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

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, http://mindfull.wordpress.com/.

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

Halloween Fun

With Halloween just around the corner , I stopped by the neighborhood ‘Dollarama’ to get inspiration for some Literacy and Numeracy centres.  It was amazing what I discovered.  Here are some of the materials and ideas that were generated by the Early Literacy and Numeracy teachers that I am so lucky to work with.

Candy Corn

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.

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!