1. Resources
Flexible Grouping is key to
Tier1 RTI
PODS: Pedagogy that is
Outcome-based,
Differentiated, and Student
Centred
Are you interested in trying to
teach with Math PODS? Click
here to see a video made by
GSSD teachers who are masters
at this type of instruction:
https://drive.google.com/file/d/0B
wKqA1qY-
aPdR2pWMjV0VDlVWmM/vie
w?usp=sharing
If you are viewing this newsletter
in hard copy, go to my blog,
www.blogs.gssd.ca/csmith/
and look under the tab “Math
Pods” for a link to the video and
other support.
”To prepare students for
Algebra, the curriculum
must simultaneously
develop conceptual
understanding,
computational fluency,
and problem-solving
skills” –National
Mathematics Advisory Panel
What Do We Do When Students Don’t “Get It”?
We work hard to ensure we address every learner in the room. We provide
direct instruction, modelling, think-alouds, and pair talk. We represent in a
variety of ways. We use manipulatives and involve students in constructing
understanding. We provide opportunities for guided practice and feedback.
We assess formatively, adjust our instruction, find other approaches, enrich,
challenge, scaffold, and address gaps. And at the end of all this, there are and
always will be some students who still need more. We know “slower and
louder” isn’t the answer! But what is?
We need time with individuals or small groups of students of like ability to
address gaps in understanding. Teaching in PODS provides this opportunity
within the classroom (Tier 1 RTI, which is just good, rich teaching and
differentiating). If we pre-assess and group according to ability (some of the
time!) we will have an opportunity at the teacher table to interview, scaffold,
and strengthen understanding for students who aren’t understanding, as well
as providing more challenging tasks for students who are ready. *
Additional individual or small group support can be offered within or outside
the classroom (Tier 2). Does your school have an RTI time block? Is there a
way to create one for your learners who need extra help?
Response to Intervention at Tier 1 refers to differentiated classroom
instruction, (see first paragraph) where we try our best to meet the needs of
diverse learners. This does not mean “individualized instruction”! …but it can
mean grouping learners in various ways including like ability groups to better
address student needs.
Tier 2 RTI is intensive teaching targeted specifically to gaps in understanding
of two fundamental abilities: literacy and numeracy, because these literacies
are required for learning in other disciplines. Tier 2 interventions target
small groups of learners, and may occur within the classroom and/or in
special time blocks set aside outside the classroom but not in lieu of regular
instruction. These interventions are very specific to filling gaps in
understanding, and involve close teacher interaction with students. These are
not time periods to finish in-class work, homework, or practice skills
independently. It is also important to note that this is time in addition to
regular core instruction.
Tier 3 RTI would be adapted or modified learning for students on Individual
Instructional Plans (IIP’s), and would involve diagnostic testing, Student
Support Teachers and/or Special Education specialists.

2. Tier 2 Math Interventions:
Math interventions focus specifically on number and pattern, as these
are the basic understandings that support other areas and are required
for success at the next level. It is recommended that for K-5 we focus on
number: developing a sense of number, place value, composition of
numbers, basic operations, computation, estimation, and automatic
recall of facts (add’n, subtr’n, mult’n and div’n), and fluency of
operation. For middle years, we focus on rational numbers (fractions).
Students need a robust understanding of positive and negative
fractions, fractions on a number line, they must be able to represent
and compare fraction, decimal and related percents. They should
encounter fractions in a variety of contexts, such as ratios, rates
proportions, and probability. These are critical foundations of algebra.
Tier 2 intervention, then, may focus on material not necessarily aligned
with current classroom topics, but certainly material that is fundamental
to understanding all subsequent topics, given the coherent and
sequential nature of mathematics.
Recommendations for math interventions:
1. Screen students (pre-assess/assess), identify at-risk learners, and
provide interventions. Looking for diagnostics? You could use
the Sask Common Math Assessments, which are organized by
grade and outcome:
https://www.dropbox.com/sh/vhuy7f3ecngo90s/AAABYQcQGIO
atsjKm24-6KE4a?dl=0
We are also have access to some diagnostics developed and
generously shared by Saskatoon Public and Saskatoon Greater
Catholic School Divisions:
SPSD has pre and post diagnostics by grade, aligned with Sask
Curriculum.
SGCSD has a diagnostic that identifies a student’s level from
Grade 1 to 9 of Sask Curriculum.
