1. Math AIMS Blitz Number Sense Thursday, March 11, 2010 Periods 1, 2, & 3

2. Period 1 – Number Sets To what number set(s) does the following belong? 1.{3, 4, 5, 6} 2.{¼, 3, ½, 15, ¾, 0} 3.{-2, 6, 5, 4, 0, 6} 4.{ , 5, 7, -¼} 5.{ } 6. { } 7. {-3, - ½, 0, 1.56, 1} 8.{3, 6.352…, 7, 9} 9.{0, 4, 8, 2,  } 10.{0, 1, 8, 6.13, 10} Number Sets (“…” means they keep going. “ “ means repeating) Counting Numbers: 1, 2, 3, 4, 5, …what you used to count Whole Numbers: 0, 1, 2, 3, 4, 5… Integers: … -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, … Rational Numbers: all of the above plus fractions and decimals that end or repeat…ratio is like fraction Irrational Numbers: Decimals that don’t repeat and don’t end (most popular irrational numbers are  (pi) and square roots of non-perfect squares )

3. Period 1 – Number Sets ANSWERS To what number set(s) does the following belong? C = Counting, W = Whole, I = Integers, R = Rational, IR = Irrational 1.{3, 4, 5, 6} C, W, I, R 2.{¼, 3, ½, 15, ¾, 0} R 3.{-2, 6, 5, 4, 0, 6} I, R 4.{ , 5, 7, -¼} IR 5.{ } I, R because the square roots are really 4 and 5 6. { } IR 7. {-3, - ½, 0, 1.56, 1} R 8.{3, 6.352…, 7, 9} IR 9.{0, 4, 8, 2,  } IR 10.{0, 1, 8, 6, 10} W, I, R Number Sets (“…” means they keep going. “ “ means repeating) Counting Numbers: 1, 2, 3, 4, 5, …what you used to count Whole Numbers: 0, 1, 2, 3, 4, 5… Integers: … -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, … Rational Numbers: all of the above plus fractions and decimals that end or repeat…ratio is like fraction Irrational Numbers: Decimals that don’t repeat and don’t end (most popular irrational numbers are  (pi) and square roots of non-perfect squares )

4. Period 2 – Finite or Infinite Finite: Countable Infinite (  ): Uncountable – goes on forever Finite or Infinite: distance Mr. Kramer descended when skydiving counting numbers whole numbers irrational numbers counting numbers between 0 and 4 rational numbers between 0 and 4 integers between 0 and 4 irrational numbers between 0 and 4 counting numbers less than 4 integers less than 4

5. Period 2 – Finite or Infinite ANSWERS Finite: Countable Infinite (  ): Uncountable – goes on forever Finite or Infinite: distance Mr. Kramer descended when skydiving finite counting numbers infinite {1, 2, 3, 4, …} whole numbers infinite {0, 1, 2, 3, 4, …} irrational numbers infinite Can you name all fractions? counting numbers between 1 and 4 finite {2, 3} rational numbers between 0 and 4 infinite Can you name all fractions between 0 and 4? integers between 0 and 4 finite {1, 2, 3} irrational numbers between 0 and 4 infinite Can you name all the decimals that don’t end between 0 and 4? counting numbers less than 4 finite {1, 2, 3} integers less than 4 infinite {… -3, -2, -1, 0, 1, 2, 3}

6. Period 3 - Number Properties Associative Property: Changes which numbers are paired together (a + b) + c = a + (b + c) or 7 + (3 + 16) = (7 + 3) + 16 Commutative Property: (think about commuting and going 2 different directions) a + b = b + a or 8 + 10 = 10 + 8 Distributive Property (distributes a value to the other values) a(b + c) = ab + ac or 6(10 + 8) = 6(10) + 6(8) Identity Property (keeps the value the same) a * 1 = a or 15 * 1 = 15 a + 0 = a or 18 + 0 = 18 Name the property shown. 1.5(x + y) = 5x + 5y 2.3 + b = b + 3 3.ab + 0 = ab 4.6(1) = 6 5.9 + (8 + a) = (9 + 8) + a 6.5 + (3 * 1) = 5 + 3 7.6 + (3 + 8) = (3 + 8) + 6 8.7 + (2 + 10) = 7 + (10 + 2) 9.3x + 6y = 3(x + 2y) 10.1(5 + y) = 5 + y

7. Period 3 - Number Properties ANSWERS Associative Property: Changes which numbers are paired together (a + b) + c = a + (b + c) or 7 + (3 + 16) = (7 + 3) + 16 Commutative Property: (think about commuting and going 2 different directions) a + b = b + a or 8 + 10 = 10 + 8 Distributive Property (distributes a value to the other values) a(b + c) = ab + ac or 6(10 + 8) = 6(10) + 6(8) Identity Property (keeps the value the same) a * 1 = a or 15 * 1 = 15 a + 0 = a or 18 + 0 = 18 Name the property shown. 1.5(x + y) = 5x + 5y Distributive 2.3 + b = b + 3 Commutative 3.ab + 0 = ab Identity 4.6(1) = 6 Identity 5.9 + (8 + a) = (9 + 8) + a Associative 6.5 + (3 * 1) = 5 + 3 Identity 7.6 + (3 + 8) = (3 + 8) + 6 Commutative (order changed) 8.7 + (2 + 10) = 7 + (10 + 2) Commutative 9.3x + 6y = 3(x + 2y) Distributive 10.1(5 + y) = 5 + y Identity