Free Resources for Math Teachers?

If you are familiar with TES.com and "Tarisa" get in touch and leave a comment below, not really sure what to do with this-was told to download files...

https://www.tes.com/

http://www.mmlsoft.com/index.php/downloads

https://mrnussbaum.com/math

Blogger vs. Wattpad

At what point is becoming a blogger just a matter of self-publication. Are you not a published author if you are a blogger?

I am working on a personal understanding of  enough is enough. If I haven't gotten published by a renowned company or press yet-will I ever? I have three more big ideas to put on paper before I find out for certain. these three big ideas are by far innovative and hopefully as wonderful as I hope they are.

The writing process of blogging is so much different than that of creative writing. What if, the line were blurred-thus "Wattpad". I am working on my travelling teacher (A teacher memoir) that obviously won't be finished until I have reached my goal of becoming a principal-even then, I may still continue to write just to show what I had done to get that far. 

Putting it all together-I am hoping to wrap it all nicely and fit it onto teacherspayteachers to help build up my digital footprint and online portfolio for future applications to school boards.

Now I am finding myself circling around in a manner of speaking, not repeating but sprreading my ideas all over (in Chinese, a person who spreads things out a long the street, a vendor, is called a "Bai Tan'Er" and my wife loves calling me this for the reason that I physically do this with my personal items at home-ALL THE TIME).

May be in a creative writing course, this is a notable process "Blog, Plot, Write." and if so-I think this may be one of my most innovative portfolio projects in class yet.

Looking forward to the end of these projects-but hot damn I enjoy seeing whats created in the end!

Vice Videos For Students and Teachers!

Changing Your World!

https://video.vice.com/en_us/video/vice-lgbt-trans-student-brought-gender-neutral-bathrooms-to-his-high-school/5a3837eb177dd437a11bef33

Toxic Tourism

https://video.vice.com/en_us/video/toxic-tourism-in-california39s-imperial-valley/5637cd24d140e599358eddab

Garbage Island/Sustainability

https://video.vice.com/en_us/video/garbage-island/563b9c912aab5c416bc75039

"The Learning Teacher"

https://heidiallum.wordpress.com/2018/04/08/from-patterns-to-algebra-the-genius-of-dr-beatty-and-dr-bruce/

This looks useful!

http://passyworldofmathematics.com/balance-beam-equations/

http://www.visualpatterns.org/

another couple shared resource form my AG Prof.

Check it future math teachers!

Effective Feedback

Can grades inhibit learning? In what ways have these resources affected your ideas about the role of feedback in math learning?

Discussion Post: 

Teachers used to feel compelled to mark copious amounts of student work and tests, and to “crunch numbers” to determine percentage marks. We now do much more assessment that is intended to inform our teaching in a manner that is responsive to our students’ learning needs. An important part of responsive teaching is feedback (self, peer, and teacher) that promotes learning.

1) Assess your own feedback practices by completing “My Feedback Practices”:

. Do not post your questionnaire – it is for your own reflection.

2) Based on your assessment of your own feedback practices and other learning in this module, set a SMART goal for improvement in your math feedback practices. Share your goal as your Discussion post.

I'll save my questionaire answers for myself but I will post a link to the PDF used: 

2) My feedback practices are sound and complete. Like everything else there is room for improvement most in the "Using Feedback to further learning" learning section. Right now, my last few years of teaching has been in a volatile department. No year is ever the same. The curriculum is the same but the expectations of the teacher are always changing to become more standardized. I have always been resilient but  still needing to change the materials I develop to meet the required amount of assessments. Funny fact: Some teachers and admin get upset with my findings after my AQ's because I raise too many questions about the system-no one wants to take the time to due their due diligence or pay the right people to get the job done. Nonetheless, my feedback practices do not reflect further teaching, the system I am currently working under now follows a strict timeline and expectation for teaching content and assessments. I spoke about this in my "Diagnostic Assessment" post, but I know I can do it. my SMART goal is below to improve my habits in regards to effective feedback:

S-I will develop a unit in Algebra that aims to meet the needs of BOTH 7/8 student Linear Equation Strand expectations

M-Each lesson regard concepts or instruction should reflect student diagnostic activities to enhance or further learned skills/knowledge

A-This goal should be achieved by the end of the Math AQ course that I am taking now. I'll know I have completed my goal once it  has been tried and tested by peers or myself.

R-This is a realistic goal because of the fact that have created a lesson plan,a unit plan, a full unit before

T-This should take about a month to complete.

