Coaching Goals 2016


At the end of last school year, the math teachers and I got together to discuss use of manipulatives and mathematical discourse. (A Balanced Approach Prezi)

During this professional learning session, we read portions of this article. Teachers were asked which of the 5 Practices they felt they needed to work on the most. Like most teachers, many felt they were already using the practices and had a difficult time selecting one on which to improve. But like any growth mindset person, we know there’s always room for growth. 

This is why one of my coaching goals for this school year is to work with teachers on improving on one of the five practices. My plan is to confer with teachers within the first month of school to establish the goal and collect data and monitor progress throughout the first semester. This falls right in line with our school goal of increasing classroom discussions. I’ll be using this book as a guide. 

My second coaching goal for the year is increasing the use of manipulatives within all math classrooms. I’m still pondering the best method for doing so. The biggest hurdle is teacher comfortability. However, I know the more they use them, the more they will become comfortable with using them. So step 1, ease teachers into use and help them feel comfortable using them. Step 2, ensure teachers are using best practices when employing manipulatives.   At my elementary school, teachers were more willing to use them as it was a high priority. Now in my middle school, it’s not as high on the list. 

If anyone has any ideas and strategies they’ve used, please leave a comment and share. 

Creating a Remediation They Want to Come to!


At the end of every 1st semester, students who failed a course are invited to participate in Comet Academy, my schools grade recovery/remediation sessions.  This year, those attending Comet Academy come for 2 1/2 hours for 6 consecutive Saturday mornings.  During our first session on January 30th, students were given a 30 questions, multiple choice pretest covering 5 key standards from 1st semester.  I was assigned the 8th graders who failed to which I was very excited.  8th grade is the one grade level I haven’t been able to infiltrate with the use of manipulatives and building conceptual understanding.

Students completed the pretest in about an hours time, followed by checking the answers of a partner.  Stunned by the results, I knew immediately, 6 sessions, even at 150 minutes a pop, wouldn’t be enough to get the students to pass the post test.  The highest score was 11 out of 30 correct, ugh!

After proposing to the math AP about the need for a math boot camp for students who failed to stabilize their foundation for high school, I got busy planning.  8th graders who failed 1st semester, whether they attend Comet Academy or not, would be pulled twice a week for 30 minutes each time for 5 weeks.  This would occur during their Connections classes (electives, specials, not the core classes).  This boot camp would only offer additional support and would not be rewarded with a grade, extra credit or anything tangible outside of a better understanding of the content.  For students who are often motivated by outside factors, I needed to ensure the activities were enticing enough to get them to come week after week.

Meaningful Practice

The standards are not new for students, therefore a mix of meaningful practice and concept development is necessary.  In their regular classroom, students are subjected to worksheet after worksheet or textbook page after textbook page for practice.  In boot camp we used a Solving Equations Bingo game to practice solving equations.  Students filled in the answers: x=3, x=11.5, x= 1 1/2, x=5, x= 17, x=4, x=17 and -72 =x into the Bingo board.  Then I read off equations in which students needed to solve in order to cover the correct answer.

We also played a game of Knockout!  This idea was taken from the basketball game Knockout!  In the basketball version, participates line up behind the free throw line, the first two people in line have a basketball.  The goal is for the second person in line to make a shot before the person in front of them in order to knock the player out of the game.  In boot camp, students sat in a straight line and the second person tried to correctly answer the math problem before the person in front of them did in order to knock them out of the game.  Here’s the PowerPoint with the game: Boot Camp 2-9 and 2-11.

To encourage collaboration, students were grouped (they chose girls against boys) and given whiteboards to record the answers to problems.  The group representatives would hold up their whiteboard showing their answers.  In order to receive a point, teams had to get the correct answer, but also shot a tiny basketball into a toy hoop.

Concept Development

To help to continue to build student understanding of solving equations and integer rules, I used lessons from Hands-On Standards and incorporated color tiles and algeblocks with lessons like this Exponent Activity.

