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MATH Get Something on the Table “A blank stare solves nothing”

MATH Get Something on the Table “A blank stare solves nothing”. The Plan?. What is the smallest possible value for the product of 2 integers that differ by 7?. To understand a question like this, I find it’s easiest to just try something. This helps me see what the problem is asking:.

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MATH Get Something on the Table “A blank stare solves nothing”

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  1. MATH Get Something on the Table “A blank stare solves nothing”

  2. The Plan? What is the smallest possible value for the product of 2 integers that differ by 7? To understand a question like this, I find it’s easiest to just try something. This helps me see what the problem is asking: “2 integers that differ by 7?” What 2 do I use? Use any! Just get started! Product Let’s pick two more Differ by 7 2 9 8 is less than 18 … Now I see the problem! 1 8 Let’s keep going! 4 -3 0 -7 -6 1

  3. The Plan? Three distinct lines, all contained within a plane, separate that plane into distinct regions. What are all of the possible numbers of distinct regions of the plane that could be separated by any such three lines? What’s the problem asking? It’s hard to say. Draw a box and draw three lines. I start to see the problem, and draw the lines differently … How else can I draw the lines? Let’s draw a box and draw three lines … Three lines drawn like this create 4 regions … This way gives me 6 regions! 7 regions!

  4. When the choir is arranged in rows of 5 people each, the last row is one person short. When the choir is arranged in rows of 6 people each, the last row is still one person short. What is the least possible number of people in the choir? (29; 30; 56; 60; 99) The Plan? What’s the problem asking? There’s 5 chairs in each row (all filled by people), except for the last row (where one chair is empty). Draw this … The choir is rearranged. Now there’s 6 chairs in each row (all filled by people), except for the last row (where one chair is empty). Draw this … I start to see the problem … 5 Chairs / Row 6 Chairs / Row X X X X X X X X X X X X X X X X X X X X X X X X X X X O X X X X O There can be 14 or 19 or 24 or 29 or 34 ... people in the band. There can be 17 or 23 or 29 or 35 ... people in the band. There could be 29 people in the band.

  5. The Plan? Melissa had 3 fewer apples than Marcia. Then, she gave 2 apples to Marcia. Now how many fewer apples does Melissa have than Marcia? Forget formulas – use real things. MELISSA MARCIA Melissa has 3 few apples than Marcia Melissa gave 2 to Marcia Melissa has 7 fewer apples than Marcia.

  6. The Plan? Gary has turtles, cats, and birds for pets. The number of birds he has is 4 more than the number of turtles, and the number of cats is 2 times the number of birds. Of the following, which could be the total number of Gary’s pets? (14; 18; 20; 22; 26) Try a single turtle. What does this mean? Turtles Cats Birds Total 10 1 5 16 nope but nowI'vegot the feel of the problem 20 Yes! 2 12 6

  7. The Plan? When x is divided by 7, the remainder is 4. What is the remainder when 2x is divided by 7? Look for an easy number to get started. Suppose I let x = 11 This is what the problem asked for – In fact, that’s why I chose 11! Now answer the problem!

  8. The Plan? Bus X travels 40 miles per hour for 2 hours; Bus Y travels 60 miles per hour for 1.5 hours. What is the difference, in miles, between the number of miles traveled by Bus X and the number of miles traveled by Bus Y ? If the problem says “suppose you have a triangle”, draw a triangle. If the problem says “suppose you have two buses”, label two buses! Forget formulas. Just draw a timeline. 40 m 1 hr 40 m 1 hr 80 Miles Bus X: 40 mph for 2 hours 60 m 1 hr 30 m .5 hr 90 Miles Bus Y: 60 mph for 1.5 hours

  9. The Plan? Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year? If the problem says “suppose you have a triangle”, draw a triangle. If the problem says “suppose you have three years”, label three years! Forget formulas. Fill in what you know. What do we know? If sales for the third year were 38 million dollars … What else? sales for the third year were double the sales for the second year. year 1 year 2 year 3 16 19 38 What else? million dollars more the second year than the first,year.

  10. The Plan? An industrial cleaner is manufactured using only the 3 secret ingredients A, B, and C, which are mixed in the ratio of 2:3:5, respectively, by weight. How many pounds of secret ingredient B are in a 42-pound (net weight) bucket of this cleaner? If the problem says “suppose you have a triangle”, draw a triangle. If the problem says “suppose you have three ingredients”, label three ingredients! Where do I start? Since the ratio is 2:3:5, why not start with that? A B C Total Not enough – let’s double everything. 10 2 3 5 Still not enough – let’s double everything! 20 4 6 10 Close. I need 42. I won’t be able to get it with whole numbers, clearly. But I also see the nature of the problem now. 40 8 12 20 Total is 42 10x 2x 3x 5x 42 8.4 12.6 21

  11. The 2 diagrams below show a circle of radius 1 inch with shaded sectors of angle x°, for 2 different values of x. One of the following is the graph in the standard (x,y) coordinate plane of the area, y, of a shaded sector with angle x°, for all values of x between 0 and 360. Which is that graph? The Plan? This is a hard one – wrestle with what they’re asking for. Read the question carefully. Look at the two circles. What are they asking? A hint: if x is small, how much of the circle does it “carve out”? How about as x gets large?sking? part of circle shaded? angle 0 0 Now I have an idea what to graph … 90 1/4 180 1/2 360 whole thing

  12. The Plan? The lead of a screw is the distance the screw advances in a straight line when the screw is turned 1 complete turn. If a screw is 2½ inches long and has a lead of ⅛ inch, how many complete turns would get it all the way into a piece of wood? If the problem says “suppose you have a triangle”, draw a triangle. If the problem says “suppose you have a screw going into wood”, draw a screw going into wood!” Make sure to label everything. What does the problem say about this screw going into the wood?

  13. The Plan? If xy = 144, x + y = 30, and x > y, what is the value of x – y? Sometimes it’s easiest to just try some numbers and see what works … x y x + y xy Nope – too much. I need two different numbers. 20 10 30 200 Still too much, but closer! 25 5 30 150 Bingo! 24 6 30 144 Now make sure you answer the right question!

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