All of these can be downloaded from my blog:
http://blogs.gssd.ca/csmith/assessment-and-data/
2. Interventions should focus intensely on whole numbers in K-5,
and rational numbers in Gr 4-8.
3. Instruction during intervention should be explicit and systematic.
During regular instruction we may skip around through math
content to show the interconnectedness of skills (spiral
curriculum). This approach may cause difficulty for students that
are struggling to master a single concept or skill (Riccomini &
Witzel, 2010).
Provide models (exemplars) of well-worked problems, have
students do think-alouds, provide guided practice and feedback.
Use frequent reviews and summaries.
4. Help students recognize underlying structures when solving word
problems.
Possible Curriculum Supports
for Tier 2 Math Interventions
KeyMath is a diagnostic tool but also
has teaching resources to target
specific gaps in understanding. The
resources include a teaching easel
with good visuals. GSSD has key
math resources available to SSTs.
Leaps and Bounds
http://www.nelsonschoolcentral.co
m/cgi-
bin/lansaweb?webapp=WBOOKSIT
E+webrtn=booksite+F%28LW3ITE
MCD%29=9780176351526
This resource was developed by
Nelson and has input from Marian
Small (strongly invested in having
students construct mathematical
knowledge). A few copies are
available in the Anna Ingham Room
Do The Math Is a curriculum
intervention developed by Marilyn
Burns, a respected researcher and
writer of meaningful math
curriculum.
http://teacher.scholastic.com/produ
cts/dothemath/
http://www.pearsoncanadaschool.co
m/media/canada/numeracynets/Nu
meracyNetsv1.html
Note that GSSD does not endorse one
resource over another at this point.
Nothing replaces intervention by a
teacher skilled in math!

3. 5. Intervention teachers need to be proficient in providing mathematical representations. They should be
well versed in math instruction and have a thorough knowledge of curriculum, assessment, and child
development.
6. Devote the first 10 minutes of each session on mastering basic facts with fluency.
7. Use rigorous monitoring of progress.
8. Incorporate motivational strategies, such as reward games or activities that still support learning
mathematical concepts or develop procedural fluency.
-National Center for Education Evaluation and Regional Assistance (2009), U.S. Dept of Education, Institute of Education Sciences
-Riccomini, J., &Witzel, B. (2010). Response to Intervention in Math. Thousand Oaks, CA. Corwin.
“It is time for the debate
regarding proficiency with
whole-number computation
and basic facts to end and
time for teachers to devote
instructional time to
computational proficiency
and automaticity of basic
facts…these types of
practice activities that build
automaticity and
proficiency…are an
essential part of Tier 2
instructional supports for
students lacking in these
areas”
-Ricommini & Witzel, (2010)
Have a Mathy Valentine’s Day!!
Web Resources:
The Numberphile: This site has
activities, graphs, software, ideas,
support, demos and more for upper
middle year to high school. There
are resources for students, including
a collection of math video sites (see
“videos” tab).
https://mathematicsforstudents.
wordpress.com/videos/
Online practice: Check out this site
for very organized online practice
(virtual worksheets). This is from
South Africa so you will need to
correlate with our curriculum, but
its pretty easy to go look around the
site.
http://www.cimt.plymouth.ac.uk
/projects/mep/default.htm
Have you checked out Estimation
180 yet? It’s a great web site for
class starters, developing number
sense, stimulating math dialogue,
and its engaging because your
class can look at reasoning from
other students all around the
world. Here’s a video that shows
you highlights:
https://www.youtube.com/watc
h?v=Rfpu42cS-6Y
Another well-loved class starter
activity is Quick Draw. This
game-like activity develops
spatial reasoning skills and math
vocabulary:
http://www.learnnc.org/lp/pages
/787 . By the way, we have a
copy in the Anna Ingham
Library!!
Resources for Tier 2 interventions in
Mathematics: http://www.intensiveintervention.org/resources/sample-
lessons-activities/mathematics
A fun multiplication game (within this lesson plan) might make a good math
station http://www.discoveryeducation.com/teachers/free-lesson-
plans/discovering-math-computations.cfm
Need a collection of quick games for practicing basic facts?
http://www.mathfilefoldergames.com/ This site always has some free
downloadables
Math Playground: Free math games to help build proficiency, as well as
tutorial videos http://www.mathplayground.com/
Great collection of practice and games: http://www.softschools.com/math/
Play Math, Love Math: https://mangahigh.com/en-us/ Mangahigh has a
vatiety of games like Pemdas Blaster (Order of Op) and Algebra Meltdown.

