-
- Functions
- Mathematics
- Middle School
- Relationships and Functions in Middle School Mathematics.
- License:
- Creative Commons Attribution
- Language:
- English
- Media Formats:
- Downloadable docs
Education Standards
Learning Domain: The Number System
Standard: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) Ö (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) Ö (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) Ö (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Learning Domain: The Number System
Standard: Fluently divide multi-digit numbers using the standard algorithm.
Learning Domain: The Number System
Standard: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Learning Domain: The Number System
Standard: 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. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Learning Domain: The Number System
Standard: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Learning Domain: The Number System
Standard: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Learning Domain: The Number System
Standard: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
Learning Domain: The Number System
Standard: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Learning Domain: The Number System
Standard: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
Cluster: Apply and extend previous understandings of multiplication and division to divide fractions by fractions
Standard: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples
Standard: Fluently divide multi-digit numbers using the standard algorithm.
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples
Standard: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples
Standard: 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. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers
Standard: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers
Standard: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers
Standard: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers
Standard: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
Cluster: Apply and extend previous understandings of numbers to the system of rational numbers
Standard: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
Numerical and Algebraic Operations & Analytical Thinking in Middle School Mathematics
Overview
This supplemental resource provides problems and activities related to Numerical and Algebraic Operations & Analytical Thinking in Middle School Mathematics.