We were discussing about surface tension driven flows and we brought into discussion one very important aspect that is surface tension driven flow of blood and to understand that how do we model the surface tension driven flow of blood we started discussing a little bit about the rheology of blood that is the constitutive behaviour expressed in terms of some mathematical model. So we suggested that there could be several complex models of blood rheology but at the same time for simplicity we prefer to use a model like this where k and n are the 2 parameters consistency index and behavioural index. Now these indices unlike many other fluids are not constant for blood and these indices sensitively depend on the composition of the blood. So see I am trying to give you a broad picture. Let us say that somebody is handling of disease blood sample that means a blood sample that carries the signature of a disease. Now there are several diseases in which because of the disease there will be alteration in the blood rheology and these parameters k and n will change and if these parameters k and n change the fluid flow characteristics will change. So if you have a micro channel or a micro capillary through which blood is being transmitted and the flow characteristics of the blood are changing then that might give an indication of the existence of a certain disease in the blood sample. So that is many times critical and let us see now that what are the parameters on which this will depend. So as I pointed out in the previous lecture that the t stars can be neglected under certain situations so t is equal to ks to the power n where this t and s we have discussed these are stress and rate of deformation dietic of dietics. Now this k and n these are again dependent on several parameters. One of the important parameters is called the hematocrit fraction. Hematocrit fraction is essentially the volume fraction of the red blood cells. So it will depend sensitively on the volume fraction of the red blood cells because we see here that the k depends on the h, h is the hematocrit fraction. So in some way see these are not in medical applications see medical applications are very complicated. So you do not always expect that equations and expressions will be derived from first principles. So these are the expressions for k and n which are given here these are not derived from first principles but these are curve fitted from a huge number of experimental data collected over the years. So I mean in that spirit you need to understand I mean there is no like first principle proof of like I mean where from these expressions come. So we will we see here that some coefficient c1, c2, c3 appear in this context and before getting into what is what should be c1, c2, c3 on what parameters those will depend let us quickly revisit the blood properties. So human plasma is transparent plasma is the watery part of the blood that is transparent slightly yellowish with a typical density of typical 1035 kg per meter cube. So it is like you can understand that it is just like water density it contains a solution of plasma proteins in an aqueous medium proteins contain about 7% of the total plasma volume and can be classified into 3 major groups albumin, globulin and fibrinogen. We discussed about fibrinogen and it is importance in the context of the constitutive behavior that if you take away the fibrinogen the t star component will go away. Plasma also contains the emulsified fats or lipids cholesterol free fatty acids hormones dissolved oxygen dissolved carbon dioxide. So this is the plasma composition now whole blood is plasma plus the blood cells. So blood cells will contain red blood cells erythrocytes red blood cells are also called as erythrocytes. So you can see like how the red blood cells typically look in these pictures WBCs or the white blood cells which are also called as leucocytes and platelets in an aqueous solution. The red blood cell count is approximately 5 million per millimeter cube which is about 40 to 45% by volume of the whole blood. As I told you that we define a parameter H which is hematocrit if you express this hematocrit by volume percentage then it is about 40 to 45% but you can well understand that it is not constant. It will vary from one individual to another individual it will vary from one diseased condition to another diseased condition. So based on the hematocrit it is possible to like describe the rheology of the blood sample. Now just to give you some idea typical dimensions of RBC like 7.8 micron in diameter. See I mean long time back when we were discussing about some introductory application introductory ideas regarding applications of microfluidics we told that biological cells are very important constituents in microfluidics and you can see that the dimension of the red blood cell see it is around say roughly 10 micron I mean I am not going into the intricacy of difference between 7.8 and 10 just say roughly 10 micron. So if it is so you see that like it is its dimension is comparable to dimensions of many microfluidic channels. So microfluidics can capture the variations over the length scales of these kinds of cells very nicely and these are typically 2 micron thick and 88 micron cube in volume its function is transport of oxygen I mean it is one of the main functions and less number of RBC will lead to a disease called as anemia. Size of WBC is significantly larger all the order of magnitude wise it is still the same but size of WBC is 16 to 22 micron for monocytes but I mean it is much reduced for lymphocytes and granulocytes I mean these are different types of WBCs so monocytes will be significantly larger but lymphocytes and granulocytes these are typically less in size WBC protects bodies from disease and normal WBC is to RBC concentration is equal to 1000 but if there is abnormal rise in WBC number that sometimes is an indicator of a disease called as leukemia. Platelets are smaller than RBC and WBC and their diameter are about 2 to 3 micron and platelet is to RBC is 1 is to 10. So you can see that RBC is the dominating type of blood cell but other blood cells have also have very significant functionalities platelets and WBCs are actively ordinarily not enough to influence the blood flow characteristics. So like one has to understand that here we are studying the or here we are going through the different types of blood cells not because we are interested as such about the biological characteristics of the blood cells but we are interested to see how they influence the fluid flow, how they influence the fluid flow. So in terms of influence on the fluid flow platelets and WBCs do not have that kind of very significant influence as RBCs have however platelets play an important role in forming blood clots that may severely interfere with the flow. And depending on formation of blood clots there can be serious conditions with in a human body which are known as strokes. So it is not an explicit control of the rheology of blood but by implicitly controlling the formation of clots it is possible that platelets can also significantly alter the blood flow. Now we have seen that it is the hematocrit that plays a significant role towards altering the blood rheology and it is the volume fraction of red blood cells. And in describing that how the consistency index and behavioral index depend on hematocrit 3 important parameters C1, C2 and C3 came into the picture. So in this particular slide we will discuss that what are the parameters or what are the factors on which C1, C2, C3 depend. So C1 depends on plasma globulin concentration and on hematocrit. So that is why you see these are not universal constants that is what I want to impress upon you that these are not universal constant. These constants will vary from one individual to the other one diseased condition to another diseased condition. See C1 increases with total plasma-albumin fraction. What is albumin? That is a protein in the blood plasma. So if there is a change in concentration in albumin then C1 will change. So see that many times you go for blood test and you go for detection of a disease or sometimes quantitative evaluation that is say blood composition test. So this is an indicator that instead of going for the blood composition test explicitly there could be another implicit way that the flow carries the signature of the blood composition through the rheology. So it might be possible that by relating the flow with the blood rheology and that with the composition of the blood it might be possible to argue about the possible constitution of the blood. C2 also increases directly with TPMA and both C1 and C2 show more sensitivity to the viscosity of the blood plasma than to any other factors related to blood cells. Now what about C3? C3 is relatively independent of plasma chemistry and appears to be remarkably constant for a given animal species. So this is a constant which is relatively independent of the blood chemistry. As C3 decreases so does the average hemoglobin concentration. So it is not so much species dependent but it is dependent on the average hemoglobin concentration and increase in shear rate will deform softer erythrocytes or red blood cells and more non-Newtonian the fluid becomes harder the cells more Newtonian the fluid is because increasing the shear rate has no effect on the