# Characteristic of Effective Instruction

## On this page...

## Teaching for Understanding

### Elementary

EngageNY - Grade 3 Module 5: Fractions as Numbers on the Number Line

Factoring, Quadratics

- Reflections on Factoring: The Process of Factoring, Factored Form, And Prime Quadratics
- How Many Quadratic Factor?
- Mystery Quadratic
- Which Quadratics to Factor?
- Analyzing the Quadratic Formula

Formative Assessment Lesson "14 Legs in a Barn"

The Mathematics Common Core Toolbox - A resource site designed to support districts and schools working to meet the challenge and the opportunity of the CCSS. Find tools and instructional materials to help better understand and to implement the CCSS in Mathematics.

The site is broken into the following three sections:

- Standards for Mathematical Practice - This section features Key Visualizations (animations) and Formative Assessment tools and tasks.
- Standards for Mathematical Content - This section features Key Visualizations (animations) that support the CCSS content standards.
- Resources for Implementation - This section features Preparation for Implementation, Studying the Standards, and Sample Scope and Sequence.

Meaningful Distributed Practice (MDP): Describing 2 and 3 D Shapes

Meaningful Distributed Practice (MDP): Equivalent Fractions

Meaningful Distributed Practice (MDP): Part/Whole Relationships, Angles, Language

Reflections on Practice: Perimeter and Area Through the Van Hiele Model - (document available to NCTM members only)

### Middle

Activity 2: Ratio Tables to the Rescue

Activity 3: Take Me Out to the Ballgame

Activity 4: Takin' Care of Business

Activity 5: Power Bars

Activity 6: Mee, Too

Activity 7: Look's Like it to Me

Activity 8 The Midas Touch

Activity 9: A New Slant on Ratio Tables

Estimations and Approximations: The Money Munchers

Increasing and Decreasing by Percents

Interpreting Distance-Time Graphs

The Mathematics Common Core Toolbox - A resource site designed to support districts and schools working to meet the challenge and the opportunity of the CCSS. Find tools and instructional materials to help better understand and to implement the CCSS in Mathematics.

The site is broken into the following three sections:

- Standards for Mathematical Practice - This section features Key Visualizations (animations) and Formative Assessment tools and tasks.
- Standards for Mathematical Content - This section features Key Visualizations (animations) that support the CCSS content standards.
- Resources for Implementation - This section features Preparation for Implementation, Studying the Standards, and Sample Scope and Sequence.

Reflections on Practice: Perimeter and Area Through the Van Hiele Model - (document available to NCTM members only)

Shaded Areas of Rectangular Grids

- Shaded Areas of Rectangular Grids: Lesson Guide
- Shaded Areas of Rectangular Grids: Launch
- Shaded Areas of Rectangular Grids: Accommodation Grids

Solving Linear Equations - Multiple Methods and Representations

Solving Real Life Problems: Baseball Jerseys

Text Messaging

Using Dimensions: Designing a Sports Bag

### High

Candy Quality Control

Check That Digit

Devising a Measure for Correlation

Reflections on Factoring: The Process of Factoring, Factored Form, And Prime Quadratics

Ferris Wheel

- Riding a Ferris Wheel and Transforming Functions: Student Handout
- Riding a Ferris Wheel and Transforming Functions: Lesson Plan

Logarithms

- Logarithms: Examples of Gentle Gradual Development Through Meaningful Distributed Practice
- Meaningful Distributed Practice-Concept Exponents and Logarithms
- Graphic Logs: Quake Story

The Mathematics Common Core Toolbox - A resource site designed to support districts and schools working to meet the challenge and the opportunity of the CCSS. Find tools and instructional materials to help better understand and to implement the CCSS in Mathematics.

The site is broken into the following three sections:

- Standards for Mathematical Practice - This section features Key Visualizations (animations) and Formative Assessment tools and tasks.
- Standards for Mathematical Content - This section features Key Visualizations (animations) that support the CCSS content standards.
- Resources for Implementation - This section features Preparation for Implementation, Studying the Standards, and Sample Scope and Sequence.

