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OER Commons is a dynamic digital library and network. Explore open education resources and join our network of educators dedicated to curriculum improvement.

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Relying on subjective judgement, teachers are no better than chance at determining whether a student needs a read aloud accommodation (Fuchs & Fuchs, 2001; Helwig & Tindal, 2003). What happens when students get the wrong accommodations?

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Chromebooks in the Classroom Quick Start Guide

available from NPR, Inc.

collaboration with CALL Scotland

Making Google Drive Docs Accessible

Penn State: http://accessibility.psu.edu/software/googledocs/

University of Michigan: https://sites.google.com/a/umich.edu/going-google/accessibility

Before downloading any extensions! Make sure you download:

Extensity - This extension helps you manage all your extensions!

Apps / Extensions

Key: X= Extension; A = App

Tip: Install one extension at a time and trial. Some conflicts have been experienced!

ChromeVox (X) - Screen Reader Support that reads items on the screen

High Contrast (X) - Change view of webpages

ChromeVis (X) - Highlight text of webpage - change size / color of text

Zoomy (X) - This extension overrides the default zoom (for text and images) for all websites. Default zoom can be set manually or automatic.

Tip: Install one extension at a time and trial. Some conflicts have been experienced!

Read & Write by Text Help (X) - Powerful toolbar inserts into Google Docs and provides an array of supports for reading.

Snapverter by TextHelp (A) - Take a picture of a document with smartphone; covert to accessible PDF.

Snap&Read Universal (X) - Text reader plus text leveler. It adjusts text complexity and reads both accessible and inaccessible text on Google Drive, PDFs, and websites.

Learning Ally Link (A) - Provide access to human narrated audiobooks. Membership based services with eligibility requirements (print disability)

Premier Literacy Solutions for Chrome (X) - A suite of literacy support tools including text to speech support for Reading, Summarizing, Dictionary. Also has Voice Dictation and Worksheet Wizard. 30 day free trial; $29.95 yr/subscription.

Read The Web 3 (X) - from Kurzweil - Text to Speech support that can read in 30 voices and 17 languages and dialects.

Readability (X) - Streamlines the presentation of web pages for easier reading.

Beeline Reader (X) - Adds color gradient to webpage text to assist with visual tracking between lines. Colors can be customized, plus has Open Dyslexic font.

Send to Kindle (X) - Send a document / webpage directly to your Kindle for reading.

Kindle Cloud Reader (A) - Read your books / documents directly in the browser.

dotEPUB (X) - Convert any webpage to an ePub file to read on compatible mobile devices.

Readium (A) - ePub document reader

My EBook Maker (A) - Create your own digital books that can be exported to other compatible mobile devices.

Bookshare Web Reader (X) -For Students with print disabilities, access to an extensive collection of digital books that can be read with text to speech directly in browser.

Newsela (A) - Newsela publishes daily news articles at 5 reading levels from grades 3-12 to drive gains in literacy.

Books That Grow (A) - Over 100 FREE ebooks at different reading levels. Teachers can assign books and monitor progress.

Fluency Tutor (A) - Student App & Teacher App - Teachers assign reading materials and students review directly in Google Drive. Provides tools to assist students with reading passages & allows them to record their reading for playback.

Copyfish (X) - Free OCR (Optical Character Recognition) extension that will pull text from an image, video or PDF.

Visor (X) - Screen Dimmer and reading aid. Provide focus for reading materials by blocking other areas of screen.

Tip: Install one extension at a time and trial. Some conflicts have been experienced!

Read & Write by Text Help (X) - Powerful toolbar inserts into Google Docs and provides an array of supports for writing.

Grammerly (X) - Spell check and grammar check while writing online

Ginger (X) - Grammar and spell check support while writing.

Co:Writer Universal (A & X) - Don Johnston's powerful word prediction tool comes to Chrome!

Mic Note (A) - Powerful note taking tool that provides dual support. Audio can be recorded while the person types. Embed PDF and PPT docs into the app. Audio is synced with the written notes. Think Livescribe Pen in the Chrome browser!

Doc Hub (Formerly PDFZen (A) - Load PDF files then type, highlight or draw directly on the form.

