# What are you sorting & why?

## Sorting is what your brain does to make sense of the world, from the moment you enter it.

You have no words or symbols yet so you sort based on sensory perceptions.

Teachers guide students to become efficient with sorting and categorizing information so that they do not become overwhelmed by the tons and tons of information their brain is constantly trying to make sense of.

Everything I sort with students is deliberately chosen with specific vocabulary and attributes in mind.

We develop vocabulary together. The vocabulary of space, shape and number.

Key vocabulary (just a sample)

right, left, horizontal, vertical, parallel, perpendicular

greater than, less than, equal to

We physically pick up and move things to put them into a sort.

We sort, sorts. Avoid binary thinking: Everything does not boil down to one of two choices like yes/ no, pretty sister/ugly stepsisters, good witch/bad witch.

We choose an attribute and stick with it. Then we look inside that group of things, see a second attribute that some of them share and sort again.

They are all gingerbread boys. They all have blue eyes. (No sort yet).

I see eyes that are circles. Pull them into a sort. Label it circle eyes.

In that sort I see they also have buttons. But some have 2 buttons and some have 3 buttons.

So from circle eyes I pull a group of circle eyes and 2 buttons. I leave the rest in the circle eyes.

This is the beginning of a hierarchical sort.

Here are some houses to sort:

This is how you learn to spatialize your teaching:

Next step make fifths from same size whole. Then compare thirds and fifths. Explain why thirds are greater than fifths.

## Grade 1 and 2 start their year with tracing and discussing shapes.

Decomposing shape directly impacts decomposing number. Build vocabulary: side, vertex, angle, regular, irregular, rotate, reflect, translate, parallel, perpendicular. Develop the reasoning needed to trust number is in number.

## Symmetry is an attribute of shape. Students of any age can study line symmetry. A line of symmetry divides a shape into 2 parts that exactly match. Actively engage students in folding and tracing to identify lines of symmetry. Sort shapes according to the number of lines of symmetry. Ideas like parallel, perpendicular, superimposing angles, equal side lengths and fractions emerge quite smoothly from just studying symmetry. USE POLYGONS, no bunnies, butterflies or hearts please.

Geri , Your materials that connect the imagery of Area models to multiplication and beyond are awesome – And so perfect for setting up the work for Junior- Senior High. Incredible alignment. This is all streamlined so beautifully. Love the flexible thinking this encourages – demands! – and the common sense approaches it develops. James Tanton, PhD

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