I also believe I could improve the ways I am getting students to reflect on their own learning. The BC curriculum that is being implemented is currently moving into a model that does this more. Using the ideas of the K/U;T;A;C model in Ontario. Instead of assigning them marks for these things, students are awarded personal merits. They have called these the "Core Competencies". I have developed a lot of resources in regards to this and I'll add some to give you examples of what I am working on. Like in Ontario, we are asked to write lesson goals on the board. We are a heavy paper based school and I have been working to make classroom management more effective for incoming teachers as well as returning teachers are in heavy content classes. The reflection process has proven very effective for students but needs to be fostered in the correct environment.

Complimentary resources to help foster growth mindsets through feedback!

http://thelearningexchange.ca/who-makes-the-biggest-impact/

http://thelearningexchange.ca/videos/feedback-and-mindset/

Meeting "Needs" in Math

A responsive learning environment “responds” to the needs of the learner.  Of everything that you have explored in this module, what is one aspect of the math learning environment that struck you as particularly important for adolescents in Grades 7 and 8? To clarify, what is crucial for students of this age in particular? Explain.

I think the most important part of learning math in a classroom-or learning environment in general is recognition. As viewed in the First Nations section of this module, there is a framework and principles of First Nations learning that takes place in a classroom. I spoke earlier about the 4th principle-Wisdom. Taking a look at that list overall is speaking to the importance of the recognition I am talking about.

When a teacher completes and IEP for a student, it is not just simply a washing of hands and responsibilities. It is a form of acknowledgement by the teacher that there are some further tasks we need to complete to ensure that this student is receiving the attention and support needed in order to say they had a fair shot at being the best they can/could be. 

Marion Small's thoughts on the BIG IDEAS are not to better categorize and or assist in the circulation of mathematics for teachers in particular, her work in the field of education is aimed at ensuring that all students (regardless of incoming mathematical skills), have a fair and equal opportunity at making the most out of a subject that they can. As much as the BIG Ideas are for the teachers, the benefits of using these ideas spill over for students to reap as well.

If needs can be identified, (no matter to the extent of which are needed) a teacher can inspire a student to do there best. Sometimes, students who try their best may not succeed or excel like others-but on an individual plane-its the best. For these students, their best is the most important thing. The next level for some of these students might be that they caught up with materials or simply, excel. Regardless, everyone needs recognition. This is something I reflect on a lot coming from an ESL teaching background.

"Diagnostic Assessments" in Math

This image resonates with me because of the fact that it requires teachers and students to realize that, 'This is where I start." Even if the student struggles to see where they NEED to arrive, having them develop that recognition of the next step is the teachers task, not just helping students get to the next spot-but knowing what the next spot is.

This image/list of accommodations resonates with me the most because of an experience I had mentioned in an earlier post in which my teachers in elementary school for negligent to provide us with, assisted learner tools (manipulatives). We were not entirely denied these tools but were certainly expected to be able to mentally comprehend the math at a very early stage of the learning process.

Generic Rubrics are something that I feel can be reflective of accessible learning as well. As an English teacher, these are useful tools for assessing For and Of learning. I like to use Checkrubrics for assessment for learning. the English Curriculum of Grades 9-12 has some excellent examples of Checkrubrics and T/I;A;U;C rubrics for different types of writing. 

The growing success documents are exceptionally good at introducing the different parts of assessment because of the constant myths of assessment. "The more work, the better its understood," to an extent, one could apply the 10,000 hours till expertise philosophy, but the reality is-NO student is spending 10,000 hours on one task in one class. This means teachers need to find an alternative mode of assessment. In China (where I am teaching now), parents get physically upset when their children are not sent home with homework or even homework for the holidays-granted most of the parents are never home, but still-what is the purpose of the homework if the student doesn't understand it in the first place OR understands it well. 

In my opinion, homework is dead-its a vehicle of information to the parents/guardians letting them know what is happening the classroom with their child. I feel homework is not a form of assessment-especially in English because their is no way to really know it was that student's work. 

Teachers are sometimes looking for ways to build marks of students-well lets mark that homework, there are two things wrong with the way this is being handled in my opinion. 1) My earlier point about homework not being used properly, and 2) Teachers are missing the fact that the number of assessments SHOULD NOT be the focus of evaluations, but the number of authentic assessments-see earlier point about English teacher's homework worries.

At this age, (I have touched on a lot) I think its most important that students get feedback and guidance. Homework as take home tasks for support from guardians is important-but not as an assessment or evaluation. Rubrics are great for providing feedback and "next steps". I think at the 7th and 8th grade levels. This is the most important time for students to be exposed to rubrics in all subjects, not math. A teacher provides good feedback, but if a student can understand how to reflect on that feedback before high school (seeing where they stand on a rubric versus where their goal is to be-ZPD), that student will be extremely successful. What I could summarize with is, assessment of learning is most important for students at the 7th and 8th grade levels at this point. Two rubrics I designed that I'll be adding into my final project are attached. 

