Look over the lessons in Chapter 7 (not including 7-8 Work Problems). Why do you think the editors of this textbook put all of this material together in one chapter? What connects all of the lessons (be specific)? Are there any lessons in Chapter 7 that do not fit in the chapter? With what units should they be inserted into? Also, do you think other lessons could be added to this chapter? If so, which ones, and why? If not, why not?
(Yes, there are many questions to answer here. You will be graded on your ability to produce well-reasoned answers.)
1) We think the editors of this textbook put all of this material together in one chapter because they are all about applying fractions.
ReplyDelete2) Usage of fraction connects all the lessons. For example, proportions is a set of two set of fractions which equal each other. And scientific notation when you divide you have to put it in fraction form.
3) Scientific notation does not fit in the chapter. They don't fit in the chapter because scientific notation can never be expressed in fraction form, unless divided by which is an operation.
4) Scientific notation should be inserted into rational and irrational numbers. They should be inserted in there because they express rational numbers in a simpler way.
5) No, other lessons should not be added to this chapter. These combinations fit perfectly together and they cover all we need to know about fractions.
The editors of this textbook put all of this material together in one chapter because when solving these problems, they all somehow relate to each other. Having to do with solving fractions and decimals connects all of the lessons. All negative exponents, scientific notation, fractional equations, proportions, ratios, and percents include decimals and fractions. Negative exponents and scientific notations both don’t fit in this chapter because they are the only ones related to exponents while all the others aren’t. They should be inserted into chapter four instead of chapter seven because chapter four deals with exponents. Also, chapter 3-7 could be inserted into this chapter because in chapter 3-7 you learn about cost, income, and value problems. In cost, income, and value problems you use percentages to solve problems just like you do for most of chapter seven problems.
ReplyDeleteGreat reasoning! I especially like the last point.
DeleteWe think that the editor of this textbook put all of these materials together in one chapter because they all have to do with manipulating percent, proportions, and ratios. For example, ratios and proportions have to do with fractions and in certain problems, we have to convert the answer into either a decimal or a percent. For Equations with fractional coefficients and fractional equations, we have to cross out the fractions which means that we are manipulating them to make the equation work. Percents and Percent Problems have to do with percents and to solve percent problems, we have to convert them into a fraction or a decimal. An example would be finding the amount of discount of an item. With scientific notation, we have to convert the first number from either decimals and fractions into whole numbers. Negative exponents do fit partially in the fact that we have to change them into fractions to solve, but they are not usually grouped with percents, fractions, and decimals. Mostly, exponents have a chapter to themselves and the negative exponents lesson should be moved to chapter 4-1: Exponents. We believe that nothing else should be added to this chapter because percents, ratios, proportions fit together. With these three, decimals and and fractions are already included which fit with this chapter.
ReplyDeleteWhy do you think the editors of this textbook put all of this material together in one chapter?
ReplyDeleteEverything has to do with fraction at least and bit and they want us to know that fractions can be used in this many methods, not just one.
What connects all of the lessons (be specific)?
Fraction connects all of the lessons because for ratios and proportions, you use fractions to simplify. For percentage, you need fractions to turn it into a decimal. Of course fractional equations use fractions too since its equations made with fractions. Scientific Notation may seem like it doesn’t use fractions but you actually use it since you can use fractions to divide two scientific notations. You also need fractions for negative exponents since you use them to change a negative exponent into a positive exponent.
Are there any lessons in Chapter 7 that do not fit in the chapter?
What doesn’t fit in Chapter 7 is Scientific Notation since the main purpose for Scientific Notation is moving decimals, not use fractions to divide.
With what units should they be inserted into?
Scientific Notation fits in the decimal unit since it mainly uses decimals. (You move decimals all the time and figure out things) In this book, there isn’t a chapter just about decimals but we can put it in units where you add, subtract, multiply, and divide decimals.
Do you think other lessons could be added to this chapter? If so, which ones, and why? If not, why not?
Yes, I think other lessons could be added to this chapter. I think the exponents section from chapter 4 (Chapter 4, Section 1) could be added to this chapter since Scientific Notation has something to do with exponents.
