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About the Learning Math Courses

Mar 27, 2020

When teachers have a deep conceptual understanding of mathematics, it can help their students develop strong mathematical skills and knowledge.…

Part A: Observing a Case Study (25 minutes)

Mar 27, 2020

To begin the exploration of what topics in number and operations look like in a classroom at your grade level,…

Track Our Progress: The Salad Bar

Mar 10, 2020

Scroll through the pictures below to see our salad-bar plates and what the larva is eating at that time. See…

Track Our Progress: Mother Knows Best

Mar 10, 2020

Scroll through the pictures below to see our ovipositrons. See the Mother Knows Best activity instructions for questions to consider.

Track Our Progress: Brassica and Butterfly Life Cycles

Mar 10, 2020

Scroll through the days below to see our Brassicas and butterflies develop through their life cycles. Then, at the bottom of…

Track Our Progress: Assessing Variation

Mar 10, 2020

Click on one of the three growing systems in either of the pictures below to see a close-up of one…

Track Our Progress: Selective Herbivory

Mar 10, 2020

Below are pictures of our Selective Herbivory systems in its initial state and at one and two days after introducing…

Program 16: Writing in Science

Jan 31, 2020

Watch the 30-minute video “Writing in Science.” Apply what you have learned in “Writing Across the Curriculum” as you watch…

Program 15: Writing Across the Curriculum

Jan 31, 2020

Watch the 30-minute video “Writing Across the Curriculum.” If you prefer to watch the video in segments, you can stop…

Program 14: Modeling Revision

Jan 31, 2020

Watch the 30-minute video “Modeling Revision.” Apply what you learned in “Learning to Revise” as you watch the extended video…

Program 13: Learning To Revise

Jan 31, 2020

Watch the 30-minute video “Learning To Revise.” If you prefer to watch the video in segments, you can stop at…

Program 12: Peer Conferences

Jan 30, 2020

Watch the 30-minute video “Peer Conferences.” Apply what you have learned in “Conversations Among Writing Peers” as you watch the…

Program 11: Conversations Among Peer Writers

Jan 30, 2020

Watch the 30-minute video “Conversations Among Writing Peers.” If you prefer to watch the video in segments, you can stop…

Program 10: Teacher-Student Conferences

Jan 30, 2020

Watch the 30-minute video “Teacher-Student Conferences.” Apply what you have learned in “Conversations With Student Writers” as you watch the…

Program 9: Conversations With Student Writers

Jan 30, 2020

Watch the 30-minute video “Conversations With Student Writers.” If you prefer to watch the video in segments, you can stop…

Program 8: Teaching a Specific Writing Strategy

Jan 30, 2020

Watch the 30-minute video “Teaching a Specific Writing Strategy.” Apply what you have learned in “Teaching the Writing Craft” as…

Program 7: Teaching the Writing Craft

Jan 30, 2020

Watch the 30-minute video “Teaching the Writing Craft.” If you prefer to watch the video in segments, you can stop…

Program 6: Reading/Writing Connections

Jan 30, 2020

Watch the 30-minute video “Reading/Writing Connections.” Apply what you learned in “Reading Like a Writer” as you watch the extended…

Program 5: Reading Like a Writer

Jan 30, 2020

Watch the 30-minute video “Reading Like a Writer.” If you prefer to watch the video in segments, you can stop…

Program 4: Fostering Choice and Independence

Jan 30, 2020

Watch the 30-minute video “Fostering Choice and Independence.” Apply what you have learned in “Reasons for Writing” as you watch…

Program 3: Reasons for Writing

Jan 30, 2020

Watch the 30-minute video “Reasons for Writing.” If you prefer to watch the video in segments, you can stop at…

Part C: Modeling Linear Relationships (35 minutes)

Jan 28, 2020

In This Part: How Square Can You Be?  In Parts A and B, you confirmed that there is a strong positive…

Students’ Understanding of Area (video)

Jan 28, 2020

Engaging Students’ in Hands-On Activities (video)

Jan 28, 2020

TerrAqua Column | Track Our Progress: Now You See It

Jan 24, 2020

Scroll through the pictures below to see a larger picture of one of our petri dishes. See the Now You…

TerrAqua Column | Track Our Progress: What Is It? | Aquatic System

Jan 24, 2020

Scroll through the pictures below to see enlargements of the aquatic habitat of our TerrAqua system. See the What Is…

TerrAqua Column | Track Our Progress: Is It Alive?

Jan 24, 2020

Click on the links below to see pictures of the components we put into our TerrAqua system. See the Is It…

Program 2: Teacher as Writer

Jan 23, 2020

Watch the 30-minute video “Teacher as Writer.” Apply what you have learned in “Building a Community of Writers” as you…

Program 1: Building a Community of Writers

Jan 23, 2020

Watch the 30-minute video “Building a Community of Writers.” If you prefer to watch the video in segments, you can…

Put It Into Practice | Connecting School and Home

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The three activities are…

Examine the Topic | Connecting School and Home

Jan 13, 2020

Extend Your Knowledge In this section, you will expand your understanding of connecting school and home literacy. You will compare…

Watch the Video | Connecting School and Home

Jan 13, 2020

Lecture In this section, you will watch Dr. Paratore’s lecture on connecting school and home literacy practices. Print Dr. Paratore’s…

Before You Watch | Connecting School and Home

Jan 13, 2020

Video Summary The video for this session examines the research and related practices for building positive home-school connections. Dr. Paratore…

Put It Into Practice | Using Assessment To Guide Instruction

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The three activities are…

Examine the Topic | Using Assessment To Guide Instruction

Jan 13, 2020

Extend Your Knowledge In this section, you will expand your understanding of assessment practices that inform your instruction. You will…

Watch the Video | Using Assessment To Guide Instruction

Jan 13, 2020

Lecture In this section, you will watch Dr. Paratore’s lecture on using assessment to guide instruction. Print Dr. Paratore’s Assessment…

Before You Watch | Using Assessment To Guide Instruction

Jan 13, 2020

Video Summary The video for this session examines assessment practices that measure student performance and progress, and inform instructional decisions.…

Put It Into Practice | Differentiating Instruction

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The three activities are…

Examine the Topic | Differentiating Instruction

Jan 13, 2020

Differentiate Instruction in a Class In this section, you will explore an activity to better understand how to group students…

Watch the Video | Differentiating Instruction

Jan 13, 2020

Lecture In the session, you will watch Dr. Paratore’s lecture on differentiating instruction for early literacy. Print Dr. Paratore’s Differentiating…

Before You Watch | Differentiating Instruction

Jan 13, 2020

Video Summary In the video for this session, Dr. Jeanne R. Paratore presents research-based principles that support the use of…

Put It Into Practice | Teaching Writing as a Process

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The three activities are…

Examine the Topic | Teaching Writing as a Process

Jan 13, 2020

Extend Your Knowledge In this section, you will expand your understanding of writing instruction by comparing the ideas from the…

Before You Watch | Teaching Writing as a Process

Jan 13, 2020

Video Summary The video for this session examines how to teach writing as a process. Dr. Jeanne R. Paratore begins…

Put It Into Practice | Comprehension and Response

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The three activities are…

Examine the Topic | Comprehension and Response

Jan 13, 2020

Reading for Meaning In this section, you will explore an activity to better understand what factors children use to comprehend…

Watch the Video | Comprehension and Response

Jan 13, 2020

Lecture In this section, you will watch Dr. Paratore’s lecture on comprehension instruction in two parts. Print Dr. Paratore’s Comprehension…

Before You Watch | Comprehension and Response

Jan 13, 2020

Video Summary The video for this session examines comprehension and response to literature in grades K-2. In her lecture, Dr.…

Put It Into Practice | Word Study and Fluency

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The three activities are…

Examine the Topic | Word Study and Fluency

Jan 13, 2020

Consider Other Points of View In this section, you will expand your understanding of word study by comparing the ideas…

Watch the Video | Word Study and Fluency

Jan 13, 2020

Lecture In this section, you will watch Dr. Paratore’s lecture on Word Study and Fluency. Print Dr. Paratore’s Word Study…

Before You Watch | Word Study and Fluency

Jan 13, 2020

Video Summary  The video for this session examines word study and explicit fluency instruction in the primary grades. Dr. Jeanne…

Put It Into Practice | Supporting the English Language Learner

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The four activities are…

Examine the Topic | Supporting the English Language Learner

Jan 13, 2020

Examine Cueing Strategies In this section you will explore an activity to better understand reading as an English Language Learner.…

Watch the Video | Supporting the English Language Learner

Jan 13, 2020

Lecture In this section, you will watch Dr. Gort’s lecture on reading instruction for English Language Learners in grades K-2.…

Before You Watch | Supporting the English Language Learner

Jan 13, 2020

Video Summary  In the video for this session, Dr. Mileidis Gort presents research-based principles that support English Language Learners’ literacy…

Put It Into Practice | Creating a Literate Community

Jan 13, 2020

Choose Activities In this section, you will apply what you have learned to your own teaching. The three activities are…

Examine the Topic | Creating a Literate Community

Jan 13, 2020

Extend Your Knowledge In this section, you will expand your understanding of a literate classroom community by comparing the ideas…

Watch the Video | Creating a Literate Community

Jan 13, 2020

Lecture In this section, you will watch Dr. Paratore’s lecture on creating a literate community in early literacy. Print Dr.…

Before You Watch | Creating a Literate Community

Jan 13, 2020

Video Summary  In this video session, Dr. Jeanne R. Paratore presents three research-based principles for creating an effective literacy environment…

Key Terms | Teaching Reading: K-2 Workshop

Jan 13, 2020

About the Learning Math Courses

Jan 08, 2020

When teachers have a deep conceptual understanding of mathematics, it can help their students develop strong mathematical skills and knowledge.…

About the Learning Math Courses

Jan 08, 2020

When teachers have a deep conceptual understanding of mathematics, it can help their students develop strong mathematical skills and knowledge.…

Learning Challenges

Jan 08, 2020

Each session of The Learning Classroom generally concentrates on a single learning theory and describes how it might be applied in a…

About the Learning Math Courses

Jan 08, 2020

When teachers have a deep conceptual understanding of mathematics, it can help their students develop strong mathematical skills and knowledge.…

Teaching Strategies

Dec 19, 2019

Watch the Video | Teaching Writing as a Process

Dec 19, 2019

Lecture In this section, you will watch Dr. Paratore’s lecture on teaching writing as a process. Print Dr. Paratore’s Writing…

Featured Classrooms

Dec 17, 2019

Classroom Videos Investigating Word Meaning Teacher: Angie Zapata Grade 3, Mathews School, Austin, TX Using a passage from Charlotte’s Web by E.…

Lens on Literacy

Dec 17, 2019

We all agree that learning to read is a critical step in a child’s education. But teaching children to read…

Video Organizer Chart

Dec 16, 2019

All lessons are appropriate for K–12 teachers of any foreign language.