viscosity of the hardened red blood cell suspension. So this is a very very important point to discuss like many times like people loosely ask a question and I have seen I mean like many interrogators troubling other people by asking that is blood a Newtonian fluid or a non-Newtonian fluid? It is actually not a very straightforward answer it depends on many things like for example it depends on the hardness of the red blood cells. So if the red blood cells are soft then they can be very easily deformed. So you can see then an increase in red blood shear rate will deform soft erythrocytes or the red blood cells and more non-Newtonian the fluid will become. However if the red blood cells are hard then the shear rate has no effect on the viscosity effective viscosity. So viscosity is a constant the apparent viscosity will not change and that means it will be like a Newtonian fluid. So whether it is Newtonian or non-Newtonian may depend on all these parameters and you can see now you see that the hardness of the red blood cell is a critical issue and hardness of the red blood cell since it dictates the rheology and hardness of the red blood cell also carries the signature of certain diseases. So it is possible to detect a disease by using the rheology of blood because I mean the hardness of the red blood cell many times is significantly altered by virtue of certain disease conditions. The parameter C1, C2 and C3 for a given sample of blood depend on the chemistry of the plasma specifically it is globular protein composition chemistry of the red blood cell specifically it is hemoglobin concentration number of that is the volume fraction of the red blood cell that is the hematocrit fraction size and degree of cellular aggregation of red blood cell and the red blood cell shape geometry and deformability mass density of red blood cell plasma and mass density of the composite whole blood. Now you see that there are so many parameters involved and each of these parameters if these are altered then the rheology of the blood will be altered and the flow through the micro channel flow of blood through the micro channel will be altered. So in a disease condition one can have unusual hydrodynamics because of the existence of certain disease in the blood. Now one important thing to understand is that in one way by which flow and shear rate and flow and rheology are coupled in two ways it is a two way coupling is that if you have altered flow you will have the altered shape of the red blood cells if you look here that depending on this is a shape diagram of the red blood cells. So you can see that with change in flow velocity the red blood cell shape will change and the red blood cell shape when it changes it might alter the flow rheology and that might in turn alter the flow. So there might be a two way coupling of course these two way coupling will be strong only if the shape change is very significant. If the shape change is not very significant this kind of two way coupling will not be there. At abnormally high flow rate and in constricted region of circulatory system red blood cell may deform and burst. This is like a severe condition of unusual hydrodynamics that if you have abnormally high flow rate and in a very constricted region I mean if the flow passage is very narrow then the red blood cell cannot sustain the shear and it will rupture and it can be a life threatening condition. Change in effective viscosity with volume percentage of red blood cell is manifested in several diseases like anemia or polycythemia. Anemia as we discussed is a decrease in normal number of red blood cells or less than normal quantity of hemoglobin in the blood. Polycythemia is a disease state in which proportion of volume that is occupied by red blood cell increases beyond the normal amount. So in the two extreme conditions you can have the disease which is related to the hydrodynamics of the red blood cells. I mean the disease is not directly related to the hydrodynamics but the disease is related to the rheology and the rheology concerns hydrodynamics. So we can relate this disease with the hydrodynamics. Now so far we discussed about how the composition of the blood so to say affects the blood rheology. Now the same blood sample when it flows through a tube, tube means it may be a capillary tube or a microfluidic channel whatever when it is flowing through a tube if we reduce the diameter of the tube what happens? So the normal intuition is that so if you have a sample, if you have a blood sample then if you have a channel of say or a tube of say 4 millimeter, 3 millimeter, 2 millimeter in size then you will have a effective viscosity of the blood sample. If you reduce the dimension from say 4 millimeter to 0.4 millimeter, 1 order less. What do you expect? Do you intuitively expect the viscosity to increase? By viscosity I am saying loosely the term viscosity it is apparent viscosity or effective viscosity. If it is not a Newtonian fluid we cannot call it viscosity. So is the viscosity expected to increase or decrease? What does our intuition say? So if you have a blood vessel which has a lower dimension then our intuition will say that actually it might increase the viscosity of the blood sample, effective viscosity because a smaller diameter means a greater constriction and the constriction will not allow the blood flow, blood to flow easily. But in reality what happens is something that is significantly different from that and this effect is something which is very very interesting and we will discuss a little bit.  But let us say let me draw 2 different diagrams. One this green colored channel is a larger diameter. Let us say this is the 4 millimeter and this is the 0.4 millimeter one. The black one is the 0.4 millimeter diameter. Now let us make a schematic of the blood cells there. We are not trying to resolve the shape of the blood cell, just trying to draw something like this. It is little bit enlarged, not in proportion just for clarity nothing more than that. So let us say that let us consider the center of this. Now here at the wall what is the expected velocity? If it is in contact with the wall, if it was in contact with the wall the expected velocity would have been 0 because of the no slip boundary condition. On the other hand at the center line there is a non-zero velocity and because of this relative tangential velocity there will be a rotation of the blood sample, blood cell. Because of the rotation in the blood cell there is a lift force that is I mean if you have a body even in a potential flow if you have a circulation, flow around the body with a circulation there is a lift force and this is something which is very common I mean this kind of lift force I mean you can see in sports balls also. So if you give a circulation to a tennis ball or a cricket ball in a certain direction the ball will tend to be floated up in the upward direction that is the top spin. So this kind of effect in fluid mechanics is called as Magnus effect. So now if you have this kind of rotation there is a tendency of a lift force. Now with a lift force if the lift force is good enough then the cell will be detached from the solid boundary and it will move towards the center line. Now can you tell that given the same flow rate in which case the blood cell will experience a stronger lift force in the case 1 or case 2. In case 1 the reason is that here the center of the blood cell is closer to the center line where the maximum velocity is there. On the other hand here it is far off from the center line. So that means the stronger the lift force what will be the effect the blood cell will very easily join the bulk flow of the center line leaving behind a cell free layer adhering to the solid boundary. Now the region close to the solid boundary is primarily responsible for the viscous behavior of the fluid. Now there if the blood cell gets depleted that is there is a depletion or cell free layer form then actually that will reduce the effective viscosity of the blood sample and this blood cell when it joins the center line will actually add to the inertia of the system because it has its own mass and therefore it will try to have a favored transport of the fluid instead of creating a resistance. So if you reduce the diameter below a threshold limit then actually the effective viscosity of the blood sample will go down instead of going up. This effect is known as Farhuse Lindquist effect and it is a very important and interesting effect in medical science it has been studied in medical science for a very long time and this effect also is important when we are doing fluid mechanics experiments with blood samples. So that has to be taken into consideration.  