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