#10037 Internally displaced Iraqis flee fighting in Mosul

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#10036 Syrian mother reunited with children she feared had drowned

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#10009 The focus of this photograph is a group of young children sitting tightly together on the floor in a dimly…

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#10001 Caring for Refugees, c. World War I

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#2003 Comparison of unsprayed conventional cotton crop and Bt GM cotton in Australia

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#2003 The color photograph is of a field of cotton. The photograph is divided to depict two different crops, which are…

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#100 Athabasca Glacier, Jasper National Park, 1917

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#101 Athabasca Glacier, Alberta, Canada, 2005

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#2573 Generating Power

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#2573 A woman sits in profile on a stationary bicycle in the foreground of the image. Her profile orientation and placement…

#2574 Bicidesgranadora (Mill/Corn Thresher)

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#8047 Migratory Mexican field worker’s home on the edge of a frozen pea field. Imperial Valley, California

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#8047 The black and white photograph depicts a Mexican migrant family in front of a makeshift shelter in California. The photograph…

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#264 Man in Doorway

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#265 Son of migratory worker from Kansas in squatters’ camp near Farmersville, California

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#268 Scenes of the northern Shenandoah Valley, including the Resettlement Administration’s Shenandoah Homesteads

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#275 Dorothea Lange in the Field, 1938

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#285 Sign advertising farmland auction, New Carlisle, Ohio

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#298 Pink Pride, Trombone Shorty

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#252 Elizabeth and Dora Mae Tengle, Hale County, Alabama

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#257 Washington, D.C. Neighborhood children

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#258 Dock Worker/Flower Sacks

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#259 Mother with her children, Oaklawn Plantation

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#261 The Blessing

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#262 Single Men Social and Pleasure Club

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#246 Supper Time

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#235 Washington, Yakima Valley, near Wapato.

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#236 Roy E. Stryker, photograph chief of the U.S. Farm Security Administration standing in street, probably in Washington, D.C.

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#237 Group of children posing under sign.

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#245 Two Children of the Mochida Family, with Their Parents, Awaiting Evacuation Bus

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#221 Zollie Lyon, Negro sharecropper.

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#224 Women being transported from Memphis, Tennessee to an Arkansas plantation

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#227 Plantation overseer.

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#228 Cotton hoer near Clarksdale, Mississippi

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#230 Roy Emerson Stryker, half-length portrait, seated at desk, talking on the telephone

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#232 Daughter of migrant Tennessee coal miner.

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#121 Dust storm, Elkhart, Kan.

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#215 Dorothea Lange, Resettlement Administration photographer, in California

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#217 Country store on dirt road. Sunday afternoon.

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#219 Franklin D. Roosevelt at desk

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#120 Toward Los Angeles, Calif.

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#5020 Columbia University, New York, 1968

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#3520 The color photograph depicts four people standing at the edge of a grassy cliff. Large pieces of earth have broken…

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#3513 How people are adapting to climate change and fighting food insecurity

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#3503 Muir Glacier and Muir Inlet, 1980

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#3038 In the black and white photograph, three young boys stand holding stacks of newspapers at their sides. It is nighttime,…

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#6029 Hubble’s Sharpest View of Mars

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#6021 Whitewater Lake Rock Viewed by Opportunity

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#6022 Late Afternoon Shadows at Endeavour Crater on Mars

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#6023 Spirit Lander and Bonneville Crater in Color

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Focus In on This Photo: Spirit Lander and Bonneville Crater in Color

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#6023 The digital-colorized image depicts a crater on the planet Mars and includes some of the surrounding area.

#6016 Spirit Mars Rover in McMurdo Panorama

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#6017 Link to a Watery Past

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#6018 Remnants of Ancient Streambed on Mars

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#6019 Matijevic Hill

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#6020 First Use of Mars Rover Curiosity’s Dust Removal Tool

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#6012 Carbonate-Containing Martian Rocks

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#6014 Blueberry Spherules

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#6007 McLaughlin Crater Image Clues

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#6008 Barchan Dunes on the Move

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#6010 A Moment Frozen in Time

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#6011 Destination, Mount Sharp Terrain

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#6004 Icy Layers and Climate Fluctuations Near the Martian North Pole

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#6004 Icy Layers and Climate Fluctuations Near the Martian North Pole

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#6005 Dry Ice Gone Wild

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#6006 Polar Region of Mars

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#1061 The Declaration by the occupiers of Alcatraz Island, the Indians of All Tribes

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Focus in on this Photo: Washington, D.C., 1963

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Dec 12, 2019

#1035

Dec 12, 2019

#1069

Dec 12, 2019

#8006

Dec 12, 2019

#1005

Dec 12, 2019

#587 Calvin Coolidge, half length, standing, facing slightly right, holding up baseball.

Dec 12, 2019

#591 Burying the dead on the battle-field of Antietam

Dec 12, 2019

#592 Paris Liberation

Dec 12, 2019

#593 Caisson in Position, Brooklyn side

Dec 12, 2019

#1011

Dec 12, 2019

#507 Saipan (Marines carrying body)

Dec 12, 2019

#508

Dec 12, 2019

#583 Brooklyn Bridge, New York City

Dec 12, 2019

#584 City Point, Virginia. Negro soldier guarding 12-pdr. Napoleon.

Dec 12, 2019

#585 Bing Miller, of the Philadelphia Athletics.

Dec 12, 2019

#121 Dust storm, Elkhart, Kan.

Dec 12, 2019

#502 Normandy Invasion, June 1944

Dec 12, 2019

#503

Dec 12, 2019

#504 Removing the wounded on Guadalcanal

Dec 12, 2019

#505 France (Flag out the window)

Dec 12, 2019

#314 The Flatiron Building

Dec 12, 2019

#315 Brooklyn Bridge, Nocturne

Dec 12, 2019

#316 St. Johns Bridge

Dec 12, 2019

#317 Vardø Street

Dec 12, 2019

#318 7:42, from the series Teenagers

Dec 12, 2019

#309 Three Mile Island Nuclear Plant, Susquehanna River, Pennsylvania

Dec 12, 2019

#310 Bird cage, aquarium and plant stand

Dec 12, 2019

#311 A Slightly Damaged House, Johnstown, Pa., U.S.A.

Dec 12, 2019

#312 Seven Young People

Dec 12, 2019

#313 Bus Rider

Dec 12, 2019

#304 Beggar-peddler on Broadway

Dec 12, 2019

Woman holding a small child and a box of Wrigley’s Spearmint gum, in front of a building on Broadway in New…

#305 Rappahannock River, Va. Fugitive African Americans fording the Rappahannock

Dec 12, 2019

#306 Rockefeller Center with Collegiate Church of St. Nicholas

Dec 12, 2019

#307 Sojourner Truth, “I sell the shadow to support the substance, Sojourner Truth”

Dec 12, 2019

#308 New York City, 1897. The organ grinder and his wife

Dec 12, 2019

#301 Dunes in Herschel Crater, Mars (detail)

Dec 12, 2019

#302

Dec 12, 2019

#303 Niagara Falls

Dec 12, 2019

Photograph shows men in morning coats and top hats standing at the side of Niagara Falls.

Envisionment Building | Making Meaning in Literature: A Workshop for Teachers, Grades 6-8

Dec 12, 2019

The Center for English Learning and Achievement (CELA) has made these two great resources available for teachers. Authored by Dr.…

Envisionment Building

Nov 19, 2019

The Center for English Learning and Achievement (CELA) has made these two great resources available for teachers. Authored by Dr.…

Case Studies

Nov 15, 2019

These four case studies are interactivities based on actual scientific research projects carried out by leading teams in the field.…

Homework

Nov 15, 2019

This series of problems leads you through the creation of a histogram and its corresponding tables for the data in…

Activity: Lesson Builder

Nov 12, 2019

Introduction Purpose Now that you have explored the envisionment-building process and revisited the joy of reading literature, we invite you…

What is Envisionment Building?

Nov 12, 2019

A Response-Based Approach to Reading Literature Judith A. Langer National Research Center on Literature Teaching and Learning University at Albany…

Teaching Strategy Workbook

Nov 06, 2019

Explore two poems using strategies from the workshops. This activity offers you an opportunity to read two poems and reflect…

#10043 Refugees waiting for work at Marsavan [i.e. Marsovan]

Nov 01, 2019

#2013

Oct 31, 2019

Listen to the Experts

Oct 21, 2019

Practice: Respond to Student Writing

Oct 21, 2019

The following drafts allow you to evaluate authentic samples of student pieces written in three different genres. Each time you…

A Closer Look (video)

Oct 15, 2019

A Closer Look is a helpful video to view first, as it provides the basis for further study. This video features:…

Authors’ Notes IV

Oct 09, 2019

Authors’ Notes I

Oct 09, 2019

Authors’ Notes III

Oct 07, 2019

Authors’ Notes II

Oct 07, 2019

Making Observations Like a Scientist

Oct 04, 2019

Catherine Rohrbaugh teaches students how to take notes and analyze text across different content areas to foster independent learning. Teacher: Catherine…

Productivity Quiz

Sep 26, 2019

Risk, Exposure, and Health Video

Aug 09, 2019

Human Population Dynamics Video

Aug 09, 2019

     

Ecosystems Video

Aug 09, 2019

   

Many Planets, One Earth Video

Aug 09, 2019

   

Build a Rubric Activity

Aug 06, 2019

Rubrics are an important tool for all teachers. They carefully explain the criteria that will be used to judge a…

Arbiter Activity

Aug 06, 2019

When you assess or comment on student papers, what are the things that you look at? Do you concentrate on…

A Writer’s Notebook

Aug 05, 2019

No one knows the anguish and joy of writing better than a writer. That’s why numbers of educational organizations believe…

Energy Challenges Video

Jul 25, 2019

   

Water Resources Video

Jul 24, 2019

   

Atmosphere

Jul 24, 2019

Atmospheric Pollution Video

Jul 24, 2019

   

Oceans Video

Jul 24, 2019

   

Interview with Stuart Davies

Jul 23, 2019

Interviewer: What is your position and who do you work for? STUART: I am the Director of the Center for…

Interview with Robert Crabtree

Jul 23, 2019

Interviewer: How did you first get involved in the ecosystem in science? BOB: When I was seven years old, and…

Interview with Penny Chisholm

Jul 23, 2019

Interviewer: Tell me a bit about your position here. PENNY: My name is Penny Chisholm and I’m a professor in…

Interview with Pieter Tans

Jul 23, 2019

Interviewer: What is the history of The Global Monitoring Division (GMD)? PIETER: I’ll start further back a little bit. Mankind’s use…

Interview with Kerry Emanuel

Jul 23, 2019

Interviewer: I’d like to begin by asking you how you first got interested in weather phenomenon. Can you think back…

Interview with Paul Hoffman

Jul 23, 2019

Interviewer: What regulates the average temperature of the Earth over billions of years? PAUL: This only really became a question in…

Interview with Andy Knoll

Jul 23, 2019

Interviewer: What makes Mars different from Earth? ANDY: If you look at a picture of Mars from one of the NASA…

Interview with Wendy Graham

Jul 23, 2019

Interviewer: Can you tell us who you are and what you do? WENDY: My name is Wendy Graham. I’m a professor…

Homework

Jul 18, 2019

Problem H1 Read the Grades 6-8 standard on data analysis and probability that was developed by the National Council of Teachers of…

Part D: Examining Children’s Reasoning (30 minutes)

Jul 18, 2019

As this course comes to a close and you reflect on ways to bring your new understanding of data analysis,…

Part C: Inferences and Predictions (35 minutes)

Jul 18, 2019

The NCTM (2000) data analysis and probability standards state that students should “develop and evaluate inferences and predictions that are…

Part B: Statistics as a Problem-Solving Process (45 minutes)

Jul 18, 2019

The National Council of Teachers of Mathematics (NCTM, 2000) identifies data analysis and probability as a strand in its Principles…

Part A: Statistics as a Problem-Solving Process (20 minutes)

Jul 18, 2019

A data investigation should begin with a question about a real-world phenomenon that can be answered by collecting data. After…