So streamlines that are closer to the center line of the channel represent fluid velocities that are faster than the ones associated with fluid streamlines close to the wall. This gradient in velocity across any suspended particulates say RBC start the cell spinning right. We have qualitatively discussed all this these are just like recapitulations in such a way that the side of the cell facing the channel center line moves in the direction of flow whereas the side of the cell facing the wall of the vascular channel moves in a direction against the flow. This leads to a drift in the particulates away from the wall resulting in the existence of a region constituted of the bulk fluid but devoid of the blood cells that is called as skimming layer. This implies that near the walls where the viscous effects are the most predominant the effective viscosity becomes less and the axial pressure gradients do not have to work as hard as it would have otherwise required to drive the flow if the blood cells were densely populating in the near wall region and hence the whole fluid appears to be less viscous okay. So again I am repeating this is a very very important phenomenon in medical sciences I mean in medical sciences whoever is studying hematology is giving a lot of attention on this specific behavior. So if you see here that if you look at this graph just to give you an idea that relative viscosity I mean it is a viscosity relative to a reference state. So this relative viscosity it is not important that you look into the numbers but see the fall. So if you take the tube diameter say 4 millimeter from 4 millimeter to 3 millimeter if you reduce your tube diameter you will see that there is not much change. But if you reduce below 0.5 millimeter that is what 500 micron. If you reduce below 500 micron you will see that there is a dramatic drop in the relative viscosity. See these are all natural ways by which nature helps in moving a fluid through a capillary and like it is not there for all fluids but this is I mean possibly nature has made the blood in living beings in such a way that the blood rheology adapts to itself to augment the flow characteristics as you reduce the diameter because as you reduce the diameter otherwise many other effects are adverse. So there should be certain favorable effects which come into the picture and this is one of the favorable effects. So with these considerations see these understandings were existing for a long time in the text of the blood hematology but these understandings were not commonly described in studying the behavior of the blood flow through microfluidic channels. So in my early days of research in microfluidics in 2005 I wrote a paper when like I brought it out that how all these parameters are actually influencing the blood flow through a microfluidic channel. So the paper was describing dynamics of blood flow through a microfluidic channel based on all these considerations and these are the summarizing features of I mean what was revealed. Now blunting of velocity profiles this we have not discussed significantly or elaborately but blunting of velocity profiles due to an axial accumulation of red blood cells as well as a streamline RBC alignment strongly influences the motion of fluid into the channel. This is something to do with the lift force that the blood cells experience as you reduce the diameter of the channel this force becomes more and more important. Influence of capillary forces increases with time. This is something which I want to discuss a little bit because this is just a summary but I want to discuss a little bit about this. Let us say that you have a capillary and there is a meniscus and the contact angle is theta. So what is the driving force on the capillary due to surface tension just due to surface tension. So perimeter into sigma into cos theta this we have discussed elaborately. Now we have to understand as we discussed that this theta is not the static contact angle value but this theta is the dynamic contact angle value. So typically for slow movement of a capillary front over a wetting surface this tan theta will scale with capillary number to the power one third. This we also we have discussed this is called as Tanner's law. So capillary number is mu u by sigma viscous force by surface tension force. So now as the fluid enters the channel forces come into the play. This driving I mean this surface tension if the contact angle is like this and if the capillary front is like this it is driving the flow in the forward direction but there is a opposing viscous resistance. These 2 forces will always be important and inertia force depending on the regime it may be or may not be important. So now if you see this driving force will try to drive the capillary but the viscous force will try to oppose. So if this is so then there might be a critical juncture when the viscous force is so strong that that might stop the flow of the fluid in the capillary but typically we see that in small capillary the static height being large the static lift the total static displacement being large it is possible that the fluid gets traversed by a large distance I mean it is not a short distance after which it stops. So what makes the fluid to traverse a remarkably large distance despite a good amount of resisting force. In the resisting force as we understand that in microfluidic or nanofluidic channels the resistance force will be quite significant. Despite that the fluid traverses a significant distance which is not something very intuitive. So something very interesting happens. So what is that? So just try to roughly look into this formula. So if the viscous force is increasing that will tend to reduce the velocity. If that reduces the velocity that reduces the theta. If theta is reduced the driving force which is proportional to cos theta this cos theta will increase because as theta decreases the cos theta increases. So you can see that this is like a natural justice to the capillary transport. So what is happening is the viscous force is trying to arrest the flow but the surface tension force is almost trying to go beyond its capacity to self-adjust to increase it in such a way that the flow can be sustained. And because surface tension is a very important force over small scales this is one of the mechanisms by which you can sustain a flow through surface tension over small scales. So this is one way by which you can sustain blood flow also. It is true for any general fluid so blood being of no exception you can sustain also blood flow through the same way. Actual accumulation of red blood cells leaves behind a lower viscosity plasma skimming layer near the micro channel wall which otherwise is a region of high rates of strain. Consequently the apparent viscosity of the whole blood sample decreases and the effect of reduction becomes significantly prominent as the size of the red blood cell approaches the hydraulic diameter of the microfluidic channel. So size of blood cell being red blood cell being not so much variable so it is basically the size of the micro channel. So you reduce the size of the micro channel you can get this effect very significantly. So this effect of reduction in the apparent viscosity of the blood as you reduce the diameter of the channel this effect may not be significantly failed for all sorts of blood vessels. It can be only failed for blood vessels which are micro capillaries but not all sorts of blood vessels so we have to remember this carefully. So we will summarize the discussion so far. We have started discussing this chapter with the concept of equilibrium contact angle that measures the relative effect of the surface forces acting at an interface when a droplet is sitting on a solid surface. This can be measured experimentally. We have derived Young's equation and Young's Laplace equation from energy minimization considerations. Vertical capillaries exhibit capillary rise or depression depending on the surface tension of the liquid used. Capillary flow dynamics equations can be derived from Navier-Stokes equation with simplifying assumptions using Lucas-Washburn analysis which yields short time and long time scale solutions. We have derived these solutions. This lump system approach can also be used to model the capillary flow in a circular capillary. Now there are certain limitations that render it is useless to explain the exact contact line mechanics and dynamic evolution of the contact angle. So exact contact line as we discussed that the lump model is good enough to give the essential capillary filling characteristics but the exact description of the contact angle is missing from the lump analysis. The concept of virtual mass overcomes some of these limitations and gives a physically realistic picture of capillary filling dynamics and why we needed the concept of virtual mass to avoid infinite initial acceleration as time tends to 0. So by incorporating all these effects and also the effect of different regimes in the velocity profile not just a fully developed regime, we came up with a model of lumped model of capillary filling dynamics of blood and we use that model for specific case study and some of the results we discussed. So far we have discussed about surface tension driven flows but we have not discussed so much of how do we modulate surface tension because I mean there is of course a straight forward mechanism by which we can alter the flow by having surface tension as a force but many times we can alter the flow by having gradient of surface tension as a force. So how can we modulate surface tension that will be our next agenda to discuss. So we will discuss about again micro flow actuation but in the context of modulating surface tension. So micro flow actuation can be possible by various means. So we have discussed about how flow can be actuated by pressure gradient and this has philosophy very much similar to how flow can be actuated by pressure gradient in large scale systems through micro