Saturday, December 11, 2021

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


Wednesday, December 1, 2021

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

Friday, November 5, 2021

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.

Tuesday, June 1, 2021

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.