Classroom Case Studies, Grades 6-8

Jul 18, 2019

This is the final session of the Data Analysis, Statistics, and Probability course! In this session, we will examine how statistical…

Homework

Jul 18, 2019

Problem H1 Read the Grades 3-5 standard on data analysis and probability that was developed by the National Council of Teachers of…

Part D: Examining Children’s Reasoning (30 minutes)

Jul 18, 2019

As this course comes to a close and you reflect on ways to bring your new understandings of data analysis,…

Part C: Inferences and Predictions (30 minutes)

Jul 18, 2019

The NCTM (2000) data analysis and probability standards state that students should “develop and evaluate inferences and predictions that are…

Part B: Developing Statistical Reasoning (45 minutes)

Jul 18, 2019

The National Council of Teachers of Mathematics (NCTM, 2000) identifies data analysis and probability as a strand in its Principles and…

Part A: Statistics as a Problem-Solving Process (30 minutes)

Jul 18, 2019

A data investigation should begin with a question about a real-world phenomenon that can be answered by collecting data. After…

Homework: Statistics as a Problem-Solving Process

Jul 18, 2019

Problem H1 Read the Grades Pre-K-2 standard on data analysis and probability that was developed by the National Council of Teachers of…

Part D: Examining Children’s Reasoning (30 minutes)

Jul 18, 2019

As this course comes to a close and you reflect on ways to bring your new understanding of data analysis,…

Part C: Inferences and Predictions (30 minutes)

Jul 18, 2019

The NCTM (2000) data analysis and probability standards state that students should “develop and evaluate inferences and predictions that are…

Homework

Jul 18, 2019

Problem H1 Many people wonder whether students need to know algebra in order to be successful in today’s world. What…

Part B: Developing Statistical Reasoning (40 minutes)

Jul 18, 2019

The National Council of Teachers of Mathematics (NCTM, 2000) identifies data analysis and probability as a strand in its Principles and…

Homework

Jul 18, 2019

Problem H1 In the Achilles and the tortoise problems in Part C, Achilles runs at a constant rate of 9…

Part E: Thinking About Technology (10 minutes)

Jul 18, 2019

In mathematics, technology can be used to learn new concepts, apply known mathematics, avoid tedious computation, and gather information. It…

Part D: Putting It Together (35 minutes)

Jul 18, 2019

Linear functions have come up in many situations so far in this session. In this section, we’ll consolidate some of…

Part C: Rates (40 minutes)

Jul 18, 2019

A rate describes how much one variable changes with respect to another. Rates are often used to describe relationships between…

Part A: Statistics as a Problem-Solving Process (25 minutes)

Jul 18, 2019

A data investigation should begin with a question about a real-world phenomenon that can be answered by collecting data. After…

Part B: Slope (40 minutes)

Jul 17, 2019

Thinking About Slope Slope is an important concept in mathematics, and in Part B we’ll explore how it is used…

Part A: Linear Relationships in Patterns (35 minutes)

Jul 17, 2019

Finding the Pattern A function expresses a relationship between variables. For example, consider the number of toothpicks needed to make…

Homework

Jul 17, 2019

These homework problems will take you through the process of statistical estimation using numerical data. You will investigate the quality…

Part D: The Effect of Sample Size (30 minutes)

Jul 17, 2019

In This Part: Sample Size 20 All of our estimates thus far have been based on a sample size of 10…

Homework

Jul 17, 2019

Part E: Critiquing Student Lessons (20 minutes)

Jul 17, 2019

In the Grades 6-8 curriculum, students are frequently asked to think about patterns, but often their “pattern sniffing” skills end…

Part D: More Problems That Illustrate Algebraic Thinking (25 minutes)

Jul 17, 2019

At the 6-8 grade level, there are many problems that prepare students for their later work in algebra. There is…

Part C: Patterns That Illustrate Algebraic Thinking (25 minutes)

Jul 17, 2019

Many students find that a context or situation helps them think about algebraic ideas. In the next problem, we’ll look…

Part B: An Example for Developing Algebraic Thinking (25 minutes)

Jul 17, 2019

The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (2000) identifies algebra as a strand for…

Part A: Classroom Video (30 minutes)

Jul 17, 2019

To begin the exploration of what algebraic thinking looks like in a classroom at your grade level, watch a video…

Homework

Jul 17, 2019

Part E: Critiquing Student Lessons (20 minutes)

Jul 17, 2019

In the grades 3-5 curriculum, students are frequently asked to think about patterns, but often their “pattern sniffing” skills end…

Part D: More Problems That Illustrate Algebraic Thinking (25 minutes)

Jul 17, 2019

At the 3-5 grade level, there are many problems that prepare students for their later work in algebra. Experiences with…

Part C: Investigating Variation in Estimates (45 minutes)

Jul 17, 2019

In This Part: Using a Stem and Leaf Plot In Part B, you obtained several different estimates for the total number…

Part C: Patterns That Illustrate Algebraic Thinking (25 minutes)

Jul 17, 2019

Many students find that a context or situation helps them think about algebraic ideas. In the next problem, we’ll look…

Part B: An Example for Developing Algebraic Thinking (20 minutes)

Jul 17, 2019

The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (2000) identifies algebra as a strand for…

Part A: Classroom Video (30 minutes)

Jul 17, 2019

To begin the exploration of what algebraic thinking looks like in a classroom at your grade level, watch a video…

Homework

Jul 17, 2019

Part D: Critiquing Student Lessons (20 minutes)

Jul 17, 2019

In the K-2 curriculum, students are frequently asked to think about patterns, but often their “pattern sniffing” skills end with…

Part C: More Problems That Illustrate Algebraic Thinking (45 minutes)

Jul 17, 2019

At the K-2 grade level, there are many problems that prepare students for their later work in algebra. Experiences with…

Part B: Selecting the Sample (30 minutes)

Jul 17, 2019

In This Part: Fair Sampling You may have noticed that your estimates for the total penguin population vary quite a bit…

Part B: An Example for Developing Algebraic Thinking (25 minutes)

Jul 17, 2019

The National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (2000) identifies algebra as a strand for…

Part A: Classroom Video (30 minutes)

Jul 17, 2019

To begin the exploration of what algebraic thinking looks like in a classroom at your grade level, watch a video…

Part A: Random Samples (15 minutes)

Jul 17, 2019

In This Part: Counting Penguins Statisticians often use a random sample to estimate characteristics of a population when the population is…

Homework

Jul 17, 2019

Part E: Summing Up (10 minutes)

Jul 17, 2019

Part D: Working with Algebraic Structures (60 minutes)

Jul 17, 2019

How might you solve equations in this new system? Note 7 Let’s start with the equation 3x = 8. Looking…

Homework

Jul 17, 2019

Problem H1 Use the table of sums for the sum of two dice to determine the more likely winner of…

Part C: Algebraic Structures (50 minutes)

Jul 17, 2019

Mathematicians have always been interested in solving equations. Over the past 150 years they have studied techniques for solving equations,…

Part B: Guess My Rule (20 minutes)

Jul 17, 2019

One way to compare algorithms is to play the “Guess My Rule” game. Here’s how it goes: • Someone makes…

Part D: Are You a Random Player? (20 minutes)

Jul 17, 2019

In This Part: Developing the Mathematical Probability Let’s return to the statistics question we considered in Part A: Can a person develop…

Part A: Comparing Operations (10 minutes)

Jul 17, 2019

Students begin to move from arithmetic to algebra (in the structural sense) when they start thinking about properties of operations…

Homework

Jul 17, 2019

We said previously that algebra has become very much concerned with operations. So far, the only operations we’ve used are…

Part C: Different Functions (35 minutes)

Jul 17, 2019

We’ve seen many different kinds of functions in the past few sessions. We’ve examined characteristics of functions, looked at their…

Part B: Inverse Proportions (60 minutes)

Jul 17, 2019

Splitting a Prize Imagine that the teachers in your school decide to play the lottery together. If they win, the…

Part A: Cyclic Functions (50 minutes)

Jul 17, 2019

Tides The following situation describes a new kind of function: Note 2 The ocean has high tides and low tides.…

Homework

Jul 17, 2019

You’ve already seen examples of exponential growth. When you have an exponential function where the constant multiple between outputs is…

Part D: Quadratic Functions (25 minutes)

Jul 17, 2019

Quadratic Functions and Differences You know that for linear functions, the difference between successive outputs is a constant. For exponential…

Part C: Figurate Numbers (45 minutes)

Jul 17, 2019

Square Numbers Now that we have a basic understanding of exponential functions, let’s move on to another kind of relationship.…

Part B: Exponential Growth (40 minutes)

Jul 17, 2019

A Salary Situation Suppose you are given two different options for salary at a temporary job. Note 5 Plan A:…

Part A: Exploring Exponential Functions (40 minutes)

Jul 17, 2019

Problems: Changing + to * In Session 5, we learned that linear functions have constant first differences. That is, every…

Homework

Jul 17, 2019

In the puzzles that follow, each shape stands for a number value of “weight.” To solve these puzzles, make the…

Part C: Bags, Blocks, and Balance (30 minutes)

Jul 17, 2019

Here are 3 balanced scales. Use your intuition about balance to determine, for each case, how many blocks have to…

Part C: Analyzing Binomial Probabilities (45 minutes)

Jul 17, 2019

In This Part: Making a Tree Diagram A tree diagram is a helpful tool for determining theoretical or mathematical probabilities. Let’s…

Homework

Jul 17, 2019

Problem H1 Invent a number game like the one from Problem D1. Draw a network that lets you figure out…

Part E: Other Kinds of Functions (45 minutes)

Jul 17, 2019

Functions and Non-Functions So far you have been thinking about functions as algorithms or machines. They take an input —…

Part D: Number Games (35 minutes)

Jul 17, 2019

  Problem D1 Draw a picture of this algorithm and use your picture to answer the following questions: If you…

Part C: Function Machines (35 minutes)

Jul 17, 2019

About Function Machines When thinking about inputs and outputs, you are thinking about algorithms as functions: You input a number…

Part B: False Position and Backtracking (30 minutes)

Jul 17, 2019

False Position The solutions to mathematical problems often involve writing and solving equations. We generally think of solving equations by…

Part A: Equality and Balance (30 minutes)

Jul 17, 2019

Equality We have been using the equal sign throughout previous sessions. In this part we are going to look at…

Part B: Mathematical Probability (50 minutes)

Jul 17, 2019

In This Part: Predicting Outcomes You can use statistics to determine whether it’s possible for a player to develop skill in…

Part B: Undoing Algorithms (20 minutes)

Jul 17, 2019

An algorithm is a recipe or a description of a mechanical set of steps for performing some task. For example,…

Homework

Jul 17, 2019

Problem H1 Sandy made some iced tea from a mix, using 12 tablespoons of mix and 20 cups of water.…

Part A: Doing and Undoing (15 minutes)

Jul 17, 2019

There are many situations, both in and outside of mathematics, where the process of doing and undoing helps you organize…

Part D: Speeds, Rates, Steepness, and Lines (45 minutes)

Jul 17, 2019

In Parts B and C we examined the proportionality of mixtures and scale models. In this activity, we will take…

Part A: Probability in Statistics (20 minutes)

Jul 17, 2019

In This Part: What Is Probability? Problem A1 Make a list of the topics and ideas that come to mind when…

Part C: Quadperson (45 minutes)

Jul 17, 2019

Playing with Quadperson This activity compares the effects of absolute and relative comparisons on a picture. Think about what would…

Part B: The Mixture Blues (45 minutes)

