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!

Counting on Fall – Math in Nature

There is a new series of books called “Math in Nature” which journeys into the natural worldThe wonders of nature are shown in vibrant cut paper collages that focus on important mathematical concepts. Each season focuses on an area of mathematics. There are many  ‘What if?’ problems presented in the text.

Counting on Fall book coverOn the day before Halloween (can you believe it!), 60 primary teachers gathered at DEC to discover and experience activities that promote number sense with Chris Hunter and myself.  We emphasized the importance of differentiating the activities to meet the need of the students.  Assessment for learning is another important aspect to consider when doing these activities with students.  Ask yourself: What do I want the students to know, understand or be able to do?

Here are some of the activities that extended from the ideas in the book:

1. Guess, Check and Estimate – (focus on estimation, referents and skip counting)Fall Leaves Picture

  • Ask the students take a collection of objects and lay them on the bare tree
  • Ask the students to ‘estimate’ how many objects are on the tree board
  • Ask the students to make a ‘referent’ of 2, 5, or 10 and pull it away from the total collection
  • Ask the students if they would like to revise their estimation (after seeing the referent)

Estimate of leaves Picture Check number of leaves Picture

2.  Bat Cave Pattern – (focus on patterning)

Bat Cave PictureWhat patterns do you see?

  • How could you model the patterns using Cuisenaire rods? (or other materials)
  • Some students may need to lay rods directly on the book.
  • Some student may need to be challenged by changing the number of bats sleeping in each row (increasing by 2)

Cuisenaire Rods in Order Picture Cuisenaire Rod Square Picture

Bat with Single Cuisenaire Rods Pic Bat with Cuisenaire Rod Pic 2

3.  Making Ten Story Mats – (focus on partitioning and number operations)Flying Geese PicAsk the students to count out a quantity of 10 objects.

  • How many different ways can you make 10 in two parts?
  • What stories can you tell about your story mat? (I counted 5 leaves on the ground and 5 floating in the sky.  How many leaves have fallen from the tree?)
  • What equations can you write about your story?

Leaves in Pond Pic4. Roll, Build and Compare – (focus on comparing quantities…more/less/the same)Bears and Berries Pic

  • Ask the students to work with a partner.
  • Each partner rolls a 10-sided die and builds the quantity rolled on their 10 frame.
  • The partners compare their quantities.  Who has more? less? Are they the same?
  • Ask the partners to determine how many more or less.

Scaredy Squirrel Pic 1 Scaredy Squirrel Pic 2