Introduction to Slope and Slope-Intercept form

 This link will take you to a list of several Virtual Nerd videos that help introduce slope and the slope-intercept form of equations that we use for many word problems involving a consistent rate of change with two variables (x,y).

https://virtualnerd.com/search/search.php?q=slope+intercept&search=1

Proportional Relationships and Introduction to Using Percents

 Video on solving proportions (finding an unknown x in a numerator or denominator, as in one fraction = another fraction. 

https://www.google.com/search?q=solving+proportional+equations&rlz=1CAJCUZ_enUS850&sxsrf=AOaemvI3rNldwlCFSM7A49ogKKDxpMWHeQ%3A1638386174788&ei=_smnYf2xL-iSwbkPjP-M-A8&oq=solving+&gs_lcp=Cgdnd3Mtd2l6EAEYADIFCAAQkQIyBQgAEJECMgoIABCABBCHAhAUMggIABCABBCxAzIICAAQgAQQsQMyBQgAEIAEMggIABCABBCxAzIICAAQgAQQsQMyBQgAEIAEMgUIABCABDoHCCMQsAMQJzoHCAAQRxCwAzoECCMQJzoNCAAQgAQQhwIQsQMQFDoLCAAQgAQQsQMQgwE6BwgjEOoCECc6BwguEOoCECc6DQguEMcBEK8BEOoCECc6CgguEMcBEK8BECc6BAgAEEM6DgguEIAEELEDEMcBENEDOg0ILhCxAxDHARDRAxBDOhEILhCABBCxAxCDARDHARCjAjoHCAAQsQMQQ0oECEEYAFDRCFjuLmDzSmgCcAJ4AoABwgGIAcsbkgEFMTQuMTiYAQCgAQGwAQrIAQrAAQE&sclient=gws-wiz#kpvalbx=_DMqnYY3gMaXhxgGOjJaQBA17

Videos on Proportional Relationships, or when y varies directly as x.  kx = y

In algebra this will also be called direct variation.

https://www.youtube.com/watch?v=CMPvYn0MaHI

https://www.youtube.com/watch?v=oowdRMr00HM

Virtual Nerd videos breaking down the Proportional Relationships topic into several parts.  This link takes you to a list of videos on the topic.

https://virtualnerd.com/common-core/grade-7/7_RP-ratios-proportional-relationships/A/2/2a/

Video on Finding a Percent of a Number.

https://www.youtube.com/watch?v=rR95Cbcjzus

Video on What Percent is it?

https://www.youtube.com/watch?v=Uf-Rl1e2I4Q

Word Wall Cards that often prove helpful with definitions and basic examples.  Open the link and click on the topic.  For example, you might click on Proportional Reasoning to get started:

https://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/2016/gr7-vocab-cards.pdf

For extra practice items, text Dan

PreAlgebra: Video introduction to Transformations of the coordinate plane

 https://www.youtube.com/watch?v=jFPqnFxyEek

Transformations on the coordinate plane.

Pre-Algebra Q2 Temperature change from minus to more minus

 The temperature on a winter Monday morning is -15.4 degrees according to a digital thermometer.  The temperature drops a little more each day.  Four days later, it has dropped 20% from the Monday morning reading of -15.4.  What is that temperature four days later after the 20% drop, measured to the tenth of a degree?

Explain in writing how you completed the task.  What did you do and in what order did you do it?

After you have completed your written explanation, pick a new starting temperature for a new problem.  Please choose a negative temperature between -1 and -9.  Then choose a percentage drop of between 20% and 40%.  After you set up the new problem, solve it yourself and be prepared to explain your problem and answer.  

Something to think about...

If we started at +10 degrees and had a 50% drop, would you expect the new temperature to be +5 degrees?  If we started at -10 degrees and had a 50% drop, would you expect the new temperature to be -5 or -15?  Why?

An answer and explanation for Q2 will be published in another post soon.

Pre-Algebra A1 Answer for filling the tank

The cost of gas for a truck is $3.59.  The gas tank holds 28.2 gallons when empty, but it is 1/5 full now.  How much will it cost to fill the tank?