First Nations Learning Perspectives

Updated/Revised: 2021

https://toronto.ctvnews.ca/ontario-school-board-regrets-burning-books-in-the-name-of-reconciliation-as-part-of-educational-program-1.5580647 

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https://sites.google.com/teltgafe.com/indigenouslearnersinmath/home

https://thelearningexchange.ca/videos/lisa-lunney-borden-integration-of-culture-in-the-classroom/?pcat=&psess=&ptit=Leaders%20in%20Mathematical%20Thinking&ps=leaders-in-mathematical-thinking

In the New BC curriculum, the classrooms were told to incorporate more aspects of First Nations Student Learning. I think personally, we have had that all along, it really comes down to the teaching styles I talked about in a previous post. I was mentioning that there were four types of teaching styles. There is the expert, the "Cool" teacher, etc. Well, while reading through the "Integrating Aboriginal Teaching and Values in the Classroom", I noticed that the fourth value/teaching principle is "Wisdom" and originally I was going to scan over that until I had my attention caught by the ideas of group talk and "humour" in the classroom. If a person has ever lived on a reserve or lived with anyone of a first nations background, you learn quickly that they have one of the most rough, yet loving sense of humors out there. Rough in regards to the material (sometimes a bit racy or unconventional), but always friendly and loving in the delivery of a good joke or tease. It is very much similar to how my Dad had brought me up, "helps ya develop a bit of a thick skin," cause ya, the world is a tough place at times and you need to know that sometimes we need to have humility (teaching number 5). With that understanding, people can become wiser, stronger, etc.

The group talk is the area in which I would like to specifically add into simple and regular textbook work. Creating small groups I would like to see something like that of the lesson plan I will have added into the end of the post.

Essentially, the class will be split up into groups and given exercises 1-2; 4-7; etc. at which point, they will need to work together with chart papers and each other to solve. Each group will be formed into a larger circle in which each group needs to solve their questions and when finished, move to another group to help them; OR have another group come help them first. the idea is that the students are given questions of increasing difficulty based on skill level, grit, etc. (as the teacher designates as fit). Students with the beginning level questions will most likely have visitors coming by to see how the base of the concepts were solved and then move around the circle until it gets to their set of questions. As a community (in a perfect learning environment), the students would have completed the conceptualisation of a new mathematical feat as a learning community-growing from one to other; scaffolding from one to the other.

Final Reflection/Thoughts on Teaching Mathematics as an English Teacher

I feel mathematics is a subject area with no real "free" support online unless you are working through tutorial sites and what not. This is certainly a subject area I feel teachers are not appropriately supported in because of the lack of willingness to exchange free resources (especially after being a teacher looking for resources). I feel there is something to be said for the people who develop resources in mathematics and hand them out, but ya-its not a wonder why teachers struggle to support mathematics for students in classrooms at times. I feel that the struggle is real and that I really learned a lot in this course in regards to creating, adapting, connecting resources. Even representing ideas from the way I see/understand it and putting it into a platform or format that students can access it.

I must say the biggest test in my readiness for teaching Mathematics would need to be the final project we needed to complete in which we needed to explain and share resources collected that ANY teacher could walk into a class and use with no prior knowledge or experience in mathematics. Funny how in British Columbia, this is generally how most Math gets taught (well if not on the mainland-for sure at the offshore schools when there are not enough teachers to go around). Nonetheless, I am looking forward to expanding my horizons and opportunities to teach things in the classroom I may not ever have expected to have taught before.

From the course, the general guidance of the professor and her positive feedback as well as “pizza project“ book that she had shared with me (I forgot to add that into my resource folder) but that was an exceptional read and would highly recommend it as well as taking this course and just reviewing module 1&2 carefully again. That was the biggest eye opening part of me-just the pedagogy of mathematics, very inspiring stuff.

A final not to all or any who are reading through. Good luck out there, it’s strange at times and tough a lot of the time when learning something new this late in the game that you might even have students who are stronger at tasks with that you. I’d also like to recommend taking the split class or a regular one any day-the possibilities for the enriched learning for the 7’s, that would have saved a colleague a lot of headache down the road. It also feels great when students say “ Oh, we learned that with .... last year!”

I get that in my English classes with a few teachers, best feeling!

