Wonderful. I want to welcome everybody who's joining us this morning, actually going into this afternoon for our second webinar in the Open for Anti-Racism series and I'm just thrilled to have some of the developers of the Math Equity Toolkit with us, which was a project out of Education Trust West and Education Trust West and I apologize. I attend your webinars, Rachel. I'm on your email list and yet I'm not sure if I can describe exactly what Education Trust West is. It's an advocacy research group around equity and education really at all sectors, but did that capture it and just doing really exciting work. That was a great description, Una. Thank you. All right and we'll share a link later for your site as well and I should say that Education Trust West is one of four centers I believe around the country all focused on advocacy and equity in education. All right, Liz, next slide please. Let's see. Don't worry. I'm going to introduce our amazing speakers here in just one second and but we do want a little call out to the William and Flora Hewlett Foundation who has been supporting this anti-racism project and is really a leader in open education, equity and anti-racism, not only in education, but really society-wide. Our focus today is the Math Equity Toolkit, which is a really exciting project around making equitable classrooms, starting first with the teachers and their need to really reflect on who they are, what they bring to the classroom, what might be their implicit biases and how to really work with their students who may be the same as them or not, but it's really that process, that learning cycle I think is what Danny and Rachel would call it and that's what they're going to tell us about today. Okay, next slide please. So I want to start by introducing Danny Wadlington. Danny brings more than 13 years of field experience, two masters of arts degree in education and educational leadership from some of the countries and I must say from some of California's top universities. She's a master math teacher helping to close the gap in numeracy acquisition for many students of color and in fact if it's okay for me to mention Danny, she is a local high school teacher here in the Bay Area as well as one of the leaders, perhaps the co-founders of Ketzel Education Consulting and she's also an experienced West African dance teacher. She uses the interconnectedness of rhythm movement and math in order to engage her students and help them own their math identities. So thank you Danny, would you like to say a few words before we jump in? Yeah, I think you got, I think you got it. Thank you. Okay, well thank you for being here and next up is Rachel Ruffalo, I hope I pronounced that correctly. She is the director of educational engagement or educator engagement, I should say at Education Trust West located in Oakland California and her career in education spans more than 20 years serving as a teacher, new school developer, school leader, consultant, researcher and advocate and throughout this she's been committed to pursuing equity and social justice. She was a first-generation college student and experienced the transformative power of education within her own family. As the director of educator engagement, she works with school districts through a multi-year process that involves mixed methods research study to identify opportunity gaps and systemic inequities and the math equity toolkit is an example of that. Rachel holds a master's in educational policy organization and leadership studies from Stanford and a master's in education and teaching and curriculum from Harvard. So thank you Rachel, would you like to say anything before we jump in? I think you got it, thank you. Okay, you both have such impressive resumes, I'm sorry if I got tongue-tied there. All right, next slide please Liz. So for those of you who might be new to the Community College Consortium, we have been around for over a decade now. We were founded right here in Northern California but we are a national organization. We work with faculty in supporting their professional development to find and adopt open educational resources and practices in order to help students be successful and to reduce equity gaps and so this particular project is really an example of that. Next slide please Liz. All right, so very quickly and I'm sorry my internet seems to have been a little slow there. So for those of you who haven't heard of the Open for Anti-Racism Project, I hope most of you have. I know that we have our faculty cohort which is our, we hope our first faculty cohort going through this process and it's a one-year program to explore how faculty can use OER and open pedagogy to make their instructional materials and their teaching practices more anti-racist. Our faculty cohort, there are 17 of them from a regionally dispersed California Community Colleges. You can see that it covers a wide range of disciplines from administration of justice through sociology, social work, chemistry, math, etc. So really spanning just a wide set of disciplines and we're so interested to see how the open pedagogy and OER works within different disciplines. And you know I know in talking with Rachel and Danny about math we had a discussion around how you know sometimes when you come to teachers initially and say math may not be taught in an equitable manner, it may not be inclusive and they're like well it's all about numbers. I mean you know what's what what does numbers have to do with equity and so I think we will hear a lot more about why that's so important, why teaching math is a key example of the need for equitable thought. All right next slide please Liz.  So the math equity toolkit, it's a toolkit of resources that were developed by really teachers, practitioners, coaches, professional development providers, and language development specialists. Although we're not going to focus on that one particularly today but I think that's a really fascinating piece as well and it's all about supporting teachers in their journey towards anti-racist instruction and helping their students to be successful and there were five strides and I think Rachel will give us a little overview around that. Today we're focusing on dismantling racism in mathematics instruction which is the first stride and there's a lot of resources online to support your further investigation of this and at this point I'm going to turn it over to Rachel and Danny. Thank you so much Una for the introduction and for the invitation to join you in your cohort and other guests today. I'm just going to share my screen. All right so as as Una mentioned we typically share this with mathematics instructors and we're just thrilled today to have an opportunity to talk more generally about the process of developing this tool to support you all in your anti-racist work in your own context and I believe that that much of the content is likely applicable to your context as well. I'm going to try to I see a spinning circle on my screen so I'm going to see if I can advance the slides. There we go. Okay there we are so you've already heard about us so I'm going to click through this and as Una said the Education Trust West is a non-profit educational equity organization focused on educational justice and closing achievement and opportunity gaps through research data policy analysis and advocacy and I would add to that also through practice and so we do partner with practitioners throughout the state through early childhood through college it's an important feedback loop to inform our policy and also to inform our research agenda oops am I okay I got a little I got shut down here okay so I'm apologize let me reopen the slides. No worries technology's always I had it all set up and now my computer is acting tired. Let me see I can also share let me okay yeah that would be great Danny. Thanks Danny if I can get it back in time for your presentation I can support you. This is the moment when I always say imagine when our students are going through right. You know it's a it's a humbling and a good reminder I think about that too like how challenging it can be for adults. All right okay thank you so much Danny. So I'm just going to share a really brief overview of the toolkit generally and then Danny's going to dive into really the heart of Stride 1 which I think is really aligned with the work of your cohort. So the the toolkit is made up of these five different tools that we call them strides and they were collaboratively developed to support teachers in providing equitable access to grade level priority math standards. Our focal student groups are black Latinx and multilingual students in grades six to eight although we have found that the principles and the practices are really applicable beyond just grade six to eight and really beyond just math. Next slide please. So why is it needed? Well we were approached because there this was in late spring where we knew that teachers are going to need to make some strategic instructional decisions due to the pandemic and to the disruption to the school year and as we started planning what this might look like to support teachers we really couldn't ignore that the gaps in access to quality math instruction pre-existed the pandemic and the conditions have just been exacerbated throughout this crisis and so we really seized this opportunity as not just to be like a COVID response type of resource but really an opportunity to transform math education and to really help educators to think about what they can do in their own context to really be much more in tuned and responsive to the needs of students while being very cognizant of the systemic racism that exists and permeates all of our our institutions and systems. So next slide please. So we definitely could not have done this alone we brought together a group of 35 amazing collaborators including Danny from all of these organizations many county offices and universities here in California as well as some national partners such as Unbounded and the English Learner Success Forum. We had teachers and coaches researchers professional development providers really a wide range of perspectives and expertise. Next slide please. We also grounded our work so we had to work fairly quickly and we brought together folks from all these different organizations and so we wanted to ground our work in some guiding principles and foundational documents so that we could have coherence and some common themes and threads throughout all of the strides and so not going to go into detail but just offering this as I think an important approach to a complex task like supporting equitable and anti-racist instructional practices. So one of the the if you can go to the next slide the first principle was that equitable access to high quality standards aligned curriculum and instruction should be universal so we used the instructional priority content from student achievement partners to help us to help guide our work in what the what of the teaching which what content. The next slide the second slide is or the second principle is that barriers to equitable access to high quality curriculum are the result of structural, racist, and biased systems not students, backgrounds, cultures, or family income. So as we think about the approach to the barriers the barrier is not the students the barrier is the system and so we really also relied on this position paper from Toldoas Mathematics for All that put some language to the moment that we are in and the opportunity to