Building Number Sense Through Routines
What if math class didn’t begin with passing out worksheets and instead began with a fun, interactive activity that encouraged talking and collaboration?
Math routines offer teachers a great opportunity to start math class on a positive note while also using precious class time in a productive way. With math routines, you can improve your students’ number sense and offer them a deeper understanding of many math concepts.
Are you sold yet? Let’s explore what this might look like.
What Are Math Routines?
Math routines are not a replacement to curriculum, but instead are warm-ups that offer a perfect start to math class. These activities help students apply number concepts in a low-stake format, which can help lower math anxiety. Plus, they can also build your class community and self-confidence in individual students.
Math routines are low-entry but also high-ceiling. In other words, they are easy to enter, but also offer lots of room to expand. In this way, math routines allow students of different math abilities to better understand concepts. These routines are effective because they facilitate the building of number sense even in students who struggle with math. With math routines, teachers can also achieve an understanding of students' thought processes.
What is Number Sense?
“As students work with numbers, they gradually develop flexibility in thinking about numbers, which is a hallmark of number sense… Number sense develops as students understand the size of numbers, develop multiple ways of thinking about and representing numbers, use numbers as referents, and develop accurate perceptions about the effects of operations on numbers.”
More concretely, number sense means that students have a grasp on the basic operations of math, the commutative, associative, and distributive properties, place value, composing and decomposing numbers, comparing numbers, and more!
If this sounds like a lot, it’s because it is! Throughout their school experiences, children need concrete experiences with math and lots of opportunities to wrestle with problems, numbers, and math concepts. It is only through practice that children can develop number sense. Maths routines provide an excellent opportunity for children to grow “their” number sense.
Examples of Math Routines
Math routines have a few defining characteristics that make them special. Most importantly, they are an interactive, class-wide event that promotes discussion. Math routines are also fairly short and can review a concept that’s already been taught in a formal lesson. With this in mind, let’s take a look at a few examples of math routines:
Clothesline Math: Each student is given a card with a number on it. Then, students have to spread those numbers out to create a number line, thinking of the spacing in between each number. Numbers are shown in different ways, such as the actual number, dots, tallies. Students do this hands-on and have to correct themselves based on where other students put their cards.
One possible extension for this activity could be using decimal places or fractions, and negative numbers instead of only whole positive numbers.
Number Talks: Provide a math problem for the class. For example, “Is 12 x 3 closer to 30 or 40?” Or, “Make the number 132. Use the numbers 200, 2, 3, 5, 9 to get there. You can multiply, divide, add, or subtract, but you can only use each number once.” Or, offer another math riddle or brain teaser.
Before asking students to work on the problem or solve it, ask students to do a “Turn and Chat.” In this activity, students talk with their neighbours about different strategies they could use to solve the problem and what they think the answer might be. Then, encourage children to share strategies with the whole class.
With the first problem, students might explain that they solved the multiplication this way: 10 x 3 + 3 x 2. Others may have solved the multiplication by memorising 12 x 3 or simply estimating. Yet others may have solved this way: 3 x 5 + 3 x 5 + 2 x 3.
Ball Toss: Use a permanent marker to write numbers all over a big, soft ball. Then, have students toss the ball. As they toss, each student says the number that their thumb lands closest to and adds it to the previous number. Students continue adding the numbers until they reach a certain threshold such as 100. Alternatively, ask students to multiply, divide, subtract, etc.
I have, who has?: Give each student a card with a number on it. Then, start the conversation by saying, for example, “I have the number five. Who has five plus three?” Or, “I have the number five, who has a number that’s less than five?” The student who has the number to which the question applies goes next, asking a similar question. Continue in this manner, asking students to use various operations and descriptions until every students’ number has been called.
Many of the activities are similar for different grade levels but get more complex for the older grades.
Other resources that you can use as a part of your math routines that also help build number sense include math boxes and Matific Online Learning Platform for games and activities. Do keep in mind that these number sense math routines are not a replacement for the actual curriculum.
How to Implement Math Routines for Best Results
To implement math routines first you need to decide which routines to use for each class, grade, or school. Then set norms for discussion. Instead of rushing to find one right answer, the discussions allow students to discover that there are many different ways to reach the answer.
Instead of asking the first student who raises their hand to say the answer, let the students put a thumbs up if they know the answer. Take it further by asking students to hold up one finger for each way they know to reach the answer. This way, all students can think of different solutions and not give up right away.
In math routines, let every student be part of the conversation. Some good sentence and conversation starters can include:
"So you're saying...,"
"Can you repeat what ___ just said in your own words?"
"Do you agree or disagree with what ___ said?"
“Can you walk me through how you thought about the problem?”
With these concepts and activities, it is good to let the students explain how they get to different solutions because the concepts build upon each other and are interconnected.
Remember, the goal isn’t only to get the problem right. Other goals include thinking flexibly, practicing manipulating numbers, talking through processes, and growing understanding in math. Help students focus on these goals by highlighting good discussions, the helpfulness of making mistakes, and the importance of solving problems with various strategies.
Do you use math routines in your classroom?