home4school Posted May 25, 2010 Share Posted May 25, 2010 1) The volume of a cube is 64 cu in. How long is its side? The answer key says: "Since 4 raised to the 3rd=4x4x4=64, a cube with a volume of 64 in cubed has sides that are 4 in long." Well, that's great if you just know in your head that 4 to the 3rd is 64, but what if you don't?!? How do you back out of the problem to find the answer? 2) The area of a square is 121m squared. What is its perimeter? If the square’s area is 121 m2, then the length of one side is 11 m. So the perimeter is 4 × 11 = 44 m. 3) The area of one face of a cube is 64 in squared. What is its volume? Since each face of a cube is a square, and the area of the face is given as 64 in2, the length of one side (edge) is 8 in.The volume is thus (8 in)3 = 512 in3. I don't even see where she would have explained this concept well enough to figure these out. The answer key is even sketchy to me. Can someone please help me understand better? Thanks, Kim Quote Link to comment Share on other sites More sharing options...
Corraleno Posted May 25, 2010 Share Posted May 25, 2010 (edited) To do these problems you need to understand what "squared" and "cubed" mean (which she explains at the beginning of the lesson); you need to understand how to calculate the area, volume, and perimeter of a square or cube (also reviewed at the beginning of the lesson, albeit briefly); and you need to know the "squares" in the times tables (e.g. 11 x 11 = 121 or 8 x 8 = 64). If you don't know the squares and some of the simpler cubes off the top of your head, you might want to make a chart to use. If the area of a square = 121 sq m, then one side has to equal the square root of 121 because the length of one side, squared, is the area. So ?x? = 121? The answer is 11. Since the perimeter of a square is 4X the length of one side, 4 x 11 = 44. If one face of a cube is 64 sq", then the length of one side is the square root of 64, since side x side = area of a square. So ?x? = 64? Once you know that the length of one side is 8", then 8 x 8 x 8 would give you the volume of the cube: 512 cubic inches. Jackie Edited May 25, 2010 by Corraleno clarification Quote Link to comment Share on other sites More sharing options...
fractalgal Posted May 25, 2010 Share Posted May 25, 2010 (edited) I agree :) ETA: Just wanted to add that for cubed roots to "back out" of the problem you would think of what number n will give you n X n X n = 64. When you are working with smaller numbers this is usually easy to see by use of estimation. Edited May 25, 2010 by fractalgal Quote Link to comment Share on other sites More sharing options...
home4school Posted May 25, 2010 Author Share Posted May 25, 2010 Well see, when you explain it, I get it! :lol: This has just been a bad day all around! I just couldn't wrap my head around that this morning and my son was looking at me like I had three heads. I have to admit, we've gone to MM6 from TT7 and it has been an adjustment! No more simple, easy word problems. But, that is why we changed, to be challenged more. Sometimes the brief explanations leave me hanging though. I'm sure if I emailed her with ??, she'd responded happily, but I knew I could get what I needed right here! Thanks again. Maybe tomorrow I need two cups of coffee before math! Kim Quote Link to comment Share on other sites More sharing options...
Corraleno Posted May 25, 2010 Share Posted May 25, 2010 (edited) If you're coming from TT7, you might actually want to back up to MM 5A. The explanations in 6A may seem "brief" because MM assumes the student has covered the material in MM5 already. There are a LOT of really good, foundational concept explanations in 5A & B, including several lessons specifically on problem-solving. MM5A covers: Basic operations plus 4 lessons specifically on problem-solving Large #s, estimating, rounding Decimals (with another problem-solving lesson) Graphing & statistics Introduction to functions MM 5B covers: Fractions (in great depth) Geometry (with LOTS of meaty problems calculating area, volume & perimeter, including unusual shapes and shapes on a coordinate grid) Integers (negative numbers) Graphing functions in the coordinate plane Percents & Ratios MM6 skims over a lot of the material that's covered in MM5, and moves quickly into deeper topics, so I think going from TT7 to MM6 would be a big jump, both in the concepts covered and the level of the problems. MM 6A covers: Operations, powers, exponents Simple equations Ratios & proportions Decimals (in great depth) Number Theory: factoring & primes, simplifying, GFC/LCM Fractions & fractional equations MM6B (not released yet) will cover: Percent Integers (in more depth) Geometry (angle calculations, congruent transformations, area/volume, etc) Statistics & probability The problems you posted are from the beginning of Ch 1 in 6A. The explanation in that lesson focuses on relating the mathematical concept of exponents to geometric concepts that were covered in considerable depth in 5B, so those are not repeated in the lesson. If your DS is struggling with these problems due to "lack of explanation," then I would go back to MM5 and review the topics he's not solid on. Otherwise, he may become increasingly frustrated as he works through 6A. I think sometimes when kids start to fall behind, parents switch programs looking for something that will work better, but they're reluctant to really back up as far as they need to, because they feel like they're already behind and they need to "catch up" ASAP. But sometimes the whole key to moving forward smoothly is to back up far enough that the foundation is really really solid, rather than just backing up a little, getting a basic but shaky scaffold in place, then pushing forward. If the foundation isn't really solid, then what you build on top of it will always be shaky, KWIM? Jackie Edited May 25, 2010 by Corraleno typo Quote Link to comment Share on other sites More sharing options...
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