really rethink mathematics for this year and every year. And then the third principle is that beliefs and language about students and their families shape how adults view and teach students and so we wanted to be very mindful of being assets oriented in our in our language in our approach and in our practices and we relied and kind of based a lot of our work on the California English Learner Roadmap especially principle number one assets oriented and needs responsive schools. And next slide please. So our group when we first began to put together the toolkit we focused on the question of what are the barriers to equity what is what is it that our toolkit is trying to support teachers to address. And we we came up with many ideas and I invite you to answer this question in your own context what barriers to equitable instruction to your students experience and I invite you to put in your response in the chat. As you do thank you Danny as you think about that I'll share some of the ones that our team came up with on the next slide. So we had many and we found that they spanned instructional barriers some were structural some were systemic and we wanted to focus on barriers that teachers have some control over in their context and those who are supporting teachers. And so you'll see we have these five that we focused on that created the basis for each stride in the toolkit and the first one that's a culturation of bias and racism in school systems and mathematics instruction is the one that we'll be focusing on today with stride one. The other four are really about teacher training curricular supports and supports for teachers to shift instruction and to build their capacity to meet students needs both in language development and social emotional and academic development. And so those are all great strides as well but we will be focusing on them today. So this is the stride that Danny will be going into more detail on dismantling racism and mathematics instruction but just want to share the titles of the other four strides with you so that you can if they peak your interest or you know people who might benefit from looking at them just want to make you aware of them. So stride two is fostering deep understanding its methods for deepening student conceptual understanding through orchestrated math discussions that build on and connect multiple strategies. Again the content is math but really the practice could span various content areas. Stride three is about environments that and practices that support students social emotional and academic developments so this one is called creating conditions to thrive. Stride four is the interconnectedness of English language learning and the development of mathematical thinking this one is called connecting critical intersection so this is the one that really aligns English language development with math content and math practices. And stride five is geared towards coaches and others who are supporting teachers in their growth their professional growth and it's called sustaining equitable practice and it shares some coaching structures that support math educators in their ongoing centering of equity principles. Again it this would be completely applicable to any teacher who is wanting to go through some reflective processes with a coach or a colleague and there's some great resources in that stride five. So I'm going to share also the webpage again equitablemath.org where you can download all of the strides or each individual stride or the whole toolkit and that's area that circled there on the next slide is a close-up of it. It is a it's okay it's a there we go it has the we did webinars we did deep dive webinars for each of the strides and so you can access the recording from each of those webinars they were presented by the content developers of each stride so those are great resources and we encourage you to share them widely and and then I think the next slide is my transition to Danny who will take you all in a deep stride a deep dive into stride one. I apologize for going so quickly but I wanted to make sure to leave as much time for Danny to share. Thank you Danny. Thank you. Thank you Rachel. All right so I am going to do a deep dive into stride one but like Rachel said the deep dive sessions that are on the website are really important and I talk a lot more there about how to use the tool so today I'm going to talk more about the purpose of the tool and like what you might learn from using the tool but if you want to learn how to actually use the tool you can you can check out that deep dive as well. So when we so when we got invited to this project or when I got invited to this project and thinking about the barriers that students face I really did think about teacher beliefs and teacher biases and how that impacts learning especially in the math classroom because we know that the outcomes for for math students are very racialized and a lot of the approaches to math have been like how do we do math better and I think that that's great right we also need to teach and engage with math in very different ways but if we don't actually address racism then we can't deal with the racialized outcomes so much of math um takes kind of a colorblind approach to the way that we have done math reform and and that then just leaves better math but not like the question is for whom right so yes we have access to a different kind of math different ways of learning math different ways of thinking about math but if they still don't encompass like this idea of racism then we haven't actually gotten to the root of the problem we fixed maybe a symptom or how it might present itself but as we know there are still racialized outcomes so we took a very racialized approach to how we um to how we wanted to to to go about addressing the barriers um barriers for black Latinx and multilingual students and what we did was we wanted to create a sort of action-based workbook to provide teachers um reflection and opportunities to really examine their actions beliefs and values around teaching mathematics and we chose a workbook approach because we know that some folks are not ready to do anti-racist work and you can't necessarily change their minds or their beliefs or their inherent biases in in a lot of ways right at first so we wanted to take an action-based approach because you can change folks actions and hopefully in the process we will change their hearts and minds um so we really wanted to start off by thinking about how does racism show up in our math classrooms right like how does it actually show up and so we know that white supremacy culture is is a part of our everyday lives it's a part of the fabric of how we walk um how we walk the the or not necessarily the world well we can argue the world but at least here in California and in our country we live in a racialized society and so if we aren't very clear about thinking about how white supremacy culture like shows up then we miss it right because white supremacy culture is one of those things that that just permeates um and we don't even realize it's it's invisibleized in a lot of ways so we really wanted to um we really wanted to visibilize how it shows up and we wanted to make clear that it shows up in in everyday teacher actions it's not like oh i'm like a lot of teachers decide oh i'm going to be racist today that's not a thing right like people don't always do that um but we can still perpetuate white supremacy culture but by engaging in what we might see is everyday typical math things and for those of us who aren't also math teachers like i'm going to give us an opportunity to think about like the ways that it shows up in math classrooms but i'm sure you can read some of these and be like oh actually do that in my class um so what i'm going to do is i'm going to on the next screen here are the here are what we saw as the ways that white supremacy cultures show up in math classrooms and i want you to take a moment to read them and if i can i'm going to put them in the chat box in case you can't read it on the screen so i mean take a minute pause real quick um i'll put them in the chat box so you can actually see them hold on i have to stop sharing don't let me do that um but what i want you to do is in the chat box if you could if you don't mind thinking about what are some of the ones that maybe you have engaged with what are the ones that you've seen happen which ones strike your mind is maybe not something that you recognized before um i invite you to um read those right now and then put in the chat box which ones you which ones you're surprised about which ones have you done which ones have you seen oh there's only one person i know that most of us have seen or done or or witnessed more than these so thank you thank you rigor is an interesting one i'll try to maybe hit on that one a little bit but feel free to add your own feel free to to share yeah the right way and the only way that happens a lot especially in math yeah the concept of rigor is really really interesting so thank you thank you i really appreciate you all feel free to keep them coming and so i think that like right like there are ones that are like kind of clear in our minds right that we might like okay it makes sense that like when we're thinking about rigor especially when we think of think think about things like grit and like the the racist um undertones of what it means to have grit and rigor and things like that um those ones are like maybe clear but maybe it's not like addressing mistakes right that one may not be as clear and so this workbook really offers you an opportunity to think about um to think about more ways in which white supremacy culture shows up in our classrooms but we can't we can't only talk about white supremacy culture because i think that right like in in sort of visualizing what white supremacy culture looks like that's like oh okay now i know maybe what i shouldn't do but what should i do instead and so i want to make sure that as you engage with the workbook or as you engage with with thinking about this that we highlighted some characteristics of anti-racist math educators um because we need to know what we should do differently and so one of the one of the first one right is it's designing a culturally sustaining math space and even if you aren't in math designing a culturally sustaining space and like an actual culturally sustaining space so not just like putting things up in your classroom or putting like posters of folks up in the classroom that has a place too i'm not trying to knock anybody who does that i do that as well um but really making sure that we design our spaces for students of color and for folks who may or may not be in our classrooms that still need to be centered right like maybe you don't have a lot of um black and brown students or maybe you don't have like lgbt students that you might see right but that doesn't mean that your space shouldn't welcome most folks so even a lot of times with anti-racist work they're like oh but i don't teach students of color well i think that like you still should send them in your classrooms because we also don't want um we also don't want our white students right to walk out into the world and not understand experiences of folks of color too right so um we have to make sure that our spaces are really culturally sustaining so think about um for example like i know that we like to think about routines but for folks of color ceremony is really important so how we open our class how