Meaningful Distributed Practice Planning: Graphing Linear Equations & Solving Linear Systems

Medicine Dosage

- Medicine Dosage Task
- Medicine Dosage Task Spreadsheet Showing Different Recursive Models
- Explanation of Two Recursive Models for Medicine Dosage Task

NCSM Great Tasks for Mathematics: Bugs, Giraffes, Elephants and More

Permutations, Combinations, and RNA

Proof with Multiple Representaions (Fido Problem)

Reflections on Practice: Perimeter and Area Through the Van Hiele Model - (document available to NCTM members only)

Resources for Teaching the Iowa Core Additional Standards in High School Mathematics

Sets, Logic, and Internet Searches

Skydiving Math

Solving Linear Equations

- Solving Linear Equations: Teacher and PD Notes
- Solving Linear Equations: Student Version
- Solving Linear Equations: Teacher Versions

Solving Linear Equations - Multiple Methods and Representations

Text Messaging

Text Messaging Problem: An Application of Systems of Linear Equations

Transformations

## Student-Centered Classrooms

### Elementary

Formative Assessment Lesson "14 Legs in a Barn"

### Middle

Activity 5: Power Bars

Activity 6: Mee, Too

Activity 7: Look's Like it to Me

Activity 8 The Midas Touch

Estimations and Approximations: The Money Munchers

Increasing and Decreasing by Percents

Solving Real Life Problems: Baseball Jerseys

Using Dimensions: Designing a Sports Bag

### High

Candy Quality Control

Check That Digit

Devising a Measure for Correlation

Ferris Wheel

- Riding a Ferris Wheel and Transforming Functions: Student Handout
- Riding a Ferris Wheel and Transforming Functions: Lesson Plan

Medicine Dosage

- Medicine Dosage Task
- Medicine Dosage Task Spreadsheet Showing Different Recursive Models
- Explanation of Two Recursive Models for Medicine Dosage Task

Proof with Multiple Representaions (Fido Problem)

Reflections on Practice: Perimeter and Area Through the Van Hiele Model

Solving Linear Equations

- Solving Linear Equations: Teacher and PD Notes
- Solving Linear Equations: Student Version
- Solving Linear Equations: Teacher Version

Text Messaging Problem: An Application of Systems of Linear Equations

## Teaching for Student Differences

### Elementary

### Middle

Estimations and Approximations: The Money Munchers

Increasing and Decreasing by Percents

Solving Real Life Problems: Baseball Jerseys

Using Dimensions: Designing a Sports Bag

### High

Devising a Measure for Correlation

Medicine Dosage

- Medicine Dosage Task
- Medicine Dosage Task Spreadsheet Showing Different Recursive Models
- Explanation of Two Recursive Models for Medicine Dosage Task

Solving Linear Equations

- Solving Linear Equations: Teacher and PD Notes
- Solving Linear Equations: Student Version
- Solving Linear Equations: Teacher Versions

## Rigor and Relevance

### Elementary

Middle

Activity 4: Takin' Care of Business

Estimations and Approximations: The Money Munchers

Increasing and Decreasing by Percents

Reflections on Practice: Perimeter and Area Through the Van Hiele Model

Shaded Areas of Rectangular Grids

- Shaded Areas of Rectangular Grids: Lesson Guide
- Shaded Areas of Rectangular Grids: Launch
- Shaded Areas of Rectangular Grids: Accommodation Grids

Solving Real Life Problems: Baseball Jerseys

Text Messaging

Using Dimensions: Designing a Sports Bag

### High

Candy Quality Control

Check That Digit

Devising a Measure for Correlation

Ferris Wheel

- Riding a Ferris Wheel and Transforming Functions: Student Handout
- Riding a Ferris Wheel and Transforming Functions: Lesson Plan

Medicine Dosage

- Medicine Dosage Task
- Medicine Dosage Task Spreadsheet Showing Different Recursive Models
- Explanation of Two Recursive Models for Medicine Dosage Task