channels also the concept is very very similar. Capillary effects direct use of surface tension forces or their differentials due to thermal or solutal gradients that is one possibility. Rotational forces that is one typical scenario is electrokinetics which is basically combination of electrostatics and hydrodynamics. We will discuss about electrokinetics I mean after a few lectures. Magnetic forces exploitation of electromagnetic hydrodynamic effects which is also called as EMHDFX. Rotational forces fluid flow modulated by centrifugal and corioli forces again we will discuss about this through the microfluidic device lab on a CD. Sound we will not discuss that particular effect in this course but it is possible to have micro flows through acoustic streaming generated by pressure waves and light as an effective actuation of micro flows by light induced surface tension modulation. So that also we will discuss. Micro flow actuation mechanism through surface tension. So generate gradients in surface tension force so we have discussed about generation of flows using surface tension so that I am not repeating but the additional concept that we will learn through the subsequent discussions in this lecture is generate gradients in surface tension force. So how do you generate gradients in surface tension force? You can generate gradients in temperature, gradients in concentration using electrical field. You can modulate contact angle through design hydrophobisation or hydrophilisation of solid substrates, a combination of these effects and so on. So we will start with that how to modulate surface tension with temperature. This is also called as thermo capillary effect. So let us go to the board and we will try to discuss what it is. For most of the fluids the surface tension is a strong function of temperature okay. So this is true for most of the fluids. For many fluids again as we increase the temperature the surface tension decreases. This is a very common characteristics of fluids of many fluids and this has something to do with the physics and chemistry of fluids over molecular scales. So let us not get deep into that but we first appreciate that the surface tension is a function of temperature. For many fluids the surface tension versus temperature is linear. But for many fluids you can get even higher order variations like quadratic types of variations and so on. But the linear variation for water for example it is a linear variation. Now let us say that there is a free surface which is flat okay. So this free surface which is flat let us say that this is the free surface of a weld pool just as an example that is you are doing some welding process and this is the free surface of a weld pool as the material gets molten. Let us say this is a high temperature this is a low temperature region molten both places are molten. So just as a physical example let us say that there is a solid work piece and you are heating it by some energy source. Let us say laser or whatever. So this wherever heating is made there is a low surface tension because surface tension for that particular fluid we are assuming that it will decrease with increase in temperature. So here surface tension is low sigma as compared to here where the surface tension is high right. So a fluid element which is located on the free surface will be stretched to move from low surface tension to high surface tension and that differential surface tension will drive a flow in this way. So similarly on the other side also same type of flow will occur and because of its inertia and to maintain the continuity you can have a circulation loop like this. So this type of flow where there is a flow due to surface tension is called as thermo capillary flow or in convection terminology this is called as marangoni convection. Now how is this convection possible? This convection is possible because the gradient in surface tension induces a stress in the fluid. How does the gradient of surface tension induce a stress in the fluid? It will induce a stress in the fluid by a mechanism or by a mechanism by virtue of which the free surface is free of shear. That means roughly speaking the shear due to viscous effects is balanced by the shear due to surface tension gradient. So that the free surface is free of shear. So how do you that means how do you get the shear due to surface tension gradient? If you get the shear due to surface tension gradient that is same as the shear due to viscous effect and these 2 effects must nullify each other so that the free surface must be free of shear. So we should also try to assess that what is the stress that is there due to the gradient of surface tension at the free surface. So we will take it up in the next lecture as we go ahead with how to modulate surface tension. Thank you very much.


Welcome to the second in a series of backstory podcasts on the topic of early childhood learning in Longmont. My name is Tim Waters, and I've been invited by the Longmont Observer and the Longmont Public Media to moderate conversations of leaders, advocates, experts, and policymakers on topics of interest and relevance to Longmont residents. This month, we're focusing on young families with young children, concerned that, as a community, we're failing both because of insufficient childcare in early childhood learning opportunities in Longmont. Not that this group is failing them. More globally, we have too many kids who are not experiencing what they need to experience. Every story about an issue or a problem you read in the newspaper or read on the Longmont Observer website has a backstory, a backstory that is typically more interesting and engaging than what gets reported as news. So this month, we're telling a story that is understood all too well by moms, dads, and grandparents with children and grandchildren under the age of six. It's a story that's less well understood by business owners and primary employers, but one with huge implications for them is one that seldom draws the kind of intensity and attention and support it deserves from local policymakers. Because of its implications for nearly every goal or objective, the school board member or city council members and county commissioners establish when setting priorities is why we're doing these podcasts, because it's so important. Indeed, this is a backstory of a challenge so complex and pervasive of such consequence and of such significance that we're telling it in a series of no less than three podcasts. We'll see if we add to this series after we finish number three. These will be produced and posted in sequence on the Observer website in Longmont's YouTube channel as well as Longmont public media. And I guess channel eight now as it's up and ready to go. Our hope is that all Longmont and Boulder County residents will understand what's at stake for all of us if we don't get this right for the youngest of us. Today I'm joined by three. We have one drop out, Ann Mocka, who is the curator of education at the museum called in with that virus that everybody's dealing with right now. So we have three outstanding experts this morning. Amy Ogilvy is executive director of Wild Plum, one of Longmont's premier preschool programs and our primary Head Start program. She's running a pretty complex program. Matt Eldred, executive director of the Learning Center. Olga Bermudis is the community coordinator for prevention hyphen, children, youth, and families for the city of Longmont. It is involved in all things city of Longmont with respect to early childhood education. So let's start by learning a little bit more.  Give us an idea of why you're in this space and who you are. You want to start? Sure, I can start. I'm Amy Ogilvy. I'm the executive director of the Wild Plum Center. I have been in early childhood education for 15 years after about 20 years working with teenagers. So what I really found was that working with teenagers, we were trying to intervene at a much later time and that if we had done a better job in the early years with ensuring good brain development and reducing traumatic experiences, preparing children for school, we wouldn't have needed to intervene with as many teenagers as we did. So I made the switch about 15 years ago to working in early childhood education because of that. All right, Olga. My name is Olga Bermudis and I've been with the city of Longmont for 11 years. So how about my sister's degree in psychology? And I really believe in the prevention. I really believe that the whole country spends a lot of money in intervention. But I really believe that we can make a big difference if we really invest in prevention. So that's what I'm here because I really believe that we invest in the little kids. We really get them ready so we're going to be able to be successful and they're going to be able to thrive in our community. All right, yeah. My name's Matt Eldren. I'm the executive director at TLC Learning Center, a 65-year-old nonprofit early childhood center here in Longmont. My early childhood experience and background probably goes back to when I was a kid. I remember having foster kids in my home when I was probably in second, third grade. So I think I've been doing early childhood my whole life. Went to school for early childhood special education and PE. And then I couldn't decide which age group I liked. So my degrees are