we close our class is actually more than just oh we should do a routine because students should follow it it's like that's that's actually part of like how we live life and so thinking about how do you design spaces um that are culturally sustaining for students um ethnomathematics is also really important it's how we deal with numbers on a regular basis there's no way that you have gotten up today and haven't and have not interacted with math or numbers there's no way you've done it already today and so ethnomathematics is really thinking about what are those everyday things that we sort of engage with that encompass numeracy or or math or mathematics even in ways we don't necessarily realize and that's goals beyond bringing like real world class like real world examples into the classroom because a lot of times what we do is we say okay we have this like thing to teach now let me figure out what in the world like does that and it's like no you walk the world and you engage in math every day why don't we bring that into our classroom and make sure our content aligns with that and so really rethinking how we engage with mathematics and how we teach mathematics in the ways that we experience them as we walk the world not just to bring in that real world content um and that's true for folks who are not math educators as well like I think we do the same thing like with ethnic studies we treat ethnic studies like content and it can be but ethnic studies is also a pedagogy and an approach and if we shift that then we can also think more widely and more broadly about how do we engage with um with ethnic studies um for two closed barriers for folks um in a in a way that's different and doesn't seem like it's just based on content there's so much work about ethnic studies as pedagogy and framework and I encourage everybody to to research that and look into it um also I know we I know we've already had some comments about what what rigor is and what rigor is not and then another day we can go more in a deep dive of like what we mean to say make rigor accessible through strong and thoughtful scaffolding and really that is important because I think a lot of times we sacrifice rigor to make things easier for folks just so that they get through it and then a lot of times we actually over scaffold even when they could just be rigorous and so really thinking about how we can redefine rigor and really think about rigor and scaffolding in a very very different in a very very different way of course we want to students of color to close the the the gap in access to STEM fields I'm not going to talk more about that one but that that's also really important especially in the Bay Area and Silicon Valley we're right here and like we are leaving out like our population even in this space and Silicon Valley doesn't match right the employment and so really thinking about that um encouraging multiple and varying ways of sharing and communicating knowledge this is so important I can't talk about how many classrooms I see students just get shut down for like doing things differently we have different ways of being and all of that has to be incorporated into our classrooms we can't we can't not do that um and it's more than just like allowing it I think whenever you get to a point where you say you can allow something we have to like check that a little bit because why is it what's allowed like we literally just exist and so how can we make sure that our students are being able to exist in spaces um the way that you know exist just exists as who they are in our spaces and communicate their knowledge um and their ways of sharing it in that way because a lot of times what happens is if someone is not explaining it the way that we taught it or explaining it the way that we think is academic you know language then they're shut down and they're thinking and that that's not okay um and this is a big one supporting students to reclaim their mathematical ancestry it bothers me when um certain uh mathematical concepts are um connected with certain people when we know they existed beforehand um and that's really important because like we just know like you know anyways I will go into that but I think that there's so much math that existed before it was recorded and worshiped in written word and that that in itself right the written what is written being valued is another form of white supremacy culture so I just want us to like really challenge that and one that's kind of missing from this list that I want to add is that we're always that anti-racist educators are always learning and unlearning um like earlier in the chat box I saw that some people mentioned like very colonial ways of thinking and that you know we are a product in our history is of that and so if we don't check right like our colonial ways of being and understanding the world then we're perpetuating these ideas so I would also add to consistently like learn and unlearn and keep in mind that anti-racism is a journey it is not a destination you can't check off any boxes and so we are continually right change as the world continually changes we also need to adapt and adapt and and alter these lists to to include more of the experiences that we that we have and yes sorry I'm reading the comments yes um so right now what I want us to do I'm going to invite us to freedom dream a little bit um so freedom dreaming is sort of imagining worlds that are just representing people's full humanity centering people left on the edges thriving in solidarity with folks from different identities who have struggled together for justice and knowing that dreams are just around the corner um not these things far off in the distance um and so what I want us to do is I'm going to take us through an activity so I invite you to turn off your camera if it is on if you'd like um and to close your eyes if it feels right and safe to do so and I'm going to walk us through a freedom dreaming exercise I'm going to walk us through a freedom dreaming exercise and I'm just going to talk us through I want you to literally not be limited right so I don't want you to think about what are these limitations what are this just really imagine what it would be like if our schools were really anti-racist if our students were thriving okay so I want us to think about our classrooms our schools our learning spaces and what they would seem what they would look like what they would feel like if we really engaged in anti-racist education at the end I'm going to invite you to share but I don't want you to focus on that part right now I just wanted to give you a heads up I'm going to talk us through this visualization as we freedom dream I want you to imagine what it would be like to do anti-racist work in your learning space what would it look like to tap into holistic aspects of what it means to exist to be to learn to teach what would it look like what would it feel like if black and brown voices stories and experiences were centered at your site what would it feel like if the languages and native tongues of multilingual students were to be honored what would it look like if black indigenous people of color were thriving what would it feel like if white students families and teachers acknowledge their individual and collective privilege and work towards liberation for black and brown lives what would it look like if white teachers families and the larger community and other folks with privilege and power gave all that up and other benefits in order to prioritize the needs of black and brown community members what would it look like what would it feel like if teachers modeled being anti-racist leaders in society what would it look like what would it feel like if admins supported them in doing so what would it feel like to build and sustain a culture of accountability self-reflection and growth I'm going to give you a minute to silently reflect on any other questions or thoughts that came up for you that may have felt like a very long 45 seconds but I want to thank you for freedom dreaming with me I'm going to invite us to breathe deeply as we transition minute count us in breathing in and breathing out so let's breathe in one more time breathe in breathe out and I invite you to open your eyes and turn on your cameras when you are ready as you are turning your cameras back on again thank you so much for freedom dreaming with me I invite you to share what were some things you envisioned when we did our freedom dreaming and what is your freedom or what is your freedom dream for your learning space and you can either unmute or write in the chat box I want to give some time and space to do that thank you all for sharing see respect all celebration spirit differences how awesome would it be to have vertical not sorry not vertical but horizontal leadership I love that idea thank you multiple languages thank you I'm going to go back one slide because you know dr. Bettina love talks about how yes we freedom dream right but that freedom dream is not far off it can be right around the corner and we have to work hard to make that happen and that's a lot of why we are doing right what we are what we are doing and so thank you all for sharing please keep them coming one way that we I love these dreams I'm really going to read them as we go so one way we thought about doing that right is to really get folks into the work and so we created this workbook with this sort of five-part plan of engaging reflecting planning and then acting on that plan and then reflecting again to think about like how was that work how was engaging in anti-racist work for all of the purposes that you all are talking about in the in the chat box like I really encourage you as you get into this if you want to work on these or as you bring this into your learning spaces like keep in mind that you have a goal and you have a vision and use the visions that you're talking about in the chat box to make your action plans to make those things happen because our dreams can be reality um and so I want to talk a little bit about I know I've said before we have a deep dive of like how to actually engage with the work but I know that not everyone here is a math teacher and I also know that some questions around how the workbook can be used are really important and so again if you want to look at just how to use it you can go to that deep dive that's on the that's on the website um on equitablemath.org but also I want to give you some some considerations um and other notes for how you might use this both in the classroom in the math classroom but also in in classroom spaces or learning spaces or even in your life if you'd like as well um so the first thing is to read Teima Okun and Kenneth Jones and Kenneth Jones characteristics of white supremacy culture a lot of the work that we do in the workbook is based on this and this is really important especially if you're not in a math classroom because it shows how it shows up in organizations and we are all part of institutions um we are all part of an institution right like even even this organization is part of larger institutions and so you can this visualizes how white supremacy culture shows up in the in our spaces and in organizations and so you can be more cognizant of those things and can challenge them as they come this article even has antidotes so they treat it like this is a problem and how do we treat it with antidotes um and so it's a really good article that is a really foundational one for anti-racist work and it was really