Answer:  $80.99   (80.9904 rounded to cents)

The tank needs 22.56 gallons to become full (80% of 28.2, because 1/5 is 20%).  Now multiply $3.59 times 22.56.

An alternate method would be to calculate the cost of a full tank, then subtract 20%.  The full tank ($3.59 times 28.2) is $101.238; do not round in the middle of the task.  20% of $101.238 is $20.2476.  Subtract $20.2476 from $101.238 and you get $80.9904.

Pre-Algebra Q1 Calculating the cost of filling the tank.

 The cost of gas for a truck is $3.59.  The gas tank holds 28.2 gallons when empty, but it is 1/5 full now.  How much will it cost to fill the tank?

Explain in writing how you completed the task.  What did you do and in what order did you do it?

After you have written the explanation of your work process, think about this question.  Can you see another, different way to complete the problem; a different process?  If you can, write out that explanation, step by step.  Once you have done that, try the second way and see if you get the same answer.

Finally, if you did any rounding of decimals in your work process, think about how that might have impacted your accuracy.  It is usually best to not do any rounding until the end.

An answer and explanation will be published in another post soon.

K12 Education needed a paradigm change before the pandemic

Click here for a two page summary of my thoughts on K12 education:

https://drive.google.com/file/d/10Q3OEnenFQPSyrbWWbf64M7v3qhpWKdP/view

Click here for my manuscript of about 100 pages, plus appendices:

https://drive.google.com/file/d/11acKOGaw-V9iscQHX6cc0fqAoqqydtff/view

Escaping the K12 Doom Loop

 Click the link to open a pdf version of my book:  Escaping the K12 Doom Loop.

https://drive.google.com/file/d/11acKOGaw-V9iscQHX6cc0fqAoqqydtff/view?usp=sharing

K12 education has never worked well for most Americans, especially those who come from poverty or distressed households.  The paradigm of moving students along by age cohort, regardless of skill mastery, puts students at an increasing disadvantage as time marches on.  Many types of school reform have come and gone, but the doom loop of the conveyor belt has never been adequately addressed.  My book details faults of the conveyor belt and offers alternatives.  You will find embedded links within the narrative that will take you to supporting materials.  I encourage you to follow the links as you go.

Comments are encouraged.  Thank you!

