Wednesday, March 30, 2016

Formative Assessment Insights Online Course Reflection

I had to write a 1500 page essay on what I learned from my online course that spanned five months, and I decided to make it a blog post complete with some links to evidence of student work. Thanks West Ed for the great opportunity. Teaching Channel: you make great videos with awesome teachers. And I got to watch more video of Dylan Wiliam before I read his book.

Here's a link to an overview of the Feedback loop: https://player.vimeo.com/external/135680818.hd.mp4?s=245f1e7392f18d912a73862d0b6c8906&profile_id=119 

My classroom practices have been influenced greatly by the Formative Assessments Insights online course by West Ed. I’m glad that I have many examples of how their structure and suggestions allowed me to develop as a teacher and give my students a chance to be a more active participant in their learning by knowing where they stand and where they can go from here. I plan to continue these strategies and by having this summary, I can reference how it was implemented in the past to implement it in the future. I documented my journey on my blog at http://joyceh1.blogspot.com so others could see how I implemented it. I also enjoyed the collaborative piece of the course where we commented on research articles with other teachers in California, and I got to collaborate over Google Docs with one team member to give and get feedback on the implementation of the course ideas.


I believe I am more equipped to anticipate and uncover my student thinking and respond to it in a more timely manner every day I step into the classroom. The future is bright when I think about the possibilities of what I can achieve with my current and future students. Seeing my students quietly focusing on giving constructive and affirming peer feedback on post it notes during gallery walks was proof I will continue this instructional routine. The activity gathered evidence of what students noticed about each other's parabolas and their features. I want to continue to introduce learning goals to students and establish success criteria with them.


Learning about building blocks was huge because it made me realize that students come from a variety of backgrounds and unfortunately it's best to assume they do not remember the required prerequisite knowledge from the previous grade level. I had already used whiteboards before, but this course reinforced how important they are in getting and giving timely feedback. Asking the right types of questions was a common theme in the videos we viewed.


Interestingly, a prior administrator that observed me advised me to give an exit ticket to inform the next day's instruction. This online course reinforced that and gave students a chance to demonstrate their knowledge in an opportunity where it would not be graded. The next day I prepared the common mistakes and asked students what was wrong with it. I also tried to encourage, when possible, to have students say what was correct about it or going in the right direction. Exit tickets are so vital I realize to meeting students where they are and responding to how they have learned or not learned a concept.


I loved all the videos of the course because I haven't been disappointed before with what I've seen on Teaching Channel. There were some familiar faces even from math teachers on twitter that I saw (Crystal).


The online course was a set of five modules. Actually, there was a Module 0. This was where you setup your Google account to share your work and learn about the Zaption video tours in addition to the NowComment interface when looking at research articles filled with teacher and student dialogue.


The first module asked you for a definition of formative assessment. Before starting the course, I believed it was only ungraded assessments such as quizzes, exit tickets, and having students write their answers on white boards. By Module 1.5, I realized formative assessment wasn’t a type of assignment, it was a complete process and cycle. It was lesson planning, assessing prior knowledge, developing building blocks (small chunks of a standard), anticipating struggles, acting on feedback, changing your plan mid-class or the next day, acting on exit tickets, and much more.


I was introduced to the Feedback Loop in Module 1.8 that addresses three questions: “Where am I going?” This consists of the development of building blocks, learning goals, and success criteria. The next question is “Where am I now?” This is where you elicit evidence of student learning, interpret that evidence, and identify the gap. Finally, “Where to next?” In this last section you take responsive action and close the gap.


In module 1.13, we reflected on a variety of Teaching Channel videos. I learned that developing success criteria with your students after they are introduced to the learning goals empowers students to take ownership of their own learning. The video modeled a growth factor lesson where the teacher was able to meet the needs of various students by allowing room to extend the idea of growth factor. Students achieved the learning goal of identifying that the growth factor was the same for three patterns, but a pair of students went a step further sharing to the class that if you graphed the patterns they would be parallel lines because they had the same growth factors but different starting values or y-intercepts.


