The ICE Model
I(deas), C(onnections and E(xtensions).
Developed by Robert Wilson (Queen’s University).
Elaborated upon by Susan Young.
the fundamentals of new learning
include building blocks such as the steps in a process, the
necessary terminology/vocabulary, definitions, details and
Ideas are only information.
What do Ideas look like?
o recognizing numbers
o knowing that a triangle has three sides
o associating heavy clouds with the probability of rain
What do Ideas-level tasks look like?
o show a “greater than sign”
o identify the parallelogram
o state the slope of the line shown on the graph
o graph the ordered pair (2, 6)
o measure this angle using a protractor
o match the unit “cm” with the appropriate expansion
o or fill in the blanks for “in the expression 5x , 5 is called
the _______, x is called the ______, and 2 is called the
Ideas are “bits and pieces” of knowledge that are best described in
terms of simple recognition or recall.
Ideas-level demonstrations are set as a basic minimum requirement
for success, fitting best with Level two of the provincial achievement
rubric. Major student errors and the continuous need for teacher
support set Level one achievement apart.
• between and among the discrete bits and pieces of knowledge
• made by the learner between the material and their own real-
• ideas are integrated into webs of information and knowledge
that is tied together so that learners are not experiencing
isolated skills, concepts, rules or symbols.
ie. This number _ is
2 less than 9
1 more than 6
small compared to 73
the number of days in a week
large compared to one-tenth
Consider the concept of seven as constructed by a young child. It is
first likely connected to the counting procedure and understood to be
less than 10 and more than 2. However, the web of connected ideas can
grow large and involved. Van de Walle, p.29
Connections are webs
• Estimate the answer to 12/13 + 7/8
• Compare squares and rectangles
• or answer questions like In how many ways can two triangles
• identify relationships between objects by stating shared
• use events from meaningful experiences to describe probability
• compare experimental results with predicted results
• discuss trends in graphs to draw conclusions about the data
• students are able to use their learning in novel ways apart from
the initial learning situation to predict how …; state the
implications of …; propose solutions for …; or validate his and
• evaluate arguments that are based on data analysis, ask “what
if” questions, discuss and defend the choice of a pattern rule, or
create problems giving rise to first-degree equations with one
• the students’ ability to use old definitions and laws to predict
new generalizations and conclusions by relating knowledge
from several areas
• student is able to reorganize prior knowledge and skills
creatively or generatively to describe or illustrate new
generalizations or concepts across strands or disciplines
Strands Ideas Connections Extensions Totals
Number Sense & Typically scores from The verbs associated with The application of
Numeration quizzes, homework. Students see how “extensions” suggest that ICE ensures that a
Procedural skills remain mathematical ideas build children need grade is more than an
Expectations selected important but should be on one another in a useful opportunities to think average of scores.
from Ontario weighted in proportion to network of connected deeply,
Curriculum other goals that reflect what ideas.
Document and the curriculum values.
categorized by verb
as I, C or E.
Spatial Sense & Extension verbs challenge ICE helps to align
Geometry Ideas are at the beginning of Students apply ideas in a students to ask questions assessments with the
Expectations selected the learning continuum. context or situation. and reason about true goals and
from Ontario important ideas. objectives of the
categorized by verb
as I, C or E.
Patterning & Algebra Extension solutions The final grade is
Ideas (only information) are Students recognize that demonstrate a student’s dependent upon the
Expectations selected at the lowest level on a mathematics is not a facility in using a variety quality of the
from Ontario rubric. laundry list of isolated of mathematical instruments that are
Curriculum rules and formulae. representations to add to used to generate the
Document and their own understanding grade. ICE can serve
categorized by verb and to better communicate to keep a balance in
as I, C or E. ideas to others. those instruments.
Total 35 50 15 100
• the students’ ability to pose problems and to invoke informed
but original experimental designs or experiential methods
Generating a grade through the use of the ICE model reflects the developmental
nature of learning and can still fit nicely into administrative expectations about