Lower School | K-Gr. 5
K - Grade 5 Academics

Learning to Make Sense of Numbers

When we talk about math we often talk about problems, equations and formulas. But behind the numbers and symbols, math is a way of thinking and exploring relationships. Factual knowledge about numbers is important, but far more valuable is the understanding of what numbers represent and how they relate to each other. This understanding, number sense, is the foundation for more complex mathematical concepts. From kindergarten through fifth grade, Lower School Math Specialist Mrs. Stacy Shaener teaches daily explorations of number relationships that get the whole class cheering about math.

Routines Are a Good Thing

Number routines are intentional daily exercises to reinforce and develop number sense. Number sense includes understanding quantities, more and less, larger and smaller, order, symbols as representations of concrete objects, and more. A student can memorize that one plus one equals two. But without good number sense, they can’t understand that adding one more to that group makes three. Number routines are a very effective way to get students thinking and talking about these types of relationships.
“I love using these because every student can participate with the group but at their level. Differentiation for varied learning abilities is built in. These routines encourage students to practice reasoning and mental math, and to use mathematical vocabulary in a very natural way. They learn to talk about their thinking and listen to others at the same time.” — Mrs. Shaener

Same But Different

In this routine, Mrs. Shaener posts two sets of numbers or number relationships on the board and asks the class to list everything that is the same or different. Rather than ask students to solve for a specific answer, she asks them to consider anything they might know about these numbers and how they relate to each other. Mrs. Shaener asks her students to justify their responses. They have to explain their thinking and through that process can often discern if they’ve made a statement that doesn’t make sense. Click here for more about this number routine from Looney Math Consulting.
Severn School elementary school students raise their hands during a lesson.
Because it is presented as an open comparison, every student can participate in the routine at their own developmental level.
Image of student math work.
It’s valuable for students to hear and see how their peers do this mental math.


In this number routine, Mrs. Shaener shows the class an image and asks them to wonder what number it represents. As students make their estimates, she reveals clues that help them narrow the choices down to a smaller and smaller set of numbers, until the big reveal at the end. After each clue, Mrs. Shaener asks the class to talk in small groups about their thinking.
Severn School elementary school students talk to each other during a math lesson.
Students practice math vocabulary and model their thinking processes as they share with their groups.
As students make estimates about the number of objects in the photo, she asks them to use what they already know about numbers. For example, a student suggested 100 for a small group of rings. Mrs. Shaener asked if they thought 100 was a big or small number and then directed them to look at the picture again. The student was able to quickly self-correct and make a better estimate after thinking about that relationship. Click here for more about esti-mysteries from Steve Wyborney. 

Severn School elementary school student looks at a photo of rings on a white board.
Mrs. Shaener invites volunteers to share their reasoning with the class as they try to solve the "esti-mystery" together.

Having a Blast Learning Math

These are just two examples of the many number routines Mrs. Shaener uses with her students. You can feel the energy in the room when they practice them — there is a buzz of excited chatter as students raise their hands high into the air. With encouraging dialogue, Mrs. Shaener teaches her classes to celebrate successes, work through struggles together, and see that process is the most important part of learning math. 
The big reveal at the end of a 1st grade "esti-mystery" routine.

Support for our Students at Every Level

We are committed to meeting the individual needs of a diverse group of learners at Severn and believe that children do best when they have a committed team of adults supporting them. Mrs. Shaener helps our Lower School students make math a priority, while also making it fun. Through professional development workshops and research, she keeps up-to-date on new and better ways to engage our kids in authentic problem-solving activities and works closely with teachers to keep every student moving forward with confidence in math.

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Lower School

Preschool-Grade 5
Chesapeake Campus
1185 Baltimore Annapolis Blvd
Arnold, MD 21012

Middle/Upper School

Grade 6-12
Teel Campus
Severna Park, MD 21146