File_001   File_005

Formative Assessment

I have to know where they are from day to day because I don’t have a lot of time to cover the material.  Therefore, each session has a connected formative assessment.  This helps me to plan differentiated lessons even within the small group of students I see on the different days.  I’ve used a two question quiz, a portion of a FAL and a Ticket out the Door pictured below.  Students were able to choose what type of question they wanted to answer which is a formative assessment within a formative assessment :-).


Special Education Math Framework


It’s been a while since I have sat down to collect my thoughts and as the Bible says, “write them down and make them plain”.  This may result in a series of multiple posts in the next coming days.


Coming back from winter break always creates the opportunity to visit every math classroom to see how teachers have jumped back into the swing of things.  I was encouraged by the many teachers who have started 2016 with a bang of differentiation, small groups and formative assessments.  I was also encouraged by the goals teachers set for themselves to improve during semester 2.  One teacher’s goal became the spring board for one of the many projects in which I am currently working.

The special ed teacher approach me to share she felt the interactive textbook wasn’t helping her students understand the concepts.  She desired to know more instructional strategies she could use to better meet their needs.  During a pre-conference, we discussed how using more hands on activities and manipulatives would help students in understanding the concepts.  This prompted the conversation of what resources would provide meaningful activities while incorporating manipulatives.  We looked at using Hands-On Standards (HOS) and resources from nzmaths.  The conference ended with the scheduling of a model lesson on implementing a HOS lesson involving functions.  During our post conference, she expressed excitement about the observations she made during the lesson.  Students were discussing the mathematics and making connections between previously taught concepts and functions.  Students were more engaged than when they worked from the textbook.  All this in the MILD special education classroom.

After seeing the lack of hands-on experiences in other special ed classrooms, the special ed AP and I discussed ways to increase this instructional strategy. What spawned from that conversation was the Special Education Math Framework for Grace Snell.

Balanced Numeracy Adapted from our district’s balanced numeracy document we developed a scope of a lesson for special ed teachers.  It was important for it to mesh with our school initiative of gradual release.  Beginning the lesson with an activity from HOS brought in the hands on experience while satisfying the whole group portion of gradual release.  As the lesson transitions to the work session where students are working independently, the same manipulatives from the HOS mini-lesson can be used and any knowledge or understanding gained can be applied.  So those teachers who find comfort in the pages of a textbook are able to stay comfortable for the time being.

Happening this Friday is an optional professional learning session on implementing HOS and using the manipulatives.  My goal is to get every special ed teacher comfortable with using manipulatives on a regular basis.  I predict when we get to that point, teachers will find the textbook does not fulfill the same need as once before.

Pythagoras Square


During the summer I had the opportunity to work alongside my math friends implementing foundations of algebra professional learning sessions. Although I was the one conducting some sessions, I also put myself in the position of a learner. One of my takeaways was using the Pythagoras Square to help build conceptual understanding of square and cube numbers as well as square roots and cube roots. 

So Wednesday morning when I was asked to cover an 8th grade class (the teacher was out and there wasn’t a sub to cover) I gladly abliged. They are working on simplifying radical expressions and the primary means of introducing this idea was through the use of prime factorization. I wanted students (and teachers) to understand the why behind the simplified solution. 

When students came into class from connections they were asked to view this model and record what they noticed and what they wondered. 

Students’ notices included: the different colors, it looks like an arrow, the figures getting larger and the similarities of a multiplication table. A few students wondered if the model could be extended. So I asked a few to jump in to help extend the model. 

We didn’t complete the entire square due to time. However, we did take the time to focus in on the perfect squares and their lengths. We were able to make the connection between the area of the squares and the radicands and the lengths of the squares and the square roots. 

From there we jumped into simplifying radical expressions.  We discussed identifying factors of the radicands and determining which factor pair contained a perfect square. 

