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This was our last TMI meeting. Sad to say after three years of work, our TMI cohort is finished. Thank you to all the participants for their hard work.

A summary of our day's events are below:

First we worked on providing feedback to each group's Instructional Intervention Sequence. We used a tuning protocol in which each group was given a few minutes to summarize their sequence and inform the listeners about their strategies. Then the group asked questions, gave feedback and finally the group with the instructional intervention sequence described what they would do to edit it.

Afterwards, we played a game called Albacheeball. The participants were divded into groups and played the game that used substitution in algebraic expressions to generate the largest numeric solution possible.

After lunch, the group watched and worked on open ended tasks. The first task was a task based on the Lucy Show called Bean Queen. Participants explored linear and exponential relationships along with the meaning of logrithmns in context of real-world problems. Secondly, participants worked on linear programming with a Furniture Problem in which they built chairs and tables with multi-link cubes and then graphed the inequalities based on constraints.

Finally the day was finished with our participants from Bardstown hosting a BreakOut activity.

This day highlighted strategies that TMI has shared with participants over the course of the project. The day began with a challenge problem from Dr. Lee.

Then, participants experienced the Apple Activity in which they examined the variety of ways we present content to students and how it affects their learning.

Afterwards, participants brainstormed strategies that they had used the most in their classrooms. Participants then took that list and played Boggle and found the MVP (actually listed their top 3 strategies).

Facilitators revisited the Instructional Intervention Sequence from June 2015. The group did live editing to improve the clarity of the instructional sequence. After lunch, participants grouped themselves by content and topic to create another instructional intervention sequence. Participants are to incorporate their instructional intervention sequence in their classroom over the next month and bring in student work to our next meeting.

Participants worked on a 3-Act Lesson that a facilitator created on scatterplots and winning Olympic data.

Our two-day summer workshop concluded our look at proportional reasoning. The following is a brief outline of activities and learning for the two days:

Day 1: Participants were given a new resouce, Total Participation Techniques (TPT). This resource was covered through jigsaw activities and a powerpoint. Participants were given a set of TPT cards they could create for their classroom.

Participants investigated direct proportional versus inverse proportional relationships. Work from the Scale City module, Sky-Vue Drive-In was highlighted in our learning. Activities from this resource along with the article from the April 2016 Mathematics Teaching in the Middle School entitled "It's a Bird, It's a Plane, It's a Dilated Superhero" were used. Participants worked together to learn about shadows and their dilations in an activity called What Math Lurks in the Shadows". The activity used a light source (cell phone flashlight was the best) and moving an object's distance from the light source.

Participants also worked on scaling the size of planets by using a variety of sports balls to show the relative size of other planets to the size of Earth.

Participants finally played games called Bump and 4 in a Row that worked with ratio creation and other math concepts.

Day 2: This day focused on developing an understanding of the similarities and differences between direct proportionality and inverse proportionality through the participation in hands-on labs. The first lab was known as Penny Bridges. A second lab was from the May 2016 Mathematics Teaching in the Middle School entitled "Spaghetti Bridges: Modeling Linear Relationships". Participants worked in groups to collect datafor both labs and then typed their data in DESMOS. Participants examined both sets of data by looking at the tables, graphs and equations to compare and contrast direct and inverse proportionality.

Another activity that examined proportionality was the Globe-Trotting activity. Participants threw inflatible globes around the room and collected the number of times land or water was found. The table of data helped to determine the percentage of the globe that is land and water.

Finally the day ended with STEM stations that focused on proportionality seen in genetics and chemical reactions. The STEM stations were organized with the Teach-Learn model in stations. Handouts of the stations and the Teach-Learn grouping cards are in the Sharepoint site.

This month's meeting highlighted the use of proportional
reasoning with reference to geometry (in particular scale factor and
dilations).Participant were lead
through the following activities:

** Card Sort based on the 3 Types of Questions with last
month's participant work on proportional reasoning question writing.

**Reading on Similarity from Marian Small on p. 97-99.

** Discovery of meaning of dilations based on hands-on
exploration of the Rubber Band Activity.

**DESMOS Activity on Dilation to show how technology
supported the hands-on approach to dilations with the rubber band
activity.