Every lesson in this chapter uses factions in a way. Even so, they are not very closely related and seems strange to put these lessons together into one chapter. Many math problems require you to change ratios, percents and proportions to fit the equation. For this reason, ratios, percents and proportions should be put together in one chapter while negative exponents should be group with scientific notation seeing how they commonly appear when using scientific notation. Finally, even if fractional equations uses fractions, it is more of an advanced section of equation problems. Though these lessons all use fractions in some way, they don’t tie in close enough to each other to be taught in one Chapter and should be taught separately. Scientific notation are closer to decimals.
ReplyDeleteGreat points. I would love to hear how you would structure these lessons within other units.
DeleteWe think the editors of this textbook put all of this material together in one chapter because the editors wanted to include important lessons to learn from the book but there was nowhere else specific to put it in because in order to know how to solve the questions, you need to learn everything else first and combine them to figure out the answer. So if the proportion sections was with the section where we first learned proportions, it wouldn’t make sense because there were things that we didn’t learn yet. Also, it does make sense that everything in this chapter has to do with fractions and using further things that were learned earlier in this chapter to solve the question and equations. What connects all the lessons together is that they are all questions involving fractions. There are lessons that do not fit in the chapter which are negative exponents and scientific notations. We say this because percents, ratios and proportions are equal to another. Ratios can be shown as proportions or percents. Negative exponents and should be inserted into chapter 4 section 1 which is exponents. Scientific notations should be inserted into the time when we first learned scientific notations but we don’t really remember where it was in the previous textbook. I don’t think there should be anything else added in this chapter because it would just mean more lessons to learn and be a bigger “mess.” Since there are already so different lessons in this chapter, adding more would make it more confusing.
ReplyDeleteGreat points, and I completely agree: adding more would make it confusing.
DeleteThis unit might look as if there are no relations between each section because they look like they’re teaching different kind of lessons. However, there are actually something in common if you look carefully, such as all being in need of applying fractions. When you look at sections like proportion, ratios, and percentage, you can see that there is a reason they all need fractions to solve. Proportion are ratios, ratios are percentage and ratios are percentages. They are considered as the same thing after solving. You can use ratios and proportions to find the ratios. However in these sections, there are some other lessons that do not fit in well as others do. Scientific notations can be considered differently, but they also relate in different ways, such as having to express the divisions in fractions.
ReplyDeleteWhere should scientific notation go? They can be considered differently? I don't understand.
Delete1. Why do you think the editors of this textbook put all of this material together in one chapter?
ReplyDeleteAll the lessons are related to dividing. Percents, proportions, and ratios are all related to dividing. Also these three topics are usually tied together in a textbook. The only thing that isn't related to dividing a lot is scientific notation. Scientific notation doesn't fit in any chapter.
2. What connects all of the lessons?
Fraction connects all of the lessons. You can write a ration as a fraction. You use a fraction when making a proportion, such as, 2/3=4/6. We learned how to solve equations with fractional coefficients (ex. x/7 + x/3 = 10), fractional equations (ex. 3/x - 1/4 = 1/12), percents that requires fractions to solve (ex. 29/100 = 29%), percents problems (ex. in order to find the percent of decrease, you solve by using this formula/equation: percent of change/100 = change in price/original price.)
3. Are there any lessons in Chapter 7 that do not fit in the chapter?
We don't really think scientific notation fits in this chapter. Scientific notation doesn't really fit in any chapter because it doesn't relate to dividing a lot. Scientific notation and exponents relates to multiplying.
4. With what units should they be inserted into?
Scientific notation should be inserted into Polynomials (Unit 4) because it teaches us about exponents and multiplying monomials.
5. Also, do you think other lessons could be added to this chapter? If so, which ones, and why? If not, why not?
No, other lessons should not be included. it would expand the topic to much. Also no other topic talks about proportions precisely. So the unit should be the way it is.
But aren't we dividing using scientific notation?
DeleteWe think that the editors of this textbook put all of this material together in one chapter to show how fraction connects all of the different topics together. It also is trying to show how to apply fractions. In Chapter 7, scientific notation doesn’t really match because it is more focused on moving decimal points. It is way easier to divide scientific notations if it is in fractions but for the other parts I don’t think it matters.The unit scientific notations should be inserted into the Rational and irrational numbers because irrational numbers have lots of decimals and scientific notation can simplify the process. I think that other lessons should not be added to this chapter because if you add more different, random topics to this chapter, it would be more complicated, jumping onto different topics in the same chapter. It would be so much harder for the students to learn all of the different things at once, and they would be confused.
ReplyDelete