foundational to um it was really foundational to the work that we did with the tool with stride one of the toolkit because we we use those definitions and that language and so a lot of times people are like I don't understand power hoarding or I don't understand what it means when it says um objectivity or things like that and so this article um from Tamelle Coon and Kenneth Jones can really help to ground the definitions of those words thank you for putting the link in Kim thank you thank you um also you can go beyond this workbook so like I said for math books right like you can use it as is other folks can also use it as is but if you're not in the math classroom think about the white supremacy culture characteristics think about how they show up every day like you can still read um how and why they show up and what's the importance of of dismantling them and you can also take into mind all of the other information as well but when you create your plan sorry I'm really bright right now when you create your plan you can um you can do it for your own context okay so the workbook too was also written for was also written like to for to address two of the white supremacy culture characteristics per month um but it's okay to maybe do one right or it's okay to say well actually you know what I need a longer month on that or sometimes your school or your your institution might be might have goals for the year that that don't necessarily align align align to the way that we presented them in the workbook so it's okay to speed up slow down do them in a different order um think about think about how what's best for your content um even though like as you can see on the picture right there's the section for engaging and then they also offer what you can do instead please try out those verbal examples so we we thought about like how do we change our language to um support anti-racist efforts and math so really try out the verbal examples um try out the classroom activities if you um are wondering like because the classroom activities are little snippets and so if you're like I think I want to try that and some of the classroom activities are not don't also have to go with math right like you can try this in your in your classroom not just in math but if you need help with some of the classroom activities feel free to email me I would be happy to connect with you especially if it's like activities or materials already have put together like just let me know we can explain a little bit more tell you how we use them in our classrooms because a lot of the class activities are things that we actually used um and have done in the in the past and are doing now so um please feel free to reach out to me or the other content developers um and for the classroom activities also please implement um the professional development there's lots of ideas for professional development as an individual as a department um as a school there's a lot that we can work on um there and so they also we also offer that professional development um we offer professional development ideas in the workbook you can also hire kids at education consulting we are doing some um we do what we do anti-racist work in general and in terms of like um professional development we have many opportunities for professional development some that are specific to this workbook but also two larger anti-racist ideas as well um but most importantly because I know that sometimes people get so caught up in the work um that we don't always come back to the anti-racist um characteristics or characteristics of anti-racist math educators and so this visual is like just for you to visualize right um you don't have to read it right now but I know that I did like a big picture of the anti-racist math educators but in the workbook there are also bullet points to unpack um each of those characteristics and suggestions for how to teach and like I said you can do this whether you're in a math classroom or not sometimes it's just about changing the context with the purpose behind the work transcends grade level and transcends content so thank you so much for listening to us and sharing space with us today um I have really appreciated um this and I want to open the floor for questions and comments you all don't have to be shy you can unmute before you can chat but well I just want to know whenever Danny is facilitating a webinar sign me up thank you absolutely I feel refreshed and inspired thank you Danny and Rachel so I can say that um it is it is very challenging when you're trying to find examples in STEM that are diverse in terms of who's being depicted um utilizing something that shows physics and um I spend a lot of hours trying to add variety of color um to my PowerPoint slides because um I always talk about the wondrous variety of people I get to meet every semester and so I try very hard to embrace that um in what I'm presenting but wow in STEM it is really challenging to find images with diversity thank you for that Teresa we um we have a wonderful set of um links um on our website and I will put that in um the chat window it's it's a good start um and um yeah uh includes um well James just presented on this this morning includes nappy dot com um and I'm I'm going to guess that um Danny and Rachel have other suggestions but I will look that one up and put it in there and I think that will that might be a start um we have some through our you know I'm part of equity mind and practitioners at our our college as well and we have some that we've come across but I'm always looking for more tools because it is a challenge absolutely well um we will um I think we'll we'll move on now to just because we're coming up on the hour but um Danny and Rachel are still here and we'll come right back around to them at the end as you think of more questions for them when I did see a few a few a few more questions um let's just finish out if we can uh and James is James the co-lead of OFAR along with myself and Liz at CCCOER is going to finish us out here great thanks and boy thank you Rachel and Danny again sign me up Danny let me know whenever you're facilitating a webinar um so we've got more goodness to come if you missed our uh webinar last month it is uh archived on the CCCOER website that was also a terrific webinar uh looking at uh uh a a colleague in political science analyzing her discipline and the represent lack of representation in her discipline and then a colleague uh talking about anti-racist pedagogical practices and discussion practices in the classroom uh in march we've got a webinar coming up that features two colleagues one from the African American male education uh and network development a mend uh talking about uh it's a group of African American males in community college leadership positions who mentor and support African American students in community colleges then we have a colleague who's been active in open education who is part of a group called Wait Whites for Racial Equity uh and the group is exactly what the name describes uh white people talking the talk and walking the walk uh for racial equity so I think that'll be a really interesting perspective uh in April in April then we have uh community college equity assessment lab uh Dr Frank Harris many of you are familiar with of the with the work by Luke Wood and Frank Harris Dr Harris has agreed to speak with us in April which will just be fantastic if you've ever heard him you know how great he is um May is to be determined and then June will be an opportunity for the participants in our O4 OFAR cohort uh to share out some of the great work that they're doing and some of the ideas and discoveries uh that they're that they're creating so look forward to those webinars uh next slide please and the next slide is a little bit more information about the March webinar again amen the organization amen you can see the description there on the screen and Whites for Racial Equity uh the description is on the screen as well so again I think that'll be a really interesting uh a real interesting webinar to see a couple of different approaches of doing the work that we're talking about to provide supports a bit outside the classroom and back to you Una All right next slide please thank you Liz I just wanted to mention to all you open educators out there that Open Education Week is uh week after next March 1st through 5th um please submit um your wonderful projects uh there and come and browse um projects from around the world so this is really a it's an annual celebration I think we're in our eighth year since 2013 um and um it's it people submit really uh literally from um you know 40 countries around the world in multiple languages um and um I'd love to see yours there as well and there's some links here on how you can get involved in other ways um CCCOER will be doing a number of um events as well that week and um if you're on our email list um you will hear about them um and um we'll post a link there to our email list in just a moment and these are just resources for you that we repeat once again our CCCOER the community college consortium for OER uh's website there and um we also point you to the wonderful resources being put together by I by our statewide academic senate uh through their OER I project and here's the email list if you would like to join that email list and hear about uh various events during open ed week and and beyond and I think we're we're just finishing out now we um do have a um we do have a survey that we ask you to take it's a very short three question survey um and um I don't know this is that easy for you to put in the chat window um and we just want to hear how how the webinar went and if you've got um thank you very much Liz and um if you've got ideas for future webinars we're we're always interested in hearing what the community needs needs to be successful in their open anti-racist work so thank you so much Danny and Rachel and um I we will be here for a few more moments so please if you have additional comments questions please jump in um you can unmic um or type in the chat and Danny's been in the chat thank you Danny for addressing some of the comments and Rachel for adding the the additional resources I would encourage everyone to check out the ed trust west website they do a lot of great work a lot of data analysis as well uh so if you're trying to understand what our students are going through they've done surveys on and what our students are facing during the pandemic just all kinds of goodness on the trust west website yeah thank you for sharing that Rachel the link and yes amazing webinars sometimes featuring California community college leaders as well so it's um really wonderful thank you all so much for the opportunity to share with you and just being conversation with you today it was a pleasure


This study proposes a novel approach to improve the accuracy of instrumented footwear for ambulatory gate analysis. Transduction learning models were developed to reduce measurement errors associated with conventional techniques while maintaining computational simplicity. These models were tested on a group of elderly individuals with varying degrees of gate and balance impairment. Results showed significant improvements in both spatial and temporal parameters, suggesting the potential of transduction learning models for improving the accuracy of instrumented footwear for ambulatory gate analysis. This article was authored by Huang Hejiang, Tuan T. H. Duong, Aishwini K. Rao and others.