Permutations, Combinations, and RNA

Proof with Multiple Representaions (Fido Problem)

Resources for Teaching the Iowa Core Additional Standards in High School Mathematics

Sets, Logic, and Internet Searches

Skydiving Math

Text Messaging

Text Messaging Problem: An Application of Systems of Linear Equations

## Assessment for Learning

### Elementary

Meaningful Distributed Practice (MDP): Part/Whole Relationships, Angles, Language

Meaningful Distributed Practice (MDP): Equivalent Fractions

NAEP - Kindergarten Tasks - Geometry

NAEP - Kindergarten Tasks - Measurement and Data

NAEP - Grade 1 Tasks - Geometry

NAEP - Grade 1 Tasks - Measurement and Data

NAEP - Grade 1 Tasks - Number and Operations in Base 10

NAEP - Grade 1 Tasks - Operations and Algebraic Thinking

NAEP - Grade 2 Tasks - Geometry

NAEP - Grade 2 Tasks - Measurement and Data

NAEP - Grade 2 Tasks - Numbers and Operations in Base 10

NAEP - Grade 2 Tasks - Operations and Algebraic Thinking

NAEP - Grade 3 Tasks - Geometry

NAEP - Grade 3 Tasks - Measurement and Data

NAEP - Grade 3 Tasks - Number and Operations - Fractions

NAEP - Grade 3 Tasks - Number and Operations in Base 10

NAEP - Grade 3 Tasks - Operations in Algebraic Thinking

NAEP - Grade 4 Tasks - Geometry

NAEP - Grade 4 Tasks - Measurement and Data

NAEP - Grade 4 Tasks - Number and Operations - Fractions

NAEP - Grade 4 Tasks - Number and Operations in Base 10

NAEP - Grade 4 Tasks - Operations and Algebraic Thinking

NAEP - Grade 5 Tasks - Geometry

NAEP - Grade 5 Tasks - Measurement and Data

NAEP - Grade 5 Tasks - Number and Operations - Fractions

NAEP - Grade 5 Tasks - Number and Operations in Base 10

NAEP - Grade 5 Tasks - Operations in Algebraic Thinking

### Middle

Activity 7: Look's Like it to Me

Activity 8 The Midas Touch

Estimations and Approximations: The Money Munchers

Increasing and Decreasing by Percents

Interpreting Distance-Time Graphs

Modeling Situations with Linear Equations

NAEP - Grade 6 Tasks - Expressions and Equations

NAEP - Grade 6 Tasks - Geometry

NAEP - Grade 6 Tasks - The Number System

NAEP - Grade 6 Tasks - Ratios and Proportional Relationships

NAEP - Grade 6 Tasks - Statistics and Probability

NAEP - Grade 7 Tasks - Expressions and Equations

NAEP - Grade 7 Tasks - Geometry

NAEP - Grade 7 Tasks - The Number System

NAEP - Grade 7 Tasks - Ratios and Proportional Relationships

NAEP - Grade 7 Tasks - Statistics and Probability

NAEP - Grade 8 Tasks - Expressions and Equations

NAEP - Grade 8 Tasks - Functions

NAEP - Grade 8 Tasks - Geometry

NAEP - Grade 8 Tasks - The Number System

NAEP - Grade 8 Tasks - Statistics and Probability

Proofs of the Pythagorean Theorem?

Ratios and Proportional Relationships

Solving Real Life Problems: Baseball Jerseys

Using Dimensions: Designing a Sports Bag

### High

Devising a Measure for Correlation

Ferris Wheel

- Riding a Ferris Wheel and Transforming Functions: Student Handout
- Riding a Ferris Wheel and Transforming Functions: Lesson Plan

NAEP - Grades 9-12 Tasks - Algebra

NAEP - Grades 9-12 Tasks - Functions

NAEP - Grades 9-12 - Statistics and Probabilty

PARCC

Resources for Teaching the Iowa Core Additional Standards in High School Mathematics