In module 1.14, I took a self-assessment, one of the formative assessment tools, and on a scale of 1-4 I rated myself at mostly 2’s and 3’s. Two of my goals I set were to use a variety of strategies to elicit evidence of student learning during class and use assessment more frequently to guide my instruction.


In Module 2, I reflected on videos where they showed a strategy that has worked for me before: turning and talking. In a whole class discussion the teacher wasn’t getting enough participation, so to build students’ confidence she had them turn and talk to confirm their ideas, to get more students to raise their hands. I liked how the teacher elicited evidence of student knowledge by using an online voting system for students to vote on their self-confidence with each success criteria. It allowed students to see which criteria students were confident in and which ones they thought they would need support in. In module 2.4 we wrote our first learning goals and success criteria. In 2.8 I reflected on how determining learning goals and success criteria answers the 3 questions of the Feedback Loop. Where am I going? The learning goals keep the end goal in mind and develop an accessible way to describe the concept or skill. The success criteria specifies what the students must demonstrate to show they achieved the learning goal. Where am I now? Learning goals help uncover prior knowledge and allow students to reference them during the lesson for academic language. Success criteria is a chance for students to self-assess or be assessed by a peer to see where they are with the success criteria. Where to next? The learning goals tell the teacher whether they will revisit or build upon a standard.


In Module 2.14, I reflected on keeping my English Language Learners and IEP students in mind prior to teaching a unit or lesson when developing the building books. I will continue to revisit the Common Core math progressions to see where students are coming from and where they are going. I noted that success criteria appears to be material that could be used on a summative assessment. Learning goals allow me to sequence the presentation of different students understanding of separate goals. Building blocks, learning goals, and success criteria are the 3 components that form the foundation of formative assessment because this work is done prior to teaching. They provide front loaded academic vocabulary and references for students throughout the day and week. All students want to know what they’re expect to learn and how they can demonstrate that knowledge. This is what learning goals and success criteria achieve. Students don’t want to be confused about what they do or do not know, and neither do we as teachers.


In Module 2.15, I developed building blocks for a standard, 8.F.4 that dealt with linear functions and their rate of change and starting points. One of the building blocks was color coding the growth of their pattern. Before writing the building blocks, I researched relevant prior knowledge by visiting the Common Core Math standards progressions (http://math.arizona.edu/~ime/progressions/) and learned that in 6th grade students had worked with equivalent ratios in tables and in graphs. In 7th grade students investigated k as the constant of proportionality in the equation, table, and graph of y=kx, as well as looking at proportional and nonproportional situations. In 8th grade they will eventually find the growth between two ordered pairs. The first building block was  “in a tile pattern the number of tiles added from one figure to the next is the growth factor, or m in y=mx+b which is the vertical height of the slope triangle” and “in a tile pattern the number of tiles in Figure 0 is the parameter b in y=mx+b and when graphed the y-intercept.” We developed the success criteria in class that involved both of these ideas in each of the multiple representations. After that, I setup a coordinate plane with them on a whiteboard and asked them to graph a linear equation. This was my pre-assessment so I could see where and which students would need further guidance. The great aspect was the success criteria being on the board for students to reference, as well as the learning goals. They then worked in their composition books and posted a picture of their work on a blog post. I documented the development of the success criteria with students at (http://joyceh1.blogspot.com/2015/11/day-60-deciphering-cc-standard-table.html).