What's going on everyone? Sam here with late in sports cards rip in 2011 top supreme football hobby case break random divisions. Here is a look again at your random results. As always, you can find these on the website under the results tab as well as the link that's currently in chat. So good luck guys. Let's do some 2011 tops supreme. I want to pull a monster mckell ashore right now. Give me all the mckell ashores. Give me all the edwin gates. What's going on everybody? No, but for real, let's see like a brady or something. That'd be kind of wild. All right, here we go.  Please come back. Please. Please lord, come back. I can't wait. That's going to be D'lone Carter to 429. There we go, AFC south. Nice. A Charles Woodson to 429. Jake locker rookie auto to 175 AFC south Washington legend Titans legend. Wow. There we go. Congrats AFC south. Jake locker and second year in domicom suit to 75. Wow, dude. NFC north. I can't believe I cannot believe I'm saying second year. No, I'm going to that's that's that's madness madness to me. Here we go. Come on, baby. Let's see something big. A locker could chuck it dude. He was so good at Washington. All right. Well, we got a redemption. So I apologize on that. There's Richard Mendenhall for the AFC north for the Steelers to 75 legend Richard Mendenhall. How he longed 429 Ryan Williams rookie. He would have been nasty if he didn't get hurt all the time. Nice one there. NFC west and then definitely probably an expired redemption. Vaughn Miller 2011 top supreme rookie autograph of Vaughn Miller. Nice one there. Six tires in 2014. So we do apologize on that AFC west. We will send it out to you. Maybe they still have it or something similar to it. Maybe we'll send you something hopefully. So Vaughn Miller AFC west. Broncos Vaughn Miller. Weird redemption card. I know. God. Next one. Yeah, right. Some sort of patch auto of some sort. There's a red Kendall Hunter. Oh man, I miss Kendall Hunter. Color match for the NFC west. There's a blue Taiwan Jones. AFC west. Absolute maniac that guy was. He was still in the NFL until like a few years ago and like nobody realized it. How about a Leonard Hankerson. No shot. We've got a one of one Christian Ponder and Leonard Hankerson. Boom. Oh my God. This is insane. What a card. Holy cow, man. Wow. You should have made that bet. I'm glad you didn't. Christian Ponder and Leonard Hankerson. Let's go. That is NFC north, Gregory H and NFC east, Brent S. We'll go ahead and random that one at the end of the break. That is fire. Let's go. Oh man. Oh man. Leonard Hankerson. That was downfield threat. That is downfield threat Leonard Hankerson. And that is where did Christian Ponder go to college? Not Mizzou. That was Gabbard. Here's an SEC guy. Wasn't he? Was he like Arkansas? Oh, we magged it. Don't you worry. There is no chance in hell that wasn't getting magged. Purple, Mike Williams. That's Buccaneers 2010 draft pick, Mike Williams. Nice one there. Got a Slam Bradford to 425. FSU. That's what it was. FSU. Nice one there. Hey, Roger Staubach is going to the NFC east. And a nice one here. He got to 50. Jersey auto Jonathan Baldwin. There we go. FSU west. God, I love seeing these guys. He was in the later traded to the San Francisco Niners for equally as legendary AJ Jenkins. FSU west, congrats on that. I cannot believe that there is a Christian Ponder and Leonard Hankerson one-of-one to dual patch auto sitting in front of me. That is insanity. There's red, the Sanjai's 3 out of 99 plus a blue Sanjai's. That is 406 out of 429. Look at that. There we go, AFC east. We've got an Arod to 429 for the NFC north. Vaughn, 11 out of 50 AFCs. We got a Shane Vareen. That is past catching legend to Shane Vareen right there. That is a classic target of a Brady dump off right there, Shane Vareen. Guy at like 1200 yards receiving from no downfield passes of more than three yards. Shane Vareen. Let's go, dude. God, this is fun. This is the best thing I've ever opened in my life is 2011 Top Supreme. This is insanity. This is insanity. Him and Steven Ridley out of the backfield. There's another Mike Williams, 39 of 99. He literally was James White before James White. There's a Greg Little, 411 out of 429. Nice. Nice one. Here we got a Ronnie. Oh, no. Ronnie Lott to 429. Okay. AFC north, Bo. Bo. I'm hitting you up, dude. How about out of 50 Ray Lewis on the Jersey Auto, the Land Shark, baby. Oh, 38 out of 50. That's nasty. That's so sick. Bo, check your emails the next day or two potentially, buddy. That's nasty. That is game use Jersey Auto. Big Ray right there. You know what that is? I am content with pulling stuff after that. I am content with that now. That's nasty. That's so sick.  I completely missed the trash game. That's literally five inches for me. New year coming back today for a reason. There you go, man. What a way to come back. What a thing to come back to. There's a Joe Nemeth, Broadway Joe, 28 out of 30. God. Jerry Rice to 429 for the Niners, AFC, or NFC West. Reggie Wayne to 429. Oh, we got another legend coming up. Oh my God. How about going to the NFC East? Number nine of 20, Jarell Jernigan. Giant's Legend. Giant's Return Man legend right there. Jarell Jernigan. I love it, dude. NFC East. Brent S with that one. God, Jarell Jernigan. That's a name right there. God, dude. This is banana land right now. What's up, Jonathan? No, that was player one. Player one on that one. There he is again. Jake Locker, 8 out of 30. Rookie for the AFC South. Big Ben, AFC North to 429. And nice to 429. There's Tom Brady, AFC East. Another Jarell Jernigan that is 9 out of 50. Nice one there. Going to the NFC East again. This is Cam Newton here. The next break, which Kenzie's breaking, that's 2012 exquisite. So that's the luck RG3 here. Giant's retired number 12 after Jarell Jernigan's tenure. Yes, they did. Yes, they did, Mark. Jamal Charles, 24 out of 99. One-off Jersey number. Color match. Oh, here we go. Rich is paying top dollar for this card. Ryan Mallett, rookie to 429. We've got a Kevin Cobb. That's pretty nasty. I believe this will be a random. We've got A.J. Green, Julio, Mark Ingram, and Daniel Thomas. So that's AFC North, Bo H, NFC South, Josh G twice, and then AFC East is Chad P. So nobody owns majority of this, 25 of 25. So this will be a random to those four divisions at the end, or three divisions. Julio really has been around forever. Julio's been around and been good forever, man. Greg Jennings put the team on my back running with a broken leg. Greg Jennings, that is right there. That's Matt in YouTube legend. There's a John Baldwin again to 429. Go. Phil Sims to 429 for the Giants. Here we've got Big Truss, Woo Woo, Lamar Jackson, MVP in the flesh. Mark Ingram, rookie Jersey for the Saints. 22 of 25. Heisman Trophy winner from Bama. First round pick for the Saints. Love it, dude. That is actual Raven's legend for one-year Mark Ingram. There's Randall Cobb, 31 of 75, rookie, still in the NFL, still on the packets. Not bad there, NFC North. That's going to be NFC West, Frank Gore, to 429, as well as CJ2K to 429. AFC South, nice one there as well, AFC South. And then really nice one for the NFC South. There's a Julio, that is three of 10 on the Julio Jones. Quad Jersey, player worn. There you go, Josh. Picking up the Julio. The Julio rookie. My God, man. The Julio Jones rookie, Jersey. CJ2K was underrated for sure. JJ Watt would be sick out of this. That'd be pretty sick, too. Got a Ma Bradshaw to 75. There's a name, Super Bowl Champ. Two-time Super Bowl Champ, I believe. Niners legend. NFC North. There's a Greg Jennings again to 429. Here is one half of quite possibly the best double trouble backfield in recent memory. There is D'Angelo Williams to 429 for the NFC South. Nice one here going to the NFC East. We've got Leonard Hankerson. Two-of-five. We are just pulling absolute bangers of Leonard Hankerson today. Downfield threat legend would randomly go off for a couple games a year. Love it. Two-of-five, Leonard Hankerson. Oh yeah, that Hawksback field in 2060 is pretty scary. That's true. Oh yeah, that was what, Tico and Freeman. Ha ha ha ha, Vaughn's getting timed out. Only four boxes to go. I wish we could just rip 2011 top supreme all day. Eric Berry, one out of 99. Nice one there for the AFC West. That's awesome. Congrats on that. Deshaun Jackson to 429. And Phillip Rivers, 36 to 429. Oh, everybody, rich shields your eyes because there's another Ryan Mallett this time. 7 of 10. Quad Jersey going to the AFC East. Nice one there, Chad B. Way cool. We just, due to it not filling as fast as we wanted it to, we just split it up into smaller breaks. Arkansas Goat. Ronnie Brown and Cadillac Williams. That was, that's true. And Auburn. They're both like pretty good NFLers too. Drew Brees, 32 of 75, NFC South on the purple. Blue, Colin Kaepernick rookie, 379 of 429 for the NFC West. And the Damakung Siu, 124 out of 429 for the NFC North. And then we've got the absolute legend is Ryan Williams. That is NFC West, 25 of 25. Nicholas S with the NFC West by way of the Cardinals. Very nice. Congrats NFC West. There's a Jerry Rice, 10 of 15 on the green for the NFC West. That's nice. The very underrated running back is Steven Jackson to 429. Brother's next. We've got Madden. What was it? Madden 12. Cover man is Peyton Hillis. Congrats on that one there, AFC North. And I believe this will be a random as well. Oh my God, the names on this. That's gonna be Ryan Williams to Marco Murray, Jamie Harper and Steven Ridley. So that's NFC West, AFC South. That is NFC East and AFC East. So yeah, that'll be a random as well. 12 to go on exquisite, baby. Reconnext, two of five. Yeah, it was his kids, I'm pretty sure. Rich, you just saved his kid's life from drowning. Oh yeah, I saw that. He was in critical condition. Yeah. Is he okay? Does everybody know he's okay? I think that he was taken off a ventilator. I think he's doing that. Okay, thank God. This box, instead of banging her out of this one. I had eight of 99 for the AFC West. Okay, he's good now. Okay, good, good, good. Thank