Teach Children to Learn

      K12 education in America is preparing children for tests, but not teaching children how to learn.  Additionally, in spite of the testing and reporting of scores, students move to the next grade level or course regardless of test result or course grade.  Students are assigned grade levels according to age cohort and moved along as a cohort until at least the freshman year of high school.  From kindergarten to ninth grade students move from year to year, even when they fail to learn the curriculum, fail to learn how to learn, and fail the standardized tests.  Not only do the failing students suffer, but the vast majority of students who appear to pass the courses and pass the tests are not mastering the curriculum.  They move on with the age cohort and begin each year with content knowledge gaps, gaps that widen with each successive year. 
     The system is designed to move students along curriculum content knowledge paths, but it fails to teach the skills required for learning.  Students are tested for content knowledge, then, no matter the test score, the students are moved on to the next level.  Teacher preparation programs and licensing criteria focus on teacher content knowledge and content transfer through lesson planning.  Teacher lesson planning preparation assumes too much.  It assumes a reasonably motivated student.  It assumes a student who wants to learn and earn good grades.  It assumes a student with adequate prior skills and knowledge.  It assumes that students are in stable family situations that support learning and promote good behavior.  
     With the exception of early elementary pre-service teachers, teacher preparation and licensing programs give only cursory attention to how students learn and how teachers prepare, assess, and reteach students learner skills.  This creates a common reality:  Students move into fourth grade (as an example) with learner skill gaps, content knowledge gaps, and a teacher whose priority is the fourth grade content that will be tested at year end.  Yes, that teacher understands that some students will need some extra support, but the demands of teaching the class the fourth grade curriculum will soon create a pace that leaves some, perhaps many, students behind.  A teacher steeped in content knowledge and trained in content delivery will often neglect the learning skill needs of students; not because they want to, but because the environment and their training steers their focus away from learner skill development and toward content knowledge gaps.
     An example that assumes a good student in fourth grade with stable life inside and outside school might illustrate the point.  The teacher assesses math readiness of the student early in the year and determines that the student is at grade level having scored well on the standard assessment of third grade content.  In fourth grade, the curriculum guide places multiplication of two digit numbers before division using a two digit divisor (for example 175 divided by 25).  The student in question struggles with two digit multiplication as evidenced by classwork.  The teacher provides support in the form of corrections of the student’s work, models of worked out solutions for other examples, and additional remedial two digit multiplication problems.  A quiz on two digit multiplication is given to the class before the first lesson on division using two digit divisors.  The student scores 80% on the multiplication quiz, but struggles with the two digit divisor classwork as he did with the two digit multiplication classwork.
     Continuing with this example, the teacher provides support in the form of corrections to the student’s division work, models of worked out solutions, and additional remedial division problems.  Recognizing that the student still has not mastered the two digit multiplication as evidenced by the 80% quiz score, the teacher also provides the student some two digit multiplication problems after doing some one on one reteaching.  The teacher also reaches back to the fundamentals of division with the student by working through some division problems using single digit divisors (for example 175 divided by 5) before reviewing the two digit division problems with the student.  As we can see, in addition to teaching the daily lessons according to the pacing guide, the teacher is providing individual content skills coaching to the students.  In this example, the student entered fourth grade on grade level in content knowledge and scored 80% on the two digit multiplication quiz.
     Assuming the teacher is providing similar content readiness feedback and support to all students, what’s missing?  Attention to learner skills and development of student agency are both missing from the teacher’s approach.  This is the norm.  This is how the teacher was trained.   This is how administrators guide teachers to help struggling students.  This is the approach parents expect from teachers.  The teacher is focusing on the student’s gaps in content knowledge and content skills.  The teacher is not addressing learner skills.  What are learner skills?  Learner skills are applicable to any content and grow over time into life skills.  Examples of learner skills that might be appropriate for a fourth grade student include:  persistence, avoiding distractions, striving for accuracy, applying prior knowledge, questioning, explaining process steps being used, and various other self-discipline or self-monitoring skills.

Habits of Mind

https://www.goodreads.com/en/book/show/6374641-habits-of-mind-across-the-curriculum

Installment 15 of Escaping of the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the fifteenth installment from the draft manuscript.  Your comments are welcome and encouraged.

Community Support

Installment #15

https://docs.google.com/document/d/1Y1OY-eEtQjaKdpWvza7qcDpFcB2wTVtpXUezxXYEDNw/edit?usp=sharing

Freedom of choice and student agency in this context means an approach that is led by an authoritative teacher who controls the environment.  The environment is age or readiness appropriate. The students in the environment are making choices among the options led by the teacher, with room to work independently or collaboratively with other students.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 14 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the fourteenth installment from the draft manuscript.  Your comments are welcome and encouraged.

Learner Empowerment

Installment #14

https://docs.google.com/document/d/1jkA2Oe7KnGaXM71Pg6Z6PQ1rLwtf8D8JmTC6JJod58U/edit?usp=sharing

Learning is personal; to be personal, the structure, the paradigm, needs to allow for that personalization.  To be personal it must include choice, albeit guided choices at first, growing to broader choices as learners develop the skills to be lifelong learners.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 13 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the thirteenth installment from the draft manuscript.  Your comments are welcome and encouraged.

Learner Competencies K12 Supportive Practices

Installment #13

https://docs.google.com/document/d/1dUdd6CmutixR9LswriRz-uKeGHqYj0gIm6oLk5d7Tms/edit?usp=sharing

The child who masters learner competencies is more likely to behave appropriately.  The child who misbehaves, exhibits inappropriate passivity, or disengagement usually has gaps in the mastery of learner competencies.  Therefore, learner competencies must be mastered at age appropriate levels before content mastery can proceed.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 12 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the twelfth installment from the draft manuscript.  Your comments are welcome and encouraged.