In Module 3.4 I added formative assessment strategies as part of the Eliciting Evidence section of the Feedback Loop. My strategies were whiteboard pre-assessment and a blog post summarizing their understanding. In Module 3.8 I watched videos to find evidence and application of five routines: activating prior knowledge, academic dialogue, questioning, observations and analysis of student work, and peer and self-assessment. In one video I liked how students used cards with terms on them to construct their own algebraic expressions to simplify rather than a worksheet of practice problems. They had ownership of the problem and their own learning in their small groups. The academic dialogue I saw was comparing and contrasting solving strategies. In my class I name a student’s method when it’s presented and students refer to it by that name. The teacher in the video used questioning to get students to analyze the complexities and simplicities of different strategies (critiquing the reasoning of others). A student tactfully critiqued another student’s graph with a question: “If the ball is at 0 height wouldn’t it be negative height when he dropped the ball? I applaud my students when I see them ask a question rather than say “that’s wrong!” This is also where I saw the clipboard with the class roster attached to the success criteria to help analyze students work in the moment. Finally, I saw self assessment when a teacher taught a mini lesson and had students assess as A, B, or C. C meant you could start your work independently, B was I have some clarifying questions, and A was I may need the mini lesson repeated. In module 3.15, I liked seeing a teacher use a graphic organizer to chunk out the creative process so students were not overwhelmed by the number of steps.


In module 4.3 I constructed building blocks for a new lesson on transformations. I elicited evidence when developing success criteria with students doing reciprocal teaching, pretending their partner was absent and explaining their thinking. I used a clipboard with success criteria to select 3 different students to address different learning goals. I sequenced the presentations by easier learning goal to most difficult. In module 4.4 I reflected on how my lesson addressed the Fundamentals of Learning: Making Meaning, Participating and Contributing, and Managing Learning. Building blocks help students work within their zone of proximal development and advance their learning forward. In module 4.10 I took notes on the seven “Deliberate Acts of Teaching:” modeling, prompting, questioning, giving feedback, telling, explaining, and directing. These reminded me of some of the Talk Moves I’ve implemented in my class.


Students were introduced to a learning goal and then developed success criteria by explaining to their elbow partner the requirements to accurately describe a specific transformation. After developing the success criteria, many students referred back to it during the lesson to help with their explanations. The clipboard I had with the success criteria on it allowed me to seek out who I wanted to present their thinking, and it helped direct my attention to the specific evidence I was looking for.


Students practiced peer assessment with post it notes during a Gallery Walk after a formative assessment lesson on Quadratic equations: http://joyceh1.blogspot.com/2016/03/day-112-estimation-exponents-fal.html


Students made video screencasts in partnerships after working through a Desmos Marbleslides activity to see how modifying parts of y=a(x-h)^2+k changed how the graph behaved.


In Module 5 I loved the Classroom Culture Inventory. I self-assessed on these aspects of my classroom: modeling of peer and self-assessment, establish norms, collaboratively creating learning goals & success criteria, model careful listening, reveal student thinking, model mistakes as a learning resource, act on descriptive feedback, and having students be responsible for their learning. I’m glad that I’ve seen evidence of all of these during the course of this year. I want to implement more self-assessment moving forward. I liked the suggestion to not make constant eye contact with the speaker and look at the whole room to encourage students to talk to the room, and not just to the teacher. Finally I went back to my self-assessment from Module 1 and was glad to see that I rated myself higher after completing the course.

My next steps are to print these checklists and inventories like Classroom Culture out and have them displayed near my desk or in a binder where I document how I am implementing these formative assessment insight strategies. I also want to reuse the building blocks I develop and add to them after teaching it again in the future. I’m so glad I took this course and have so many more tools and resources to use.

Monday, March 28, 2016

Spring break blog post.. Grades FAQ

After having discussions with students, parents, and teachers online, I've summarized my concept based grading system at the following page: Grading FAQ.

Saturday, March 26, 2016

Day 129: WODB Terms, Exponents & System of Exponentials

My colleague Mrs. Alibhai didn't have a substitute during my 1st period prep and I took the chance to do Mr. Stadel's File Cabinet task followed up with a very quick Graham Fletcher's Sugar Cubes volume task.

Two students shared the two most popular solving methods. Some students got the surface area of each face and divided it by the area of a post it. Others divided all the dimension by 3 to see how many post it notes wide and tall each face of the file cabinet was.

