1. “Mathematics is not a race. It is more important
to have depth and connections than procedure
and speed.”Jo Boaler, math educator, author,
co-founder of youcubed.org
CHRISTINE BLESSIN
christine_blessin@sd33.bc.ca
Twitter @GalBlessin
KATHLEEN MITCHELL
kathleen_mitchell@sd33bc.ca
Twitter @kath_mmitch
All slides available at www.slideshare.net, search Blessin
Mitchell
2. Build common language and capacity in terms of
• Instructional strategies
• Computational strategies
• Small-group instruction
Goals for this session
8:30 9:30 10:30 11:30 12:30
SNAP Break Number Talks Small Group Instruction
3.
4. Our Goal
To talk to you about the WHY, WHAT and HOW
of Chilliwack’s district numeracy assessment and
prepare you to use SNAP in a purposeful way
with your students.
5. What would the perfect
math assessment do?
How would it be formed?
What data would it yield?
What effect would it have
on the student?
6. Let’s dream about assessment…
https://www.teachthought.com/pedagogy/the-perfect-
assessment/
• not pass/fail but rather start here and move forward
• a tool that promotes understanding
• serve as “stairs” instead of “hurdles”
• should not cause anxiety (teacher and students)
• provide usable data to inform & revise instructional planning
• show short term and long term progress
• multiple entry or starting points
• a learning experience in itself
• aligned with curricular standards
7. • District Strategic Plan
– Up until this point there was no baseline numeracy
data being collected in the district.
• Need for effective balanced assessment
• Practical for teachers and student-friendly
WHY was SNAP created?
8. WHAT is SNAP?
• District numeracy assessment for grades 2-7
created by Chilliwack teachers
• SNAP is unique in many ways: it creates a
measurement of achievement, but it is also a
practice tool for students that impacts
instructional practice.
9. Target Learning Standards
Grade Number Sense Operations
2 Up to 100 2-digit addition
3 Up to 1000 3-digit subtraction
4 Up to 10 000 Multiplication: 1-digit X 3-digit
5 Up to 1 000 000 Division: 3-digit ÷ 1-digit
6 Thousandths to Billions Division with decimals
7 Negative integers Finding the percentage of a number
GOAL: That all students be proficient in their grade-
level target learning standards by year end.
10. Curricular Competencies
Fully aligned with the BC Math
Curricular Competencies.
• Reasoning and Analyzing
• Understanding and Solving
• Communicating and Representing
• Connecting and Reflecting
Graded on a performance scale with
the curricular competencies built into
the rubric.
11. How teachers and students benefit
from SNAP
Targeted practice of specific skills needed for
proficiency in number sense and operations.
12. How teachers and students benefit
from SNAP
• Used as a formative assessment, SNAP drives
strong instructional practice and purposeful
planning
– High Yield Routines
– Small group instruction
13. How SNAP has positively changed
instructional practice in our district
math
• Teachers reaching out
• Popularity of math Pro-D
• After-school series
• Manipulatives
• Interest in small group
numeracy instruction
• Most current research-
based resources into
schools
14. How teachers and students benefit
from SNAP
SNAP lends itself to the development of growth
mindset in students.
18. • What are they?
• How will students become better mathematicians
through number talks?
• How will you get started with number talks?
• What are the key components of good number
talks?
Goals
19. What are number talks?
Brief daily practice during which students
mentally solve computation problems and
talk about their strategies.
In Number Talks, there is a de-emphasis on
speed and right answers and an added
emphasis on process and communication.
20. Students will become better mathematicians by…
Learning to work with numbers and arithmetic
properties flexibly.
35 – 18 =
35-10=25
-5
20
-3
17
35-
20=15+2=17
35-18
+2 +2
=37-20=17
21.
22. Learning to depend on sense-making
rather than algorithms
Students will become better mathematicians by…
24. Becoming empowered as mathematical thinkers.
Students will become better mathematicians by…
25. Getting started with number talks
Dot cards establish
• there are many ways to see or do any problem.
• we need to communicate our thinking clearly so that
others can understand.
• we are all responsible for trying to understand other
people’s thinking
With dot cards, students only need to describe what they
see, and people have many different ways of seeing.
26.
27.
28.
29.
