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


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).


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


integer


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.


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.


coordinate


Which of the following is a coordinate?

a. a and b

b. 3 and 5

c. -2.2

d. (5, -20.5)


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.


inequality


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


absolute value


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


Write the absolute value of -23.75?


less than


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”


Which of the following is correct?

a. 7 > 76

b. 8 < 9

c. 26 < -26

d. -2.32 > 1.4309

7

8


irrational number


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


Which of the following is an irrational number?

a. 3.14

b. 2.12121212121212121212121212121212 . . .

c.

d. 5.111111111111111111111111111111112151118651218. . .


real number


A real number is a number that is either a rational number or an irrational number.


True or False

-82.1111111111111111 . . . is a rational number.

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



Convert 22/7 to an equivalent form?

(any real mathematical symbol is acceptable)


decimals


Write 73.973 in expanded form?


percents


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%


Write 3 / 4 as a percent?

a. 80%

b. 75%

c. 70%

d. 60%


integers


Integers are real numbers.

They make up the set of whole numbers:

• greater than zero,

• less than zero, or

• equal to zero.


Which of these is an integer?

a. 62.53

b. .28

c. 4/1

d. 537,685


exponents


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


Evaluate:

24 = ____


Evaluate:

73 = ____


square roots


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


Evaluate:

= ____16


Understand fractional meanings


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



the bottom number (y) is the

a. denominator, divisor

b. denominator, dividend

c. numerator, divisor

d. numerator, dividend



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.


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



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


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°


2. Which of the following shows the numbers in order from greatest to least?

a.

b.

c.

d.


a. 8 and 9

b. 9 and 10

c. 10 and 11

d. 11 and 12

3. is between which two whole numbers?


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?


a.

b.

c.

d.

5. Which of the following numbers represents the greatest amount?

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CIM MathStrand A: Number Sense MA.A.1.3.2 Understanding Relative Sizes of Integers and Fractions