For the volume task, students estimated how many sugar cubes were in a box. Then they were given the answer. The Act 2 video showed the dimensions of the base. They figured out the height, the final missing dimension. I asked students how their work related to a formula. So, I stressed the connection between the division and substituting, multiplying, and then dividing.

The WODB I used all day long was from a Google slides I got from La Cucina Matematica and I can't give the author credit, let me know if you made it because I like it. It was a challenging one for some students.

The basic format of class was share out, review an power of a power problem with a coefficient to reinforce order of operations, as well as a problem where students were dividing power numbers with negative exponents.

It truly uncovered gaps in students understanding of adding and subtracting integers. Then students took their assessment with exponents, identifying functions, and the angle relationship vocabulary skill.

After the first go round 2nd period each class I singled out 27x^2 and asked what's the 2 called? (exponent) What's the x called? (base). Is 27 part of the base? There were mixed answers in every class. In one class I discussed it is the base of the exponent if there were parentheses around the 27 and the x.

The first class, like most classes, had trouble with the top left. I like how they said instead of only one with an exponent of 3, they said it's the only odd exponent, the rest are even. I liked seeing students use the words divisible, factor, and coefficient.
A common misconception was 45 was not divisible by 3. Many students were quick to say 15 times 3 is 45. So, I asked how we could build off that fact. So, they realized it was the only that had a factor of 5.
I modeled for students how to simplify 2y(4x^3)^2. On last week's assessment students mistakenly multiplied the coefficient by the coefficient in parentheses first. I said that this was not the order of operations because the exponents operation hadn't been used first.
Here is the dividing power numbers example problem. It uncovered a lot of weaknesses in integer operations. A majority of students are still not fluent with power numbers with negative exponents and how to write them as a power number with a positive exponent.

In 5th period I loved Moreen saying that the top left had the only coefficient that could be cube rooted and get a whole number as a result. They also noticed the coefficient of 45 could not be written as 3 to a power of a whole number.
I didn't take a picture of the board in accelerated, but I reviewed how to write an exponential equation from 2 coordinates. I modeled how we substituted the ordered pair into y=a*b^x for each coordinate, and then divide them by each other to make the a values become 1. Then they solved for b, and then substituted that into one of the equations to solve for a. Then substitute a and b into the standard exponential equation.
Here is a ratio problem I want to use in the future.
I want to use this visual pattern I found on Twitter. It looks interesting, especially question 3.

Thursday, March 24, 2016

Day 128: Triangle Sum Theorem & System of Inequalities

In anticipation of a discussion on triangles and the triangle sum theorem, I used this shapes WODB from Mary Bourassa:

In a majority of classes students pointed out the bottom right being a right triangle as well as the isosceles triangle in the top left. When students mentioned the obtuse triangle, I asked if there were any other shapes with obtuse angles? They realized the hexagon did so bottom left was the only shape with exactly 1 obtuse angle.
I asked students what we call the "pointy side" of a triangle. Some wanted to say vertices, which I told them was the plural for vertex.
One class said the top right was the only one with an even amount of sides.
More observations.
In the classwork, I gave students a few minutes to solve for the missing angle of a triangle. In 5th period I made the connection between showing an addition problem followed by a subtraction problem as showing work, and the 8th grade level of work of writing an equation, simplifying, and solving for x. It was a great comparison.

After 4 different volunteers shared the equations and the solving process, I explained that they had just proven the triangle sum theorem, and demonstrated the desmos feature where if you drag any of the three vertices the angles sum does not change.

Then students applied this skill to triangles with algebraic expressions as their angle measurements, where they had to solve for x and substitute it later to find the other angles. This will be on the assessment the week we get back from spring break.
Students rearranged 4 sets of 3 color coded duplicated triangles. They arranged them so that the 2 marked angles and the unknown angle lined up to form a straight line, or straight angle.