Awesome Screenshot (X) - Capture image from screen; annotate; save to Drive

Kami (Formerly Notable PDF for Google Drive )(A) - Do more with PDF files - View, Annotate, Share and Collaborate

Mindomo (A) - Mind Mapping tool. Google Drive integration. Real time collaboration

MindMup (A) - MInd Mapping tool/website. Share finished work to Dropbox / Google Drive. Real time collaboration.

Gliffy Diagrams (A) - Create flowcharts, brainstorming tool

Dictanote (A) - voice rec. free and pro version (pro= $9.99/yr)

Speech Pad (A) - voice recognition, plus has the ability to transcribe audio

Typing Club (A) - Educational games as typing training

Tip: Install one extension at a time and trial. Some conflicts have been experienced!

Calculator (A) - Simple electronic calculator for basic computation.

GeoGebra (A) - "Free dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy to use package."

Number Line (A) - Provides student's with a tool to visualize number sequences.

Learning Tools / Teacher Tools / Classroom Management

Tip: Install one extension at a time and trial. Some conflicts have been experienced!

Supports for Executive Function / Organization /Time Management

OneTab (X) - Condense all open tabs into single tab. Open tabs are displayed as a list. Reduce up to 95% of memory.

Google Drive (A) - Productivity suite of tools to support collaboration

Tab Resize (X) - Split screen to view multiple tabs at one time.

Clipboard History 2 (X) - Go back to ANY item you copied to the clipboard.

myStudent Homework Planner (A) - Organization tool for planning, scheduling, task reminders

Livebinders (A) - Organize, share resources

Symbaloo (A) - Symbol driven home page to launch favorites

Listly (X) - Copy information from web sites to make your own lists.

Maker Apps

STEM Fuse Educate (A) - instantly accessible standard based curriculum

Soundcloud (A) - Tool to record audio and share via web.

Twisted Wave (A) - Powerful audio editing suite. Similar to Audacity.

WeVideo (A) - Video editing tool for Chrome

Design Something (A) - Create 3D designs in your Chrome Browser

Lego Builder (A) - Create Lego designs

SOLE 64 (A) - Learn programming

Switch Accessible Apps

Augmentative and Alternative Communication (AAC) apps

Cough Drop AAC - Web based AAC system that works on Chromebooks

Other

Remote Desktop (A) - Allows a remote connection between your Chromebook and any other computer via the Internet.

Clarisketch - (A) - Narrate photo captures with annotation; others play back video clip. Similar to Explain Everything. NOTE: ONLY WORKS IN CHROME OS

Movenote (A) - Open a Google Doc and embed video directly into file!

Skiblz Cam (X) - Screencast application - no audio (yet!)

Split Screen (X) - Allows you to show two browser windows side by side.

Apps for Common Core (X) - Resource for apps related directly to common core standards.

Ed Puzzle (A) - Allows teacher to build UDL type assignments with video, embedded audio and quizes.

Chromnitweet (X) - Tweet directly from the Omnibox (url window).

Watch the two part webinar series, Going Google, I hosted for the Center for Technology and Disability

Part 1: Using Google & Chrome Supports as AT

Part 2: Chrome Apps & Extensions

Chromebook How To Video Channel from You Tube

Hixson Middle School - Resource Page for Chromebook Program

LSR7 Chrome Resource Page

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mmatp.com/chromeAT Get Yours Today! Chromebooks in the Classroom Quick Start Guide available from NPR, Inc. Listen Listen to my interview with @iplante from the BAM! Radio Network: Evaluating Chromebooks as an Assistive Device Download Chromebook Apps and Extensions for Learners with Dyslexia collaboration with CALL Scotland Chrome Resources Google Chrome Assistive Technology Toolbox GAFE Resources...

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Peekapak | Award-winning Social-Emotional Learning Curriculum and Games

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Peekapak | Award-winning Social-Emotional Learning Curriculum and Games

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Peekapak | Award-winning Social-Emotional Learning Curriculum and Games

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Peekapak bridges the gap between the class and home - with character education lesson plans, progress tracking & communication tools.

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Woot Math Review for Teachers | Common Sense Education

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Woot Math Review for Teachers | Common Sense Education

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Woot Math is an adaptive online curriculum that focuses on fractions, ratios, and decimals. It includes narrated tutorials and targeted practice. Teachers set up student accounts (with student names, usernames, and passwords) and students log in using this info and a teacher code. Woot Math Polls is part of Woot Math and is a standards-aligned tool that can be used to create warm-ups, exit tickets, quizzes, and formative assessments.

