CIM MathStrand A: Number Sense MA.A.1.3.2 Understanding Relative Sizes of Integers and Fractions.
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Transcript of CIM MathStrand A: Number Sense MA.A.1.3.2 Understanding Relative Sizes of Integers and Fractions.
CIM MathCIM Math Strand A: Number SenseStrand A: Number Sense
MA.A.1.3.2 Understanding Relative Sizes of Integers and Fractions
VocabularyVocabulary Day 1Day 1
Negative numbers
VocabularyVocabulary Day 1Day 1
What are negative numbers?
a. All numbers less than or equal to zero
b. All numbers less then negative 1 (i.e., -1).
c. All numbers equal to or less than negative 1 (i.e., -1).
d. All numbers that students don’t want to learn.
e. All numbers less than zero (i.e., 0).
VocabularyVocabulary Day 1Day 1
What are negative numbers?
Negative numbers are numbers that are less than zero.
Examples: -3
-0.472
-1/2
-984.32794078
-46 3/8
-83
VocabularyVocabulary Day 1Day 1
integer
VocabularyVocabulary Day 1Day 1
What is an integer?
a. An integer is a whole number.
b. An integer is a negative whole number.
c. An integer is a positive whole number, zero, or a negative whole number.
d. An integer is a number that can be written as a ratio of two numbers.
VocabularyVocabulary Day 1Day 1
What is an integer?
An integer is a whole number that can be written as a positive whole number, zero, or a negative whole number.
The numbers . . . , -4, -3, -2, -1, 0, 1, 2, 3, 4, . . . consisting of the negative whole numbers, zero, and the positive whole numbers are called integers. -3 and 31 are both examples of integers. They contain no decimals or fractional components.
VocabularyVocabulary Day 1Day 1
coordinate
VocabularyVocabulary Day 1Day 1
Which of the following is a coordinate?
a. a and b
b. 3 and 5
c. -2.2
d. (5, -20.5)
VocabularyVocabulary Day 1Day 1
What is a coordinate?
A coordinate is a pair of values that represent a point on a coordinate plane, also known as an ordered pair, (x,y).
The coordinate plane is also known as the Cartesian Coordinate System. It is made up of a horizontal and a vertical number line that intersect at right angles, called the x-axis and y-axis respectively.
VocabularyVocabulary Day 1Day 1
inequality
VocabularyVocabulary Day 1Day 1
What is an inequality?
An inequality is a math statement formed by placing a less than or greater than sign between two expressions.
For example, 1 < 2 or 3x + 3 > 6 - y
VocabularyVocabulary Day 1Day 1
absolute value
VocabularyVocabulary Day 1Day 1
What is absolute value?
Absolute value is the distance of a number from zero on the number line. It is written as |n|, where n is a real number.
For example, |-4| = 4 or |x| = x and |-x| = x
VocabularyVocabulary Day 1Day 1
Write the absolute value of -23.75?
VocabularyVocabulary Day 1Day 1
less than
VocabularyVocabulary Day 1Day 1
The phrase “less than” is a form of inequality where the real number prior to the phrase or symbol is smaller than the real number that follows the phrase or symbol.
For example, 6 < 3 means “six is less than three”
and
y < x means “y is less than x”
VocabularyVocabulary Day 1Day 1
Which of the following is correct?
a. 7 > 76
b. 8 < 9
c. 26 < -26
d. -2.32 > 1.4309
7
8
VocabularyVocabulary Day 1Day 1
irrational number
VocabularyVocabulary Day 1Day 1
An irrational number is a real number that cannot be written as a fraction, and as a decimal neither repeats nor terminates.
For example, π = 3.141592653589793238462643383279 . . . Or – 0.1112131415161718192021 . . . are both irrational numbers
VocabularyVocabulary Day 1Day 1
Which of the following is an irrational number?
a. 3.14
b. 2.12121212121212121212121212121212 . . .
c.
d. 5.111111111111111111111111111111112151118651218. . .
VocabularyVocabulary Day 1Day 1
real number
VocabularyVocabulary Day 1Day 1
A real number is a number that is either a rational number or an irrational number.