Jul 17, 2019

Comparing Mixtures The scientists at the research lab for Whodunit Jeans are trying to decide on just the right shade…

Part A: Two Different Meanings of “More” (15 minutes)

Jul 17, 2019

Problem A1 Suppose there are two classes in a school, one with 20 students and one with 25. If the…

Homework

Jul 17, 2019

Is there an association between the length of your forearm (elbow to wrist) and the length of your feet? The…

Homework

Jul 17, 2019

Problem H1 Look at this table: Input Output 1 6 2 10 3 14 4 18 5 22 6 26…

Part C: Qualitative Graphs (90 minutes)

Jul 17, 2019

Introduction to Qualitative Graphs Thinking algebraically helps us to develop different ways of representing real-world situations. You may have chosen…

Part E: Summing Up (20 minutes)

Jul 17, 2019

At the beginning of this session, we learned that finding, describing, explaining, and predicting with patterns are some of the…

Part D: Counting Stairs (60 minutes)

Jul 17, 2019

Problem D1 Here is a problem in which you can use patterns to make predictions. Count the number of blocks…

Part B: Reasoning About Situations (45 minutes)

Jul 17, 2019

Eric the Sheep Here’s a simple number puzzle that leads to a surprisingly challenging investigation. Note 3 It’s a hot…

Part C: Different Uses of Variables (25 minutes)

Jul 17, 2019

In the toothpick problem, we used a variable to describe the relationship between the number of toothpicks and the number…

Part B: Patterns in Situations (45 minutes)

Jul 17, 2019

Problem A5 describes several different ways to extend the pattern given in Problem A1. When a sequence of numbers is…

Part A: What Do You See? (40 minutes)

Jul 17, 2019

Finding a Pattern Patterns are everywhere around us. We use patterns to organize what we see and hear and to…

Part A: A Framework for Algebraic Thinking (15 minutes)

Jul 17, 2019

What does algebra mean to you? For many of us, the word “algebra” conjures classroom memories of xs and ys,…

Homework

Jul 17, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences.   Problem H1 Assume…

Part C: Problems That Illustrate Measurement Reasoning (55 minutes)

Jul 17, 2019

In this part, you’ll look at several problems that are appropriate for students in grades 6-8. For each problem, answer…

Part B: Reasoning About Measurement (40 minutes)

Jul 17, 2019

Exploring Standards The National Council of Teachers of Mathematics (NCTM, 2000) has identified measurement as a strand in its Principles…

Part A: The Concept of Area (25 minutes)

Jul 17, 2019

To begin exploring what the teaching of measurement might look like in the classroom, participants in the Measurement course first…

Homework

Jul 17, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences. Problem H1 Assume that…

Part C: Problems That Illustrate Measurement Reasoning (55 minutes)

Jul 17, 2019

In this part, you’ll look at several problems that are appropriate for students in grades 3-5. For each problem, answer…

Part B: Reasoning About Measurement (40 minutes)

Jul 17, 2019

The National Council of Teachers of Mathematics (NCTM, 2000) has identified measurement as a strand in its Principles and Standards…

Part D: Fitting Lines to Data (60 minutes)

Jul 17, 2019

In This Part: Trend Lines In Parts A and B, you confirmed that there is a strong positive association between height…

Part A: The Concept of Area (25 minutes)

Jul 17, 2019

To begin to explore what the teaching of measurement might look like in the classroom, participants in the Measurement course…

Homework

Jul 17, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences.   Problem H1 Assume…

Part C: Activities That Illustrate Measurement Reasoning (55 minutes)

Jul 17, 2019

In this part, you’ll look at several short activities that are appropriate for students in grades K-2. As you read…

Part B: Reasoning About Measurement (40 minutes)

Jul 17, 2019

Exploring Standards The National Council of Teachers of Mathematics (NCTM, 2000) has identified measurement as a strand in its Principles…

Part A: The Concept of Area (25 minutes)

Jul 17, 2019

To begin exploring what the teaching of measurement might look like in the classroom, participants in the Measurement course first…

Homework – Grades 6-8

Jul 16, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences.

Homework

Jul 16, 2019

Problem H1 Reptiles need the sun to get them going. Many large dinosaurs had to have large fins or plates…

Part C: Problems That Illustrate Reasoning About Number and Operations (55 minutes)

Jul 16, 2019

As this course comes to a close and you reflect on ways to incorporate your new understanding of number and…

Part C: Designing a Water Tank (35 minutes)

Jul 16, 2019

Imagine constructing an open-topped water tank from a square metal sheet (2 m by 2 m). You would cut squares…

Part B: Surface Area and Volume (40 minutes)

Jul 16, 2019

Determining the Relationship In the previous part, you learned that the relationship between perimeter and area is dynamic; namely, the…

Part A: Area and Perimeter (45 minutes)

Jul 16, 2019

Constant Perimeter If you have 72 ft. of fencing and you want to use it to make a rectangular pen…

Homework

Jul 16, 2019

Problem H1 The shapes below are pyramids. A pyramid is named for the shape of its base. The left shape…

Part B (continued): Reasoning About Number and Operations – Examining Students’ Reasoning

Jul 16, 2019

Here are scenarios from two different teachers’ classrooms, each involving students’ developing ideas about number and operations. Snippets of students’…

Part B: Volume Formulas (60 minutes)

Jul 16, 2019

Cross Section Method In Part A we found that we can determine the volume of rectangular prisms or boxes by…

Part B: Contingency Tables (20 minutes)

Jul 16, 2019

In Part A, you examined bivariate data — data on two variables — graphed on a scatter plot. Another useful…

Part A: How Many Cubes? (60 minutes)

Jul 16, 2019

Volume and Nets A net is the two-dimensional representation of a three-dimensional object. For example, you can cut the net…

Part A: Scatter Plots (45 minutes)

Jul 16, 2019

In This Part: A Bivariate Data Question Have you ever wondered whether tall people have longer arms than short people? We’ll…

Homework

Jul 16, 2019

Problem H1 A circle is inscribed in a square. What percentage of the area of the square is inside the…

Part B: Area of a Circle (60 minutes)

Jul 16, 2019

Transforming a Circle Let’s further examine the formula for area of a circle, A =  • r2. How do we interpret…

Part A: Circles and Circumference (60 minutes)

Jul 16, 2019

Circumference Perimeter — or distance around — is a measurable property of simple, closed curves and shapes. When the figure…

Part B: Reasoning About Number and Operations (40 minutes) – Exploring Standards

Jul 16, 2019

The National Council of Teachers of Mathematics (NCTM, 2000) has identified number and operations as a strand in its Principles…

Homework

Jul 16, 2019

Problem H1 If the area of each of the smallest two triangles in the tangram below is equal to 1…

Part C: Scaling the Area (35 minutes)

Jul 16, 2019

Similar Figures What happens to the area of a figure if we scale it up or down (i.e., enlarge or…

Part B: Exploring Area With a Geoboard (50 minutes)

Jul 16, 2019

Subdividing Area Let’s further examine the concept of area, using a geoboard. The unit of area on the geoboard is…

Homework

Jul 16, 2019

Problem H1 Conduct your own comparative study. It can be an observational study or an experimental study. The questions below…

Part A: Measuring Area (35 minutes)

Jul 16, 2019

Measuring a Surface Think of some situations that involve the measurement of area. How would you determine these areas? For…

Part A: Observing a Case Study (25 minutes)

Jul 16, 2019

To begin the exploration of what topics in number and operations look like in a classroom at your grade level,…

Homework

Jul 16, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences. Problem H1 Assume that…

Part C: Problems That Illustrate Reasoning About Number and Operations (55 minutes)

Jul 16, 2019

As this course comes to a close and you reflect on ways to incorporate your new understanding of number and…

Part B: Reasoning About Number and Operations (40 minutes)

Jul 16, 2019

In This Part: Exploring Standards The National Council of Teachers of Mathematics (NCTM, 2000) has identified number and operations as a…

Homework

Jul 16, 2019

Problem H1 At a distance of 160 m from a tower, you look up at an angle of 23 degrees…

Part C: Steepness and Trigonometry (45 minutes)

Jul 16, 2019

Measuring Steepness Since early times, surveyors, navigators, and astronomers have employed triangles to measure distances that could not be measured…

Part C: Comparative Experimental Studies (65 minutes)

Jul 16, 2019

In This Part: Measuring Short-Term Recall Now we’ll move on to an investigation of comparative experimental studies. We’ll begin with a…

Part B: Measuring Heights of Tall Objects (35 minutes)

Jul 16, 2019

Measuring With Shadows What other methods exist for measuring indirectly? One such method is to use shadows. For tall objects…

Homework

Jul 16, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences. Problem H1 Assume that…

Part C: Problems That Illustrate Reasoning About Number and Operations (55 minutes)

Jul 16, 2019

As this course comes to a close and you reflect on ways to incorporate your new understanding of number and…

Part A: Indirect Measurement With a Transit (40 minutes)

Jul 16, 2019

Similar Triangles One way to measure indirectly is to use similar triangles. In similar figures, corresponding angles are congruent, and…

Part B: Reasoning About Number and Operations (40 minutes)

Jul 16, 2019

In This Part: Exploring Standards The National Council of Teachers of Mathematics has identified number and operations as a strand in…

Homework

Jul 16, 2019

Problem H1 Draw any quadrilateral. Then draw a point anywhere inside the quadrilateral, and connect that point to each of…

Part A: Observing a Case Study (25 minutes)

Jul 16, 2019

To begin the exploration of what topics in number and operations look like in a classroom at your grade level,…

Part C: Geo-Logo (40 minutes)

Jul 16, 2019

In Part C, we explore the interior and exterior angles of a figure as well as the relationship between the…

Part B: Angles in Polygons

Jul 16, 2019

Classifying by Measure Print several copies of the sample polygons (PDF) and cut out the polygons. These are based on…

Part B: Comparative Observational Studies (35 minutes)

Jul 16, 2019

In This Part: A New Raisin Question Let’s begin our investigation of comparative observational studies by returning to the raisin problem…

Part A: Angle Definition (20 minutes)

Jul 16, 2019

Since the time of the ancient Greeks (about 500 B.C.E.), angles have been measured in terms of a circle. In…

Homework

Jul 16, 2019

Problem H1 The meter was originally based on the size of the Earth, with the distance from the equator to…

Part A: Comparative Studies (15 minutes)

Jul 16, 2019

Many statistics problems require you to make comparisons. You may be interested in comparing salaries for different professions, for example,…

Part B: Metric Units (85 minutes)

Jul 16, 2019

As we’ve seen, the base unit for length (or distance) is the meter. Meter comes from the Greek word “metron,”…

Homework

Jul 16, 2019

Problem H1 The number line shown below has seven points labeled with numbers or letters. The line is not drawn…

Part C: Fibonacci Numbers (30 minutes)

Jul 16, 2019

In This Part: The Fibonacci Sequence For the final activity in this session, we’ll look at an interesting application of ratios…

Part B: Decimals and Percents (45 minutes)

Jul 16, 2019

In This Part: Percent as Proportion The word “percent” means “out of 100.” See Note 6 below. For example, 49% means 49 out…

Homework

Jul 16, 2019

Problem H1 For the allocation below, find and interpret the MAD, variance, and standard deviation.        You will…

Part A: Models for the Multiplication and Division of Fractions (45 minutes)

Jul 15, 2019

In This Part: Area Model for Multiplication In the past, you may have learned particular algorithms for the multiplication and division…