Kyle came in at lunch about yesterday's 100^1/2 problem. He rewrote it this way. I also asked him what 10 squared was and substituted it for 100 in parentheses. He saw how that was one of the methods to solve. He also noticed the patterns of 100 squared, 100 to the 1st, and 100 to the 0, with 100 to the 1/2 snuck in between.
In accelerated students did WODB with the linear equations in y=mx+b form. It had y=4x, y=-2x+4, y=3x-1, and y=x+7. Unfortunately I didn't take a picture. I like that Markos said y=x+7 didn't belong because if you add up the VISIBLE m and b values you get an odd number.

I did not photocopy the separate graphs of 2 inequalities to show how they overlapped unfortunately, but students graphed it in their composition books independently to start class and compared notes on how they shaded it. Then they practiced it with another graph. I showed them mine halfway through. Then they looked at how many regions there were when an inequality intersected a parabola. There were 5. Students had to test to see which region to shade. I think some started to see the pattern that greater than was above the line and less than was below the line.

Tomorrows assessment will have solving linear inequalities, interpreting and graphing their solutions.

Wednesday, March 23, 2016

Day 127: WODB, Exponent Mistakes & Linear Inequalities

I ran into science teacher Mr Coff who had a sex ed t shirt on sent to him by a company. I couldn't get over it.
Students had sex ed week.
Couldn't get over it.
Thanks Andrew Gael for the WODB:
One student mentioned that the top right is the only that when you square it you get the same number.

I like how students pointed out that the bottom right had white numbering, while the rest were black.
After reviewing a homework problem that reviewed all of the definitions from yesterday: corresponding, alternate interior, and same side interior angles. They had to write equations when given expressions and set them equal to each other when the angles were congruent.
We also discussed how to write a mixed number for a division problem with a remainder.
For class, I gave students 10 minutes of independent work time before presenting their solutions. I made a mistake in 3rd period and did not target which problems I wanted to focus on while 2nd and 4th period brought up the problems I was hoping and anticipating they would need practice on.
Jarren came up with this reasoning for exponent mistakes w/o my assistance.
Continuing to make that jump to seeing that no factors in the numerator left means there's a 1 in the numerator.
Justin and Joey explained the (-2)^3. It differed immensely from -6^2 's discussion. I wish we talked more about how there was a coefficient of -1 even though it wasn't entirely visible.
I like how Ella's explanation had a diagram.
In accelerated students worked on a fraction WODB that the other classes had already done. They graphed 4 inequalities independently and quietly and focused. Then they applied inequalities to real life situations regarding poverty and the U.N.
My dad helped me hang my tv on the wall the complete the day.

Tuesday, March 22, 2016

Day 126: WODB Linear Functions, Angles & Linear Inequalities

Today's WODB for all classes was the following linear functions:

For some reason, many students in multiple classes said that the bottom right graph was the only one with "negative association." I replied that a scatterplot that had points going down was negative association. They eventually came up with negative slope.
I also prompted students to add on to thoughts of the top right being the only one that passes through the origin (0,0). I liked when students mentioned bottom left was the only one with a negative y-intercept.
This class found that the top left was the only one with a negative x intercept. We also discussed what was true about what was visible which had to be added to some observations. For example. the bottom left was the only one that intersected only one axis.
In each class we came up with conjectures for corresponding, alternate interior, and same side interior angles. I stressed that interior comes from being in between the parallel lines.

More conjectures again.
Then students used the conjectures to find angles by writing and solving equations. This proved to be quite challenging for them. Some moved on to identifying if angles were corresponding, alternate interior, same side, straight, or none of these.

In accelerated we reviewed two of the homework problems first. I targeted one where you had to divide by a negative on both sides which then reversed the direction of the inequality sign. We had not covered that last year. To demonstrate this I had students write 12 and 8 with and ask which inequality symbol should I put between them. They said greater than. Then I divided both sides by -2, and they said ahh.. they saw that the inequality couldn't face the same direction anymore. I should have demonstrated with a positive number as well to show it didn't change the direction because students asked about that later.

