Written by Rebecca Forchuk, Principal

DMG Professional Learning Day, November 23, 2018

Students
come to math class with different interests and understanding of concepts, but
regardless of where they are on the continuum, students are adaptable. Teachers can enhance learning when we plan
for this variability in math. Exploring
instructional strategies that consider this variability was the focus of Dr.
Morris Gibson’s staff learning day on November 23

^{rd}. I had the opportunity to learn, alongside the staff, from their admin team and Wanda Dechant, Designer of Professional Learning, Calgary Regional Consortium.
Kevin,
Principal of DMG, pointed out the importance of warm ups in math and made
connections to other areas of life: athletes warm up, musicians warm up and so too
should mathematicians. The benefits are:

Bridges
transition time for students.

Allows students
to shift to mathematical thinking.

Builds
confidence through successful math opportunities that are at the right level.

Provides effective,
yet easy, differentiation opportunities when using open ended or ‘low floor,
high ceiling’ tasks.

Reviews prior
learning and provides formative assessment to teachers.

Makes thinking
visible; students hear/see the thinking of others

(Adapted
from DMG PowerPoint slide 27, Nov 23

^{rd})
There are several warm ups that develop the 7
processes of math, which are foundational to mathematical
understanding. This week we are going to explore one of
those warm ups:

__Warm Up #1: How Many Dots__

Ask students:

**“How many dots do you see?”**

Flash
the picture for three seconds on the Smartboard. Warn students it will be F-A-S-T! If you need to show it again, do so. But again, make it quick – three seconds or
less. The purpose of this task is NOT a correct
answer.

Ask
students to share how many dots they saw.
Try to get variability in students’ answers.

Here
comes the mathematical thinking. Ask:

**“How did you see the dots?”**

While students share how they
saw the dots, the teacher captures the student’s visual representation on chart
paper or Smartboard by doing two things:

- Draw lines from dot-to-dot to represent how they saw the dots.
- Write down the equation that represents their visualization.

The
picture below demonstrates what your chart paper might look like after students
show their thinking:

(Taken from DMG PowerPoint Slide 33, Nov 23

^{rd})Picture 1: How teacher "saw" the dot card |

I participated in this warm
up twice: once with Div 1 teachers and again with Div 2 teachers. Figure 1 shows the diverse ways in which everyone
on staff saw the dots on this card. Each division of
teachers came up with entirely different ways to visualize the same dot card! See Picture 1 for the various ways teachers saw the dot card.

Through
our discussions after the task, we came to consensus such a warm up can develop
the

**processes**of**visualization**,**reasoning**,**communication**and**estimation**. This task also develops:- Spatial reasoning
- Positive mathematical mindset
- Understanding there is a variety of perspectives in math
- Understanding there are multiple pathways to arrive at an answer.
- Ability to subitize

At the end of the session,
admin tasked teachers with homework: try one of the warm ups from the session
before their next PLC meeting. It is clear that students as young as Grade 1 can
benefit from “How Many Dots.” It really demonstrates variability when a student
visualized the dots as a picture of a fish – what a unique way to see them!

This proves to be a great low floor, high
ceiling task. Dot
cards (just Google “dot cards math” to find an endless number of them) can be
simple and range in complexity:

Example 1:

Example 2:

Example 3:

Watch the blog over the next few weeks when we explore more Math Warm Ups that develop number sense, processes of math, and growth mindset based on professional learning at DMG!

A
big thank you to the admin and staff at DMG for inviting me to their session
and sharing their learning journey!