Sixth Grade

Power Standards

• Solve mathematical problems, including those in real-world contexts, involving multiplication and division of fractions. (6.NS.1)
• Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12, including in real-world contexts. (6.NS.4)
• Find and position rational numbers, including integers, on a horizontal or vertical number line; find and position pairs of integers and other rational numbers on a coordinate plane. (6.NS.6)

Concepts and Skills

* Power Standard Content

• Use models and equations to multiply fractions, including mixed numbers (whole by fraction, fraction by whole, fraction by fraction)
• * Use models and equations to divide fractions, including mixed numbers (whole/fraction, fraction/whole, fraction/fraction)
• Solve decimal problems using all four operations
• Divide multi-digit whole numbers using a standard algorithm
• * Find the greatest common factor for two whole numbers less than or equal to 100
• * Find the least common multiple of two whole numbers less than or equal to 12
• Find the prime factorization of a number; write using exponents
• Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation
• Order rational numbers using inequalities
• Explain that absolute value of a number is its distance from zero
• * Represent rational numbers on a number line
• * Find and position pairs of integers and other rational numbers on a coordinate plane (four quadrants)
• Find distance between two points on same horizontal or vertical line

Language Usage

• A student in 6th grade will demonstrate the ability to apply and comprehend critical language by interpreting the problem, choosing the appropriate operation, explaining a solution strategy, comparing the location of numbers on a number line, and describing the location of coordinates on a graph.

Content-Specific Vocabulary

• Factor
• Product
• Multiples
• Greatest Common Factor (GCF)
• Least Common Multiple (LCM)
• Decimal
• Divisor
• Dividend
• Quotient
• Fraction
• Numerator
• Denominator
• Inequalities
• Rational
• Integer
• Negative
• Positive
• Number line
• Coordinate plane/graph
• Origin
• x-axis
• y-axis
• Quadrants
• Horizontal
• Vertical
• Absolute
• Value
• Equation

Process-Specific Vocabulary

• Algorithm
• Locate
• Order
• Compare
• Less than
• Greater than
• Graph
• Solve
• Position
• Plot
• Represent
• Explain

Essential Understandings

• The factors and multiples of numbers are used to classify and compare numbers.
• Integers allow values to be described relative to a fixed point.
• Situations dictate a need for different operations.

Factual Guiding Questions

• How can I find the factors of numbers? Multiples?
• What common factors and common multiples do the numbers have?
• What strategies can be used to multiply fractions? Divide fractions? Add, subtract, multiply, divide decimals?
• What does the absolute value of a number represent?
• Why does zero not have an opposite?

Conceptual Guiding Questions

• What do the factors and multiples of the numbers tell about the situation?
• Will the strategies and algorithms we have developed apply to all fractional quantities?
• How do decimal operations compare to fraction operations?
• What does comparing locations of numbers on a number line tell you about the numbers?
• How are opposites related?

Engaging/Debatable Guiding Questions

• Will breaking a number into factors help solve a problem? What relationships are revealed by doing that?
• What is the most efficient strategy for dividing fractions?