One thing added to this post that I was not going to add until I saw it worthwhile (I certainly see it worthwhile now) was two questions we needed to ask about the course/concepts learned to the professor,

1) How do students best make the jump from concrete understandings and applications to more theory and thought based concepts?


A: I see moving from concrete to abstract as "fading" instead of a "jump".  The symbolic/abstract is only meaningful if students have truly conceptualized, and concrete and visual understanding is key in getting there.  Cycling back to the concrete for every new layer of a concept is important (e.g., when learning operations with fractions, for example).  That is why I love the Tap into Teen Minds resources about "concreteness fading" and the "progression" resources such as the "Progression of Fractions".


2) would it be reasonable to expect a grade 8 students could learn grade 9 linear functions, substitutions/factoring and graphing instead of just moving to an equation with more than e unknown variable?


A: As for your second question, I can barely get my 8s through the important aspects of the P&A curriculum by the end of the year according to my Board's Scope and Sequence document.  We certainly get into graphing in grade 7 and 8 and I go into point of intersection of two rules when we get into solving equations later in the year.

Language Enhancement Strategies Through Unconventional Means

Readathons in class

Book Reviews (NOT REPORTS)

Banned Book Reviews

Historical Documents/Artifacts (Show and Tell)

Book Displays/Study Notes

Book Talk/Cafes

LGBTA Awareness Actvities

Charity Events

Gallery Walks

ESL Tutorials/Book Buddy systems (Hosted by students)

Poetry/Short Story Contests (NOT ASSESSMENTS)

Teaching Algebra with Manipulative Pieces

To begin, I am working on an elaborate collection of resources for teaching Algebra to Grade 7 and 8 students, i have a post discussing this already-however what I found exceptionally interesting is this package located at this URL

https://www.saultschools.org/cms/lib/MI17000143/Centricity/Domain/137/a2tam.pdf

it contains printable sheets that can be utilized as manipulative pieces just as tangible pieces could as well. It is interesting to see the substitution tiles. Chapters specifically looked at are also quite useful for class teaching strategies/using manipulative pieces (for example, looking at Chapter 3 "Solving equations").

I am currently diving into the commonsense/org lesson plans and checking out how they are utilizing manipulative pieces to teach Linear Equations in grade 7.

 https://www.commonsense.org/education/lesson-plans/solving-linear-equations-using-manipulatives

Excellently laid out and described lesson plans.

I'll be posting again with resources I am sure!

Open and Parallel Tasks for Grade 7 and 8 Students

The discussion today is open and parallel tasks, specifically I will be using the example of "Pepperoni on a Pizza" to discuss the ideas of open and parallel tasks for a grade 7 class; and "number of rocks in the elementary class's playground" as an example of open/parallel tasking in a grade 8 class.

Grade 7 "Pepperoni on a Pizza"
Marion Small's Big Idea: Number and Operations, "Numbers Tell How Much or How Many"

Open Question: "How many pepperoni are on a pizza? (personal size 12"/30cm)

Parallel Task:
Task A- "Decide on a number of how many pepperonis might be on an extra large pizza (16"/40cm), then create a formula that can show tell people how many pepperonis are on ANY size pizza"
Task B- "What is a fraction that best describes the Pepperoni to Cheese ratio?"

Rationale:

Students are interested in this idea because of a couple reasons, one might be that they get pizza afterwards (hint, hint); whereas another being that maybe its just not something they ever really thought about. While all students are specifically focused on the number of pepperoni-there is a task B that is mean't to be more difficult because it is relying on the use of fractions. To fathom the task itself the students are expected to step back and break the pizza up into a fraction/slices, afterwards decide what an appropriate fraction might be that represents the number of pepperoni on the pizza; divide that between the number of slices and then relate the number of pizza slices with more cheese than pepperoni on them. This is also a great opportunity to get students started with manipulatives as it is a bit of a broader idea.

Grade 8 "Number of Pebbles on the Playground"
Marion Small's Big Idea: Number and Operations, "There are many equivalent representations for a number or numerical relationship. Each relationship may emphasize something different about the number or relationship."

Open Question:"What is the weight of a single pebble?"

Parallel Task:
Task A- "What do you think the number of pebbles on the playground is?"
Task B-Devise a way of measuring the number of pebbles in the on the playground as efficiently as possible.

Rationale:

Students are working on data management; measurement as well as number sense and numeration depending on the relationships between size and volume. The students will most likely have difficulties when try to fathom a task like counting those stones and then creating a formula to show its possible growth based on the size of the playground.