Students access a progression of adaptive lessons through units organized by topic and presented as notebooks, and they view their progress through units. Student home pages show 12 lessons (which look like sticky notes) per screen: Completed ones are shaded, future ones have locks. Each lesson begins with a short (1-2 minutes) narrated example, followed by a series of practice questions, sometimes with further tutorials and more questions. At the end of the lesson (each of which are about 10 questions long), a student earns 1-3 stars depending on quantity correct, and the next lesson is unlocked (it's now gray, with a "new" sash). The site's adaptiveness makes it so that the "next" lesson may or may not be sequentially next -- sometimes it's a review of content that needs some extra attention, and sometimes it skips ahead to a more complex concept. At any time, previous lessons may be redone; new problems are provided, and the adaptive feature still works. Students can also earn pens, badges, and trophies.

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Woot Math is an adaptive online curriculum that focuses on fractions, ratios, and decimals. It includes narrated tutorials and targeted practice. Teachers set up student accounts (with student names, usernames, and passwords) and students log in using this info and a teacher code.

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Edulastic Review for Teachers | Common Sense Education

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Edulastic Review for Teachers | Common Sense Education

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Teachers can use Edulastic with all students if they are required to -- or want to -- track assessment data related to standards. Teachers should help students register in class to ensure that everyone is able to use the program. In addition, for classrooms with one-to-one devices, it would be beneficial to have students take some assessments in class to allow for questions and practice. Once all students understand how to navigate the program, teachers can share assessments both in and out of class. As students complete assessments, teachers can individualize instruction for those who struggle with a specific standard, or they can re-teach a particularly difficult standard to the entire class. Teachers can use Edulastic seamlessly with Google Classroom and Clever. Teachers are able to preview assessments and review questions from the student's perspective and assign flexible points as they target their individual class needs.

Continue reading Show less

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Teachers can use Edulastic with all students if they are required to -- or want to -- track assessment data related to standards. Teachers should help students register in class to ensure that everyone is able to use the program.

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20 Websites for Free Reading Comprehension Worksheets

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20 Websites for Free Reading Comprehension Worksheets

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20 Websites for Free Reading Comprehension Worksheets

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20 Websites for Free Reading Comprehension Worksheets

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Welcome to my Freebies Page!

Please enjoy these freebies from my Teachers Pay Teachers Store Games 4 Learning

On this page your will find Printable Math Games Freebies, Printable Phonics Games Freebies and also Seasonal Games and Puzzles! ENJOY!

Math Bump Games Freebies

Place Value Games for 2 Digits Freebies

Place Value Worksheets for 2 and 3 Digits Freebies

Addition Board Games Freebies

Subtraction Board Games Freebie

Multiplication Board Games Freebie

Cut monkeys to help kids master basic multiplication.

Division Board Games Freebies

Cute and colorful, these monsters will help kids to master basic division facts. Enjoy!

Math Pick, Flip, Check Card Freebies

No Prep Math Games

Snowman Math Bump Games Freebies

Phonics Game CVC Freebie

Phonics Game Silent e Freebie

Phonics Game R Contolled Vowels Freebie ar er ir or ur﻿

More Christmas Freebies

Valentine's Day Math

Christmas Math Games and Puzzles

Pumpkin Smash Game

Pumpkin Smash Game - Printable 2 player game sheet. Enjoy!

Math Problems and Brain Teasers Freebie

A collection of 7 Math Brain Teasers Cards

Halloween Math Board Games

There are 2 Halloween math board games that review numbers to 20 and numbers to 100.
Available at

Phonics Board Games

These Word Change games are great for CVC and Silent e review!

Addition Tic Tac Toe and Multiplication Tic Tac Toe

Tic Tac Toe game boards to practice addition and times tables.
Kids love Tic Tac Toe and now they love these math games too!

Word Boards

Have fun using these as a board game or word building activity.

Short Vowel CVC Fishing Board Game

Easter Freebies

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Please enjoy these freebies from my Teachers Pay Teachers Store Games 4 Learning On this page your will find Printable Math Games Freebies, Printable Phonics Games Freebies and also Seasonal Games and Puzzles! ENJOY! Cut monkeys to help kids master basic multiplication. Cute and colorful, these monsters will help kids to master basic division facts.

