Big Results in a Small Amount of Time

On May 17, 2016 over 150 teachers gathered to explore, discuss and make Big results 1connections.  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 Number Sense Routinesunderstanding 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:Big results 3

Quick images

  • Big results 4Students are shown pictures displaying groups of objects or symbols, viewing each for only a few moments.
  • Students are encouraged to take a ‘picture’ Big results 5and 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 Around the Circle – Whole class participation. Each student says a number as you count around the circle.Big results 6
  • 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 Big results 7moment and ask questions. The goal is not just practice rote counting, but to engage the children in reasoning, predicting and justifying.

Number Talks

Big results 9Conversations with the whole class that are usually about 5 – 10 minutes in Big results 8length.

  • 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.Big results 10

Which One Doesn’t Belong – (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?Big results 11
    • 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!

Basic to the Basic ~ A Better Way – Part 2

Report cards, snow, flu and tired bodies didn’t stop over 50 teachers from attending the second part of ‘Back to the Basics’.  It always amazes me that these dedicated teachers attend after school workshops to network, share and learn together.  Thank you all for caring so much about your students and helping them to make sense of mathematics.  We all agreed that we want our students to understand the basic addition and subtraction facts by applying strategies that make sense.  Please continue the conversations and building the important foundation with our young learners.

part 2

Back to the Basics – A Better Way

Pic1Another amazing group of over 70 primary teachers met after school to learn more about teaching the ‘Basic Addition and Subtraction facts’ in a meaningful way on February 12, 2014.  This was part one of a two-part series.  I am always so thrilled to see the dedication of hard working, caring teachers who want their students to truly make sense of mathematics.

It is so important for the students to establish a firm foundation of ‘Number Sense’ before teachers start presenting strategies to help students understand the facts.

We know that students still need to “know their facts”, however, memorization and timed drills didn’t work for many students (and still doesn’t).  Some of our struggling mathematicians have been drilled for years and still struggle as they enter high school. .  A structured, thoughtful and systematic approach is required for all students to build understanding, fluency and application of the basic addition and subtraction facts.  Teachers need to provide ‘direct instruction’, guided practice, and then independent practice. The concept behind the ‘gradual release of responsibility’ is so important in providing the opportunity for all students to build understanding.

Many of the ideas presented are taken from Carole Fullerton’s resources.

Mastering the Facts SubtractionNumber SenseMastering the Facts Addition

“Mastery of the facts is very different from memorization of them.  Mastery depends on the co-existence of overlapping competencies as shown in the following diagram…”


“Promoting these competencies through direct instruction, rich tasks and meaningful practice will allow our learners to truly master the facts.”                                                            Carol Fullerton, 2012

Let’s provide the opportunity for all students to build a strong understanding of the basic addition and subtraction facts.  Stay tuned for Part 2!

Daily Math Investigations Part 2

Daily Math Investigations Part 2 took place in Surrey on November 21, 2013.  Around 70 DMIdedicated teachers left their classrooms and report card writing (some very eager for a break) to explore, discover, share and network together.

If you’d like to get a copy of “Daily Math Investigations’, please go to Carole Fullerton’s blog,

The focus of the session was on ‘Rich Routines’ from Daily Math Investigations.

Rich Routines are:

open-ended thinking tasks done in larger groups

more structured, but not boring

concepts worth revisiting

increase in complexity as they are explored over and over

active and engaging for all students

DMI Post 1

Rich Routines are questions/investigations posed during a whole group time.  We have suggested a variety of routines that are predictable in nature but are engaging and open-ended enough to meet the needs of all the students. Here are some of the routines we discussed from the resource:

  • All About NumberDMI Post 3
  • Cuisenaire InvestigationsDMI Post 4
  • Exploring the Open Number Line
  • Exploring the 100’s chartDMI Post 5
  • Numbers of the Day
  • Counting CollectionsDMI Post 6
  • Messing with Data
  • Sort it Out
  • Teeter Totter Tales

Check out the new Entry Tasks that were introduced at yesterday’s session.
Many of the tasks were taken from the Numeracy Centre Fun section of the blog.

