Facilitator’s Guide
Math K-6
Geometry Progression
In Practice
Session Description
Participants will engage in activities and discussion focused on the Common Core State Standards
Geometry Progression.
Goal of the Session
•
•
To explore the K-6 Geometry Standards for Mathematics
To experience a math activity that focuses on deeper understanding of the classification of
shapes.
Materials

Post-it notes, scissors, tape, poster paper, projector
Handouts

Copies or e-version of the K-6 Geometry Progression –
http://ime.math.arizona.edu/progressions/
Pre-session Preparation
1. Review the Power Point and Facilitator’s Guide.
2. Review the Geometry Progression.
3. Decide if you need to provide copies or access to the electronic version of the Geometry
Progression
TIME
5 min
CONTENT/ACTIVITIES
MATERIALS
Introduction and Objectives
Slides 1-3
Go over Objectives and discuss the flow of learning Geometry
in the CCSS-M by going through the flow chart on Slide 3-5.
15 min
Learning Progression
Slide 4-5
Handout:
Let teachers read through the slides.
The Geometry Progression
Document
Then ask them to read through the overview. P2-5


10 min
The Common Core State Standards in mathematics were
built on progressions: narrative documents describing the
progression of a topic across a number of grade levels,
informed both by research on children's cognitive
development and by the logical structure of mathematics.
Give the participants plenty of time to read this section,
recognizing that teachers often don’t have the luxury to
just read.
Today we are focusing on the Geometry Progression
which can be found at
http://ime.math.arizona.edu/progressions/
Think, Ink, Pair, Share
Slide 6-9
Ask participants to read pages 2-5 of the geometry
progressions document and then do a think pair share
activity about what they read in the overview.
They should:
Think about what they read.
Note important ideas.
Share ideas with a partner
Share ideas with the whole group.
2 min
Most Important Goals for K-6
Slide 10
Read through the slide.
K-5 Geometry Progression in Practice
TIME
3 min
CONTENT/ACTIVITIES
MATERIALS
Levels of geometric thinking
Slide 11-12
Review these ideas
At the analytic level, students recognize and characterize
shapes by their properties.
A student might think of a square as a figure that has four
equal sides and four right angles. Different components of
shapes are the focus at different grades, for instance second
graders measure lengths and fourth graders measure angles.
7 min
Let’s do Some Math
What can we do to facilitate the development of geometric
thinking?
Each group of 4-6 people will
need 100 post-it notes,
scissors, tape, markers and a
piece of chart paper.
We need to engage students in geometric thinking focusing
on the geometry standards at their grade level.
The presenter needs a piece
of chart paper and a marker.
Slide 13
Today we will experience a lesson that does just that.
Introduce the lesson.
This lesson is called the Four Triangle Problem it can be found
in the MATH by all Means Geometry Grade 3 Marilyn Burns
Replacement Unit. Written by Cheryl Rectanus Distributed by
the Cuisenaire Company
Begin the Lesson:
Ask participants “What shape is a post-it note?”
Have participants do the activity on the slide
Discuss
Post a piece of Chart Paper
Label it, “Geometry Words” add to the chart as vocabulary is
discussed.
Add Square, Triangle, and Diagonal…
K-5 Geometry Progression in Practice
TIME
3 min
CONTENT/ACTIVITIES
Guess My Rule
Slide 14
Tell the participants that we will be putting triangles together
to make new shapes.
However, we are going to follow a rule…Ask them to guess
the rule.
Rule:
Sides that touch must be the same length and match up
exactly.
5 min
The Four Triangle Problem
Slide 15
Go through the slide
Discuss congruence.
Remind participants to follow the rule.
NOTE: Identical shapes could be different colors or in
different positions. Transformations (reflections, rotations or
translations) do not result in new shapes, they are the same
congruent shape, just shifted, turned or flipped.
Rule: Sides that touch must be the same length and match
exactly
10 min
Shape Search
Slide 16
Tell the participants that they will be working with their table
teams to find all of the possible closed shapes that they can
make with 4 triangles.
They need to follow the rule.
You can ask them to predict how many shapes they might
find.
Visit all groups and help them to keep looking for shapes
There are 14 non-congruent shapes.
K-5 Geometry Progression in Practice
MATERIALS
TIME
10 min
CONTENT/ACTIVITIES
Shape Sort
Slide 17
Once most groups have found all 14 shapes ask the groups to
design a sort that would help move their students forward in
their geometric thinking.
The sorts can vary depending upon the grade level.
Possible sorts include
Number of sides, Types of Polygons, Figures with lines of
symmetry vs. no lines of symmetry etc.
Each group should tape their shapes onto a large sheet of
chart paper displaying the sorting technique they used.
Ask the groups to display and share their posters and their
thinking.
10 min
Connect to the Geometry Progression
Slide 18-19
Participants should take a few minutes to think about which
part of the progression they would address with this problem
They can use the progressions document or refer to the
geometry content standards.
Lead a discussion to summarize their findings.
2 min
Deeper Understanding
Slide 20
Consider the quote
5 min
Reflections
Slide 21
Ask Participants to consider the questions on the slide.
Discuss
3 min
Wrap-Up
Slide 22
Review resource
K-5 Geometry Progression in Practice
MATERIALS
Chart Paper, Markers, Tape