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**MA.A.1.3.2 Understanding Relative Sizes of Integers and Fractions**

CIM Math Strand A: Number Sense

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Negative numbers Vocabulary Day 1

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**What are negative numbers?**

All numbers less than or equal to zero All numbers less then negative 1 (i.e., -1). All numbers equal to or less than negative 1 (i.e., -1). All numbers that students don’t want to learn. All numbers less than zero (i.e., 0). Vocabulary Day 1

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**What are negative numbers?**

Negative numbers are numbers that are less than zero. Examples: -3 -0.472 -1/2 -46 3/8 -83 Vocabulary Day 1

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integer Vocabulary Day 1

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**An integer is a whole number. An integer is a negative whole number. **

What is an integer? An integer is a whole number. An integer is a negative whole number. An integer is a positive whole number, zero, or a negative whole number. An integer is a number that can be written as a ratio of two numbers. Vocabulary Day 1

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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 and 31 are both examples of integers. They contain no decimals or fractional components. Vocabulary Day 1

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coordinate Vocabulary Day 1

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**Which of the following is a coordinate?**

a and b 3 and 5 -2.2 (5, -20.5) Vocabulary Day 1

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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. Vocabulary Day 1

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inequality Vocabulary Day 1

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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 Vocabulary Day 1

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absolute value Vocabulary Day 1

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**For example, |-4| = 4 or |x| = x and |-x| = x**

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| = or |x| = x and |-x| = x Vocabulary Day 1

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**Write the absolute value of -23.75?**

Vocabulary Day 1

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less than Vocabulary Day 1

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**For example, 6 < 3 means “six is less than three” and **

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” Vocabulary Day 1

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**Which of the following is correct?**

7 > 76 8 < 9 26 < -26 > Vocabulary Day 1

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irrational number Vocabulary Day 1

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**– 0.1112131415161718192021 . . . are both irrational numbers**

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 = Or – are both irrational numbers Vocabulary Day 1

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**Which of the following is an irrational number? 3.14 **

Vocabulary Day 1

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real number Vocabulary Day 1

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

Vocabulary Day 1

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**True or False -82.1111111111111111 . . . is a rational number.**

Vocabulary Day 1

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**Conversion of fractions**

Pre-requisite Skills Day 2

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**Conversion of fractions**

¼ = .25 1/3 = .33 (repeating) ½ = 4/8 = 3/6 = 500/1000 = .5 = 50% 10/1 = 10 / 0 = undefined Pre-requisite Skills Day 2

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**Conversion of fractions**

Convert 22/7 to an equivalent form? (any real mathematical symbol is acceptable) Pre-requisite Skills Day 2

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decimals Pre-requisite Skills Day 2

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Write in expanded form? Pre-requisite Skills Day 2

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percents Pre-requisite Skills Day 2

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**16 / 80 is the same as 16 divided by 80.**

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 Skills Day 2

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Write 3 / 4 as a percent? 80% 75% 70% 60% Pre-requisite Skills Day 2

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integers Pre-requisite Skills Day 2

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**Integers are real numbers.**

They make up the set of whole numbers: greater than zero, less than zero, or equal to zero. Pre-requisite Skills Day 2

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**Which of these is an integer? 62.53 .28 4/1 537,685**

Pre-requisite Skills Day 2

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exponents Pre-requisite Skills Day 2

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**An Exponent is a number that appears as a superscript next **

What is an exponent? An Exponent is a number that appears as a superscript next to 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 Skills Day 2

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Evaluate: 24 = ____ Pre-requisite Skills Day 2

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Evaluate: 73 = ____ Pre-requisite Skills Day 2

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square roots Pre-requisite Skills Day 2

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**A square root is the number that is multiplied by itself to **

What is a square root? A square root is the number that is multiplied by itself to get the number that is being evaluated. For example, √16 = 4 because 4 · 4 = 16 Pre-requisite Skills Day 2

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Evaluate: = ____ Pre-requisite Skills Day 2

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**Understand fractional meanings**

Pre-requisite Skills Day 2

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**A fraction is made up of two parts: the top number (x) is the **

denominator, divisor denominator, dividend numerator, divisor numerator, dividend Pre-requisite Skills Day 2

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**A fraction is made up of two parts: the bottom number (y) is the **

denominator, divisor denominator, dividend numerator, divisor numerator, dividend Pre-requisite Skills Day 2

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**A fraction is made up of two parts: the numerator (x) **

and the denominator (y) The bar between the two numbers means “divided by,” “out of”, “per”, or “over” (i.e. “x over y”). The top number is the dividend and the bottom number is the divisor. Pre-requisite Skills Day 2

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**4 ÷ 5 = 5 Г4.0 = .8 e.g. = When you convert a fraction,**

you may solve it by dividing the numerator by the denominator. The numerator becomes the dividend and the denominator becomes the divisor of the operation: X ÷ Y = Y ГX In this case, the bar between the two numbers means “divided by.” The top number is the dividend and the bottom number is the divisor. 4 ÷ 5 = 5 Г4.0 = .8 e.g. = Pre-requisite Skills Day 2

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**x over y = x out of y = x per y**

A fraction is made up of two parts: The bar between the two numbers 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 Skills Day 2

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**e.g., miles per hour; dollars per week**

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 Pre-requisite Skills Day 2

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**1. The coldest temperatures ever recorded for the four U. S**

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? –48°, –37°, –55°, –66° –66°, –55°, –37°, –48° –37°, –48°, –55°, –66° –66°, –55°, –48°, –37° Practice Day 3

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

Practice Day 3

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**3. is between which two whole numbers?**

a. 8 and 9 b. 9 and 10 c. 10 and 11 d. 11 and 12 Practice Day 3

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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, 0.75 Practice Day 3

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

d. Practice Day 3

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____________________ Examples: All the numbers that can be written as fractions. Each fraction must have a nonzero denominator. Rational numbers can.

____________________ Examples: All the numbers that can be written as fractions. Each fraction must have a nonzero denominator. Rational numbers can.

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