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

  • 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 – 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?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!

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What Really Counts?

In April I was extremely lucky to attend the NCTM conference in Boston Massachusetts. I listened to a fabulous session titled ‘Counting Matters: Why We Should Pay More Attention to Counting’. The presenters (Elham Kazemi, Allison Hintz, Kassia Omohundro Wedekind, Teresa Lind, and Angela Chan Turrou) were so enthusiastic and engaging. I knew I had to return to my district and try some of the routines presented from Jessica Shumway’s book ‘Number Sense Routines’.

With great excitement I collected materials and ventured out to several schools to try out my new discoveries. Thanks to all my wonderful colleagues (Sarah Schnare, Carrie Donahue, Cara Johns, and Amanda Crawford) for sharing their students with us. My wonderful friend and ‘partner in crime’, Lillah Martin, joined me on the journey. We learned so much from the students that we needed to share the experience with others.

On May 12 an amazing group of around 80 teachers met and uncovered the power of two ‘counting routines’ in the Primary classrooms (counting collections and choral counting). I am always astonished by the devotion of teachers who attend after school workshops. The group explored counting collections, and choral counting while making connections to important math concepts and seeking out patterns.

Learning to count while simultaneously developing a sense of quantities and number relationships is an important foundation for students. Counting is more than repeating a rote sequence and recognizing the numerals. Counting has proven to be important to lay the foundation for understanding of the base-ten system, operating on numbers and problem solving. When students develop competence, they not only count with accuracy and ease, but will also develop the sense of the quantity of numbers they are working with. The focus moves from knowing the number they landed on to making reasonable estimated and noting the reasonableness of the outcome of the counting.

I challenge you to try out these routines with your students to uncover the important math concepts and rediscover the joy of counting.

Please check out this link http://tedd.org/ for additional information. Again, thanks for the amazing presenters and Twitter friends of the NCTM Boston session.

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Read a Story, Explore the Math

I feel honored to have spent time with over 90 amazing Primary teachers at the BCPTA conference in beautiful Victoria B.C. on October 24, 2014. What a wonderful group of dedicated teachers who love to learn some different ways to support their learners.

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Everyone loves a good story. Teachers love reading them and students love hearing them. What better way to set the stage for a math lesson. Last May 2014 Carole Fullerton and I collaborated together to create a new resource Read a Story: Explore the Math. IMG_7014

This resource promotes the teaching of important math concepts through the exploration of delightful children’s books. Many of these books are newly published and all have the potential for students to engage in math and provide opportunities to explore in meaningful ways.

IMG_1618At the conference we shared most of the books, some of the activities and tried a few for ourselves. We explored the tasks with Cuisenaire rods, dominoes, two sided counters, ten frames and dice. By using the manipulatives the students are encouraged to make connections to the concepts and represent their thinking in concrete ways.IMG_0980

Stories allow us a shared experiences. They engage us emotionally, and make us curious about the world. Carole and I hope that this resources will provide ideas for possibilities to pair stories with mathematical investigations that will inspire rich mathematical thinking in your students.

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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.

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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, http://mindfull.wordpress.com/

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

Patterns, Patterns, Everywhere!

Pattern

The capacity to pattern – to establish a pattern core, to repeat and name it – is an essential skill in mathematics learning.  Students who can pattern can predict what comes next with confidence.  They know that there is order – to the manipulatives they use, to the days of the week, to the sequences of their days.  The capacity to pattern is a necessary pre-requisite for success in algebra – to be able to predict ‘down the line’ is the foundation of algebraic thinking.  Students should be able to represent it in language and actions.  Students who are competent with patterning will be able to identify and correct an error in an existing pattern. Students should be able to extend a pattern off of both ends (beyond both the start and the end) and to represent it in language and actions.

Patterning with colour or another physical attribute is the precursor to skip counting. When students build patterns with a pattern core of 2 elements, the number of objects in their pattern increases by 2 each time. To find the total number, then students can skip count by 2’s.  In this way they follow a new pattern:  skip a number, say a number, or skip 1, say 2, skip 3, say 4 etc.  Skip counting requires sets of objects to be counted.  Success with skip counting depends on being able to subitize, and see groups at a glance.

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