I came up with these ideas while I was reading through Marion Smalls and ___ text, "More Good Questions: How to Differentiate Secondary Mathematics Instruction". I was reading through, trying to really grasp and understand the purpose as well as meaning of the open/parallel questions. Having the examples really made it applicable for me.

More information:

http://www.teachertoteacher.com/newsletter-archive/jan2010-newsletter.html

BC's Core Competencies-FINALLY UNPACKED!

http://learningcommons62.sd62.bc.ca/information-centre/digital-text-books/core-competencies/

Analysis of a 3-Part Math Lesson

In our course we came across this excellent example of planning lessons to help intermediate students succeed in class, socially and individually.

Check it out here-->

http://www.edugains.ca/newsite/math/supporting_classroom_practices.html

We are keeping in mind Marion Small's following BIG ideas.

 Measurement Big Ideas (Marian Small):

     - A measurement is a comparison of the size of one object with the size of another.

     - The same object can be described by using different measurements.

     - The numerical value attached to a measurement is relative to the measurement unit.

    - Units of different sizes and tools of different types allow us to measure with different levels of precision.

     - The use of standard measurement units simplifies communication about the size of objects.

     - Knowledge of the size of benchmarks assists in measuring.

     - Measurement formulas allow us to rely on measurements that are simpler to access to calculate measurements that are more complicated to access

Questions

1) Let's look at the expectations and big ideas for this lesson.

    a) What are the grade 9 expectations for this lesson?  

    b) Which grade 7 and 8 expectations would support the learning in this grade 9 lesson?  To clarify, which expectations in grades 7 and 8 would be foundational for this lesson? 

    c) Which of Marian Small’s “big ideas” for measurement would encompass the learning in this lesson?

2) Identify learning goal(s) for this Grade 9, 3-Part lesson and list possible success criteria.

3) What was the format of the consolidation for this lesson?  What does consolidation do for the learning in this case?

4) What role does student voice play in the learning for this lesson?

5) Group problem solving can look like organized chaos. 

    a) What classroom management strategies are shown? List all strategies that you observed during this lesson.  

    b) Choose one classroom management strategy from the lesson.  Explain its use and effectiveness. 

    c) What other management strategy would you try for this lesson or has worked for you during group problem solving situations?

Success Criteria

• I have thoroughly analysed a 3-Part lesson.
• I showed my understanding of module content (e.g., big ideas, learning continuum, learning goals and success criteria, 3-Part Lesson, etc.).
• My assignment is organized.  My communication expresses my understanding and analysis clearly.

_________________________________________________________________________________

In our online course we are asked to break down and discuss a grade nine math class as shown in the "Teaching Through Problem Solving" link on this page shown above.

Write-Up;

The Grade 9 expectations of the Academic level that would be reached are in the Overall Expectation of "Determine through investigation, the optimal values of various measurements"; as well as "solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures" from the Measurement and Geometry Strand; Specifically the expectations being completed/achieved are the following:
-determine the maximum area of a rectangle with a given perimeter by constructing a variety of rectangles, using a variety of tools (e.g., geoboards, graph paper, toothpicks, a pre-made dynamic geometry sketch), and by examining various values of the area as the side lengths change and the perimeter remains constant
-explain the significance of optimal area, surface area, or volume in various applications (e.g., the minimum amount of packaging material; the relationship between surface area and heat loss);

NOTE: I believe actually, the Curriculum document's overall expectation of ""solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures" is completed to an extent, but not the specific extent to which the curriculum is actually asking for. In particular the specific expectation seems to be asking for this to be accomplished with irregular shapes as it prepares students for trigonometry and trig functions. So, although in regards to semantics, the expectation is met "overall", its not met specifically.

This understanding has grown from grade 7 and 8 curriculum foundations built in elementary school through the Math curriculum. In Grade 7,the overall expectation that will eventually lead to the growth of a student's understanding in surface area may be "determine the relationships among units and measurable attributes, including the area of a trapezoid and the volume of a right prism." Specifically, Measurement Relationships  in which ;"solve problems that require conversion between metric units of area (i.e., square centimetres, square metres) (Sample problem: What is the ratio of the number of square metres to the number of square centimetres for a given area? Use this ratio to convert 6.25 m2 to square centimetres.)"; and "solve problems involving the estimation and calculation of the area of a trapezoid".