God. There's a Alex Green to 429, excuse me, 429. As well as a, oh man, what a name on this last one. That is to Marco Murray to 429. On the rookie. Nice one there. A little bit of a corner issue. I guess we could probably send an empty box and wrap it right. See why not? Send an empty box and do this next one. I was obsessed with this guy in college. Like when he was in college, I was legitimately obsessed with this guy. How about 16 of 90? Titus Young, Boise State legend. That is trick play legend. That is absolute monster next to Austin Pettis with Doug Martin in the backfield. Titus Young. Going to the NFC North. That's a name right there. That is somebody I completely forgot about even existed. Unbelievable. Titus freaking Young, everybody. All right guys, let's do a quick random. We're going to random the two of five quad relic, both of them, and that's 25 of 25, as well as the one of one Christian Ponder and Leonard Hankerson. Man, what a couple of names in this. We'll do a quick recap and then I will turn it over to Kenzie and we'll break some squizz. Quad receiver. I can't believe I'm typing in Jamie Harper. I'm typing in a card to random for Jamie Harper in the year 2023, as well as Leonard Hankerson and Christian Ponder. That's insane. Ponder, Hankerson. That is the first and last time we'll ever type that duo into the random. All right guys, let's do these randoms. I'm going to start off with the wide receiver quad. That's going to be the NFC North with AJ Green, NFC South of Julio, NFC South as well with Mark Ingram and NFC East with Daniel Thomas. Nobody owned more than two of these spots, so it will go to random. Good luck. We'll start on this. Going to roll each of them seven times. So we've got one, two, three, four, five, six, seven. Going to the NFC North with AJ Green. Seven times on the running back quad. Two of five, got Ryan Williams, NFC West, DeMarco Murray, NFC East, Jamie Harper, NFC South and Stephen Ridley, NFC East. Seven times. One, two, three, four, five, six, and seven. NFC South on that one with Jamie Harper. I can't believe Jamie Harper's bringing that card home. And then seven times on the dual one of one, Christian Ponder and Leonard Hankerson, dual RPA between the NFC North and the NFC East. Good luck, everybody. One, two, three, four, five, six, and seven. Going to the NFC North. NFC North. Congrats on that one. Let's do a quick recap, everybody. We had the Brady, number to 429. Ryan Mallett to 10. Mark Ingram to 25. Julio Jones to 10. Titus Young to 90. Ryan Williams to 25. Jarell Jernigan to 50. Shane Vereen to 50. Jake Locker to 175. Legend. John Baldwin, Jersey Otto to 50. That is Jarell Jernigan, Jersey Otto to 20. That is Leonard Hankerson, RPA to a five. We had the Vaughn Miller, unfortunately, expired redemption. We had the Ray Lewis, 38 out of 50. That's so nasty. And the one of one dual, Christian Ponder, Leonard Hankerson. That'll do it for the break, guys. Thanks again for the fill. Next up, Kenzie's coming over with some exquisite-


In this presentation we will discuss the weighted average inventory method using a periodic system. The weighted average method as opposed to a first in first out or last in first out method, the periodic system as opposed to a perpetual system. We want to keep the other systems in mind as we work through this comparing and contrasting. We're going to be working with this worksheet entering this information here. It's important to note that this worksheet is a worksheet that can typically be used with any of these inventory flow type problems of which there are many. We have first in first out, last in first out, the average method. And then we have a perpetual and periodic system which can be used with any of those methods. It's also possible for questions to ask for just one component such as cost of goods sold or ending inventory. And therefore it can seem like there's more types of problems that we can have in that format as well. If we set up everything in a standard way, even if that weighs a little bit longer for some types of problems, it may be easier because we can just memorize that one format to set things up. This would be a format to do that. This would be breaking up the information into three components. Purchases, cost of merchandise sold, and inventory or ending inventory. Within those three components we're going to have the quantity, the unit cost, and then the total cost in each of these three sections. And then we'll enter the data through this worksheet as we go starting this time with the beginning inventory. So this is where we started at the beginning of the month, in this case the month of March. We're going to say the beginning inventory is 100 units costing $50, 100 times 50 being $5,000. We're going to put that same $5,000 out to the total column just to give an indication as we go through this worksheet of what the total is in its own distinct column out in the total section. So there we have that, 5,000 units, that's where we start. If we look at our trial balance, it will be in order, assets, liabilities, equity, revenue, and expenses, debits, non-bracketed or positive numbers, credits bracketed or negative numbers, the debits minus the credits equaling this zero. So we have net loss in this case, meaning revenue of zero minus these expenses 5,3 and 9,920 giving us a loss of 10,720. We're focusing here, of course, this time being the inventory on inventory. This 5,000 matching what we just put into our worksheet, that is our beginning balance, that's where we start. Next, we will have a purchase of 400 units at $55. We're going to put that into our worksheet in the purchasing section. Remember that the purchases will not differ no matter what method we will be making, whether that's FIFO, LIFO, AVERAGE, PERPETUAL or PERIODIC. It will be what it is in March. It was 400 units that we purchased at $55. Notice the rising prices from 50 to 55 for the inventory units we are purchasing, same units, costs going up. That's going to be the standard assumption that will happen. You want to just remember it going one way as if cost increase would be the norm. And then if it goes the other way, then we can kind of just reverse some of the effects that would happen. So in other words, as costs rise, what's going to be the effect on ending inventory and cost of goods sold under the three methods, LIFO, FIFO and AVERAGE, and then reverse the effects, obviously, when costs then fall. So we're going to have the 400 times the 55, that'll be the 22,000. Then we're going to do our average calculation. Now, it's possible since we're doing a periodic system to just do all of the purchases and then calculate the average at the end. But we're going to calculate the average as we go to get practice calculating the average. It can be something that people find a little bit more confusing because of the weighted average that we will be using. So what we're going to do is we're going to calculate our average by putting the calculation all under this line, under this date line. Again, moving this amount down. So there's our 100 units at 50 or 5,000. Then we're going to move this column over and there's our 400 units at 55. So we started at 100 units at 50. We got 400 units at 55. What we want to do now is create the average. Now, I'm going to show the wrong way to do this first of all and then we'll calculate the weighted average. So the normal average of just the two prices would be 50 plus 55. Those two numbers divided by two would give us an amount right in the middle of them at 52.50. Which seems reasonable. 52.50 seems reasonable. However, it's not exactly right because there's a lot more of the 55 units, 400, than the 50 units, 100. And therefore the weighted average taking that into account would be closer to the 55 than to the 50. So that's the mistake we just have to kind of avoid. How are we going to do this? We're going to take the total here, the total dollar we've spent, and the total units and then divide those out. So it can look a little bit confusing on the worksheet because we're first going to calculate or sum up the units, 100 and 400. We're not going to sum up the unit cost. That doesn't really make any sense because it's the unit cost. We can sum up the total here, 5,000 and 22,000 for 27,000 and then take this 27,000 divided by 500. So now we're simply taking the 27,000 divided by 500 and that gives us the 54 which is closer to this number that's the weighted at the 400 units. So we get 54 as our total. If we pull that out to the outer column then the 27,000 what is what should be on our financial statements in ending inventory and our trial balance. We're going to record the journal entry here now. Here's going to be our new thing that happened. We purchased another 400 units for 22. We're going to adjust inventory. Inventory has a debit balance. We're going to make it to go up by doing the same thing to it. This is another debit of 22,000. Then the other side is not decreasing cash but increasing the liability accounts payable. Therefore we will increase accounts payable by the 22,000 posting this out then. We have the inventory. Inventory is up here. It started at 5,000. It's going to go up by the 22,000 to 27,000. Then we have the accounts payable. Counts payable 12,150 going up by 22,000 to 34,150. Note once again this transaction is going to be the same no matter what method we are using. If we see everything here we're going to say that we're still in balance. No effect on net income. The purchase of inventory was not expensed at the time of purchase. It will be expensed but not till it's used in order to generate revenue in accordance with the matching principle. That will be when we sell it in the form of cost of goods sold. However, under a periodic system we're not going to get around to recording that cost of goods sold until the end of the time period until we do a physical count the end of the month, the end of March in this case. Next transaction we're going to say that there's