Session 8: Homework

Jul 15, 2019

Problem H1 Show how to use Cuisenaire Rods to model 3/4  2/3. Problem H2 a. The shaded part is 5 1/4. Specify…

Part C: Absolute and Relative Reasoning (30 minutes)

Jul 15, 2019

Rational numbers or fractions can be used in many different ways. One source of confusion, especially with fractions, is the…

Part B: Fractions With Cuisenaire Rods (45 minutes)

Jul 15, 2019

In This Part: Representing Fractions With Rods Rational numbers are a “ratio” of one value to another. It’s common to think…

Part A: Interpreting Fractions, Units, and Unitizing (45 minutes)

Jul 15, 2019

In This Part: Interpretation of Fractions We know that a fraction, as a “rational” number, is a ratio of two numbers.…

Homework

Jul 15, 2019

Problem H1 a. Find the fractional equivalent for 0.142857. b. Find the fractional equivalent for 0.142857142857142857…. Problem H2 Shigeto and Consuela were…

Part C: Ordering Fractions (25 minutes)

Jul 15, 2019

There are several ways to compare fractions, many of which use benchmarks or intuitive methods and do not require computation…

Part A: Metric System Basics (35 minutes)

Jul 15, 2019

History The metric system was introduced in France in the 1790s as a single, universally accepted system of measurement. But…

Part B: Decimals to Fractions (30 minutes)

Jul 15, 2019

In Part A of this session, you learned that the decimal representation for every rational number was either a terminating…

Part A: Fractions to Decimals (65 minutes)

Jul 15, 2019

In This Part: Terminating Decimals  In Part A of this session, you’ll examine the process of converting fractions to decimals, which…

Homework

Jul 15, 2019

Problem H1 Prime numbers have exactly two factors. Now find some numbers that have exactly three factors. What do these…

Part B: Looking for Prime Numbers (45 minutes)

Jul 15, 2019

In This Part: Locating Prime Numbers In this part, we’ll continue a mathematics tradition begun by Eratosthenes of Cyrene (276-194 B.C.E.)…

Part E: Measuring Variation (45 minutes)

Jul 15, 2019

In This Part: Mean Absolute Deviation (MAD)  We will now focus on how to measure variation from the mean within a…

Homework

Jul 15, 2019

Problem H1 Imagine that you are playing the Between game with a partner. Player A picks a decimal number between…

Part C: Precision and Accuracy (30 minutes)

Jul 15, 2019

Measuring With Precision We have learned that physical measurement involves error and that every physical measurement is an approximation. This…

Part B: The Role of Ratio (45 minutes)

Jul 15, 2019

Ratio and Scale Measurement is the process of quantifying properties of an object by comparing them to some standard unit.…

Part D: Deviations from the Mean (30 minutes)

Jul 15, 2019

In This Part: Tallying Excesses and Deficits In Part B, we looked at excesses and deficits when we moved coins in…

Part A: Measuring Accurately (45 minutes)

Jul 15, 2019

Conservation, Transitivity, and Unit Iteration In Session 1, we established that in order to measure something, we have to (1)…

Homework

Jul 15, 2019

How Large Is It? This table shows the height to the shoulder and the weight of several species of buffalo.…

Part D: Summing It Up (10 minutes)

Jul 15, 2019

What is measurement? Measurement is the process of quantifying the properties of an object by expressing them in terms of…

Part C: Nonstandard Units (30 minutes)

Jul 15, 2019

Print this PDF and cut out the small and medium triangles to fit into the shapes. Problem C1 Using two…

Part B: Which Rock Is the Largest? (65 minutes)

Jul 15, 2019

Measuring Surface Area You can measure a number of attributes of rocks — for example, surface area, volume, and weight.…

Part C: Using Line Plots (30 minutes)

Jul 15, 2019

In This Part: Creating a Line Plot  Remember the line plots you worked with in previous sessions? If you reshuffle your…

Part A: Comparing Rocks (15 minutes)

Jul 15, 2019

Measurement is used in all aspects of daily life, as well as in such fields as engineering, architecture, and medicine.…

About the Learning Math Courses

Jul 15, 2019

When teachers have a deep conceptual understanding of mathematics, it can help their students develop strong mathematical skills and knowledge.…

Part A: Models for Multiples and Factors (75 minutes)

Jul 15, 2019

In This Part: The Venn Diagram Model The numbers 24 and 36 have certain things in common, including many common factors…

Homework

Jul 15, 2019

Problem H1 The number abcabc (where each letter represents one particular digit) is divisible by 7, 11, and 13 for…

Part C: Factors (35 minutes)

Jul 15, 2019

You saw that you could devise tests for such numbers as 6 and 18 based on their relatively prime factors.…

Part B: Divisibility Test (50 minutes)

Jul 15, 2019

In This Part: Developing Testing Rules  Another way to examine the characteristics of base ten numbers is to look at the…

Part A: Alpha Math (35 minutes)

Jul 15, 2019

“Alpha math” problems, where each letter stands for one digit of a number, can help you identify some of the…

Part B: Unfair Allocations (25 minutes)

Jul 15, 2019

In This Part: Fair and Unfair Allocations The average for a set of data corresponds to the equal-shares allocation or fair…

Homework

Jul 15, 2019

Problem H1 Explain the diagrams that illustrate 124 using the following models: a. The partitive (or equal groups) model b.…

Part C: Colored-Chip Models (35 minutes)

Jul 15, 2019

In This Part: Addition In this section, we will use manipulatives to model addition, subtraction, multiplication, and division with positive…

Part B: Area Models for Multiplication and Division (45 minutes)

Jul 15, 2019

In This Part: Multiplication with Manipulatives Models and manipulative materials can help make multiplication and division with integers more tangible. They…

Part A: Fair Allocations (25 minutes)

Jul 15, 2019

In This Part: The Mean The term average is a popular one; it is often used, and often used incorrectly.…

Part A: Meanings and Relationships of the Operations (40 minutes)

Jul 15, 2019

In This Part: Addition We will begin our look at the various meanings for each of the operations and the laws…

Homework

Jul 15, 2019

Problem H1 Write the base five numbers 1234five and 1.234five as base ten numbers. Problem H2 Find the base ten…

Homework

Jul 15, 2019

Problem H1 Determine the Five-Number Summary for each of the remaining data sets of raisin counts from Session 2, and…

Part C: Place-Value Representation in Base Ten and Base Four (40 minutes)

Jul 15, 2019

In This Part: Examining Base Four  In Part C, we shift our focus to the base four number system. You will…

Part B: Exponents and Logarithms (35 minutes)

Jul 15, 2019

As you saw earlier in this session, one way to represent each power of two is to write the base…

Part A: Base Two Numbers (45 minutes)

Jul 15, 2019

In This Part: Base Two The number systems we’ve been looking at so far in this course use 10 digits…

Homework

Jul 12, 2019

Problem H1 Divide the number 1 by the numbers 1 through 10 consecutively. What conjectures can you make about rational…

Part C: Examining Zero (50 minutes)

Jul 12, 2019

In This Part: The Behavior of Zero The real number system is a positional system. In such a system, the…

Part B: The Size of Infinity (35 minutes)

Jul 12, 2019

Infinity is infinitely large, right? But is it possible for one infinite set to be larger than another? Infinity is…

Part A: Number Sets (35 minutes)

Jul 12, 2019

In This Part: Relating Number Sets We will continue our focus on the number line and the relationships among the…

Teaching Strategies: Lesson Study

Jul 12, 2019

When the Third International Mathematics and Science Study (TIMSS) was conducted in 1996, more than 60 percent of American math…

Homework

Jul 12, 2019

Think back to the finite system of units digits that you explored in Part A and answer the following questions…

Teaching Strategies: Listening to Students

Jul 12, 2019

According to veteran teacher Steve Reinhart, students can sometimes be the best instructors. In an April 2000 article in Mathematics…

Lesson Plan 2: Skeeter Populations and Exponential Growth

Jul 12, 2019

Overview: In this lesson, students will learn to model situations mathematically. Specifically, students will perform investigations on the growth of…

Lesson Plan 1: Mathematical Modeling, Circular Movement and Transmission Ratios

Jul 12, 2019

Overview: In this lesson, students will learn to use mathematical models to represent real life situations. In particular, they will…

Part C: Building the Number Line (35 minutes)

Jul 12, 2019

After exploring a number system different from our own, we are now ready to begin examining the real number system.…

Mathematical Modeling

Jul 12, 2019

Mathematical Modeling Mathematical models are useful tools for engineers who study the effects of traffic on a bridge, telephone companies…

Teaching Strategies: Concepts First, Skills Later

Jul 12, 2019

Teacher Peggy Lynn’s mathematics classroom probably looks different from many classrooms you have seen. That’s because Peggy teaches math in…

Teaching Strategies: Questioning Techniques

Jul 12, 2019

Educational philosopher John Dewey said: “What’s in a question, you ask? Everything. It is a way of evoking stimulating response…

Lesson Plan 2: Very Varied – Inverse Variation

Jul 12, 2019

Overview: This lesson teaches students about inverse variation by exploring the relationship between the heights of a fixed amount of…

Lesson Plan 1: Be Direct – Oil Spills on Land

Jul 12, 2019

Overview: This lesson teaches students about direct variation by allowing them to explore a simulated oil spill using toilet paper…

Direct and Inverse Variation

Jul 12, 2019

Part 1: Direct Variation Direct variation is a critical topic in Algebra 1. A direct variation represents a specific case…

Part E: Finding the Five-Number Summary Numerically (30 minutes)

Jul 11, 2019

In This Part: Locating the Median from Ordered Data In Part D, we used noodles to help us visualize the concept…

Teaching Strategies: Instructional Decision Making

Jul 11, 2019

This slogan appeared on a basketball T-shirt several years ago: “Just elevate and decide in the air.” The phrase could…

Teaching Strategies: Affective Domain

Jul 11, 2019

Affective refers to those actions that result from and are influenced by emotions. Consequently, the affective domain relates to emotions,…

Part B: Comparing Number Systems (15 minutes)

Jul 11, 2019

How does the number system you’ve been working with in Part A relate to the real number system you usually…

Part A: A Simpler Number System (70 minutes)

Jul 11, 2019

In This Part: Addition in Units Digit Arithmetic Stated simply, a number system is a set of objects (often numbers),…

Lesson Plan 2: Bigger and Smaller – Exponent Rules

Jul 11, 2019

Overview: This lesson will teach students about several of the rules regarding exponents. It uses a situation from Alice in…

Lesson Plan 1: Overrun by Skeeters – Exponential Growth

Jul 11, 2019

Overview: This lesson provides students with an introduction to exponential functions. The class first explores the world population since 1650.…

Exponential Functions

Jul 11, 2019

Exponents An exponent is mathematical shorthand that means a number is multiplied by itself repeatedly. An exponential function is a…

Part D: The Box Plot (25 minutes)

Jul 11, 2019

In This Part: Five-Number Summary with Measurement Data Now we’ll look at how you can represent the Five-Number Summary graphically, using…

Teaching Strategies: Patterns

Jul 11, 2019

Educator Marilyn Burns describes algebra as “the generalization of arithmetic.” The same definition is given in The Mathematics Dictionary (4th…

Teaching Strategies: Rule of Four

Jul 11, 2019

“High school students’ algebra experience should enable them to create and use tabular, symbolic, graphical, and verbal representations…” So begins…

Lesson Plan 2: Curses and Re-Curses! It’s Happening Again.