These previous lessons from Grade 7 Mathematics are some of the first examples of exposure to measurements on a 3-dimensional shape to which students are deducing an understanding. The relationships that students develop at this level are crucial because if they are unable to make the connections of a relatively uncommon whole shape such as a trapezoid, to that of a more common whole shape like a square or rectangle, than the student will be trying to develop that relational understanding at a time where they are supposed to be further developing that understanding. I was a student who had "fallen between the cracks" of mathematics when I was going through school and to no fault of mine or my teachers, I just was never really encouraged or had teachers that they themselves were confident in their mathematical skill level enough to try "something different" for students who just were mathematically delayed at particular stages. The hardest part was getting to Grade 10, I was in Grade 9 applied Math and my teacher requested my parents move me to academic grade 10 instead. Big mistake because there was such a disconnect between what the teacher allowed us to learn with in applied grade nine to that of which was expected of us in grade 10 academic. Until the lat three or four years had I actually decided to go back, study and redetermine the importance of mathematics in my life. I am glad I did. Sorry for the personal narrative.

Furthermore in Grade 8, Overall although students are not looking at a cylinder, cone or pyramid in this particular example (grade 9 classroom example), the students who have completed the act of finding the necessary information to complete the task as instructed for a particularly sized object; meaning that it is correct to say that the overall expectation in which students will be able to/will have "determine the relationships among units and measurable attributes, including the area of a circle and the volume of a cylinder". The students would have certainly relied on the experience gained from the completion of the overall expectation, "research, describe, and report on applications of volume and capacity measurement;" because in order to do the research and reporting, students would have worked together and also communicated with not just classmates they are working with but the rest of the class who observes their work. Specifically, students who have succeed in "research, describe, and report on applications of volume and capacity measurement; determine, through investigation using a variety of tools and strategies;" Students in the video were able to use charts, and manipulatives to describe and understand the question that the teacher had posed to the class in the beginning. Along with the idea of investigation in general, it was noticed that a student was able to take the idea of the surface areas of all the cubes and utilize the fact that although the cubes together made a large surface area; could it be that the shape changes to maximize the "SA"? This thinking that the student exemplifies could be argued as nourished in his past experiences of completing the specific expectation of, "the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula (i.e., Volume = area of base x height)". Realistically, the skills that students are applying to the specific expectations are related to the growth of their particular understandings of tasks they they will face in the future, for example teachers can note that within the following expectation students are utilizing the problem solving skills (math process) to "determine, through investigation using concrete materials, the surface area of a cylinder; solve problems involving the surface area and the volume of cylinders, using a variety of strategies." Students who completed "solve problems involving the estimation and calculation of the circumference and the area of a circle" will have found the experiences helpful because of the simple acquirement of skills needed to estimate and hypothesize in the creation of numbers to manipulate.

From this longitudinal  perspective its recognized that Marion Small's BIG ideas to which teachers can apply to this particular lesson is, "The same object can be described by using different measurements." as well as "Measurement formulas allow us to rely on measurements that are simpler to access to calculate measurements that are more complicated to access". These BIG ideas of Marion Small are represented in this particular lesson through the investigation that the students participate in when determining the Surface area of the Cube. The apprehension of ideas through individual manipulation of numbers is important to note as well. The teacher in the lesson specifically mentions that regardless of the numbers of cubes used, there could be a connection to the overall optimization. He encourages students to manipulate the numbers that he originally shares with the students. Through the success of specific students, the class becomes successful when sharing ideas at the front of the class. These are the two BIG ideas that best resonate with me in regards to this lesson. 

The learning goals of this lesson as I might described them to my students are:

1. Expressing mathematical ideas in different ways
2. Measuring the maximum area of an object with some similar size sides and some different size faces

The role of consolidation in the lesson as presented, is done in a number of ways. The Lesson consolidation is done through the designing of chart with findings after the experimentation and exploration process. Students as a group are to go to the front of the class and present findings along with methods of process. Choosing only a select few is a productive method for the teacher's lesson and student's time, however it does send a negative message to the groups who were not able to present. If there are ways of consolidating through more accessible means to all students with a given amount of time (much like how we do in the ABQ through discussion posting), this may assist in a stronger consolidation for students. This idea of more time on "accessible" consolidations, could also factor into differentiation of student learning in which students who are ahead can continue ahead while the teacher reviews with specific students who need it.

The role of the student voice in this lesson is layered. The students are communicating which is not only a Math Process as discussed by the ministry as an essential tool; but also a skill utilized to consolidate the learning that has occurred in the class. The students who are able to use their voice have participated and represent the more vocal and confident side of the class. As noticed in the video, there are students who are not documenting the process or discussion, it is sometimes the voice that can also motivate students to share their ideas in order to avoid the act of writing when tired or not interested enough to invest in the written documentation aspect of the lesson. For the teacher the role of the student voice is also to assist the students within a group support each other.

