provided for you (there are questions for each grade level, from kindergarten to fifth grade).
4. Have students talk with a partner about their answers, strategies, and thinking. 
5. Students share their thoughts with the class. 

Here’s a visual image from Talking Math that includes questions for students in grades K-5, along with references to the standards at each grade level. TK teachers can use the grade K questions.

You can also use the following Math Transformations slide deck to access more visual images. One of my favorites in the deck features jelly beans. Notice in the following vignette how the jelly bean image engages a group of fourth graders in problem solving. The teacher begins by showing them this photo:

Then she asks,“What would you need to know in order to make a good estimate of how many jelly beans there are in this box? What questions might you ask yourself? What decisions might you have to make?” 

The teacher gives her students time to think, and then has them talk with a partner before eliciting ideas from the class.

Students come up with several ideas that can help them make good estimates. 

“I’d need to know how many rows and columns there are.”

“I’d need to know if there are the same amount of beans in each little holder.”

“About how many beans there are of each type or color.”

“I’d have to decide whether I’m going to add or multiply.” 

Next, the teacher asks students to estimate how many jelly beans there are altogether. They discuss their answer and strategy with a partner before sharing with the class. 

Laying the Foundation for a Successful Year

The math routines outlined in this post are little gems that pack a big punch. They have the potential of yielding lots of learning in a short amount of time. These routines can be used with any math curriculum material, and they don’t require much preparation. The routines spark curiosity in the learner, give them opportunities to communicate their math thinking, build their toolkit of strategies for solving problems, reveal patterns and structure in our number system, and help students see the world through a mathematical lens. 

The first few weeks of school are crucial in setting the tone and laying the foundation for a successful year of learning mathematics that supports sense making, independence, and engagement. Introducing these math routines is an important part of laying this foundation, and we hope you try them out!