**Television Problems from Teaching Fractions and Ratios for
Understanding based on similarity. (p. 83-84
and #33 from p. 94)

**Participants shared how they have used TMI strategies in
their classroom. Susan Strange shared a website: www.interactmath.com. Maggie Blanton shared the math stations she created on slope-intercept and standard form of linear equations.

**Introduced Scale City from KET with video

** Scale City activities highlighted with 5 stations

Today's focus was on multiple representations. Our instructional strategies/activities included the following;

Inch, Centimenter, What's the Difference?--hands-on lab that focuses on discovering the scale factor between inches and centimeters by utilizing data collection, tabling and graphing.

Talk Partners Revisited--participants did a Jigsaw of Chapter 4 from Shirley Clarke's Outstanding Formative Assessment. Participants highlighted "aha" moments or facts they had forgotten about in the incorporation of random talk partners.

DEMOS integration--Jordan Marcum shared his integration of Marble Slide from the DESMOS teacher site as a way to help students understand slope.

3 Types of Questions--participants practiced writing open questions in the forms of reversibility, flexibility and generalization. These questions will be used for a future activity.

3-Way Tie--participants saw how this Math Tool can be used not only as a vocabulary tool, but also as a template for multiple representations.

Marian Small p. 94-96--read the research behind how proportionality manifests itself in multiple representations (NAGS Rule).

Borax Lab--participants used increasing teaspoons of borax detergent in water and measured the change in temperature as more teaspoons of borax were added. Proportionality and whether the data created a linear or non-linear relationship.

www.graphingstories.com--participants looked at this website as a way of helping students understand how to graph real-world scenarios and also a way to reinforce vocabulary.

Monthly TMI meeting focused on proportional and
non-proportional relationships.

We read
Marian Small p. 83-86 and compared and contrasted the characteristics of
proportional and non-proportional relationships and outline our findings using
a Top Hat organizer from the Math Tools book.

We explored proportional and non-proportional relationships with labs
such as the Penny Circle (a Dan Meyer 3-Act Lesson with a DESMOS connection)
and Picture This! (lab in which one participant held up a ruler and another
participant took a picture of the other holding the ruler with their
I-phone).

We also completed stations
over proportional and non-proportional based on a FAL by the same name.

Our new resource distributed was It's All
Relative flipbook over proportional reasoning.We completed the following activity:Proportionality and Unit Rates (A24-25) and Proportional or Not?
(A38-39).

At the end of the meeting,
participants shared their student work over proportional reasoning.

This meeting focused on proportional reasoning as it relates to unit rates. We also explored the incorporation of FALs and math labs into the classroom curriculum. Below are the highlights of the activities:

Card sort over the 3 types of questions (reversibility, generalization and flexibility)

Participants categorized the questions that were created by fellow participants in September's homework into the 3 types of questions)

Formative assessment lesson...Comparing Strategies for Proportional Problems

Participants looked a various strategies from student work given in the FAL in order to address misconceptions that some of their students may exhibit during proportional reasoning units.

Dan Meyer's 3-Act Lessons

Participants were introduced to the real-world applications that Dan Meyer provides in his 3-Act Lessons and blog posts. We examined the Rope Jumper 3-Act Lesson as a way to introduce unit rate.

Marian Small's Proportional Reasoning p. 68-72.

Participants read and worked selected problems from this book. Great conversation was led over the use and purpose of tape diagrams. Also multiple representaitons were addressed as a means of helping students to persevere in their mathematical thinking. If one method does not work, students need other methods in which to solve problems.

Math Labs on indirect measurement using a mirror and shadows.

Participants worked on the two aforementioned labs. After working the labs, participants discussed how to implement.

KET lesson entitled, "How Many Noses are in Your Arm"

This lesson was introduced as a means to show that real-world connections can lead to engaging tasks.

At the beginning of the day, participants received what they ordered from their $1000.

This meeting began the focus on proportional reasoning that we will have for the rest of the project. Below is a list of activities that we completed:

Participants revised their questions from the previous month based on feedback from the carousel activity. Final drafts were shared with the group.

Kicked off our study of proportional reasoning with a video from mathsnacks.com entitled Bad Date.

Participants brainstormed possible topics and synonymns for ratios and proportional reasoning they teach in their classroom.