4. Effective Strategies for Math Intervention:
1. Explicit, direct, systematic instruction. Each intervention session should recall and then build on content
from the day before. Repetition is helpful (don’t let it become painful though! There are creative ways! Use
cards, dice, games, technology—not worksheets!...but track carefully)
2. Practice of automatic recall of facts and quick computations. Procedural fluency is a skill that can be
strengthened with practice, and once students improve in this area they will have more confidence in
mathematics and will feel a sense of empowerment. This is a quick and easy way to develop improvement
to reinforce a growth mindset. Students that don’t develop mental math/procedural fluency are
disadvantaged as they move up through the grades. They will process slowly, and be operating on cognitive
overload as their thinking is tied up applying strategies and basic computations rather than grasping more
difficult, abstract concepts that are introduced in higher grades.
3. Think-alouds: Teacher models them so students can learn to think-aloud. The person doing the most (on-
topic) talking in a classroom is doing the most learning! Students need to verbalize their thinking to
consolidate ideas. Teachers need to know what a student is thinking in order to guide them or determine if
they’re on the right track.
4. Providing exemplars or interleaving worked examples: Scaffold learning for students by leaving every
second practice problem solved, with all steps shown. For these examples, students study the work. You
may ask them to say or write a description of each step. Then they do the next problem on their own.
5. Summarizing and note taking: Students make summaries of instructions or content for themselves.
6. Specific, non-graded feedback: Providing students with specific verbal or written feedback on their work
and progress that is not shadowed by a grade is one of the most effective learning tools.
7. Teach metacognitive strategies: Help students reflect on what helps them learn, what conditions are
conducive to their learning, what growth have they experienced.
8. Teach vocabulary explicitly: Math is a language- and is symbol-rich. Students can’t express what they don’t
know. We need to use word walls and continually refer to them, so students can articulate their learning,
reasoning, and questions.
References: Gregory, K., Cameraon, C. & Davies, A. (2000) Self-Assessment and goal Setting. Courtney, BC: Connections Publishing.
Hattie, J. (2012). Visible Learning for Teachers. New York, NY Routledge.
-National Center for Education Evaluation and Regional Assistance (2009), U.S. Dept of Education, Institute of Education Sciences
-Riccomini, J., &Witzel, B. (2010). Response to Intervention in Math. Thousand Oaks, CA: Corwin.

5. SUM conference May 1-2 2015. Look for developments
on smts website: http://smts.ca/
SPDU workshop Supporting Engagement in Mathematics
(I recommend this! Its good!)
April 21, 2015 Cheshire Homes
2903 Louise Street Saskatoon, Saskatchewan 9 -3:30
For More info
https://www.stf.sk.ca/portal.jsp?Sy3uQUnbK9L2RmSZs02CjV3
Jh9YwRCfE60DNZzQih7Ls=F
SPDU workshop When Johnny Can’t Multiply
Developing a Learning Progression for Multiplication and
Division February 26, 2015 McDowell Conference Room
Saskatchewan Teachers’ Federation, Saskatoon 9 a.m. - 3:30 p.m.
https://www.stf.sk.ca/portal.jsp?Sy3uQUnbK9L2RmSZs02CjV4uYDjOe9zOAX/
7MW4wsuk4=F
Metacognitive Strategies
Some of our formative assessment focuses on how well students are picking up and mastering course material.
Moving beyond content to understanding is the goal of UbD. A significant aspect of teaching students
understanding is having then actively immersed in the learning process, by continually monitoring their learning,
evaluating their performance, and being aware of what helps them learn. Only through an awareness of learning
can students set goals for themselves. John Hattie lists Self Reflection and Goal Setting, Metacognitive Strategies,
and Self-reported Grades as among the most effective classroom practices.
Some formative assessment tasks focus more on helping students reflect on their learning in this way. It can be as
simple as asking for a few reflections at the end of a lesson, unit, or task. Here are a few quick “exit cards” from
Gegory, Cameron, and Davies (2000):
A First:
The easiest part was…
The hardest part was…
Date:______Signed________
One Word Web Card Exit Pass
Two things I learned…
--
--
One question I have
--
Math Coach
Blog:
www.blogs.gs
sd.ca/csmith/
smithersmath
@gmail.com