Early Algebra

I’ve been in a number of junior classrooms lately looking at how we use pattern rules for growing patterns. Visual representations can significantly help with this, and the transition to an algebraic representation.

There’s usually a disconnect between how we use pattern rules in late primary / early junior, and the transition to algebraic representations later on.

Consider this number sequence:    5, 7, 9, …

In grade 3 we tend to accept “Start with 5 and add 2 each time”

But the algebraic representation is 3 + 2n

The difference is that algebraically, we add something to each stage including the first stage.

I’ve always thought about the idea that we seem to change the idea of the pattern rule over the grades without being explicit about it to the students.  So should we just start with the pattern rule that correlates to the algebraic representation?  In words, should it be something more like “Start at 1, and add 2 to every term (including the first one)”?

This is easier for students to see pictorially or with manipulatives.

Visually

IMG_2142

 

In words

Start with 3 and add 2 each time

 

 

Algebraically

3 + 2n

Number Sequence

5, 7, 9, …

To test this out I visited a grade 4 class who had been exploring growing patterns (but not visually).

When asked to draw their own pattern for Start with 1 and add 2 each time, most drew pattern similar to alg2
But a couple drew alg1

Over the course of a 20 minute discussion and students defending their point of view, the entire class decided the second representation actually depicted the given pattern rule better.

 

 

Early Years Summer Math

Kindergarten teachers and DECEs participated over the summer in a full day session on early numeracy.

Key Concepts discussed included:

The complexity of Early Mathnumberrelationships
Myths of Early Math
Key Number Sense Areas
Developmental Pathways in Number sequences, Counting, Subitizing, Part Part Whole Relationships, Near Numbers, and 5/10 anchors.
Instructional strategies in the early years

 

Summer Learning – Student Math Camp

This past summer grade 2 and 3 students from Little Falls PS and Romeo PS participated in Summer Math Camp, honing their skills while having fun. mathcampkids
mathcampcook 36 students attended a morning camp focused on Math for three weeks in the early summer.   The goal of the three weeks was to prevent summer learning loss and to create a positive mindset about Math.  The morning consisted of mental math review, a three part lesson, a focus on a new addition strategies, math games to review the concept, some snack preparation (baking) and inquiry.  In the afternoon students participated in a recreation program including swimming, outdoor games and other fun opportunities.

The program was a great success with students attitudes changed and math knowledge increased significantly.

Thanks to all program participants and teachers and the grant that made this possible!

 mathcamp5