Edu

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Common Core MATH

There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from.

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Use precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.(find patterns)

PK K

count stuff, describe shapes

1

(1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.

2

(1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. All up to 1000.

3

(1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes

4

(1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. Up to 1,000,000

5

(1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.

6

(1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers

((2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)(common factors 36 + 8 as 4 (9 + 2).), which includes negative numbers;

(3) writing, interpreting, and using expressions and equations v=d*t; and (4) developing understanding of statistical thinking.

7

(1) developing understanding of and applying proportional relationships;

(2) developing understanding of operations with rational numbers and working with expressions and linear equations;

For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

(3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

8

(1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem

For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

high school math

• Number and Quantity
• Algebra
• Functions
• Modeling
• Geometry
• Statistics and Probability

on Is Algebra Necessary?

http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?smid=pl-share

'[D]efenses of algebra ...are... unsupported by research or evidence, or based on wishful logic...It would be better to reduce not expand the mathematics we ask young people to imbibe'

I was interested, that research would be explained, faulty logic analyzed. A page of evidence follows implicating algebra in the high school dropout rate and the college dropout rate.

In most colleges, out of the 40 courses taken to get a bachelors degree only one needs to be a math class (and maybe one a science course). They are often classes like the author speaks of - quantitative reasoning, citizen statistics or the philosophy, history or art of math. The problem is, in order to be eligible to take that one math class, you have to pass the accuplacer, the placement test most incoming college freshman must take. If you fail it you have to take algebra. For the author, the whole 'requirement of higher mathematics comes into question' because of this.

Shall we reduce the requirement from one class in college to maybe 1/2 a class? Eliminate the eight grade level Accuplacer placement requirement. Reduce it to maybe just long-division?

Unfortunately the same argument to eliminate algebra could also be made for reading and writing. At my alma-mater, UMASS Boston, the biggest bar to graduation was the writing test that everybody had to take: desks lined up wall to wall in the gym. The topic was unknown til the moment you opened the packet, in my case it was a question on an excerpt from a novel by Jamaica Kincaid and another from a non-fiction source.

Turns out it is pretty easy to graduate from high school not really knowing how to read and write. You can even be in the National Honor Society in Boston Public Schools. It is a little harder to scam the math.

The people who run the schools define the job of the urban high school teachers of english/humanities classes is to tell the students what the book was about and how it shows how a character has overcome adversity. And then we tell them how to write it down. Then they pass all the high- stakes exams and they are declared successful.

Even my best students were quick to admit that they never really read the books. Why would they? But they could tell the story. Give them a passage from the story they just recounted and they would be flumoxed. Beyond the scripted writing and their personal narrative they were unable to respond in writing to something new. I'm not sure how they get by in college. Maybe the adjunct don't have the time to read papers or check for plagiarism as they teach 6 classes for $27,000.

It is hard to write if you don't really read, hard to frame a problem if you cannot reason abstractly. Perhaps colleges are irrelevant for basic knowledge and skills.

Most of what the average American knows about math or physics or biology or chemistry or foreign language comes from what they learn in High school. A typical bachelors degree recipient hasn't really had to study these in college. And under the authors plan, that would be reduced.

High school is where it is at.

Students are pretty good at talking. The challenge for teachers is to have students actually read and be able to respond in writing to the words they have read. Brain cells fire, neural connections are established in the interplay of sentences and ideas.

The same is true for the study of mathematics. You could probably teach fruit flies the long division algorithm. The problem with algebra is the process of turning a problem into relations that can be expressed. In large part this is a reading problem. The algebra whose requirements the author disparages is essentially to understand y = mx +b. How does something change linearly in relation to something else, the weighting of the consumer price index based on energy costs for instance. Ok so there is a little bit of quadratics, we have to know not everything is linear, double the span of that wind turbine and you catch 4 times the energy, for example.

American education needs some innovation but innovation is tough to come by in the Obama/Duncan, Stand_for_Children race to the top-down control by corporate consultants. There are plenty of interesting things to read but for the most part they are not in textbooks. 600 page 9th grade algebra textbooks with their daily pacing guide and chapter and online tests on some phony worthless algorithm created to fill those pages are an atrocity.

The algebra concepts you need for a college degree or to get 700 on the SAT's could be written an 4 8/12x11 sheets of paper. You probably should learn that. Makes solving problems easier.