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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

Critical Language

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

Concept-Based Connections

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?