On May 17, 2016 over 150 teachers gathered to explore, discuss and make connections. After a long day at work, these teachers eagerly investigated and shared ideas regarding how to use ‘5 Mathematical Routines’ (Quick Images, Counting, Number Talks, Number Lines and Which One Doesn’t Belong) in their classrooms. These 5 – 15 minute routines help to develop a mathematical community, provide regular practice on mathematical concepts, develop number sense and computational fluency with the students.

“The ultimate goal is that students make connections over time, build an understanding of relationships among numbers and operations, and ultimately apply their number sense understanding to problem solving.” ~Jessica Shumway

These routines are directly connected to the B.C. revised curriculum. The focus on curricular competencies to ‘show what you know’ (the content) is embedded in all of these routines. Each routine has a slightly different emphasis and purpose, but all of them focus on communicating, thinking and working together (the Core Competences). The structures of routines may include being part of a ‘warm up’, daily math investigation, mini-lesson, guided math group, or a ‘reflect and share’ session.

Here is a description of the 5 routines focused on during the session:

**Quick images **

- Students are shown pictures displaying groups of objects or symbols, viewing each for only a few moments.
- Students are encouraged to take a ‘picture’ and visualize the image in their head.
- Students are asked to share their thinking about the images shown (i.e. How do you see it?)

**Counting**

- Counting Around the Circle – Whole class participation. Each student says a number as you count around the circle.
- Counting Collections – Partner work. Each pair is given a collection of objects to estimate, count and record the count.
- Choral Counting – Whole class participation (or small group). The teacher decides on a number to start on and then a number to skip count by. The teacher records the number, pausing the count at a strategic moment and ask questions. The goal is not just practice rote counting, but to engage the children in reasoning, predicting and justifying.

**Number Talks**

Conversations with the whole class that are usually about 5 – 10 minutes in length.

- Intended to help develop conceptual understanding and efficiency with number.
- The teacher presents a mental math problem.
- Students are asked to think about the problem and then share solutions and explain thinking.
- The teacher acts as a facilitator to guide the conversation.

**Number Lines**

- Numbers are represented as points and distance on a line.
- They provide representation of the relationships of number and the spatial sense of quantities and magnitude.
- Teachers use number lines to represent numbers and support reasoning about them.
- Open number lines provide flexibility in thinking. Students are asked where they might place a number in relationship to another number.
- Open number lines are also used to help students add and subtract numbers and demonstrate their reasoning.

**Which One Doesn’t Belong – wodb.ca** (see examples on this website)

- Students are presented with four different numbers, objects or shapes (that are alike and different in many ways)
- Questions are asked:
- What do you notice?
- What makes all the items alike?
- What makes them different?
- Which one doesn’t belong?

- Students explain and justify their choice

Each of these routines only take a small amount of time but when used consistently…they will help to build your students’ understanding, confidence and ability to communicate their thinking. Are your students able to make connections, communicate their thinking and see themselves as competent and confidence mathematicians?

Please see the PowerPoint presentation and resources connected to this post on the Big Results in a Small Amount of Time page for more examples and clarification.

Take the time out of your day to use one of these 5 routines and let me know how it goes!