For students who were still new to it, I wrote "when you multiply or divide by a negative on both sides of an inequality, the direction of the sign reverses."



In the classwork, students tested whether coordinates were on the line of the equation y=-2x+3 graphically as well as algebraically by using the equation. This lead right in to me passing out green sticker dots and 8 coordinate pairs for students to test if they were solutions. The results were awesome. We had 2 misplaced points that students pointed out. Grace saw that the equation of the line was the "boundary point" and that everything to the right was a possible solution. They said there were infinite solutions. The class discussion was focused and productive.

Then students moved on to a graph in the book that was shaded on the other side of the line. They were asked what inequality this represents. Students reasoned it was the same inequality, except the direction of the inequality was reversed. Then they were asked to reason about what would you do to the graph to make it y<2x+3. This was great. Jason came up with it must be a hollow or invisible line like on the number line. Then he reasoned that it must be a dashed line. He earned a 3 second clap from the class for coming up with it, knowing he had not known that prior to today. I pointed out to one group that that was what the textbook philosophy is about, build the understanding yourself on your intuition and thinking.

There wasn't time to practice the 4 practice problems, but we will jump right into that tomorrow, then start 9.3.1, applying linear inequalities to real life world problems.

Always a good result when students are empowered to get out of their seat to contribute to a graph.
What a great activity. I reused my algebra walk laminated posters from earlier in the year and drew the boundary line on there. I asked students what we should do to signify all points to the right were solutions. They said shade it, so I did with the expo marker.

Monday, March 21, 2016

Day 125: WODB Probability / Angles & Alg tiles inequalities

I titled today's WODB "Probability." I reminded students that they had prior experience in 7th grade with spinners and using a paperclip and a pencil to do experimental probability. Here is what students reasoned about, thanks to Chris Hunter coincidentally for both of them, this and the algebra tile one for Algebra I:
Plenty of conversations await.

I like that 2nd period noticed the bottom left was only one where the probability of green was greater than 0 and less than 1/4. It didn't work if it was just less than 1/4 because top right had no green.
I like top left that probability of orange is less than 25 percent.
This class mentioned how the bottom left was the only one that has the smallest and largest angles.
I like bottom left: only one where P(purple) is less than 25%. The standard bottom right of blue being only one without a 1/4 or 25% chance.
To start class I wanted to review and activate students background knowledge with 3 warmup problems:


  1. Review what a right angle looked like, and solve for a missing angle. I challenged students to write an equation if they could. Also complete the sentence <x and 18 degrees are complementary angles.
  2. Given 135 degrees and a straight angle, solve for missing angle y and complete the relationship sentence. They are supplementary angles.
  3. Given one angle degree, 93 degrees, and a missing angle, identify they are vertical angles and congruent.
I asked students if they knew a way to remember complementary and supplementary. I mentioned that complementary has 1 p, and if you reflect p over the y-axis you get 9, or 90 degrees. Supplementary has 2 p's, so write 2 p's, reflect it, and you get 99, or 90+90. I'm not sure if this falls into the #nixthetrix category or not, let me know. I also pointed out that complimenting someone's hair is spelled differently then a complementary angle (sums to 90).

Then students investigated tracing paper and different angles such as corresponding. Tomorrow we will introduce alternate interior, same side interior, and corresponding. I'm thinking of doing a color coding activity with it tomorrow, because the names can get confusing when they are brand new. Students come up with conjectures on when they are congruent or sum to 180 (same side interior).




In accelerated students chewed on this Which one doesn't belong? It was totally awesome.
Prepare for some vocabulary and factoring!
I love that the top left is the only one that was a perfect square trinomial. A student first said that it was only one that can be written as (x+2)^2. I asked students to add on and they identified the type of trinomial. Since students were completing the square on the assessment, I took the opportunity to reiterate that in x^2+4x+4 the c or third term, is the middle term divided by 2 and then squared. I should have made the connection that the b/2 is represented by the 2 inside the parentheses.

