Week 1 - Big Ideas in Numbers

Question 1

Define Big Ideas in Numbers

Answer 1

An idea central to the learning of mathematics

Links numerous mathematical understandings into a coherent whole

Question 2

Big Idea #1 explanation
Numbers

Answer 2

Numbers - The set of real numbers is infinite, and each real number can be associated with a unique point on the number line (for example, there is no greatest or least integer on the number line)

Question 3

Big Idea #3
Equivalence

Answer 3

Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value (for example, 1/2 = 2/4 = 4/8)

Question 4

Language of Mathematics

Unique Language

Answer 4

• Own symbols (x, -, +, =)
• Own vocabulary (coefficient, hypotenuse)
• Own grammar (multiplication, precedes, addition)
• Own semantics (meaning of words)

Question 5

Language of Mathematics

Vocabulary

Answer 5

• Three students (adjective); The answer is three (noun)
• Pronunciation (fifteen, fifty)
• Million (very big number); milli (very small)
• 3 is a higher number that 1 (cardinal)
• First is higher than third (ordinal)
• Fractions: two fifths (cardinal over ordinal)

Question 6

Language of Mathematics

3 components

Answer 6

Words which have the SAME meaning in English and in Mathematics
e.g. above, more, profit, increase

Words which have DIFFERENT meaning in English and mathematics
e.g. power, rational, variable, volume

Words which have meaning ONLY in mathematics
e.g. coefficient, hypotenuse, vinculum