30. Key Components of Number Talks
1. Classroom Environment and Community
Building a cohesive classroom community is essential for
creating a safe, risk-free environment for effective
number talks.
Students
are comfortable in offering responses.
are comfortable questioning themselves and their
peers.
are comfortable investigating new ideas and strategies
31. Key Components of Number Talks
2. Classroom Discussions
Why share and discuss computation strategies?
o Clarify thinking
o Consider and test other strategies to see if they are
mathematically logical
o Investigate and apply mathematical relationships
o Build a repertoire of efficient strategies
o Make decisions about choosing efficient strategies for
specific problems
32. Key Components of Number Talks
3. The teacher’s role
o Facilitator
o Questioner
o Listener
o Learner
33. Key Components of Number Talks
4. The Role of Mental Math
Build on number relationships to solve problems instead
of relying on memorized procedures.
Mental Math
o Rely on what you understand
o Be efficient with number to avoid holding numerous
quantities in your head
o Strengthen understanding of place value. See
numbers as whole quantities, not in columns.
34. Key Components of Number Talks
5. Purposeful Computation Problems
Carefully crafted, just right problems that guide
students to focus on specific mathematical
relationships.
Ex: If you are wanting students to build on tens, and using
tens as friendly numbers…
20 X 4 30 X 3 20 X 10
19 X 4 29 X 3 19 X 10
19 X 9
37. Transparent Algorithms in contrast
with Standard Algorithms
Transparent Algorithms:
• number oriented rather than digit
oriented.
• left-handed rather than right-handed.
• offer a range of flexible options rather
than “one right way.”
38. Benefits of Transparent Algorithms
• Fewer errors
• Less re-teaching required
• Students develop number sense
• They are the basis for mental
computation and estimation.
47. Goal
• Present you with some practical ideas for
setting up small group numeracy instruction in
your classroom
• Provide you with a helpful tool to help you
organize some strategy groups for your
students (based on fall SNAP formative data)
48. Small Group Math: Key Questions
• Why small group math instruction?
• How can you organize for small groups?
• What can the rest of the class be doing
while you meet with small groups?
• How to plan for targeted, meaningful small
group lessons?
49. Why Small Group Math Instruction?
• Allows you to teach each group at an
instructional level that maximizes learning
• Increased one-on-one time with each student
• Targeted and specific to student needs based
on data
• Immediate Feedback
• By using this approach with both language arts
and mathematics it is easy to establish and
teach consistent routines and procedures
(mirroring the procedures and routines of Daily
5 for example)
50.
51. Making Math Stations Work
• Create a sense of urgency
• Make expectations clear
• Give choice
• Let go of managing everything they do
• Let go of assessing everything they do
• Give time to share and reflect at the end of
each block
52. What Can it
Look Like?
Planning and
Process can be
messy – that’s
okay!
54. Possible Stations
• SNAP practice/ Zoom Into SNAP
• Fact Fluency / Math Games (Math with
Someone)
• Exploring/problem solving with
manipulatives (Hands-on)
• Technology (laptops, iPads)
• Desk Work (Math by Myself)
65. Desk Work (Math by Myself)
MATERIALS
• Workbooks
• Exercise sheets
• Math journal
• TpT
How to assess?
Accountability?
66.
67. Teacher Feature
Now that everyone is
doing something
meaningful, you can
meet with your small
groups.
68. Teacher Feature
MATERIALS
• Whiteboards
• Manipulatives
RESOURCES
• Carole Fullerton Books
• JUMP
• Balanced math program of your choice
• Building Math Minds and other recommended
websites on snap.sd33.bc.ca
72. The Importance of Reflection
“How did I grow as a mathematician today?”
• Consolidates the learning
• Holds students accountable
• Promotes growth mindset
• Promotes independence and problem solving
• Allows students to self-evaluate and set new goals
I’m very pleased to have the opportunity to do this session on number talks. Number talks are one of the most effective routines or exercises in developing students’ number sense.
Math is an open and visual subject and all math problems can be solved using different methods and pathways.
This is actually a great learning opportunity for teachers. We often have our methods for performing operations in our head and by hearing the way our students are thinking and being exposed to many different strategies definitely adds to our toolbox of strategies.