Completed a Standards Dig in which participants divided into grade level groups and rread the standards for ties to ratios and proportional reasoning. Groups both shared out and charted the exact standards.

Participants completed an activity called Ratio Rambler that dealt with ratios or fractions and the possible relationships they could model (part to part; part to whole; whole to part) with two-color counters.

Participants were given the Marian Small book on proportional reasoning to read and use for Ratio Rambler activity.

In the afternoon, participants worked in groups on 4 math stations that focused on ratios and proportional thinking.

Homework: Participants are to either write questions using the 3 types of questions or create a math tool that deals specifically with ratios and proportional reasoning.

Materials given: 2 reams of card stock (blue and green), 45 individual white boards, 2 personal laminators, Marian Small proportional reasoning book.

This meeting focused on two main topics:effective questioning and TI-Nspire calculator activities.

Participants learned about 3 Types of Effective Questions which were generalization, reversibility and flexibility. Participants worked examples of each. Then they were divided into grade level groups in order to transform a common textbook problem using the 3 types of questions. Afterwards, partcipants completed a feedback carousel in which ideas for revisions were given.

Participants worked more with their TI-Nspire calculators with rational number TNS files.

Participants also played fraction card games: factor find and fraction rummy.

Materials given out: chart paper, 3 reams of cardstock, chart markers, expo markers, laminating film

This two-day session highlighted the culminating project that the TMI participants had been working on--instructional intervention sequence. Below are highlights for Day 1:

Participants examined student work examples from the Math Tools book.

Groups worked on their instructional intervention sequence while receiving feedback from facilitators.

The versatility of algebra tiles were highlighted through a hands-on exploration of how to model signed number operations, combine like terms and distributive property.

The use of the area model on the TI-Nspire to model how to multiple/divide rational numbers.

A variety of formative assessments linked to the learning target, "I am learning to solve linear equations" from the Math Tools book.

Day 2:

Participant groups presented their instructional intervention sequence in 10-minute intervals.

The use of algebra tiles for multiplication of polynomials was highlighted in a hands-on investigation.

Participants were shown how to update their operating system for their TI-Nspire.

Participants played a whole class game entitled Kaboom. The purpose of the game is to build fluency in solving linear equations.

Materials received:

Each school was given the set of dies for cutting algebra tiles.

Each teacher was given three backs of both red and blue thick foam for creating their own classroom set of algebra tiles.

We had three main topics that we learned about during the June days.

First we focused on learning how to use our new TI-Nspire CX calculator as a demonstration tool for Tier I interventions. Participants learned how to use the calculator, download software and retrieve teacher notes/student activity pages.

Second, participants played a variety of games that would help to build conceptual understanding and fluency. Our introductory game was Proportion Creation and after lunch we played linear dominoes.

Lastly, the participants were given the new Harvey Silver book, Math Tools for Grades 3-12. A scavenger hunt and background research was highlighted during the session.

A project was included as a way in which participants showcase their learning from the first full year of TMI. The breakdown of the project occurred as follows:

Day 1: homework included participants brainstorming topics or concepts that many students have misconceptions about in math.

Day 2: participants formed grade-level groups and worked on creating an instructional intervention sequence with at least two activities. Groups have to fill out the template and provide any handouts or instructions for other TMI participants to replicate the activities. Groups will present their work on the second day of the July two-day meetings.

TMI focused on consolidating the year's learning
through a day of data collection activities.Participants experienced the following activities:

Wingspan vs. Height

Disk Diameters

Desmos Teacher website--Central Park

All Knotted Up

After lunch, participants went to break out sessions
based on grade level taught. The middle
school group explored proportional reasoning with activities from the Georgia
Education Department website: Constant
Dimensions (use of non-standard units to measure) and Analyzing a Graph. They also worked on the task Stacking Cups
from the X's and Y's of Algebra Flipbook (TMI Resource participants already
have in their possession). The high
school group explored exponential growth with an M & M activity.

At the end of the day, participants completed an
evaluation form that provided TMI feedback on today's session and also ideas
for possible topics to explore this summer and next year. Finally participants chose their summer
dates. Those dates are as follows: June 17-18 and July 7-8.

