A child playing in the sink empties a short, wide glass of water into a tall, thin glass of equal volume. The child believes that the tall, thin glass contains more water. This means that the child has not yet reached which of Piaget's stages? A. Sensorimotor B. Preoperational C. Concrete Operational D. Logical/Formal Operational
The correct answer is C. Concrete Operational stage. In this stage, children are between 7-11 years old and this is when they become more logical in CONCRETE thinking, which means that they develop inductive reasoning (they can reason from specific situations to general concepts) but they have not yet developed deductive reasoning (deducting the meaning of specific situations from the general concepts that they know such as conservation of water regardless of equal volume of the container). After the child develops the ability to think logically in the abstract and develop deductive reasoning (such as the idea that a quantity remains the same despite changes in its shape or container), then the child will have entered the formal operational stage.
Example ACT English grammar section: [So biologists decided to look for wolves themselves. They have flown to elk and deer wintering areas, ridden horses and snowmobiles through the mountains, and __THROWING__ back their heads and called out....] Choose the answer choice that will make the underlined, capitalized word the best expressed idea that is also consistent with correct English grammar: A. NO CHANGE B. throw C. threw D. even thrown
The best answer choice is D. even thrown. Many students might choose C. threw, but we notice that the verb "thrown" is in past perfect tense, which is the same tense as the previous verbs. [So biologists decided to look for wolves themselves. They have FLOWN to elk and deer wintering areas, RIDDEN horses and snowmobiles through the mountains, and __THROWING__ back their heads and called out....] "Ridden" and "flown" are also in the same tense, so using "throw," "threw," or "throwing" would not make sense in the sentence as the ACT English section looks for consistency in an answer so as to make the writing flow more easily to get the author's message across in the most efficient way.
The equation ((x^2)-2x+1)/(ax-2) = (-4x+3) - (8/(ax-2)) is true for all values of x except 2/a where a is constant. What is the value of a?
The easiest and quickest way to solve this problem is to first multiply each side by the denominator which is (ax-2). This will help us combine like terms more easily. The end of step 1 should look like this: (x^2)-2x+1 = (-4x+3)(ax-2) -8 The next step is to get rid of the parentheses by using the FOIL method: So the equation should look like this: (x^2)-2x+1 = -4a(x^2) +8x +3ax -6 -8 Next, combine any like terms on the right side (aka. reducing the right side): It should look like this: (x^2)-2x+1 = -4a(x^2) +8x +3ax -14 The last step is where most people get stuck and this is key to solving the problem. We have to understand that the coefficients (the numbers in front of the variables) are equal to each other on the same side for each like variable. So, you can set the (x^2) from the left side EQUAL to the -4a(x^2) on the right side. When you cancel out the (x^2), you can just solve for a. This is how the process looks like: 1(x^2) = -4a(x^2) 1 = -4a Thus, a= -1/4 Notice that there is no need to mess with all the other variables like 8x or 3ax because when there are multiple variables (x and a) in an equation, we can set equal the like terms from both sides of the equation to cancel x and get the value for a.