Also, I may have had the image zoomed in but a student claimed the top left tile was an xy tile. He wanted to measure it, so I invited him to and he was correct. It was 20 by 21 cm on the SMARTBoard. I don't know if this is true or just the way the image was zoomed in.

To confirm the a, b, and c values were all even for the bottom right, I asked N to tell us the equations for each corner because he must have written them down when he was analyzing them. They also found top left was the only one with less than 5 x tiles.

Is there only 1 for bottom left? Bottom left is only one with more than 4 unit tiles?

Oh I forgot, I absolutely love the statement for top right: it's the only one where (x+2) is not a factor. Someone also added that when add a b and c, you do not get a number divisible by 3. I don't know how that student found that!
The bottom right was only with more than 5 x tiles. Nicholas earned a 3 second clap when you said bottom right was "only one where a, b, and c in ax^2+bx+c are all even numbers.
During class students practiced solving linear inequalities and interpreting the solutions as well as graphing the solutions. One had no solution, infinite solution, so those were new. Also, the homework tonight has an inequality where you divide by a negative on both sides, so I want to have a student discuss that tomorrow and show a little experiment where you multiply both sides of an inequality, add, multiply by a negative, and then divide by a negative to stress how the direction of the inequality sign switches in those instances.

Students solved a system of equations, and then an inequality about a tree that had to be at least a certain height and no more than a height.

Davin explaining each of his solution methods.

Davin demonstrated how if you have 4 times as many Turks as Kurds, and a total of 66 million residents in the country of Turkey, how many of each? He showed a system of equations elimination as well as Kramer's rule that he had learned on his own. It was a great review for me!

We are going to read the problem and Jeffrey is going to introduce his solution method that we didn't have time to go over here.

Sunday, March 20, 2016

Day 124: Identifying functions & Solving & Graphing Inequalities

Today's WODB from Erick Lee provided plenty of great discussion points periods 2 through 5:
I wanted to see how students used the academic language of fractions when describing which one did not belong. In one class we almost went too long with it, so I think I'm going to have to try to set a timer for it if I want to keep it as the warmup.
Most students mentioned that 5/3 was an improper fraction, and I mentioned that improper makes it sound like there's something wrong with it. I emphasized that there's nothing wrong with it, it actually can make it easier to work with at times. 
 I asked students what exactly is an improper fraction? Some said the numerator is larger than the denominator. So I asked them that all improper fractions are greater than what number? 1.

I liked that they said 2/10 is only one not in simplest form. I reminded students that that means it can't be reduced to an equivalent fraction. I love that a student noticed 2/5 is the only whose reciprocal can be written as a mixed number. Seeing them test their ideas before sharing them was great to see.

Students took notes last week on identifying functions represented as tables and graphs. I introduced vertical line test last Friday. Since it was 2 day lesson, and I wanted students to practice more interpreting, we used the pre-Common Core Algebra 1 textbooks. I got the idea from Ms. Demailly because she had assigned HW out of it. By the way I'd be open to suggestions on how else to introduce and reinforce this concept.
For accelerated, we discussed these parabolas WODB (thanks Mary Bourassa and WODB.ca):

I liked that students noticed the top left was the only one with a line of symmetry on the y-axis and a positive and negative x intercept. One student noticed bottom right stops because it has no arrows. His peer built off that idea and said that because of that it will never have a y-intercept. The one thought I added to "only one with its vertex on the x axis" was it was the only one with an odd number of x-intercepts. I also like how when a student mentioned bottom left was only one that opens up, another student added it therefore it is the only one that has a minimum.
Before students started the class work, I asked them how to graph x>1 and x<=-3. They thought about it, then students told me to make a number line, make a boundary point that was open on 1, arrow right for x>1. I also reminded I wanted 1 number to the left and right of the boundary point labeled. So, for x<=-3 they said put -4,-3,-2, and a closed boundary point on -3, arrow shaded left.

They practiced reading number line graphs, solving 2 step linear inequalities.

overall, great ending to the week.