This meeting highlighted several instructional activities. We began the day with a Block Lab Mini Math Challenge. Participants learned about the importance of slowing down instruction and providing students with multiple exposures and contexts to instruct on slope and y-intercept. The NAGS rule was also highlighted as a means of demonstrating multiple representations in the math classroom.

We then watched the Seamus video and talked about sound instructional strategies for our classrooms. Afterwards we revisited silent teaching with an example entitled The Power of Exponents. Special consideration was given to ensuring that teachers focus on the debriefing and discussion portion of silent teaching. it was also noted that teachers need to make sure that while ending a silent teaching lesson, it was important for students to write down their findings such as their shortcut or rule they developed from the silent teaching lesson.

After lunch, teachers were debriefed on the first rounds of observations with several celebrations of great teaching we saw. Teachers were introducted to a new game entitled Flyswatter. This game is a review game to promote fluency in numeracy and vocabulary.

We ended the day with teachers receiving feedback on their CRAs through a tuning protocol.

Teachers were given a new book entitled How Students Learn and each school was given a new die of base ten blocks for their accu-cut maching. If any teacher did not receive their materials, please let us know.

Several items were covered during this meeting. We discussed the importance of clearly written tasks with the activity entitled T-Time Baby. We completed a CRA task called The Shape of Things. A new instructional routine called Silent Teaching was demonstrated. Finally we completed a fish bowl activity over a tuning protocol. Participants are to have a completed CRA for a tuning protocol during the October meeting.

During our August meeting, teachers
learned about how they could use pattern blocks in designing learning
experiences for their students.Participants
experienced several “Mini Math Challenges” that demonstrated a strategy called CRA (concrete-representational-abstract).

The teachers took some time to reflect
on how much we had learned about growth
mindset, learning powers, and talk
partners and to share how these integral components of learning culture have been implemented in their classrooms since
the beginning of the school year.
Participants explored how this idea of building a learning culture in
their rooms related to the Kentucky Teaching Framework (PGES) in Domain 2,
Establishing a Culture for Learning.

Before leaving for home, participants
gathered the resources they were given:

1.Accu-Cut Machines

2.Foam

3.Seven dies to
make various manipulatives

All of the electronic resources we used
for the meeting have been uploaded to the TMI Home
Page in the Meeting Resources tab in the folder labeled August
28, 2014.

If you have any trouble accessing any
resource we used, be sure to contact one of the facilitators.

Our July 17^{th}session began with some number line
problems that utilized the number line in the addition and subtraction of
fractions. The problems
helped teachers better understand how to use their number line as a tool to
increase students’ conceptual understanding of equivalent fractions and of
addition and subtraction of fractions.

After a review of how to implement growth mindset, learning
powers, and talking partners in their classrooms, we looked at an overview of
the domains included in the teacher Professional Growth and Effectiveness
System (PGES) and how growth mindset, learning powers, and talking
partners contribute to Domain 2—Classroom Environment.

The afternoon was spent exploring multiple ways of modeling
addition, subtraction, multiplication, and division of fractions. The
homework for the evening was to explore the “flipbooks” received in June.
Participants were to choose a topic and see how the “flipbook” dealt with
Potential Challenges and Misconceptions, ideas for teaching strategies (In the
Classroom), and Meeting Individual Needs.

Day two began with some problems fromConnected Math. The
problems highlighted various ways students could understand operations with
fractions through a more contextual and concrete approach.

Other morning learning opportunities revolved around discussion
of what their investigation of the “flipbooks” revealed and we also discussed
chapter 5 fromTeaching
Mathematics Meaningfully.

After lunch, participants dealt with several classroom scenarios
highlighting difficulties students have in math class and how they might designRtIin their classroom to address the
difficulties.

Finally, participants were asked to specifically describe their
plan for the beginning of 2014-15 to:

1.facilitate
the development of growth mindset with their students,

2. teach and focus on learning powers (meta-cognitive strategy), and

3.talk partners.

Also, participants were to select a math concept they
planned to teach early in the year and design a plan that integratedCRA in their RtI plan. The teachers’ plans
were displayed and presented to the whole group.

In July, participants received Shirley Clarke’s Outstanding
Formative Assessment: Culture and Practice. Their homework for the August
28^{th}meeting is to
read chapters 2 and 4. There is a reading guide posted in the teacher
resources for July. This book will also be used extensively in the
2014-15 school year as teachers continue to work on learning culture in their
math classroom.