in special education and physical education, K-12. And then I went and did a master's in school administration. So I started working with adults with disabilities in college as kind of a way to pay the bills, became the director of that program before I graduated from college and then moved here to Colorado in 2000 and been working in youth services and early childhood services since we moved to Colorado in 2000. Yeah, I'm biting my tongue because having spent a lifetime in education, administration, and working with folks, I was going to make a comment about the difference between working with adults and young children and where the biggest challenges are. Yeah. But I won't make a comment. That's a different question. That's a different question. All right, here we go. More substance specifically relevant to the things we're doing in the Longmont and the Longmont area. And to start with, I just want to remind folks that Longmont City Council has adopted seven goals for the city and this panel is aware of these. The goals include priorities like housing, economic development, environmental protection, and workforce preparation. One of the goals that will have an integrated systems approach that leverages human social capital to provide high quality pre-K learning opportunities for all of our children so that they have a good start in life. Some may wonder why that's a goal that a city would set. So Olga is the key person in the city staff who helps to translate that goal to reality. Why would we have that goal and what does it mean? Well, why we have that goal is because I really believe that city council members understand that investing in the early childhood education is going to help the city. It's going to help the county to save some money in the long term. So through children, youth, and families, we have been working through this goal and providing high-quality trainings over trends. We develop several collaborations with the county, with the Corral Department of Education, and we are providing evidence-based trainings. So there are a lot of trainings in the community, but we are interested in trainings that really have been tested and they provide some results. So we did the TSS goal. I don't know if you guys remember that. We worked with the Aspen Center and the teachers were able to utilize some data right there and implement that with the classroom. So they were able to create some curriculums and get some results right there with the kids. And instead of getting a curriculum that was good for all 20 or 15 kids, it was a little bit more personalized and tailored to the different needs that the kids were having. So we have been making a lot of progress, providing a lot of trainings over trends. We also collaborated with the BULE Foundation. We applied for grants, and even they increased the amount of money that they provided last year. We went from $25,000 to $30,000, and that helped us just to provide more training and also enhance some of the programs that we have. For example, we have the Reading League. So we have some volunteers. We train them with the school district collaboration, and they go to the school and they read to the kids for 45 minutes to the kids that have been identified that they need some support. So yes, we are working toward increasing that high quality of training and opportunities for the kids. We also have a program, the Mayor's Book Club. We send some books, and the data shows us that 87% of the kids are improving. So we have 487 kids, and 87 is a pretty good number, showing some results. So the parents report, we send a pre-test and post-test. And parents are saying that the kids are asking us to be read, so that's an improvement right there. And they know some letters, and they know how to read short letters. Right there, we are making a lot of work toward improving the high quality of early childhood education. So I think that's an example of some of the different programs that we have in order just to work toward that goal. So I'm going to do a follow-up on this, and I want you to think about this and invite all three of you into the response. And I may answer the question myself, having been in this. I'll say again for this podcast and for this panel, I come to this experience with a volunteer hat on. I'm a volunteer with the Longmont Observer, and now with Longmont Public Media. You all know that I also wear a city council hat. Sometimes it's hard to tell the difference between the two or to take the one. You also have a little education experience. So I might put my city council hat on in response to this question depending on how deep you want to go with it. But everything that Olga just described, kids more interested in reading, reading scores improving, levels of parent satisfaction, given the things that she described already. And by the way, those are part of an answer to a question I'm going to ask later is how do people get involved? Because I'm guessing you wouldn't mind having more volunteers for the reading lead in the other kinds of things that we've talked about. But the question for me with a council hat on is their relationship between quality early childhood education and other city of Longmont goals like reducing housing insecurity, strengthening economic development efforts, protect the environment, assure a well-prepared workforce, and what I'll add to those is a bigger idea of quality of life. We hear a lot today in council chambers. We read it in the news just in conversations. People concerned about quality of life and that quickly gets connected to growth that some people see as out of control, homelessness that needs to be solved, having to wait too many left turn arrows to get a left turn because I have traffic congestion, which are all concerns about the quality of life for generally people who have some. This conversation is about those who we would like to experience more in terms of getting an early start in life. So what do you see as the connections between a quality start and the other goals that the city council has set?  So where are our most opportunities or where are our most liabilities in the lack of development or how do we best provide high-quality opportunities for kids to develop? So if we know that, if we agree that 90% of this is the brain, or our brain is happening by the time we turn five, I always tell people that it's not everything I needed to know I learned in kindergarten, everything I needed to know I learned by the time I started kindergarten.  We are learning our habits, our tendencies, our negotiating skills, our social skills, or the lack of those things. And so opportunities to high-quality, early learning and education really gives kids the best chance to succeed. Not just be kindergarten ready, but be ready for life. And you talked about the workforce, you talked about homelessness. If our children at two and three and four years old are learning how to play in the sandbox, they will be better prepared to learn in school. They will be less likely to bully in middle school. They will be more likely to communicate as an employee or an employee in life. And ultimately there'll be a better contributor in our community than the lack of. And so all of these things have statistics and demographics with them. We know that kids that have access to early learning opportunities are more likely to graduate from high school. They're less likely to drop out. They're more likely to be employable. They're more likely to be employable at a higher level. And all these things speak to just the things you're talking about, being able to afford housing to be able to keep and maintain a job. Less likely to have children at an earlier age, the teenage pregnancy rate is lower for those that have high quality learning opportunities. Those are all key factors I think. And very, very early on at two and three and four years old, we're either getting it right or we're not getting it right. And if I look at it from a parent perspective, I look at it from the perspective of a parent who has high quality childcare for their child is more likely to go to work, not miss work. So it reduces absenteeism from the work environment, which helps with economic development. It helps employers have a stable workforce. There's not as much turnover because parents are able to know that their children are safe, loved, cared for and getting a great education on top of that. So I think that from a parent perspective and a business perspective, the early childhood education is critical. If we don't have enough of that, then parents are forced to stay home, which lowers incomes in the community. It makes a smaller workforce of people to be available for employers to hire. So I think that that early childcare piece is just as important as things like housing and that kind of thing. So I really believe if the kids are able to thrive and parents are thriving, we're gonna have a really strong community. But if we don't provide the adequate resources for the parents, parents are gonna be not being able to do the job, gonna be able to maintain the job and they're gonna be able to, even the kid, just being able to access or have better jobs with a good pay scale. So in a county with almost zero unemployment in every economic development initiative tied to workforce, right? Who's prepared and how many to step