VocabularyVocabulary Day 1Day 1
True or False
-82.1111111111111111 . . . is a rational number.
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Conversion of fractions
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Conversion of fractions
¼ = .25
1/3 = .33 (repeating)
½ = 4/8 = 3/6 = 500/1000 = .5 = 50%
10/1 = 10
438624 / 0 = undefined
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Conversion of fractions
Convert 22/7 to an equivalent form?
(any real mathematical symbol is acceptable)
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
decimals
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Write 73.973 in expanded form?
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
percents
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Write 16 / 80 as a percent?
16 / 80 is the same as 16 divided by 80.
16 / 80 = .2 = 2/10 (10/10) = 20 / 100 = 20%
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Write 3 / 4 as a percent?
a. 80%
b. 75%
c. 70%
d. 60%
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
integers
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Integers are real numbers.
They make up the set of whole numbers:
• greater than zero,
• less than zero, or
• equal to zero.
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Which of these is an integer?
a. 62.53
b. .28
c. 4/1
d. 537,685
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
exponents
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
What is an exponent?
An Exponent is a number that appears as a superscript nextto a number called a base. It tells you how many times the base needs to be multiplied. The entire number is called a power.
For example, 24 = 2 · 2 · 2 · 2 = 16; 4 is the exponent
a8 = a · a · a · a · a · a · a · a; 8 is the exponent
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Evaluate:
24 = ____
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Evaluate:
73 = ____
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
square roots
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
What is a square root?
A square root is the number that is multiplied by itself toget the number that is being evaluated.
For example, √16 = 4 because 4 · 4 = 16
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Evaluate:
= ____16
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
Understand fractional meanings
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
A fraction is made up of two parts:
the top number (x) is the
a. denominator, divisor
b. denominator, dividend
c. numerator, divisor
d. numerator, dividend
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
A fraction is made up of two parts:
the bottom number (y) is the
a. denominator, divisor
b. denominator, dividend
c. numerator, divisor
d. numerator, dividend
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
A fraction is made up of two parts:
the numerator (x)
and the denominator (y)
The bar between the twonumbers means “divided by,”“out of”, “per”, or “over” (i.e. “x over y”).
The top number is the dividend and the bottom numberis the divisor.
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
When you convert a fraction,you may solve it by dividing the numerator by the denominator.
The numerator becomes the dividendand the denominator becomes the divisorof the operation:
X ÷ Y = Y ГX
In this case, the bar between the twonumbers means “divided by.”
The top number is the dividend and the bottom numberis the divisor.
e.g. = 4 ÷ 5 = 5 Г4.0 = .8
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
A fraction is made up of two parts:
The bar between the twonumbers means “divided by,”“over”, “out of”, or “per.”
x over y = x out of y = x per y
= 7 over 8 = 7 out of 8 = 7 per 8
Pre-requisite SkillsPre-requisite Skills Day 2Day 2
A fraction is also used for units of measure:
The bar between the two numbers means “per.”
e.g., miles per hour; dollars per week
PracticePractice Day 3Day 3
1. The coldest temperatures ever recorded for the four U.S. states beginning with the letter “W” (Washington, West Virginia, Wisconsin, and Wyoming) are –48°, –37°, –55°, and –66°. Which of the following shows these temperatures ordered from least to greatest?
a. –48°, –37°, –55°, –66°b. –66°, –55°, –37°, –48°c. –37°, –48°, –55°, –66°d. –66°, –55°, –48°, –37°
PracticePractice Day 3Day 3
2. Which of the following shows the numbers in order from greatest to least?
a.
b.
c.
d.
PracticePractice Day 3Day 3
a. 8 and 9
b. 9 and 10
c. 10 and 11
d. 11 and 12
3. is between which two whole numbers?
PracticePractice Day 3Day 3
a.
b.
c.
d. 2.5, 5, 0.75
4. For which set of three numbers is the second number exactly between the first and third numbers of the set?
PracticePractice Day 3Day 3
a.
b.
c.
d.
5. Which of the following numbers represents the greatest amount?