Please feel free to email me atpamharned1@yahoo.comor any of the other facilitators if
you have questions about or difficulty accessing any of the summer’s resources.

Thanks to all of you for your attendance and for all the work
you did during June and July to get prepared for the upcoming school year.

Our first day of the June summer session began with a feedback
session. First
we began by reviewing about 1)growth
mindset, 2)learning
powers(a meta-cognitive
strategy), and 3)talk
partners. After
reviewing, participants were put in grade-level groups and asked to share how
they had implemented each of the above components of classroom culture and
how their practices had impacted student learning.

The afternoon of day one was spent gaining a more in-depth
understanding of Response to Intervention (RtI) and an instructional
strategy, Concrete-Representational-Abstract (CRA), that can be used
when teaching a variety of mathematical concepts.

On day two, participants experienced a variety of strategies for
teaching conceptual understanding of comparing fractions. One such strategy was
by creating a “fraction kit” that allows students (and teachers) how to
visually compare fractions using the fraction bars.

Participants were given some time to process many of these
strategies and to grapple with how these strategies might extend to addition,
subtraction, multiplication, and division of fractions. Also,
participants were introduced to several websites that would allow the use of
technology to aid conceptual understanding of fractions and operations with
fractions.

During our two days in June, participants received several
resources, including:

1.“flipbooks”: Zeroing in on Number and Operations (grades 5-6),
Zeroing in on Number and Operations (grades 7-8), and The Xs and Whys
of Algebra (These books provide insight into these key ideas, some
common misconceptions students might have, and some ideas for strategies to use
to when teaching various math content.)

2.Shirley Clarke’s DVD, OUTSTANDING Formative Assessment, that
contains many video clip that address components of classroom learning
culture and how some teachers are successfully implementing them in their
classrooms.

3.Teaching Mathematics Meaningfully(This text will be used during the 2014-15 year to help
participants understand why students have difficulties with math and how
they, as teachers, can use formative assessment to identify
those difficulties, and to intentionally plan instruction to address
students’ difficulties in their math classrooms.)

The first Timely
Math Interventions (TMI) teacher meeting was held on Tuesday, February 25,
2014. This grant is facilitated by the Partnership Institute for Math and
Science Education Reform (PIMSER) and is funded by the Math & Science
Partnership from the Kentucky Department of Education, Office of Teaching and
Learning. The participating teachers are from Bardstown Independent,
Bell County, Jessamine County, Lincoln County, Powell County, and Washington
County. Meetings are held in Lexington at the UK/Lexmark Center
for Innovation in Math and Science Education.

In our first meeting, participants were
oriented to both the goal and the content focus of TMI. The goal of the
project is to help teachers experience and to implement strategies that can be
used for Tier 1 intervention in the mathematics classroom. With that
focus, teachers began learning about growth mindset versus fixed mindset.
They participated in activities that help students learn about what a growth
mindset is and they experienced activities to create a classroom culture
that helps each student to develop a growth mindset.

The content focus of
TMI is to foster number sense and algebraic thinking and to learn how these two
strands in mathematics promote student success in algebra. Participants
began their content focus with a search of the 5^{th} through 8^{th} grade
standards. The standards highlighted were those dealing withfluency and number lines. After the
standards “hunt,” participants worked on number line activities that would
provide opportunities for their students to build conceptual understanding
of sets of numbers at each grade level. Each teacher left with a number
line they could use in their own classroom to facilitate these and other such
number line activities.

When teachers return
in March, they will report ongoing strategies being implemented that
foster their students’ development of a growth mindset and they will
report on the number line activities they are implementing in their
classrooms.

Thanks to all the
teachers for their participation and enthusiasm in this first TMI meeting!
All the facilitators look forward to working with each of you for the next
two to three years as we increase our understanding and expertise in helping
students to be successful in algebra and in helping to make Kentucky’s high
school graduates college and career ready.

(All
the resources used in our first meeting have been uploaded to the
Teacher folder under February 25, 2014. To access the resources from Tuesday's meeting,
click on Meeting Resources on the left of this page. There is an
Administrators' folder and a Teachers' folder; click on the Teachers folder and
then on the February 25, 2014 folder.)