Decomposing or breaking apart the subtrahend
Using the same difference (thinking of subtraction as a distance)
Rounding the subtrahend to a multiple of ten and then adjusting
We often find in math that our students have very fragile skills and a shallow understanding. They are relying on rules and procedures that they’ve memorized, but they don’t understand the numerical relationships that provide the foundation for these rules.
Any deviation from the context in which they learned the algorithm (or the procedure) can lead them to confusion and mixing up rules.
“Is this the question where you….”
“Am I allowed to…”
Algorithms are certainly useful tools: they are reliable and efficient. But they often conceal very important concepts about place value.
We see these words, communicate, explain and justify, weaved throughout the entire math curriculum because these skills are necessary to be proficient in mathematics. In the past, one could be proficient in math by being able to compute quickly, but we have equipment to do that now. To be proficient in math in the 21st century, people need to be able to problem solve, compute flexibly, justify their solutions and explain their reasoning.
In January the first cohort of secondary students wrote the new numeracy assessment and only 5% of students that wrote it were proficient in explaining and justifying their reasoning. This tells us that we need to practice this skill in mathematics and number talks are an excellent avenue for practicing this skill.
They will learn that they have ideas worth listening to and that being quick to get the answer is irrelevant to being successful in mathematics.
We start with dot cards.
The purpose of starting with dot cards is to remove any negative emotions about math from the exercise.
Dot cards don’t trigger math anxiety. We are simply looking at dots and counting them and everyone can do that.
It takes time to establish a community of learning built on mutual respect, but if you consistently set this expectation from the beginning, students will respond.
An important cornerstone in building a learning community is helping students realize that mistakes are opportunities for learning.
Wrong answers are used as opportunities to unearth misconceptions and for students to investigate their thinking and learn from their mistakes.
Our role shifts from being the information giver and confirming correct answers, to being a facilitator, questioner, listener and learner.
Facilitator and Questioner: Keeps the discussion focused on the important math and help students learn to structure their comments and wonderings. Guide the students to build on your purpose by asking questions like, “How does Jenny’s strategy connect to the ideas of Joey’s strategy?”
Listener and Learner: Become more interested in HOW they arrived at their answer and WHY. You will begin to understand how they are making sense of the math and use that information to help them see how numbers are interrelated in different operations.
Hi, I’m Kathleen Mitchell, Math and Science Helping Teacher. I normally teach Math 7/8/9 at Chilliwack Middle School in French and English.
I’m so thrilled to get a large group interested in Number Talks and I hope you all leave excited at the potential that this powerful routine will have on your students’ number sense and their confidence in working with numbers.
It really is a next-to-no prep routine
A simple, low-prep station that is purposeful and directly connected to the curriculum is a SNAP station. Here you could have groups of students working on a SNAP poster together, or for independent work you could use the zoom into SNAP templates which include only one competency. So for example you could look at Reasoning and Analyzing, which would be the number line and skip counting. The focus of your small group instruction could determine where you want to put the SNAP station in your rotation. If students go through the SNAP station before coming to their small group with you, you can quickly assess it which could help guide your lesson.
A common station is a fact fluency station of a math game station. Committing facts to memory is an essential skill for freeing up working memory and estimating. Notice I said committing facts to memory and not memorizing. There is a difference. When students commit facts to memory, it means they have learned those facts based on strategy. So if they forget a fact, they rely on strategy. For example, if a student forgets 6x7 and they truly understand their facts, they may think, well 6x6 is 36 so one more 6 would be 42. But a student that has simply memorized would have to count up by 6s.
So timed drills are discouraged. They often cause anxiety which masks knowledge, and they don`t address flexible thinking. Fluent means efficient, accurate and flexible.
A common station is a fact fluency station of a math game station. Committing facts to memory is an essential skill for freeing up working memory and estimating. Notice I said committing facts to memory and not memorizing. There is a difference. When students commit facts to memory, it means they have learned those facts based on strategy. So if they forget a fact, they rely on strategy. For example, if a student forgets 6x7 and they truly understand their facts, they may think, well 6x6 is 36 so one more 6 would be 42. But a student that has simply memorized would have to count up by 6s.
So timed drills are discouraged. They often cause anxiety which masks knowledge, and they don`t address flexible thinking. Fluent means efficient, accurate and flexible.