 We concluded the lesson by students completing 10 problems on a worksheet left by the teacher for the substitute. I looked over the papers afterwards and realized some students didn’t quite understand how to write the answer once they determined the square root. For example, they would record the square root of 64 as square root of 8, not just 8. Other students needed help making the connection of identifying the perfect square strategy to the prime factorization strategy. 

Anyone who has followed for a while could guess my next step, pulling small groups. Within the groups students built squares using color tiles as we discussed square numbers and square roots. For students who recorded answers inaccurately we looked at a square made of 9 color tiles. By determining the length students were able to see why that answer is recorded as 3, not square root of 3.  For students who needed to make a connection between identifying the perfect square and the prime factorization strategies, we looked at how the prime numbers can show the lengths of the perfect square. 

I’ll have to check with the teacher to see how students faired on the common formative assessment given on Friday. 

The Beauty in Seeing


We’ve been working on solving percent problems for a while now. The concept of identifying percent of a number was introduced using a double Numberline similar to what is shown below. 

I’ll admit, when I was in grade school I recall solving percents by cross multiplying. But as with most procedures, I didn’t understand how that strategy connected to the concept of percentage. I just knew the steps to follow to get the correct answer. Fast forward to me implementing a percentage lesson with my students, I was determined to make sure students understood the meaning of percent and applied it to finding the percent of a number.   My initial thought was the double number line would be perfect for this. 

Using a lesson from Lessons & Activities for Building Powerful Numeracy, students were introduced to modeling part of a whole using the bar model. 

(Side note: This post was accidentally updated to an older version. I will try to catch the essence of the published post.)

Students struggled making the sense of the bar model, so we looked at it as a double number line. 

This version helped some students but there were some who still had trouble visualizing it.  For those students, strip models were introduced. 

Percentage Strip Models

Students were given a strip of paper. One side represented 100%. It was split into 10 equal parts making each part 10%. Students were able to see the 10% + 10% that the 20% hash mark represented. The same strip was flipped over and another quantity represented. Students could use the percentage side to find say 30% and flip the strip to determine the equivalent amount to 30% of the whole. 

After this, the concept clicked for those who were once confused. And beautiful things like these started to happen:

Young lady torn paper from her notebook to make strip

Random strips left behind after class

There was even a student who torn their scratch paper during our common assessment to make a strip model. 

Of course this wasn’t the only strategy discussed. Others came from the unit work, Getting Percentible from nzmaths. I wanted to take a amount to emphasize the beauty in seeing. 

*Sorry this version is not as well written as the original. Realizing I had accidentally updated an older draft (using the app on two different devices) really took the wind out of my sail. *

Elementary and Middle I Thee Wed


As an elementary teacher, especially the past few years being an elementary math coach, I have become accustomed to using tools such as base ten blocks, rekenreks, counters, beads and other things of that nature to help students make sense of numbers and operations. I’ve seen firsthand the tremendous growth students show in understanding when they use the tools to help identify patterns, create written representation and make conjectures about the mathematics.

As I’ve been going through the GA Frameworks for 7th grade to help me make sense of the 7th grade standards, I noticed the occasions of using manipulatives are not as frequent as they are in elementary. So I thought what better way to hit multiple birds with a really huge stones. Why not marry the two, elementary manipulatives with middle school concepts.

Let’s take for example, the addition and subtraction of integers. What’s the go to manipulative with that? Two colored counters! There are common misconceptions that come along with using the counters only. Not fully understanding zero pairs or when subtracting removing the counters instead of bringing in zero pairs are ways this tool hinder student understanding. Why not instead use a modified rekenrek as explained in my insertion into this frameworks task.



To connect quantity of integers, movement on a number line and patterns of adding and subtracting integers, why not use a bead string.


I even found a way to sneak in a number talk into a unit on operations with rational numbers.

I saw it as a great opportunity to remove the warm up problems prominent in upper grades and insert a chance to have discussions about strategies as we do quite often in elementary.

I’m feeling more comfortable with this content, more at home with my conceptual way of thinking.