Learner Competency Resources

Installment #12

https://docs.google.com/document/d/1PUnRBLKb9JMj_JoPwwi8xuxyrYonyeZf4RXGzjYBbmA/edit?usp=sharing

A key point is that learner competencies grow within the child and enable the child to be a good learner of content as a lifelong learner.  Learner competencies are key to graduating productive citizens into the community. Learner competencies must begin early and grow through K12.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 11 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the eleventh installment from the draft manuscript.  Your comments are welcome and encouraged.

Metacognition -- A Step Toward Student Agency

Installment #11

https://docs.google.com/document/d/1Nwcuw3-RCOLXlzjC-FJRPpFRTIRfQ2ThtJxI2MKv56Y/edit?usp=sharing

Metacognition is a learner competency that grows with guidance and experience. Student agency builds intrinsic motivation.  Development of learner competencies is fundamental for student agency.  

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 10 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the tenth installment from the draft manuscript.  Your comments are welcome and encouraged.

Habits of Mind -- Learner Competencies

Installment #10

https://docs.google.com/document/d/1MetNnGpNzCOpJYdFZYaTmwFgUI5x8oJUyqTH_99IYFA/edit?usp=sharing

I would suggest that these habits of mind are the goal of what I’m calling learner competencies.  K12 education will be transformed for students when habits of mind are central to teaching and learning; not assumed or dismissed by the conveyor belt, but central to teaching and learning.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 9 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the ninth installment from the draft manuscript.  Your comments are welcome and encouraged.

Learner Competencies are the Key Ingredients

Installment #9

https://docs.google.com/document/d/1qwxJhhqwAJSWrfCkg4Wd3tmBvwy6JHcGH6knWEcB9Fw/edit?usp=sharing

Before we address content areas we must address what it takes to be a competent learner.  When one has the competencies or behaviors or skills or intrinsic motivation to be a learner, content learning may proceed.  When those learner competencies are absent or deficient, both learning and behavior suffer.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 8 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the eighth installment from the draft manuscript.  Your comments are welcome and encouraged.

The Conveyor Belt Fixes Mindsets

Installment #8

https://docs.google.com/document/d/1bSfh812DlA9aHJqlHt96CiRDDb0ivFWYE47A77538z8/edit?usp=sharing

In my observation, today's student is learning from experience that achievement, particularly individual achievement, does not matter for them.  They get a year older, take more tests and move to the next grade with their age group; regardless of test scores, course grades, or learning.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 7 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the seventh installment from the draft manuscript.  Your comments are welcome and encouraged.

The Faulty Logic of Binary Choice

Installment #7

https://docs.google.com/document/d/1OdDeNAzNsejsSYP72PPKqGVutRvgAYatErp-u0F-jIA/edit?usp=sharing

The conveyor belt and traditional grading are not only hurting students in the “lower” half of the cohort, but also those in the “upper” half, even the top performers.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.

Installment 6 of Escaping the Doom Loop

Escaping the Doom Loop is my draft manuscript describing issues and solutions for K12 public education.  My January 11, 2020 blog post gives a summary.  This is the sixth installment from the draft manuscript.  Your comments are welcome and encouraged.

The Conveyor Belt is the Core Problem

Installment #6

https://docs.google.com/document/d/1lt57bBSc0gJ2DDFUWtPmAkI-d_Oz5G0N4s6jFID35Jw/edit?usp=sharing

There is no credible research or educational theory that suggests or supports the conveyor belt.  It is a result of prioritizing a factory model ahead of learning.  The conveyor belt is assumed and silently accepted. It has no champion or advocate; it’s just the way it’s always been.  Despite the clear evidence that it doesn’t work, it has gone unquestioned until now. It is the central reason that school reforms fall short of their goals.

Future posts will examine the current paradigm and new paradigm in greater detail. The blog archive on the right of the landing page presents blog posts in calendar order. The posts themselves are displayed with the most recent first, on the left side of the landing page.