a sale of 420 units at $85. Now if we were using a perpetual inventory system we would have to record the reduction of inventory and the cost of goods sold along with the sale into our worksheet. We're not looking at the worksheet here because we're in a periodic system and we're not going to record that component until the end of the period with a physical count. What we will record is just the journal entry just to demonstrate this journal entry, the sales journal entry which will be the same under the two methods a periodic and perpetual the second piece being the difference. So remember that if we make a sale on a merchandising company we typically assume that it's going to be a perpetual system and we often break out that journal entry and thinking about it into two journal entries meaning we have the sale side and then we have the inventory or cost of goods sold side of the journal entry. The sale side we can think of as similar as if we were a merchandising company and we can just eliminate the inventory and say hey what would happen if we had a sale or did services and got paid or on account meaning we got an accounts receivable what would be the journal entry. This is not affected. Accounts receivable has a debit balance we got more of it people OS money therefore accounts receivable will go up with another debit so we're going to debit accounts receivable and then we're going to credit something and something will be revenue that revenue for a service company might be fees earned or it might be revenue or income and it could be called sales for a merchandising company but it's all just a revenue account. So it's going to go up in the credit direction of the normal journal entry that we see whenever we make a sale whether it be merchandise or a service type business accounts receivable going up revenue going up. Then we have the second component that we typically think of when we make a sale as a merchandiser meaning we sold merchandise inventory should be going down and the related cost of goods sold should be going up. We're not going to record this under a periodic system that's the difference between a periodic system and perpetual system for the decrease in inventory and related cost of goods sold expense at the point at the end of the period the end of the month in this case the end of March after we do a physical count. Why? Why would we do that? Why would we not decrease the inventory? We know the inventory went down and it's probably just the sophistication of the system. If we have a clerk or someone recording these sales it's easy to know what the sales price is but this sales price has nothing to do with the cost of goods sold or in other words the cost of goods sold might have been used to make that sales price but there's no direct relationship between these two things. The sales price is known when we make the sale so 420 times 85 that's the 35 700. That's what we want to focus on collecting the revenue and making the sale at the point of sale. We don't want to spend all of our time training people how to record the cost of goods sold or inventory if they have to do it manually because that could take some time especially if there's multiple products that we are selling. If however it's an electronic scanner system that does it at that point in time without us even needing to know what the cost is then that makes it a lot more doable to do a perpetual system which would be better from an accounting standpoint. If we don't have that sophistication we may be using a periodic system which will simplify the process but we know that it won't be entirely accurate until the end of the time period. So if we post this out then accounts receivable debit balance we're posting this 35,000 to it going from 44,900 up by 35,700 to 80,600 then the revenue is going up from zero we're posting this revenue up from zero by 35,700 to 35,700 if we look at our full transaction we're back in balance net income is going up drastically went up a lot went up by 35,700 so 35,700 minus these expenses is 24,980 so that's going to be our net income note it's really not exactly correct now of course because we haven't recorded the cost of goods sold and that's going to be substantial expense that we haven't recorded we haven't recorded the decrease in inventory so our assets are overstated we will do so at the end of the time period the end of the month the end of March. Next we have on 3,18 purchased 120 units at $60 per unit so once again we'll be in the purchases column this will be the same as in any method first in first out last in first out average perpetual periodic these purchases are what they are this is what we will actually pay for the inventory we're going to have the 120 units at $60 note the rising prices from 50 to 55 to 60 that's not because the units got better that's not because we're buying better widgets or better inventory the prices just going up and that's going to be the standard prices increasing the standard for these types of problems the standard for practice as well due to inflation if nothing else the 120 times the 60 will give us the 7,200 now we're going to calculate the average once again remember that if we're doing a periodic system we could calculate the average basically at the end and sum up all of them but I want to calculate the average each time we make a new step because this is the most complex component typically what we're going to do is draw a line here we're going to bring this amount down so this is what we had before we had 500 units at $54 that's $27,000 then we're going to pull over the new information here's the new information what we are not going to do when calculating the average what you want to avoid be careful of is to just take the amounts the 54 plus the 60 the 54 being the old average plus what our new inventory costs and taking that and dividing it by 2 what's the problem with that it looks like a reasonable number but it's not taken into account the weighted average it's not taken into account that we have 500 units at $54 and only $120 at $60 and therefore this number should not be right in the middle but leaning towards the $54 so instead what we're going to do is sum up the total units we have the $500 and the $120 then sum up the total amount that we paid for those units $34,200 and then we'll do the division problem that division problem being the $34 $200 divided by the $620 units giving us a number of $55,16 note it's not going to round specifically to the penny that's okay that happens in practice we're going to round it to the penny because we're talking about dollars and cents here so we're going to say that calculate that that number here is going to be this number divided by this number or the total dollar amount divided by the quantity so that's going to give us the $34,200 that we want to get to on our trial balance now in our financial statements we're going to do that recording the journal entry the journal entry will be the same under any method FIFO, LIFO, AVERAGE because it is a purchase that's not the side that differs the side that's differing is when we make the sale so we're going to say that inventory has a debit balance we need to make it to go up so we're going to do the same thing to it another debit so here's the debit to inventory the other side is not going to be paid with cash we're going to increase the liability so the liability has a credit balance we're going to increase the accounts payable therefore by a credit of $7,200 posting this out then we have the inventory in the journal entry the inventory up here in the assets we started with $27,000 it's going to go up by $7,200 to $34,200 then we have the accounts payable we have the accounts payable here it's at $34,150 we're going to increase it in the credit direction $7,200 to $41,350 so there's going to be our transaction this $34,200 matches what we just calculated on our worksheet the $34,200 the inventory worksheet supporting the inventory amount reported on the trial balance or the balance sheet here's going to be the full transaction we still have the $34,200 or back in balance indicated by the green zeros no effect on net income no effect on these accounts the revenue or expense accounts we will be affecting the revenue expense accounts by the inventory that we purchased not at the point of purchase but at the time we sell the inventory in the form of cost of goods sold however under the periodic system we won't be recording that until the end of the period when we do the physical account we're going to do another purchase here purchase 200 units at $62 so we are going to be in the purchases column once again the $200 unit purchase at $62 note the rising prices going from 50 to 55 to 60 to 62 same units, unit cost going up because of if nothing else inflation that will be the norm you want to think that it can go down but you probably want to think the norm will be increasing prices and then reverse your thought process for it to go down the 200 times to 62 gives us $12,400 we're going to calculate our average now and we could do this at the end of the time period under a periodic system for the average method we're going to do it as we go, this being the key component to the average system calculating that average cost to do so we're going to draw a line under our last date line and we're going to be putting this new information here taking this $620 down just copying that down and then we're going to pull over our new information and once again we're going to say what not to do which is a common common error in calculating this and that's going to be taking the 55.16 plus the 62 or the two prices and just dividing by two that's an average but it's not the weighted average because it's right in the middle of those two costs and it should be leaning towards the $620 it being weighted higher it having more inventory in it so what we're going to do instead is we'll sum up the $620 and the $200 to get the $820 then we'll sum up the $34,200 and the $12,400 amount to