So here are the test questions and answers with the first answer, the traditional math answer (TMA) and second answer, the 2015 Common Core (CCSSM) answer.
1. What is counting?
TMA - "one, two, three four five etc" with no sense of what the numbers actually mean.
CCSSM - "one, two, three, four, five etc" understanding that three is one more than two and four is one more than three and that when you count five objects the word "five" refers to all five objects not just the last one counted. This is the idea of cardinality and is key to understanding number,
2. What is addition?
CCSSM The above is only an algorithm, a piece of arithmetic. Knowing just this is useless in
problem solving. To problem solve you need to know the concepts of joining, separating,
comparing and part-part-whole if you want to use addition or subtraction in anything useful. .
3. What is multiplication?
CCSSM Just like addition and subtraction the above is just an algorithm, a piece of procedural
knowledge. It doesn't help you decide which operation to use in problem solving. You'll need to
know the repeated addition, multiplicative comparison concepts as well as a few more to be know
whether to divide or multiply
4. What is division?
CCSSM See above
5. What is Pi?
TMA: 3.14 etc
CCSSM Yes, but this doesn't help a whole lot. Pi is a ratio between the diameter and
circumference of a circle. The circumference is always just over 3 times the diameter; or, if the
diameter is 7 the circumference is 22.
6. What does the 0 mean in 308?
TMA: A place holder
CSSMIt means there are 0 tens. Place holder is a meaningless term than has no conceptual
value. Children need to learn initially that each place in place value has a value.
7. What is 1/2 divided by 1/4?
TMA: "Change the sign and invert the second fraction"
CCSSM This is virtual nonsense and doesn't help at all. Knowing that the problem is asking
how many 1/4s there are in 1/2 is of far more value especially in a world of calculators.
8. Make up a word problem for # 7 above.
TMA: I can't
CCSSM: How many 1/4s in the first half of a football game
9. What do you get when you reduce 4/8?
TMA: 1/2 Unfortunately, most children being taught to "reduce" a fraction think that 1/2
is smaller than 4/8 because the word "reduce" means to make smaller and the two numbers.1
and 2 are smaller than 4 and 8. I joke about reducing 4/8 to 4/8
CCSSM; You don't use the word "reduce" fractions because children think 1/2 is smaller than
4/8. You rename or regroup 4/8.
10. Why do you put a comma after every three digits in a large number?
TMA: Because that's what you do
CCSSM Because it marks the repetition of 100, 10, 1 in each place value referent
11. What is area?
TMA: length times width
CCSSM this only allows you to measure the area of regular shaped objects. Area is the two
dimensional concept of coverage. You can find the area of your hand by tracing it onto squared
paper and counting the squares.
12. What does a degree measure in geometry?
TMA: It measures angles
CCSSM It measures the rotation of an angle about a point. This is the only way you can explain
why an angle is 45 degrees 4 inches from its origin and still 45 degrees 4 feet from it;s origin.
Children must understand what they learn at the developmentally appropriate level; this is why the common core is so good.