Enjoy and remember to …

Get them engaged

Get them thinking

Get them reasoning

Daily Math Investigations

Old CalendarThe daily calendar has been a routine in many primary classrooms since the 1970’s when Math Their Way created it. It was revolutionary in those days. It was viewed as an opportunity to expose students to patterns and counting.  Calendar was considered an important part of daily math instruction.

In its original form, it was a fairly passive experience for children. Most young learners watched as one of their peers completed a pattern, listened as others counted, or chanted along with the group. While we recognize the value of daily exposure to mathematical ideas, the passive nature of this imagining of calendar often did not meet the needs of many of our learners.

What we have learned and are continuing to learn about the brain, how children acquire mathematical concepts, and developmentally appropriate practice has lead us to re-examine this traditional approach.

Carole Fullerton and I decided we needed to “Kill the calendar”!  In many of the IMG_0580classrooms we were working in, students (not to mention the teachers) often seemed disengaged with the calendar routines. We decided to create the resource called ‘Daily Math Investigations’. In this resource, we present a more active, participatory version of “calendar” – a daily opportunity for students to truly engage with meaningful math concepts, to play with materials, to process, think, and problem-solve. The tasks, questions and problems we have included in this resource are intended to inspire thoughtful math investigations into number, shape, measurement and pattern. Daily Math Investigations allow students to explore math concepts in real and embedded ways.

Daily Math Investigations are an opportunity for students to think and play with mathematical ideas. Teachers present tasks and pose questions that are intended to IMG_1059promote curiosity about numeracy concepts. In opening up the kinds of questions we ask, we include more students in the learning of math, and help to address the range of learners in our classrooms. A combination of entry tasks and rich routines allow for balance between whole group, small group and independent learning, a chance for students to explore the math at their level.

A monthly calendar gives us interesting information. We can use it to mark important events, like an upcoming holiday, a student’s birthday or a school celebration. Highlighting these events on a calendar and counting the days until they happen is fun for students.

IMG_1012For many of us, calendar time (and all of the activities associated with it) is ingrained in our script for primary teaching. It’s important, however, to consider carefully the purpose of these tasks – and more importantly, their effectiveness. We don’t believe in ‘throwing the baby out with the bath water’. But ask yourself, “What should I keep?”  “What should I let go?”

Ask yourself a few questions:

1. Are the pieces of my calendar routine truly relevant?
2. Are students talking about the math?
3. Are the students engaged?
4. Are the students doing math?

Thank you, Carole, for sharing your wonderful ideas.  If you’d like to get a copy of “Daily Math Investigations’, please go to Carole Fullerton’s blog,

On October 22, 2013 over 80 amazing teachers attended an afterschool in-service about ‘Daily Math Investigations.’  As they entered the room, they were invited to ‘engage in’ and explore several ‘Entry Tasks’.  The room was full of conversations, discovery and engagement.  They were talking and doing the math.  This is the vision for all primary classrooms.  What do you think?

IMG_4547 IMG_4551 IMG_4552

Number Talks – Big Results in a Small Amount of Time

I am always amazed at the dedication teachers have to attend after school workshops to explore ways to support their students.  Over 90 wonderful teachers gathered together to learn about ‘Number Talks’ on September 26, 2013.


Number Talks is one of the powerful vehicles for helping students to reason with numbers and build a solid foundation for algebraic thinking.  Teaching mathematics as a sense-making process is important for students to understand the math they are doing.  Number Talks is a daily whole group activity that takes 5 – 10 minutes which involves the solving of mental math tasks.   They promote flexibility with numbers, shared learning and increased confidence.  The purpose of Number Talks is to help students develop computational fluency, as well as number sense. We discussed ways to incorporate Number Talks into classrooms and get ‘big results for a small amount of time’ for students.  Please view the presentation and attached resources to gain more information about this simple activity to include in your daily routines.

Book CoverStudent