into these jobs? What I'm hearing from this group is that over the long run, the closer we get to having it right for kids zero to five, every other initiative is strengthened or enhanced. I wanna come back just for me to classify and match some of the skills you were talking about. All of that sounds like executive function, right? The parts of the brain to give kids a chance to plan, to sequence, to solve problems. Yeah, persist. Well, that's where I was gonna go with persistence. What we know, you get that part of the brain, right? Grit, right? We read a lot about grit today. And the ability for kids to persist and overcome over the long run, Trump's IQ points, right? It's a stronger predictor, right? There's more data tied to grit and persistence in terms of academic achievement data than a whole bunch of other potential predictors like IQ points. All right, so we have both formal in YouTube, well, all three of you, formal pre-K learning opportunities. Most of us would think about that as preschool, right? There's also informal education that occurs in conjunction with, or in in conjunction with, and outside of preschool classrooms. We would have had a panelist this morning, Ann Maka from the museum as the education curator, but she woke up with the same virus that we're all dealing with right now, and it finally caught up with her. But she's put together in partnership with colleagues in the savory Valley School District, a killer program, a killer app, right? I mean, they've got a cool informal education program. Olga, how familiar with Discovery Days and what they've done with this program? Right, so Hildren and children of the families, we collaborate a lot with the museum. So we help them recurring, we help them with some of the programs. So the idea with the scary programs is being able to have some programs for anybody in the community. So they are open to anybody in the community. And also we are trying to look for families that need some resources as well. So in the past, we collaborate with, we have a program, the summer news program. So when we have recreation, we have the museum, and we have the library, and we provide some arrangements activities. So the museum having also part of that. So the idea is that we have different activities for all the kids, community members can apply for and the scholarships. And they range from really early learning to teenagers. We have teenagers learning about theater. We have kids learning about camping or an older kids learning about the natives here in Colorado. So it's a really diverse group that they have and a really different variety of programs. It's only a sports, we're just only about reading. It's really, they integrate different elements. I would also just add that the museum is committed to folks who can't typically afford to attend this sort of programming to get them there. So they give us 40, 10 punch passes every year for our families to be able to go out and experience those programs and be a part of it. To benefit from the informal learning experiences. Exactly. Along with what you're doing. Absolutely. All right, so talk about, we've got some pretty, I think, impressive informal education program that has occurred, right? And I know Anne wants to expand that program. The other side of the story from the school district is equally as powerful in terms of what they've done. That program works for discovery days between the museum and the Innovation Center. And then all the other things you've talked about are a show up in those institutions as well. You two bring a vast experience and expertise in terms of formal pre-school learning opportunities. In this case pre-schools or pre-K pre-schools. So talk to us, how would you recognize or what would you advise others to look for? Like decision-making parents or policy makers? If we're gonna invest more in pre-school learning opportunities, formal and informal, or pre-K learning opportunities, what are the best investments, right? That get us the kind of returns we're talking about. I think Matt and I both agree quality is the first thing. And as a parent who is out trying to find a childcare center, trying to find a pre-school, they really wanna be looking for quality educators. Matt and I've done some work to really trying to find what those are so that parents are able to live for those when they're out doing that search. So some of those things include having highly trained staff. Matt and I both have a bachelor's degree or higher level staff in our pre-school program. So these folks have gone to Early Childhood Education College. That they're using a research-based curriculum with the work that they're doing. So it's not something they've just kind of pieced together and they think the kids might think, look at rainbows is fun, but that there's really some scaffolding and some sequencing in learning that the children are doing through those curriculum pieces. We also really believe that a high quality program incorporates the entire family. So they're looking at health, mental health, nutrition, the needs of the family, and they're addressing that full range of things.  That there are many more resources that are being provided to families and services for children, children are being screened for disabilities and we're making sure that we're catching those concerns early so that they're addressed at a younger age and they don't carry on into the later school years as well. Yeah, I guess I would add to that. And I would maybe challenge into the listeners and viewers when I think of high quality early childhood opportunities, you mentioned pre-K or kindergarten readiness and I want us to really think about when does that start? And in my mind, if we start that at pre-K, we've lost four years of the opportunity to build this brain. And so if you think of it as a house, would you put the planning into the last, the paint on the walls if you don't have the guts of it right in the foundation? And so I really think that and this is, I don't think this is earth shattering, but we know that the best intervention is early intervention. And so especially for our kiddos that have developmental delays, physical delays, cognitive delays, if we can catch those at six weeks and eight weeks and 12 months, rather than at three and four and five years old, we know that kids are like sponges, right? They are learning at a fast pace. And again, going back to if 90% of your brain is developing by age five, we've got to start that at birth. And that is a process of educating families. It's a process of giving care to children. And just like the things that Amy talked about, those aren't just preschool indicators or levels of quality, those really can happen. Really, when this kiddo is seeing their first breath in this world, that's really when the opportunities are for these high quality learning opportunities, not only for those that are able, but those that are not as able or are disadvantaged. So I think it's really even more critical to look at those earlier years, even in pre-K. I think we also want to give a shout out to our quality rating system in the community. So the state of Colorado has a quality ranking system, level one through level five, level five being the highest quality and level one being your meeting basic licensing requirements in your program. And so we have two level five centers in Longmont. They are the Aspen Center and Third Avenue Preschool. And then we have eight level four programs. So TLC is one, all four Wild Plum Center sites are four of those eight. Junior Jets, KinderCare, Primrose, and that's all of them. So just want to give a shout out to level four, level five programs. And again, those indicators of quality are something that are set by the state. So if you're looking around and you're looking at a program called Colorado Shines, it is similar to what the idea was that in hotel or restaurant services, you have an experience, right? A level one star to a five star rating. The better your experience, the better the stars. The idea is that this- More of the stars? The more the stars, the better. Not that you're seeing stars afterwards, but the better your experience was. And that's kind of the idea. And so if you look at childcare centers or early childhood learning opportunities, they are rated based on the quality indicators of all these things we've just talked about at the state level. And that is one level of quality indicator. And at this point, it is still voluntary. So there are some level ones and twos that I would say are lower on the quality level, but a very high quality because it is still a voluntary system for the state of Colorado to participate in that. So it doesn't mean that lower level centers are not quality, just means that maybe they haven't even gone through the process or they're just starting the process of being rated through the state. Well, and also we have the informal childcare educators that are not part of this scale. They don't have all the stars, but some of them are provided really good services in our community. If you think 25% of the kids attend to the informal childcare, so right now we have a great opportunity. A lot of them are doing really good work. And a lot of the children that are in our programs are in those informal learning settings at other parts of the day or weekends or late