Jul 11, 2019

Overview: In this lesson, students learn about basic recursion by exploring patterns in the data they generate from two simple…

Lesson Plan 1: The X Factor – Trinomials and Algebra Tiles

Jul 11, 2019

Overview: This lesson will teach students to factor trinomial expressions of the form x2 + bx + c. Students will…

Properties

Jul 11, 2019

Part 1: Factoring Quadratic Expressions Factoring is the process of rewriting a number or expression as a product of two…

Teaching Strategies: Alternative Assessment

Jul 11, 2019

The educational community today is focusing more and more on assessment. High school exit examinations are being used to determine…

Part C: Quartiles and the Five-Number Summary (35 minutes)

Jul 11, 2019

Let’s go back to your 12 ordered noodles, arranged from shortest to longest on a new piece of paper or…

Teaching Strategies: Developing a Community of Learners

Jul 11, 2019

In a collaborative classroom, students are willing to share their opinions. They are enthusiastic about discussing mathematics in the interest…

Part B: The Median and the Three-Number Summary (35 Minutes)

Jul 11, 2019

In This Part: The Median Another useful summary measure for a collection of data is the median. As you learned in Session…

Teaching Strategies: Building Understanding

Jul 11, 2019

People who have developed expertise in particular areas are naturally able to think effectively about problems in those areas. Understanding…

Teaching Strategies: Appropriate Use of Technology

Jul 11, 2019

“Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.” The…

Part A: The Data Set (20 minutes)

Jul 11, 2019

In This Part: The Data Set When working with a large collection of data, it can be difficult to keep an…

Teaching Strategies: Manipulatives

Jul 11, 2019

Manipulatives:  An old Chinese proverb states: I hear, and I forget; I see, and I remember; I do, and I…

Teaching Strategies: Strategies for Teaching English Language Learners

Jul 11, 2019

According to the U.S. Department of Education, if the population of children in this country were evenly distributed geographically, the…

Lesson Plan 2: Hassan’s Pictures – Linear Programming and Profit Lines

Jul 11, 2019

Overview: This lesson helps students learn to find the feasible region in a linear programming problem, to graph a family…

Lesson Plan 1: Left Hand, Right Hand – Solving Systems of Equations

Jul 11, 2019

Overview: In this lesson, students compare the speed at which they write with their left hand to the speed at…

Systems of Equations and Inequalities

Jul 11, 2019

Part 1: Systems of Equations A system of equations involves the relationship between two or more functions and can be…

Lesson Plan 1: The Phone Bill Problem – Linear Functions

Jul 10, 2019

Overview: In this lesson, students will learn how to write an equation of a linear function when given a set…

Lesson Plan 1: Miles of Tiles – The Pool Border Problem

Jul 10, 2019

Overview: In this lesson students will recognize patterns and represent situations using algebraic notation and variables. Time Allotment: One 50-minute…

Part D: Ordering Hats: (35 minutes)

Jul 10, 2019

In This Part: Understanding the Question In Parts A-C of this session, you learned several ways to organize numerical data by…

Variables and Patterns of Change

Jul 10, 2019

Part 1: Translating Words Into Symbols Translating words into symbols is equivalent to modeling a situation using an equation and…

Part C: Relative and Cumulative Frequencies (30 minutes)

Jul 10, 2019

The frequency histogram and grouped frequency table for the 52 time estimates contain similar information to the stem and leaf…

Part B: Histograms (30 minutes)

Jul 10, 2019

In This Part: Constructing a Histogram Like the line plot we explored in Session 2, the stem and leaf plot is…

Part A: Organizing Data in a Stem and Leaf Plot (55 minutes)

Jul 09, 2019

In This Part: How Long Is a Minute?  Let’s begin with a problem you saw in Session 1, How Long Is a…

What is Envisionment Building?

Jul 09, 2019

The Center for English Learning and Achievement (CELA) has made these two great resources available for teachers. Authored by Dr.…

Session 2: Homework

Jul 09, 2019

Problem H1 For the following data sets, create line plots, frequency tables, and cumulative frequency tables. Use your results to…

Part E: Bar Graphs and Relative Frequencies (30 Minutes)

Jul 09, 2019

In This Part: Frequency Bar Graphs The line plot is a useful graph for examining small sets of data. It’s especially…

Part D: The Median (25 minutes)

Jul 09, 2019

In This Part: From Ordered Lists and Line Plots A common way to summarize data is to use numerical summaries, many…

Part C: Frequency Tables: Making a Table (40 minutes)

Jul 09, 2019

In This Part: Making a Table  As you saw in Part A, a line plot is a graphical representation of data.…

Homework

Jul 09, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences. Problem H1 Interview a…

Part C: Problems That Illustrate Geometric Reasoning (55 minutes)

Jul 09, 2019

Geometric Reasoning Problems, Part 2 In this part, you’ll look at several problems that are appropriate for students in grades…

Part B: Developing Geometric Reasoning (40 minutes)

Jul 09, 2019

Introducing van Hiele Levels The National Council of Teachers of Mathematics (NCTM, 2000) identifies geometry as a strand in its…

Authors and Literary Works

Jul 08, 2019

Student Work

Jul 08, 2019

This section features student work from Lisa Espinosa’s unit on representation featured in Workshop video 8. Samples include: One student’s…

Commentary

Jul 08, 2019

Student Work

Jul 08, 2019

This student work section includes three letters written by Laura Alvarez’s students in Workshop video 7. As a culminating project,…

Part B: Line Plots (40 minutes)

Jul 08, 2019

In This Part: Counting Raisins Let’s begin with a recap of Problem B7 from Session 1. 1. Ask a Question How…

Commentary

Jul 08, 2019

Teaching Strategies

Jul 08, 2019

Authors and Literary Works

Jul 08, 2019

Part A: Patterns in Variation (10 minutes)

Jul 08, 2019

To answer a statistical question, we collect data, which consist of measurements of a variable. When the measurements we collect…

Student Work

Jul 08, 2019

This section includes samples of student work from Workshop video 6, in which Stanlee Brimberg’s students explored the African Burial…

Commentary

Jul 08, 2019

Teaching Strategies

Jul 08, 2019

Authors and Literary Works

Jul 08, 2019

Authors and Literary Works

Jul 08, 2019

Student Work

Jul 08, 2019

This children’s book about the 1963 March on Washington for Jobs and Freedom was researched, written, and illustrated by one…

Commentary

Jul 08, 2019

Teaching Strategies

Jul 08, 2019

Student Work

Jul 08, 2019

This section features drafts of “Where I’m From” poems written by Kathryn Mitchell Pierce’s students in Workshop video 4. The…

Commentary

Jul 08, 2019

Teaching Strategies

Jul 08, 2019

Authors and Literary Works

Jul 08, 2019

Homework

Jul 08, 2019

Problem H1 We used a metric tape measure to measure the lengths of 20 pine needles to the nearest millimeter:…

Student Work

Jul 08, 2019

This section includes two samples of student work from Workshop video 3, Sally Brownfield’s unit on Indian residential schools. Samples…

Commentary

Jul 08, 2019

Part D: Bias in Sampling (20 minutes)

Jul 08, 2019

In This Part: Population and Sample In data analysis, we use graphs, tables, and numerical summaries to study the variation present…

Teaching Strategies

Jul 08, 2019

Part C: Bias in Measurement (20 minutes)

Jul 08, 2019

In This Part: Testing Your Measurement Bias Measurement is never perfect, and we can always expect measurement errors in our data.…

Authors and Literary Works

Jul 07, 2019

Student Work

Jul 06, 2019

This section features sample work from Workshop video 2, in which Akiko Morimoto’s students explored works by Judith Ortiz Cofer…

Commentary

Jul 06, 2019

Teaching Strategies

Jul 06, 2019

Authors and Literary Works

Jul 06, 2019

Student Work

Jul 06, 2019

This section features sample student work from Carol O’Donnell’s unit on dual identities and multiple worlds in Workshop video 1.…

Commentary

Jul 06, 2019

Part B: Data Measurement and Variation (65 minutes)

Jul 06, 2019

In This Part: Asking Questions and Collecting Data Let’s start our exploration of statistics by focusing on the first two steps…

Part A: A Problem-Solving Process (15 minutes)

Jul 05, 2019

The word statistics may bring to mind polls and surveys, or facts and figures in a newspaper article. But statistics…

Part A: Geometry and Reasoning (25 minutes)

Jul 03, 2019

The study of geometry in high school is often associated with proof — usually an axiomatic development with a focus…

Homework

Jul 03, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences.   Problem H1 Interview…

Part C: Problems That Illustrate Geometric Reasoning (55 minutes)

Jul 03, 2019

Geometric Reasoning Problems, Part 1 In this part, you’ll look at several problems that are appropriate for students in grades…

Part B: Developing Geometric Reasoning (40 minutes)

Jul 03, 2019

Introducing van Hiele Levels The National Council of Teachers of Mathematics (NCTM, 2000) identifies geometry as a strand in its…

Authors and Literary Works

Jul 03, 2019

Designing the Classroom to Support Understanding

Jul 03, 2019

Kristen Ferrales explains how she intentionally designs her classroom to create an effective learning environment. Teacher: Kristin Ferrales School: The Urban Assembly…

Facilitating a Socratic Seminar

Jul 03, 2019

Kristen Ferrales demonstrates how having students write to prepare for discussions creates a deeper understanding of the topic and leads…

Bringing It All Together – History/Social Studies

Jul 03, 2019

Integrating Reading and Writing This final unit presents ways to integrate the reading and writing methods covered in the previous…

Using Student Data to Plan Instruction

Jul 03, 2019

Amanda Westenberg discusses her technique of using student performance data to drive instruction. Teacher: Amanda Westenberg School: Rangeview High School, Aurora, Colorado…

Thinking and Communicating Like a Historian

Jul 03, 2019

Steve Lazar discusses how teaching his students the specific language of his discipline gives them the tools to better discuss…

Developing Questions that Promote Discussion

Jul 03, 2019

Co-teachers Addie Male and Raeann McElveen discuss how to get students to develop questions that generate good classroom discussion. Teacher: Addie…

Using the Socratic Method in History

Jul 03, 2019

Co-teachers Addie Male and Raeann McElveen prepare students for a Socratic seminar by using multiple sources, student-generated questions, students’ personal…

Presenting Facts as Evidence

Jul 03, 2019

Elisabeth Shanley’s students debate the successes of the Aztec and Inca civilizations using evidence from their research. Teacher: Elisabeth Shanley School: Parker…

View & Analyze (Video)

Jul 03, 2019

Watch the Video As you watch “Routes to Culture,” take notes on Mr. Muirhead’s instructional strategies, particularly how he groups students…

Argument Writing

Jul 03, 2019

Introduction The previous unit focused on practices that support the reading and analysis of text for developing interpretations. This unit…

Part A: Geometry as a Problem-Solving Process (25 minutes)

Jul 03, 2019

The study of geometry can include both problem solving and connections to other areas of mathematics (arithmetic, algebra, etc.). Too…

Expanding Academic Language

Jul 03, 2019

Lili Velo explains the importance of learning and practicing academic language to help students interpret historical texts, especially in a…

Class Context

Jul 03, 2019

I think using authentic materials is essential. My students were very excited at the idea that this was a real…

Homework

Jul 03, 2019

Solutions are not provided for these homework problems, since answers will vary depending on individual experiences.   Problem H1 Interview…

Analyzing Complex Text

Jul 03, 2019

Michelle Brenner’s students analyze an excerpt from Mark Twain’s The Adventures of Huckleberry Finn by gathering evidence to support their point of…

