SD COUNTS
Strands of Math Proficiency – Adding It Up
Mini-Foundations Agenda
NOTES:
 Items in this color are available in the Adding It Up section of the Foundations binder from Spearfish ’06.
 Items in this color relate to copies of the text, Adding It Up- the PDF for chapter 4 was emailed to you on May
9th. The pages from chapter 1 will have to be copied.
 Agenda & power point are available in your email. Johny is putting together a meaningful practice packet
that will be coming soon.
 Brenda’s Blocks Task—this problem was from one of our earlier trainings—we used this in place of the water
task!

Welcome and Introduction
Materials:
1. Markers
 Introduce Me?
2. Buy Treats 
10 min.
 Share Objective for today’s session:
3. Agenda & POWER
o Participants will have an increased understanding of
POINT
the five strands of mathematical proficiency
4. PDF of chpt. 4
o Participants will have an introduction to classroom
5. Projector & Screen –for
applications for the five strands of mathematical
showing video &/or power
proficiency
point
o Participants will have an increased understanding of
the research supporting inquiry-based mathematics
in teaching and learning.
 Today we will be using a key chapter from Adding It Up
o Goals of Adding It Up
 Represents a synthesis of the research on
mathematics learning
 Provides research-based recommendations
for teaching, teacher education, and
curriculum for improving student learning.
 Provides advice and guidance for
educators, researchers, policy makers, and
parents.
o Today will focus on Chapter Four
 Explain the variety of tasks
o Some tasks are more challenging because I want
you to experience mathematics from a student’s
perspective; all are designed to model one or more
of the strands of mathematical proficiency.
 Roles and Rules
o Group Work: Choose: Time Czar; Recorder,
Reporter.
o Rules: (student helper scribe and post)
 Take care of yourself….bathroom location
 Respect and value everyone’s
thinking…today we are all learners.
 Anyone want to add to the way we will
work together today?????
Comment: Say something like, “If this were a math class, I’d have
more people share…(rushed because of the time constraints)”
SD Counts Summer Institute
Strands of Mathematical Proficiency
1

45 min.
Strands of Mathematical Proficiency – Developing Background
 Divide group into five groups by counting off.
 Assign Reading
o Every one Reads Pgs. 115- middle of 118
o Each group also reads the information on their
strand.
 Conceptual Understanding – pgs. 118-120
 Procedural Fluency – pgs. 121-124
 Strategic competence – pgs. 124 – 129
 Adaptive Reasoning – pgs. 129 - 131
 Productive Disposition – pgs. 131 – 133
 Directions:
o Read assigned parts individually (10 minutes)
For the sake of time, groups may divide their pages
o
o
o
Materials:
1. Adding It UP chpt. 4
2. Highlighters- if giving
individual copies of chpt.
3. Pencils
4. Frayer Model Handout
5. Chart paper & markers
6. Understanding Strands of
Mathematical Proficiency
Handout
GROUP WORK (20 minutes)
Within your group, select a recorder, reporter, and a
time czar.
Locate worksheet in packet – explain sections—use
this as your group discussion guide:
 Strand name in the middle oval
 Working Definition—this is the definition
written in your own words…not

copied out of the text
Examples: May be problems or
scenarios….whatever will convey
to the large group the essence of
this strand.
o
Work with your group to create a Frayer Model
(on chart paper) that will describe your strand to the
large group.
THINK ABOUT:
-What do you see your students doing? How
would you know that this strand is being
developed? Evidence?
o
Report Out: Groups share and answer questions
(10 minutes) USE: Understanding Strands of
Mathematical Proficiency Handout
o
REFLECTION: (if time) Using your journal (or
reflection guide) write any questions you still have
about the 5 strands of mathematical proficiency?
How will you increase your understanding?
SD Counts Summer Institute
Strands of Mathematical Proficiency
2

30 min
Scale Problem: Brenda’s Blocks
 Group into ___ groups depending on number in group
 Provide with Handout: Brenda’s Blocks Task
 Task:
o Give participants 10 (15?) minutes of private think time to
work the problem.
o Get into groups and discuss strategies/answers
o Using chart paper, have each group illustrate the strategies
that they used to solve
o Each group shares strategies
 Further Discussion if time:
Discuss or journal what strands of mathematical proficiency
were represented with this problem? What evidence would
you give to support your thinking? Ask for individuals to
share reflections.
Materials:
1. Chart Paper
2. Pencils & markers
3. Individual problem
worksheet from earlier
training

30 min.
*This will
be rushed!
Making the Case
1. Introduction: Why all the discussion around inquiry – based
mathematics? Why should we consider thinking in a
different way about how we teach mathematics and how
students learn mathematics? (Brief whole group discussion)
5 minutes
Materials:
1. Adding It Up chapter 1
(pgs. 15-21) *make copies
2. Pyramid Partners
Process Handout
3. Pencils
4. Stop Watch
5. Bell
2.
There is compelling evidence in your text that speaks about
the need for changes. Let’s take a minute to read what the
“experts” say about that.
3.
Individually, please read from Chapter 1 in Adding It Up.
Please read individually, pgs. 15 – 21. You will be talking
with a partner about these two questions?
a. What implications for teaching and learning were
alluded to in the text?
b. What questions did this reading raise for you?
4.
You will have 10 minutes to complete the reading.
5.
Explain Pyramid Partners Process – Pass out worksheet
(explain process) 5 minutes
*Round One: 5 minutes
*Round Two 5 minutes
6.
Large Group Discussion: (5 minutes) What kinds of
questions did this raise for you? Keep track of the questions
and address those that come up over and over again.
7.
If there is any time, this would be a great place to share
videos or testimonials from teacher leaders!
SD Counts Summer Institute
Strands of Mathematical Proficiency
3

Acrobats, Grandmas, and Ivan (procedural fluency)
Lots of different ways to solve the problem.
*Goal- shows procedural fluency.
30 min.
1.
Introduce problem.
a. How many grandmas/grandpas in the audience?
b. In this problem, you will know who won the first
two round of the tug-of-war and you will need to
figure out who won the final round. The first two
Materials:
1.
2.
3.
Problem worksheet
Chart paper
Markers
rounds give you the information you need
to decide who won the final round. (Pass
out worksheet and give directions for working.
2.
3.
4.
Work the problem individually? Share your solution with
group?
Record all solutions on chart paper.
Share with the large group and explain your thinking.
Large Group Discussion
1. How many strategies did we have to solve this problem?
(Book…Method of substitution, Given points, fractions (two ways)
and a reasoning paragraph) What strands of mathematical
proficiency are represented. Explain your thinking.

25 min.
BASIC SKILLS & final math activity: How Many Rows and
How Many in Each Row. (Optional – Depending on Time)
1.
Open with an Article about Basic Facts in Conceptual
Understanding Concept. – if time allows, jigsaw each section
or highlight key points in order to answer questions raised on
power point.
2.
Meaningful Practice- How Many Rows? How Many in
Each Row.
a. Pass Out Handouts and Review Directions
b. Ask participants to partner with someone at their
table.
c. Pass out Die
d. Play!
Discuss meaningful practice
3.

5 min.
Materials:
1. Hand out a copy and use
Questions About Basic
Skills handout to answer
QUESTIONS on power
point slides.
2. Game Handouts –
Directions and Game
Board Dice
3. Johny is putting together
a meaningful practice
packet
Closure
1. Summarize the day
2. Questions, Comments
SD Counts Summer Institute
Strands of Mathematical Proficiency
4