nights or things along those lines too, right? So I've got a question that I'm gonna ask about resources and where they are and are they adequate and where others that may be underutilized? But that ties more specifically to some of what we're doing through the city. In order for every child in this community to be accessing the kinds of quality experiences with formal and informal, we're talking about, we have to have a pretty good idea of how many of those kids there are in this community. So the mayor's summit last spring, which all three of you were seriously involved with helping to design and prepare for, what do we think we've learned in the run-up to that? You knew it before, but what did the rest of us learn in that summit in terms of the kinds of access and the kinds of quality you just talked about in relationship to need? Are we addressing 100% of the need? The goal is all of our kids. Well, I think that we ought to identify four specific needs, right? One of them is transportation, that we have at this point the capacity to really work on that. A lot of the parents mentioned that they work, some of them work really early and the childcare is not even open at that time. So I think that we put that in the back burner and now we're working with staff development. We identified the staff development as something that we can work now and we're already creating a plan for that. So high quality of staff development. So some of the educators mentioned that they would like to attend, but the cost is really high and sometimes just to attend to these trainings, they have to go to different places. So what we're doing is just bringing some that high quality of trainings here in Longmont and also bringing some coaching. Some of them mentioned I attend to these trainings, but then I struggle and when I'm going to implement those new tools or techniques, I need some support. So now we're bringing some coaching. So that's some of the things that we learn, okay? We know that there are evidence-based programs, we know the ones that are working, but I think that we learn that by providing coaching and providing that assistance, we can make a difference because they can't implement really the things that are learning in these trainings. I would say- I'm gonna go back to my question of what's the, if we think about gap analysis, right? We have a solution, we have a need. The question is how much of a gap exists between demand and supply? Right, so I was headed there. I think that one of the things we learned from the summit was that it's really hard to nail down really live solid numbers of what the need is. What I can tell you is for the low income that's 100% of federal poverty or below population in Longmont, we have a need of about 400 spaces for those children to find their way into preschool. You have to pair that with the fact that we just don't have enough centers. If we have enough money, we don't have enough seats. Right, we don't have enough seats. The other thing we don't have is a workforce. So there are not enough people to hire to become the educators of these children with the kinds of quality background we want those educators to have. It's quite difficult for us to find high quality staff and it takes a lot to get there and retain them. So to give you a couple of numbers, we know that there are 32, and this is a spot in time and sometime in 2019 when we got this data. So it is outdated as of today. But we know that we have around 32 licensed homes in Longmont. We know we have about 40 licensed childcare centers in Longmont. And the capacity of those are all different from, a home might be two children and a center might be 150, 180. So the capacity is different from a home to a center. But we know that of the licensed homes, and again, when we get back to quality, the licensed homes that are 32 of those and only 6% of those are at those levels, four and five of quality through the state. On the flip side, on the centers, we know that we have 40 licensed centers and 25% of those licensed centers are at a level four and five. Now again, it doesn't mean that they're not quality because they're a one or two or three, but we know that the higher quality ones that have gone through the ratings are at those levels. Those numbers are still very low to the birth rate of Boulder County and specifically Longmont to what the need is of the workforce for our youngest children birth to five. You layer on top of that, like Amy just talked about, our childcare assistance programs are those that could access other programs. We have some super programs, the Colorado childcare assistance program, or CCAP, is a program for eligible families based on their annual household income and the size of their family. Those two things that they qualify, there are 28 of the 40 providers in Longmont that are CCAP providers. Now they might have one child, 12 children, 20 children, but they're at least a CCAP provider. Of the homes, 28% of those homes are CCAP providers. It is still very much under what the capacity or what the need is to serve the children in the community. And the CCAP program goes up to 235% of the federal poverty level, so it covers a much larger span of income levels. It's one assistance program. We're gonna come back to CCAP and what it means and how utilized or unutilized or how accessed or optimized or sub-optimized it is. Cause those are all issues. Here's the number that stuck with me and all the data, that's impressive. In fact, I would like a copy of what you just did when we're out of here, but somebody told me a long time ago, a mentor, Tim, don't ever believe that the facts speak for themselves or that the truth will set you free. Neither of those things are true much of the time. So I'm gonna translate all those data to meaning. So the meaning that stuck for me out of that Mayor's Summit last spring was that we have at least 500 kids every day parked somewhere with all the good programs, right? And the good experiences kids and families are having. We still have 500 kids and you mentioned if we had 500 seats or if we had the money, we don't have 500 seats, but all those things. So we have, we'd still have capacity issues we need to address. And we have kids who are underserved, right? So here's the question. So to provide more formal and informal learning opportunities for children, it does require additional funding. Sure. If we think about the importance of quality, which is, which some of what Olga talked about in terms of professional development and making certain that people, individuals are ready or this rating system that entities, right, programs are ready, all takes us towards quality. But there's investments we have to make there. Reliability, right? Seems to me to be an equally significant concern that they'll be there next week, next month, next year. So when my infant is involved, there's a, he's in a quality program or she that might be there for them until they're ready to go into a preschool program or into a kindergarten classroom. And that they've had consistent caregiving. Yeah, there's a reliability. The other third, for me, big variable is sustainability. And that would all go back to funding, right? And in this case, funding, given what we think we know the cost of quality are, right? You commented Amy at the outset about the challenge, right, in terms of the workforce and how many are there and why they stay or don't in terms of what the benefits are with the remuneration given the back, given I know a little bit about your background and your staff and I'm just, I shake my head. You must work magic to keep that kind of talent for the resource available. I mean, it's your personality, I can tell. So are there resources that are underutilized? And I want to go specifically back to CCAP and what we are or are not doing, are we spending every dollar in Boulder County of Colorado Child Assistance Program money effectively? And then what would it take, big picture, right? Now our last panel was about big picture. So I'm asking if you think big picture cost, there was a study that just came out from the Economic Policy Institute that shared some numbers about what this is really gonna cost and if we're serious about it. So turn that into a question.  