Part C: Activities That Illustrate Geometric Reasoning (55 minutes)

Jul 03, 2019

In this part, you’ll look at some activities designed for students in grades K-2. As you read each activity, answer…

View & Analyze the Video

Jul 03, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Part B: Developing Geometric Reasoning (40 minutes)

Jul 03, 2019

Introducing van Hiele Levels The National Council of Teachers of Mathematics (NCTM, 2000) identifies geometry as a strand in its…

Class Context

Jul 03, 2019

I encourage communication between students as much as possible. If you’re asking a friend, Can you lend me a pencil?…

Reading Like a Historian

Jul 03, 2019

Lili Velo uses historical context to teach students how to analyze historical documents. Teacher: Miroslaba “Lili” Velo School: Tennyson High School, Hayward,…

Class Context

Jul 03, 2019

One of the things I just love about teaching languages is that we can deal with math, science, geography, social…

Citing Evidence from Primary Sources to Support Arguments

Jul 03, 2019

In LeRoy Votto’s classroom, students read, annotate, write about, and discuss Wendell Phillips’s speech “The Philosophy of the Abolitionist Movement.”…

Part A: Geometry as a Problem Solving Process (25 minutes)

Jul 03, 2019

The study of geometry can include both problem solving and connections to other areas of mathematics (arithmetic, algebra, etc.). Too…

Classroom Case Studies, 3-5

Jul 03, 2019

In the previous sessions, we explored geometry as a problem-solving process. You put yourself in the position of a mathematics…

Classroom Case Studies, K-2

Jul 03, 2019

In the previous sessions, we explored geometry as a problem-solving process. You put yourself in the position of a mathematics…

Class Context

Jul 02, 2019

Part of what I do as a foreign language teacher is try to open students up to what goes on…

Class Context

Jul 02, 2019

I try to create activities that allow students to express likes and dislikes. This is most important in a second…

Close Reading of a Primary Source

Jul 02, 2019

Ann Pember’s students discuss the meaning and role of the USA Patriot Act after reading an article from the New York…

Homework

Jul 02, 2019

Suggested Reading Van de Walle, John A. (2001). Geometric Thinking and Geometric Concepts. In Elementary and Middle School Mathematics: Teaching…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Part C: Cross Sections (45 minutes)

Jul 02, 2019

Slicing Solids A cross section is the face you get when you make one slice through an object. Below is…

Class Context

Jul 02, 2019

I think it’s important that we touch upon history, science, math, and all the other curricula in our Spanish class…

Class Context

Jul 02, 2019

A real challenge to a teacher at this level is to give kids new information and find ways for them…

Part B: Nets (30 minutes)

Jul 02, 2019

Nets with Regular Polygons Imagine unfolding a cube so that all of its faces are laid out as a set…

Part A: Platonic Solids (45 minutes)

Jul 02, 2019

Platonic solids have the following characteristics: All of the faces are congruent regular polygons. At each vertex, the same number…

Class Context

Jul 02, 2019

Creative activities make the language the students’ own. It’s not the teacher’s language or the textbook language; it becomes the…

Identifying Evidence from Multiple Sources

Jul 02, 2019

Jesse Gore teaches students how to analyze evidence from primary and secondary sources in order to defend ideas. Teacher: Jesse Gore…

Reading and Analyzing Texts

Jul 02, 2019

Homework

Jul 02, 2019

Problem H1 Draw any triangle on your paper. Find the three midpoints and connect them in order. Explain why the…

Part C: Trigonometry (35 minutes)

Jul 02, 2019

Right Triangles Ratios The word “trigonometry” is enough to strike fear into the hearts of many high school students. But…

Class Context

Jul 02, 2019

When they are able to connect something that happened 2,000 years ago with something that’s happening today, they become invested…

Class Context

Jul 02, 2019

When I design a lesson, the first thing I plan is the outcome. What kinds of things do I want…

Blended Learning: Evaluating Source Material

Jul 02, 2019

In this lesson on the Industrial Revolution, Andrea Gambino Rhodes assigns primary and secondary source material to student groups based…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 02, 2019

I really believe that having student-centered learning is so much more powerful than the teacher standing in front of the…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 02, 2019

It’s all about setting the stage and comprehensible input — hearing that wait time before I expect them to start…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 02, 2019

Students are very curious about culture. Making connections to that culture and comparisons between theirs and ours is very important…

Flexible Grouping to Promote Learning

Jul 02, 2019

Darby Masland uses flexible grouping to foster understanding of texts and vocabulary. Teacher: Darby Masland School: The Urban Assembly Institute of Math…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 02, 2019

It’s very important to teach in the target language. I keep the class in German as much as possible. I’m…

Blended Learning: Purposeful Instruction

Jul 02, 2019

Andrea Gambino Rhodes discusses the ways in which she chooses primary sources to frame her lesson to engage students, such…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 02, 2019

When you’re teaching high school students, you have to keep the intellectual level up so that it maintains their interest…

Class Context

Jul 02, 2019

When you start speaking to students in a target language from kindergarten on, they’re really trained to take all of…

Reading and Responding Like a Historian

Jul 02, 2019

LeRoy Votto’s students discuss their thoughts on Wendell Phillips’s speech “The Philosophy of the Abolitionist Movement.” Teacher: LeRoy Votto School: The Urban…

Class Context

Jul 02, 2019

When the students did this activity, they became the people in the city. Having built the buildings, they took a…

Big Ideas in Literacy – History/Social Studies

Jul 02, 2019

Introduction Welcome to the history/social studies content-specific units on disciplinary literacy. These next four units explore disciplinary literacy in history…

Part B: Similar Triangles (35 minutes)

Jul 02, 2019

A mathematics teacher likes to astound her students with tricks that can be explained through mathematics. Before the class studies…

Reading, Writing, and Responding to Poetry

Jul 02, 2019

Students in Ben Berman’s creative writing class expanded their study of figurative language by reading and considering two poems about…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Part A: Scale Drawings (50 minutes)

Jul 02, 2019

Finding a “Good Copy” Here is a picture of a panther:   Problem A1 Which of these pictures is a…

Class Context

Jul 02, 2019

Students have to speak French constantly to have a high degree of ability to speak the language. It has to…

Homework

Jul 02, 2019

The coordinate geometry that you first worked with in Session 6 is useful for describing transformations. Before looking at how…

Teacher Collaboration Across Disciplines

Jul 02, 2019

Andrew Spinali meets with the 7th grade content area literacy team that he established among his colleagues. They talk about…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Bringing It All Together – English

Jul 02, 2019

Introduction Brenda Green, executive director of the Center for Black Literature, ends her weekly radio show by saying: “The reader…

Part C: Translation Symmetry and Frieze Patterns (60 minutes)

Jul 02, 2019

Translation Symmetry and Frieze Patterns A translation or slide involves moving a figure in a specific direction for a specific…

Class Context

Jul 02, 2019

I like to do content-based lessons because I think the students enjoy it. It’s language that is meaningful to them.…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Writing Workshop: Using Mentor Texts and Graphic Organizers

Jul 02, 2019

Andrew Spinali has students work on sequencing techniques to help them develop theme in their writing. Teacher: Andrew Spinali School: Parker Middle…

Class Context

Jul 02, 2019

I think from experience, I have come to realize that, short of being in the country, a film portrays the…

Part B: Rotation Symmetry (30 minutes)

Jul 02, 2019

Determining Rotation Symmetry If you can rotate (or turn) a figure around a center point by fewer than 360° and…

Part A: Line Symmetry (30 minutes)

Jul 02, 2019

In Session 5, you saw three ways to move figures around: rotation, reflection, and translation. If you can move an…

Writing in English

Jul 02, 2019

Introduction One important way we study written texts in the English language is to reproduce and revise them for personal,…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Homework

Jul 02, 2019

Problem H1 Find the height of an equilateral triangle with the following side lengths: a. 1 centimeter b. 2 centimeters…

Class Context

Jul 02, 2019

I think the most valuable lesson that my kids can take away from my room is that language learning is…

Part C: Applications of the Pythagorean theorem (35 minutes)

Jul 02, 2019

Finding Missing Lengths The Pythagorean theorem is useful for finding missing lengths. If you can find a right triangle in…

View & Analyze the Video

Jul 02, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Part B: Proving the Pythagorean Theorem (65 minutes)

Jul 02, 2019

What Is a Theorem A theorem in mathematics is a proven fact. A theorem about right triangles must be true…

Class Context

Jul 02, 2019

Language is a tool of communication. If I only ask students to do what’s on the sheet of paper, that…

Part A: The Pythagorean Theorem (20 minutes)

Jul 02, 2019

Calculation Area Here is a square drawn on dot paper: Problem A1 Come up with a method to find the…

Identifying Theme Through Close Reading

Jul 02, 2019

Kelly Johnson helps her students determine the theme of the book they have been reading—Breath, Eyes, Memory by Edwidge Danticat—by supporting…

Homework

Jul 01, 2019

Problem H1 You can make your own tangram set from construction paper. Start with a large square of construction paper…

Part C: The Midline Theorem (55 minutes)

Jul 01, 2019

The Midline Theorem In this part, we will begin to use segment notation. Optional: About Segment Notation (see below). Let’s…

View & Analyze the Video

Jul 01, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 01, 2019

A lot of the teaching at this age level starts and ends with songs. That is a way for children…

Part B: Cutting Up (50 minutes)

Jul 01, 2019

You can solve each of the following problems in more than one way. Try to find several solutions; then pick…

Part A: Tangrams (15 minutes)

Jul 01, 2019

Exploring Tangrams A tangram is a seven-piece puzzle made from a square. A typical tangram set contains two large isosceles…

View & Analyze the Video

Jul 01, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

English in the Real World: A Sports Journalist

Jul 01, 2019

Introduction The Real World videos in the Reading and Writing in the Disciplines course support teachers’ daily efforts to effectively…

Class Context

Jul 01, 2019

In middle school, we have to constantly think about engaging and motivating students. I could have just shown them pictures…

Homework

Jul 01, 2019

Problem H1 Lines p and q are parallel. Find the measures of all of the numbered angles. Explain how you…

Reading in English

Jul 01, 2019

Part D: Thinking with Technology (15 minutes)

Jul 01, 2019

Now that you’ve had some experience with dynamic geometry software, discuss or reflect on the following problems.   Problem D1…

Part C: Circles

Jul 01, 2019

A circle is the set of all points in a plane that are equidistant from a given point in the…

Guided Instruction for Independence

Jul 01, 2019

Jennifer Roberts asks students to compare two characters from The Cask of Amontillado by Edgar Allan Poe using evidence they have gathered…

Part B: Parallel Lines (45 minutes)

Jul 01, 2019

Properties of Angles Parallel lines are two lines in the same plane that never intersect. Another way to think about…

Class Context

Jul 01, 2019

  The things that they do in class — activities, language tasks —have to be from the student, from whatever…

Part A: Introduction to Geometer’s Sketchpad (25 minutes)

Jul 01, 2019

Dynamic geometry software like Geometer’s Sketchpad allows you to construct and manipulate geometric figures. Such software can help you discover…

Revising with Teacher and Peer Feedback

Jul 01, 2019

Ben Berman discusses unveiling the craft of writing by teaching students how to give and receive feedback on creative pursuits.…

Homework

Jul 01, 2019

A quadrilateral is a polygon that has exactly four sides. Here are some definitions of special types of quadrilaterals: A…

View & Analyze the Video

Jul 01, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 01, 2019

  It’s very helpful, I think, being a second-language learner myself. You know the process. You know what frustration you…

