Download AIMS Math Blitz 03112010 Per 1 - 3

Math AIMS Blitz
Number Sense
Thursday, March 11, 2010
Periods 1, 2, & 3
Period 1 – Number Sets
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 15, 10 , 26 but not 25 or 16)
To what number set(s) does the following belong?
6. { 26 , 51, 0, 5}
1. {3, 4, 5, 6}
2. {¼, 3, ½, 15, ¾, 0}
7. {-3, - ½, 0, 1.56, 1}
3. {-2, 6, 5, 4, 0, 6}
8. {3, 6.352…, 7, 9}
4. {, 5, 7, -¼}
9. {0, 4, 8, 2, }
5. { 16 , 25 , 0,  2 }
10. {0, 1, 8, 6.13, 10}
Period 1 – Number Sets ANSWERS
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 15, 10 , 26 but not 25 or 16)
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
6. { 26 , 51, 0, 5 } IR
2. {¼, 3, ½, 15, ¾, 0} R
7. {-3, - ½, 0, 1.56, 1} R
3. {-2, 6, 5, 4, 0, 6} I, R
8. {3, 6.352…, 7, 9} IR
4. {, 5, 7, -¼} IR
9. {0, 4, 8, 2, } IR
5. { 16 , 25 , 0,  2 } I, R because
10. {0, 1, 8, 6, 10} W, I, R
the square roots are really 4 and 5
Period 2 – Finite or Infinite
Finite: Countable
Infinite (): Uncountable – goes on forever
Finite or Infinite:
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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
Period 2 – Finite or Infinite ANSWERS
Finite: Countable
Infinite (): Uncountable – goes on forever
Finite or Infinite:
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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}
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
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