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!

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!

BCAMT New Teachers’ Conference

The BCAMT New Teachers’ Conference was held in Surrey, B.C. on February 16, 2013.  The participants were eager to extend their knowledge and understanding about helping their students understand the math they are doing.  Throughout the day there was a clear message that students need to be engaged in their own learning and comprehend the math they are doing.  I presented a session for a wonderful group of K – Gr. 2 teachers about building a solid mathematical foundation using one of the many tools available.  We focused on using ten frames to develop number sense.  The group agreed that by using ten frames students are able to use a visual organizer to help them make sense of subitizing and partitioning numbers.

New Teachers’ 2013

NWMC 2012

I want to ‘Thank’ all the wonderful teachers who attended my workshop at the Northwest Mathematics conference in Victoria, B.C. this weekend.  It was one of the last workshops offered for the day and these teachers were absolutely amazing!

The presentation focused on ‘The Big 3’ (subitizing, partitioning and patterning) which are essential in building a solid mathematical foundation in early primary. These concepts are interconnected and embedded in each other.

Our young learners should know what it looks like to behave like a mathematician – seeing sets without counting, breaking up sets and putting them back together again and patterning and predicting.  They are capable of doing the important work of a mathematician.

I have attached the power point and activities we explored, played and discussed at the session.  Please let me know if these activities help you to develop a solid numeracy foundation for your students in a differentiated way!

What Do They Know?

What Do They Know? – PLENTY!

On October 1, 2012 I had the pleasure of working with 70 Early Primary teachers to explore the “What Do They Know?” numeracy assessments for Kindergarten and Grade 1.  I have posted the materials presented at the workshop on this blog.

The “Early Years” is a time for exploring- for play, talk and investigation. Students need to be engaged in meaningful activities that allow them to discover and make important connections in authentic ways. The teacher’s role is to uncover how students make sense out of mathematical explorations and conscientiously build upon those understandings. We see so much capacity in our students when we know what to look and listen for!

Research and the wise teachings of John Van de Walle and Marian Small indicate that there is a set of key math concepts for students to understand in their first years of school.  The capacity to see quantity at a glance without counting (subitizing), the ability to partition numbers (break numbers apart and put it back together again) and to pattern are all indicators of success in early numeracy.

The “What Do They Know?” assessments were written by Carole Fullerton and myself.  We wanted to design a less formal and more embedded in the classroom practice assessment tool.  Carole and I field tested the assessment with many classroom teachers across the province.  These assessments (Kindergarten and Grade 1) seek to find out – in an authentic and classroom familiar way –what the students know.  There are instructional components for each assessment that suggests ideas of building on to the students’ understanding.

Please try out these assessments with your students and discover ‘what they know’ and how to support them in continuing to become successful mathematicians. Enjoy!  I know I do!