Teaching Argumentation Skills

Jul 01, 2019

Dan Guerrero challenges his students to construct arguments using academic language and terms. Teacher: Dan Guerrero School: Tennyson High School, Hayward, CA…

View & Analyze the Video

Jul 01, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 01, 2019

I expect them to learn the culture. I expect them to appreciate the language and the culture foremost. That’s the…

Collaborating and Writing: Components of Close Reading

Jul 01, 2019

Kelly Johnson discusses strategies she uses to get her students to read, discuss, and write about the emerging theme as…

One-on-One Conferences

Jul 01, 2019

Wendy Barrales has a one-on-one conference with a 6th grader who needs help applying strategies to define an unknown word.…

Part C: Definitions and Proof (45 minutes)

Jul 01, 2019

Definitions Definitions and proof both play essential roles in mathematics. Definition is crucial, because you need to know what something…

View & Analyze the Video

Jul 01, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Part B: Classifying Polygons (40 minutes)

Jul 01, 2019

Polygons can be divided into groups according to certain properties. Concave polygons look like they are collapsed or have one…

Part A: Hidden Polygons (20 minutes)

Jul 01, 2019

Identifying Polygons Polygons are two-dimensional geometric figures with these characteristics: They are made of straight line segments. Each segment touches…

Class Context

Jul 01, 2019

Around 95 percent of the time I speak Arabic. I feel it’s really important to speak in Arabic all the…

Homework

Jul 01, 2019

Problem H1 More than one feature can be combined into a triangle. Decide which of the following combinations are possible.…

Engaging Students in Authentic Reading and Writing

Jul 01, 2019

Jenee Ramos engages students in reading and writing about topics that are relevant to their lives. Teacher: Jenee Ramos School: Brookline High…

Part C: Building Towers (45 minutes)

Jul 01, 2019

In Part C, you will apply what you’ve learned about the properties of figures to a construction task.   Problem…

Reading and Writing in English

Jul 01, 2019

The following education experts appear in this video: Dale Allender is an assistant professor at California State University in Sacramento, where…

Class Context

Jul 01, 2019

  By listening to them—when they are participating, when they are talking to each other—it shows me, did they understand…

Part B: Linkage-Strip Constructions (40 minutes)

Jul 01, 2019

A triangle has three sides, but not just any set of three lengths will make a triangle. Use linkage-strips to…

Big Ideas in Literacy – English

Jul 01, 2019

Introduction The English language arts classroom has always been the primary place where students are taught academic literacy practices. These…

Using Document-Based Questions for Historical Writing

Jul 01, 2019

Amanda Westenberg uses grouping techniques, peer revision, self-revision, and teacher feedback to address the skills needed to write a document-based…

Engaging Students in Authentic Reading and Writing

Jul 01, 2019

Jenee Ramos engages students in reading and writing about topics that are relevant to their lives. Teacher: Jenee Ramos School: Brookline High…

Part A: Different Triangles (20 minutes)

Jul 01, 2019

In the following problems, you will draw a variety of triangles and take note of their differences. Note 2 Drawing Triangles…

View & Analyze the Video

Jul 01, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jul 01, 2019

  That’s the ideal, that kids are teaching each other. When that happens, it’s awesome.… I’ll put this student who’s…

Fostering Close Reading

Jul 01, 2019

Amy Miles builds students’ close reading skills and creates an opportunity to dig into complex text to foster deeper understanding…

View & Analyze the Video

Jun 28, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jun 28, 2019

  My classroom is very intentionally filled with tables and not desks because I feel that tables promote conversation, and…

Using Scientific Discourse

Jun 28, 2019

Students learn how to apply scientific reasoning to new problems and then communicate about it with peers. Teacher: Mary Murphy School: The…

Bringing It All Together – Science

Jun 28, 2019

Integrating Reading and Writing The previous units highlighted ways in which reading and writing can be integrated into different aspects…

View & Analyze the Video

Jun 28, 2019

As you reflect on these questions, write down your responses or discuss them as a group. Before You Watch Respond…

Class Context

Jun 28, 2019

The point of the activity is to show them how to negotiate. So it is not just like, “Do you…

Polishing Writing

Jun 28, 2019

Jenee Ramos uses a writing workshop approach to peer revision to help students practice their writing techniques across different genres.…

Writing for New Media

Jun 28, 2019

Jane Cunningham engages her students with a journalism podcast project in which they create their own podcasts about a subject…

Using Technology to Develop Writing Skills

Jun 28, 2019

Jane Cunningham and her colleague Mike McSweeney discuss the creation of an English unit on journalism, which promotes skills such…

Class Context

Jun 28, 2019

  I cannot call it learning a language if there is no authentic opportunity for students. If you don’t use…

Science Literacy: Reading and Writing Diagrams

Jun 28, 2019

Students use models to explain how the relative positions of the Sun, Moon, and Earth determine Moon phases, eclipses, and…

Power Writing for Science

Jun 28, 2019

Amy Miles uses a “power writing” exercise to build writing skills and reinforce background knowledge. Teacher: Amy Miles School: Health Sciences High…

Peer Teaching

Jun 28, 2019

Dr. Amanda Micsenyi raises the bar for a particularly eager student, challenging him to read additional articles about HIV/AIDS and…

Building Knowledge from Multiple Sources

Jun 28, 2019

Dr. Amanda Micsenyi leads her ninth grade class in a literature study of the timeline of HIV/AIDS. Students read and…

Reading and Writing in Science

Jun 27, 2019

The following education experts appear in this video: Meena Balgopal is an associate professor at Colorado State University in the School…

Writing in Science

Jun 27, 2019

Learning Vocabulary in Biology

Jun 27, 2019

Mary Murphy uses an engaging narrative to help students understand protein synthesis. Teacher: Mary Murphy School: The Urban School of San Francisco…

Organizing Ideas from Multiple Sources

Jun 27, 2019

Lynn Gilbert helps students create a graphic organizer for multiple resources and various types of texts; her ultimate goal is…

Assignments + Projects

Jun 27, 2019

View & Analyze the Video

Jun 27, 2019

Video Summary In “Engaging With Communities,” Patsy Lightbown, Professor Emeritus of Concordia University in Montreal, discusses ways of providing students…

Before You Watch

Jun 27, 2019

Annotating Across Disciplines

Jun 27, 2019

Catherine Rohrbaugh teaches students how to take notes and analyze text across different content areas to foster independent learning. Teacher: Catherine…

Reading In Science

Jun 27, 2019

Assignments + Projects

Jun 27, 2019

Blended Learning: Acquiring Digital Literacy Skills

Jun 27, 2019

Jennifer Roberts discusses the ways in which she incorporates the use of computers into her classroom. ​​Teacher: Jennifer Roberts School: Point Loma…

Analyzing Anecdotal Evidence

Jun 27, 2019

Dan Guerrero demonstrates how he uses anecdotal evidence as a way to engage others in a discussion of ethics and…

View & Analyze the Video

Jun 27, 2019

Video Summary In “Planning for Assessment,” Understanding by Design education consultant Allison Zmuda describes the components of a good assessment…

Creating a Classroom Culture

Jun 27, 2019

Darby Masland explains how a class-wide focus on standards helps students meet learning goals more effectively. Teacher: Darby Masland School: The Urban…

Supporting Claims with Evidence and Reasoning

Jun 27, 2019

Chemistry teacher Martin Berryman shows how to help students write strong claims based on evidence, reason, and the interpretation of…

Assignments + Projects

Jun 27, 2019

View & Analyze the Video

Jun 27, 2019

Video Summary In “Valuing Diversity in Learners,” Professor Marjorie Hall Haley of George Mason University in Virginia talks about ways…

Thinking and Communicating Like a Biologist

Jun 27, 2019

Amy Sheck leads students as they read and discuss a scientific paper on biofilms, design and propose an experiment, and…

Before you Watch

Jun 27, 2019

Assignments + Projects

Jun 26, 2019

View & Analyze the Video

Jun 26, 2019

Video Summary In “Rooted in Culture,” Professor Alvino Fantini from the School for International Training in Brattleboro, Vermont, discusses the…

Big Ideas in Literacy – Science

Jun 26, 2019

Introduction Disciplinary literacy in science is challenging and highly rewarding. It involves more than what we traditionally think of as…

Learning in a Blended Classroom

Jun 26, 2019

Leon Young explains how he integrates technology into the classroom to support blended learning. Teacher: Leon Young School: REALM Charter School, Berkeley,…

Assignments + Projects

Jun 26, 2019

View & Analyze the Video

Jun 26, 2019

Video Summary In “Subjects Matter,” Patsy Lightbown, Professor Emeritus of Concordia University in Montreal, addresses the balance between form and…

Before you Watch

Jun 26, 2019

Blended Learning: Using Technology to Learn Math Concepts

Jun 26, 2019

Leon Young uses technology in the classroom to facilitate communication among peers and to support differentiated instruction of small learning…

Collaborating to Extend Mathematical Understanding

Jun 26, 2019

Derek Boyd explains how he differentiates activities to teach specific mathematical concepts. Teacher: Derek Boyd School: MetWest High School, Oakland, CA Grade: 9…

View & Analyze the Video

Jun 26, 2019

Video Summary In “Delivering the Message,” Professor Paul Kei Matsuda of the University of New Hampshire addresses how a consideration…

Before you Watch

Jun 26, 2019

Reading and Writing in Mathematics

Jun 26, 2019

The following education experts appear in this video: Jacob Foster is the director of science and technology/engineering at the Massachusetts Department…

Delivering the Message

Jun 26, 2019

Learning Goals How do you organize an effective written or oral presentational task that has students focus on a particular…

Bringing It All Together – Mathematics

Jun 26, 2019

Introduction You have now had a number of opportunities to consider what it looks like to incorporate the disciplinary literacy…

Real World Mathematics Collaboration

Jun 26, 2019

Students in Stephanie Brown’s class work together in teams to problem solve and develop a system of equations for a…

Creating Opportunities for Mathematical Discourse

Jun 26, 2019

Sarah Langer engages students with a multistep group project that uses their understanding of graph theory. Students work together to…

Assignments + Projects

Jun 26, 2019

Fostering Student Engagement

Jun 26, 2019

Laura Mourino discusses her commitment to engaging students in a variety of tasks by acknowledging individuality in learning and making…

Writing to Deepen Mathematical Understanding

Jun 26, 2019

Laura Mourino assesses formative understanding by having her 10th graders write letters answering four key questions about a unit circle.…

Using Math Vocabulary to Articulate Understanding

Jun 26, 2019

Derek Boyd shows how reinforcing vocabulary helps students understand and retain content. Teacher: Derek Boyd School: MetWest High School, Oakland, CA Grade: 9…

View & Analyze the Video

Jun 26, 2019

Video Summary In “Person to Person,” Professor Joan Kelly Hall of Pennsylvania State University addresses the importance of the talk…

Individualized Instruction as a Formative Assessment Tool

Jun 26, 2019

Kelly Gay gives students an opportunity to explain their thinking, or a line of learning, about mathematical word problems as…

Writing for Mathematics Understanding

Jun 26, 2019

Stephanie Brown’s students first work individually and then in groups to construct viable mathematical arguments by critiquing each other’s reasoning.…

Writing in Mathematics

Jun 25, 2019

Annotating Word Problems

Jun 25, 2019

Kim Dinh teaches students how to determine important information to solve mathematical word problems. Teacher: Kim Dinh School: Health Sciences High and…