Classroom management strategies that were used by the classroom teacher are the use of an "Exit Ticket"; "Gallery Walk"; "Think Pair Share"; to which I believe that the most effective one used was the Exit Ticket. In my opinion the Chart Paper was an exit ticket for the group. This was effective because the students are most likely eager to share their ideas on the paper, this way the teacher and students can see their work on display which also signals that "Hey, I did this too!" The chart paper is an accumulation of the groups ideas (in most cases) and this is also important because if there are students in groups who are unsure of what is happening in the class, it is a good time for them to sit back and observe. It might actually be a stronger tool if the students were given a checklist of things that thy need to do to succeed in this lesson. for example, if the classroom teacher had given a page that has a series of "I statements" where students can check as "completed" and "not yet" Checkrubric; the teacher list some of the following things,

1. I have shared an idea; Write idea shared below
2. I have written something on the chart paper; Write your contribution below
3. I have Participated in the presentation of our data and experience to someone else
4. I have asked a question to our group members to see if they understand
5. I have asked a group member if my understanding of the topic is correct

 However for this lesson I think I much rather would have done a bit of a "Socrative Circle", in which two groups are working together, to prod for questions to possible answers. Instead of just speaking and sharing (which some students did not do because there could only be one speaker at a time), they would be expected to think about what they could ask to get a complete and clear answer from another "visiting" group. This could even be done and different groups could be given different shapes? Different manipulatives? This is a basic classroom and seems to be an applied mathematics 9 class which is also worth considering when developing lessons. Students who are not engaged may benefit from having access to different resources or being placed in a group with people they are comfortable with. 

Sources:
http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf
http://www.edugains.ca/newsite/math/supporting_classroom_practices.html
https://vimeo.com/193163993

Content Area Specific Collection of Resources

Our course has asked us to complete the following task.

You will curate a useful collection of resources and teaching ideas for a content area of grade 7 or 8 mathematics.

1) Choose a content focus that will benefit your own teaching of grade 7 or 8 (or both, especially if you are preparing for a split class) math.   

The content area can be very specific or broader. For example, if you are thinking of fractions or proportional reasoning:

• specific: adding and subtracting fractions;
• broader: fractions
• even broader: fractions, decimals, percents.
• very broad: proportional reasoning

Please beware that a broad focus may be difficult to manage. If you are unsure about what to choose as a content focus, or if you are unsure of your choice, ask your instructor for feedback before you begin.  The choice of focus area is really up to you and should meet your needs.

2) Gather resources and ideas related to your content focus.

These may include pretty much anything that you may find helpful:

• manipulatives (concrete and digital/virtual)
• websites
• games
• lessons (including rich tasks, 3-Part lessons, guided instruction)
• assessment tools and ideas (for, as, of learning; including feedback)
• report card comments
• differentiation
• learning environment aspects that encourage the learning

3) Choose a presentation format.

You can choose to present your assignment in a format of your own choosing (e.g., PowerPoint, Prezi, Google slides, word document, etc.). If it is not a typical presentation format, please check with your instructor to make sure it is okay and that she will be able to access it.

• Include examples, visuals, active web links and perhaps embedded videos. 
• Note all of your sources and include a list of references at the end.

Keep in mind that you want this assignment to be easy to use for yourself, and hopefully for a colleague if you wish to share it.  For this reason, make sections and headings, use sub-titles, and make captions or anecdotal notes.  

*This assignment could become part of your teaching portfolio and be a good artifact to share during an interview.

Success Criteria

• I have included a variety of resources and ideas that show my understanding of effective learning of the math content area that I selected.
• My collection will be effective in helping students to develop enduring conceptual understanding.
• My collection shows thoughtful reflection on course content.
• The format of my assignment is organized, is easily enhanced by adding other resources that I find, and allows for easy use by me or by another colleague.  My communication is clear and concise.
• I have included a page of references (see Assignment 1 for an example).

What I am asking myself now is, what area do I particularly need to grow in? Looking at a more difficult perspective, I may refer to Grade 8 Mathematics Curriculum's "Patterning and Algebra" strand. Overall the expectations I will refer to will be, more broader and generalized really (so, all of them).

What do I have so far-probably more than I know. I will certainly use this opportunity to unveil the 3-Act Math Lessons I have been working on as well-more particularly to this project, the other subject specific ones will be unveiled at a later time.