get to the $46,600 and then we can do our average, we're going to take the total dollar amount the $46,600 divided by the $820 units giving us an average of $56,83 rounding up not worrying about the fact that we have all these decimals we're going to use it rounding to the pennies talking dollars and cents so that's going to give us the $56,83 that's going to be this number divided by this number, there's the total that we are going to be reporting on the financial statements we will now record the journal entry for that new purchase, the purchase of the $12,400 remember that the journal entry will be the same under LIFO, FIFO average, periodic, perpetual all of them, this is not an estimate we're going to say that the inventory started at the debit balance and we're going to increase it, we bought more inventory with a debit of that $12,400, we're going to credit not cash, but the liability of accounts payable increasing the accounts payable posting this out, we have the inventory here going to the inventory there starting at $34,200 increasing by $12,400 going to a total of $46,600 here's the accounts payable there that's going to be posted here, we've got a credit balance starting at $41,350 increasing $12,400 to $53,750 noting that the inventory that we end up with is supported by our inventory worksheet, now we're going to do the inventory count at the end of the time period this is what we're going to do in a periodic system in order to record the cost of goods sold for the entire period what we have not been doing for the entire period and record the related reduction in inventory something we haven't done so you'll note that as we go in our worksheet we've just been doing purchases and we've been increasing and increasing with purchases not recording the decrease in the inventory for the sales and we're going to do that at the end of the time period due to and with the help of a physical count and the cost of goods sold calculation cost of goods sold calculation a mandatory calculation something we really have to know both in terms of units and in terms of dollars the format will look like this beginning inventory plus purchases gives us goods available for sale or mount available for sale minus the ending inventory will give us cost of goods sold that's going to be our calculation now note that a multiple choice question might ask you for any component just give you three one unknown for this formula they might give you the beginning of the unknown for example or the purchases as the unknown now you could write this formula as beginning inventory plus purchases skip the subtotal beginning inventory plus purchases minus ending inventory equals cost of goods sold and write it out as an algebraic equation giving any of these unknowns then as long as we only have one we would then be able to find out any of these amounts so keep that in mind you don't want to remember multiple different equations to figure out for example purchases or beginning inventory you want to remember one equation cost of goods sold that can answer any of those types of questions you do need to know the subtotal however by name even if you don't use it in the equation if you pull it out for an equation because some problems will refer to it as well as in practice we're going to do this calculation first for the units and then we'll do the same calculation in terms of dollars we started with a hundred units that's what we began with we purchased 720 units 400 plus 120 plus the 200 in the purchases section that gives us 820 available that doesn't mean we had 820 at any given time in our warehouse but within the widget warehouse we had 820 go through it meaning we started with 100 we purchased 720 we may have sold items throughout here we don't know what we sold but we know what we purchased and therefore had available for sale hence the name, goods available for sale and that's 820 then we're going to do the physical count so we're going to say there's 240 widgets left in the widget warehouse so there's 240 left so if we had 820 we could have sold 240 are still there given our physical count then the difference between the two is 580 that's what we sold in terms of the widgets it is possible that we had shrinkage or theft or spoiler or something as well which is why the perpetual system would be nice to use because it can verify or better verify that type of problem but our assumption is it's sold and the assumption is that the shrinkage of any kind breakage, theft is in material and in relation to it and therefore we're going to record this entire amount to cost of goods sold so note what we did here we just basically said hey this is the amount we had available and then allocated it out between either what's still left in Indian inventory and what has been sold we're going to do that same thing with dollars it would be a very easy conversion if the dollar amount were the same throughout the entire period but very often it is not even though we're talking about the same widgets we're not buying different types of things it's all the same but the dollar amounts are increasing so that makes it a little bit difficult if we see this then we're going to say well we started with $5,000 that's our beginning balance we know that we purchased 720 and we purchased them for $41,600 we can't convert from $720 to $416 easily because of the different dollar amounts but we know what we purchased we can just look at the GL and say hey we increase inventory that's how much we're going to pay it's not an estimate this is what we're going to pay $22,000 plus $7,200 plus $12,400 that's a given that's not an estimate and so if we add those two up we're at $46,600 that's where we stop now we're going to allocate that out between ending inventory and cost of goods sold however we know that there's 240 units that we're still in ending inventory but now we have to figure out our conversion here because we need to know which of those units we purchased some for $50 some for $50 some for $60 some for $62 that's what we'll do now in the average method and the average method because we've been calculating it as we go is nice and easy right now we're just going to say well yeah some of them cost $50 $55, $52, $60 whatever but they all cost around about an average if we average them all out a weighted average of $56 and $63 so we're going to say whatever we sold in this case 580 units those 580 we sold for this $56.83 about if we multiply 580 times $56.83 we get $32,960 $93 and that's our cost of goods sold this is the cost of goods sold we haven't been recording the entire time period it's the cost of goods sold that we would record every time we make a sale under a perpetual system the cost of goods sold we are now recording for all sales happening during the time period in our case the month the month of March month of March so we have 820 units that we had before minus the 580 means we still have left 240 so we did this allocation of the 820 units 580 have been sold and 240 are still left they are at $56.83 if we multiply 240 times the $56.83 we get $13,639 $02 so now we can fill out the rest of this form we can say okay the ending inventory is $13,939 $639 $02 and we could subtract this out then and notice we did take off the rounding here so here we have the pennies here we remove the pennies it's just rounding so if we take off the $46,600 minus $13,639 we get the $32,961 which is also matching this amount $32,960 rounding $961 that ties out we're going to do our final journal entry now this would be the journal entry that we would see under a perpetual system every time we record a sale or similar one at least one that would be reducing inventory and recording cost of goods sold but under a periodic system as we are doing now we will only see it one time at the end of the period whatever period that may be for our case the month the month of March so we're going to record the reduction of the inventory for the entire time period we're going to make it go down by doing the opposite thing a credit and the related cost of goods sold cost of goods sold is an expense it's going to go up in the debit direction bringing net income down so here's the cost of goods sold and there's the inventory so once again this is the journal entry we would see each time under a periodic system as we record sales it's going to be the second half of the sales transaction but under a perpetual under a periodic under a perpetual under a perpetual system but under a periodic system we're only going to record it for the entire sales all sales made during the period at the end so if we record this here's cost of goods sold here's cost of goods sold here it's going to go from zero way up by the 32,961 to 32,961 here's inventory here's inventory it's at 46,600 it's going to go way down by 32,961 to 46,639 this number now matching the 13,000 in Indian inventory this number now matching our cost of goods sold calculation so note that before we did this transaction our net income was way too high and now it's way lower so that's going to be the case for the periodic system our net income cannot be trusted until we do this transaction the cost of goods sold being huge for a merchandising company typically also our assets will be way overstated until we do this end of period adjustment because once again the inventory is typically a fairly large asset and it's not being reduced as we make the sales so we gotta wait till the end of the period to have an accurate number there if we look at the comparisons here's our calculation here's our worksheet here's our trial balance we can see that we have the ending inventory here we have the ending inventory on the trial balance which would be on the financial statement we have the ending inventory on our worksheet we have the cost of goods sold here on the cost of goods sold calculation on our merchandise cost of goods sold worksheet and then we have the cost of goods sold here on our trial balance as well which would also be on the income statement