And so it is college tuition to highly educate a young infant toddler preschooler. So we know that that's right now the going rate and some of that is high and some of that is low, but those are the costs that it takes to have a child in childcare or in a formal or preschool setting. So we know that those are the numbers. We also know that the workforce is vastly underpaid and the challenge is that as we do a better job of educating our folks, giving them professional development, giving them coaching opportunities, their level of education rises to bachelor's and master's level and where are those folks going? Are they gonna stay in a preschool, making an hourly wage of $14 to $16 an hour or are they gonna become a preschool teacher in a district or a kindergarten teacher in a district with better resources, health insurance and all the things that are most important to us. And so I think we've kind of got a double edged sword. We want to better train our staff and give them opportunities for higher quality, which then gives these children a better opportunity. But on the flip side, we're losing some of our early childhood teachers to other great professions. And so those are the challenges in dealing with the cost of care and the cost of quality, which is keeping staff. So it really comes down to money. If we could pay our most qualified staff more to be competitive with other industries, we would not lose them to other industries. That's really what comes down to because these folks are working people in our communities, just like the rest of us. We have a mortgage and light bills and children and things like that. So we've got to do a better job of paying our early childhood professionals. And we've got to do a better job of a multi-tiered funding source to fund this. You talked about CCAP. CCAP is in Boulder County. Boulder County committed, I came in two years ago now, but in the last couple of years, CCAP is again, it's a state program that's funneled down to the counties and individual municipalities. And typically it's somewhere around 70% of the market rate, right? So if the market rate is $1,100 or $1,200, we might be getting 70% of that. And so that has been a real deterrence for the early childhood business owner. Why would I take CCAP at 60, 70% when I could take a kid at $1,400 a month? Which one would you take if it was surely about running a business? Boulder County committed to raising the level of CCAP so much that taking a CCAP child now is not a financial loser to the drain or draining on your business anymore. And I think that's a real commitment to our county that is committed to taking the dollars that they get and matching those dollars to better financially support the children that are eligible for CCAP. So that's one thing that has happened. That has raised, I think, the level of providers or the number of providers that are taking CCAP now. But I still think that's an undereducated group. More providers should take CCAP because it is not a financial drain anymore on the organization. It actually is a more sustainable model. All right. The CCAP opportunity, is that money that goes directly to parents or does that go to the provider? It goes to the provider. To the provider. The child. If a parent wants to know if they qualify, how would they find out? They need to go through the process to... It's an application for the process with Boulder County. All right. So we're gonna, I'm gonna come to a couple of closing questions here. And one about is how people get involved if they want to. But before we do, I just wanna make a statement. Since we don't have anybody from the school district here and having spent as much time as I spent in that field, I just wanna to reinforce what it means. You're talking about having children school-ready, right? So when they step into a kindergarten, their executive function is optimized, right? You set the stage for deferring gratification, for planning, which is the persistence, right? For problem solving. What that means for a school district is, the ability to use, first of all, likely a reduced number of referrals for special education, which we know most of those occur in the first couple of years in school. Because teachers don't know what to do with kids who haven't developed in this way. So you see a spike in special ed referrals for five and six year olds.  And the cost associated with over the next 10 or 11 years is astonishing. Title I, dollars that flow to schools that have more student needs. The ability to free those dollars up to use them in other ways and less on remediation, which is how they're used, right? To supplement what's going on in schools. So the implication for kids is profound. For families is equally as profound. Sorry, I didn't mean to bump it. It's exciting. But for the system, it frees up resources to use in so many different ways if we get it right for our youngest. Why all of us have a stake in the youngest by the time they step into a kindergarten classroom. All right, I'll get off my soap box. If people are, we've talked some about people, if they're motivated to get involved, how do they do it? So what's your advice? Somebody says, God, that is important enough. I'm willing to dedicate a few hours a month a week. Well, I've seen several options, you know, actually next week coming up, we're going to show the film, No Small Matter. That's one way to get involved. On the 30th? On the 30th. In the museum? In the museum. So from 5.30 to see who have like a quick dinner. And from six to eight o'clock, we're going to be showing the film and then we're going to have discussion. So that's one quick way to get involved. So look on the website, you know, we have our link right there so people can register. So that's one, one way. Another way it could be through the Broad Eyes Coalition. So this is a coalition, a group of community members and also different organizations. Broad Eyes has been around for a long time. I have been around, I want to say probably what, like, it's 2003. Yeah. Thank you, Amy. Are you right there? Yeah, it's actually the first person to write it. So right here, right there, you know, this coalition was created just to promote high quality of education. So right there does one opportunity to get involved. Also, we have the Boulder County Early Childhood Council. Early Childhood Council, Boulder County. Boulder County does one way.  So just by being able just to read through this and learn about few concrete tools, few things that you can do with your kid, that's one way to get involved. We also have parents involved in education. It is a program where we provide childcare, we provide dinner, and those are educational sessions for parents. And so the kids will be playing and learning at the same time that parents are learning something. And also we have some parenting classes, you know, through the youth center. So we have the LENA program and we have also the North Train Parenting Program. So the kids and parents are learning at the same time, the same topic. But you know, it's tailored to the kids in that kind of vocabulary. And the parent is learning on our scope. At the end of the day, they get together and they practice that skill. That's one way to get involved. So they can walk into the family youth center. Absolutely. Or they can email us, they can walk to the youth center and we will connect them. They can also join the board of directors of either of our nonprofit organizations. So that's a great way to get involved as well. All right. Yeah. I'll assume the invitation in this session like we did the last, the second Monday of every month at three o'clock in the afternoon, at least for the time being, we have a coalition that's growing around this. And anybody and everybody's invited to show up at three o'clock at St. Peter's Episcopal Church. So, I'm sorry, state steam at Episcopal Church. You're right, thank you. So here's your back. This is part of the backstory on early learning opportunities along that. And the reason it's so important, I'm gonna say again, the stakes that we all have in this are enormous. They're huge if we don't get it right for the youngest of us. So thanks for being here, panel. For those of you who listen, thanks for staying with us. Stay tuned for the third of these podcasts. That's your backstory.


Hello and welcome to the session. In this session we discuss the following question which says the diagonal of a cuboid is root 29 meters. If its length and breadth are 2 meters and 4 meters respectively, then find the height of the cuboid. Before moving on to the solution, let's recall the formula for the length of the diagonal of a cuboid. This is equal to square root of a square plus b square plus c square where we have a is the length of the cuboid, b is the breadth of the cuboid and c is the height of the cuboid. This is the key idea that we use in this question. Let's proceed with the solution now. In the question we are given the length of the diagonal of the cuboid and we are given the length and breadth of the cuboid. We need to find the height of the cuboid. So we have the length of the diagonal of a cuboid is equal to square root of 29 meters and we have the length of the cuboid say a equal to 2 meters then breadth of the cuboid that is b is equal to 4 meters. We need to find the height of the cuboid say c. Now from the key idea we have that the length of the diagonal of a cuboid is equal to square root of a square plus b square plus c square that is square root of length square plus breadth square plus height square that is we have square root of 29 which is the length of the diagonal of the cuboid is equal to square root of length square that is 2 square plus breadth square that is 4 square plus height square which is c square. We have to find the value for c. Now squaring both sides we get 29 is equal to 2 square plus 4 square plus c square that is we have 29 is equal to 4 plus 16 plus c square or you can say that c square is equal to 29 minus 20. Thus we have c square is equal to 9 or you can say c is equal to plus minus square root of 9 that is c is equal to plus minus 3. Now that the height cannot be negative so we neglect the negative value for c and we take the value of c as 3 so we get c is equal to 3 meters or you can say that height of the cuboid is equal to 3 meters. So 3 meters is our final answer. This completes the session. Hope you have understood the solution of this question.