Here is what I have for Algebra so far (overused and unknown).

kahnacademy.com

Socrative.com

Edmodo.com/Spotlight

Kahoot.com

https://www.thoughtco.com/what-is-algebra-why-take-algebra-2311937 (rationale of algebra)

https://www.thoughtco.com/top-apps-for-algebra-2312096 (apps)

https://www.thoughtco.com/how-to-write-expressions-in-algebra-2311934

https://betterlesson.com/lesson/521023/solving-multi-step-equations-with-candy-day-1-of-4?grade=20&subject=1&from=bl_directory_no-keywords_eighth-grade_algebra_mt-lesson_521023_title

https://www.thoughtco.com/exponents-and-bases-2312002

https://www.thoughtco.com/improve-algebra-content-vocabulary-poetry-4025375

https://www.thoughtco.com/report-card-comments-for-math-2081371

https://whenmathhappens.com/3-act-math-alg1/

https://mathscribe.com/algebra1/index.html?grade-8

Thanks Prof. Box!

The professor of the Math course I am taking has posted some other valuable resources that helped me AGAIN find the missing components to the 3-Act Math problems with the extension activities!

I really hope this goes as well as I am imagining.

Just need time to put it all together-Oh Sammy boy-keeping me up at night, but Dad loves ya man.

Check out the resource!

http://passyworldofmathematics.com/balance-beam-equations/

Fact: China's government does not recognize men as "stay at home parents" and therefore does not give fathers a paid leave from work to care for their children. FML. To top it off, my wife only has five months of paid leave...Take us back to Canada!

Post from C. Hodson

I am sorry in advance for borrowing your post info, but this is something I will be returning to when working on my 3-Act Math problems. I don't think I have ever read something quite as helpful as this in an AQ/ABQ course post before...SWEET!

C. Hodson (2018)

Grade 7 Number Sense and Numeration

– add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms;

– demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number (e.g., ½ + ½ + ½ = 3 x ½ );

Grade 8 Number Sense and Numeration

– represent the multiplication and division of fractions, using a variety of tools and strategies (e.g., use an area model to represent ¼ multiplied by 1/3;

– solve problems involving addition, subtraction, multiplication, and division with simple fractions;

I like to use measuring cups (and cooking or baking) to demonstrate and assess understanding of fractions.  Fraction circles, strips and rods are used at earlier grades and also have their place in the intermediate classroom.  However, for students who have already decided they don’t like math or for those who are disengaged/disinterested, I like to incorporate baking as much as possible.  It’s less stressful for me to bake with intermediate students; they don’t require the same supervision to use the oven or other cooking tools.

I begin by introducing measuring cups and sand.  How can we get 1 cup when we don’t have a 1 cup measure?  How can we get 4 cups when we don’t have a four cup measure?   Bringing the sand table from kindergarten sparks some interest and invites students to play.  I increase the complexity of the question as students become more comfortable.

Baking is a great way to test conceptual knowledge of fractions too.  I can differentiate my assessment by giving different tools to each group.  For students who are in the concrete stage, I give the exact measuring cups they need.  1/4, 1/3, 1/2, and 1.  They still need to demonstrate that 3/4 equals ¼ + ¼ + ¼ and that ½ = ¼  

For groups who have mastered this, I give mismatched measuring cups.  For example, if they need 1/3 of a cup of one ingredient, I might give them a set of cups that is missing the 1/3 cup measure.  How will they measure 1/3 cup?  Or I might only provide 1/3, 2/3 and 3/4 cup measures when they need 3 cups of something.  What’s the easiest way to measure 3 cups?  How can they measure 3 cups with the fewest movements?

For students who truly understand how adding and multiplying fractions work, I ask them to double or triple the recipe, and write the recipe out for me before we start baking.

I did this with four groups, all differentiated in some way, but all baking the same recipe.  The proof is in the pudding…or in this case it was in the cookies.  How did they look? Taste?  What did we learn?  What would we do differently? 

You do have to be willing to risk some failures, but students are highly motivated when they get to eat their work.  They are also more willing to look at their mistakes when they don’t taste right (especially if we are planning to bake again soon).

Using measuring cups helps to move students from concrete to more abstract thinking because they help students to see the relevant use of fractions.  They are different than the manipulatives typically used – fraction strips, circles, rods, etc.  Using a different manipulative reinforces concepts that have already been attained, but for those who were not successful may provide another opportunity to learn.  Measuring 1/3 of a cup three times and filling the 1 cup measure with sand highlights that 3 x 1/3 is the same as 1 whole.

 (Always double check that your measuring cups are measuring what you think they are.  Is your 1/3 cup accurate?  Will 3 of them actually give you 1 cup when you measure it out.  Sometimes the measuring cups from the Dollar Store are off a bit.  You may also have to teach how to use dry measuring cups – level the top.)