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Free online cool math kids games and activities for children. Improve your calculation skills with these fun games. Use on an IWB in the classroom or PC or Mac at home to teach your child maths skills. Age range 7-11 years, primary key stage two, elementary grades. Great for homeschool teaching.

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By Jenn Osen-Foss, MAT

If your child has trouble with math, a graphic organizer can help. Graphic organizers help kids break down math problems into steps. They're great tools for figuring out what's being asked in a word problem or which operation to use. Kids can also use them to learn new math concepts.

There are many types of graphic organizers. The five here could work for students of all ages. You and your child can adjust them depending on your child's needs and the math problem or topic.

Each graphic organizer comes with instructions and one or two samples of what it looks like filled in. You can print them out and have your child fill them in by hand. (If your child struggles with writing, you can write in the problem and let your child do the rest.)

Tell us what interests you

About the author

About the author

Jenn Osen-Foss, MAT is an instructional coach, supporting teachers in using differentiated instruction, interventions, and co-planning.

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If your child has trouble with math, a graphic organizer can help. Graphic organizers help kids break down math problems into steps. They're great tools for figuring out what's being asked in a word problem or which operation to use. Kids can also use them to learn new math concepts.

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Evidence-Based Practices — Exceptional Children

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Evidence-Based Practices — Exceptional Children

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Evidence-Based Practices - Exceptional Children

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Specific Learning Disabilities / Evidence-Based Practices

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Creative free ideas, lesson plans and activities to teach first grade students.

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Use the tools on this page to help prepare your lessons. For your convenience, we have also included links to resources available on Kids' Place.

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https://online.maryville.edu/online-bachelors-degrees/liberal-studies/problem-solving-games/

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A video tutorial is also available to demonstrate how to use this applet.

Modes

How Many: Identify how many items or empty squares there are.

Build: Drag a certain number of items to the frame.

Fill: Determine how many items are needed to fill the remaining squares.

Add: Drag items to complete addition problems.

Choosing Play All from the Games menu will randomize which of the four games is played.

Options

The items to be used can be chosen in the upper left corner: circles, bugs, stars, or apples.

How to Use

The Next button advances to the next problem.

The Done button should be clicked when a student believes that she has correctly completed a frame.

The number buttons at the bottom of the screen can be used to enter an answer, or the computer keyboard can be used.

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The four games that can be played with this applet help to develop counting and addition skills.

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Table of Contents

Please note: Although we have taken care to create all files so that they are as accurate as possible, some files may not print accurately. Computer and printer settings may affect the accuracy of items such as rulers and protractors.

If items are photocopied on transparencies, they may also be distorted through this process.

New Blackline Masters have now been included. Click here to view the list of new BLM files.

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Please note: Although we have taken care to create all files so that they are as accurate as possible, some files may not print accurately. Computer and printer settings may affect the accuracy of items such as rulers and protractors. If items are photocopied on transparencies, they may also be distorted through this process.

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Games Index HTML5 Games Flash Games Elementary Games Puzzle Games

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Game Boards for Homemade Games

On this page you will find a few printable blank game boards. The boards can be printed on card stock or if you will be making "file-folder" games, print on heavy paper and glue inside of a file folder. After printing the game boards, be sure to look at Game Board Assembly if you need instructions on how to make the two printed board halves one whole game board. If you are having trouble printing the files, look at the Printing Suggestions.

Game Board Types

I have two game board types to print. One type is the Start to Finish game style in which the game has distinct starting and ending places. The other type is the Race Track game style in which the player goes around and around the board track until something happens to make the game end.

About the Game Board Templates

Some of the templates are completely plain while others have some marking on them. Some are in color and some are not. I've included images to help you decide if you want to print any. The files are pdf and that means they are not editable. I know that is a disadvantage, but I made most of the templates from drawings, only one was made with a word processor.

Printable Blank Dice

Yes, I have Printable Blank Dice and if you don't like what I have, go look at my Cube Templates. There you'll find printable cubes, or we can all them die on this page, in several sizes and, not only that, they are doc files so if you have die images that you want on your dice, then you can add it to the doc file before printing.

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On this page you will find a few printable blank game boards. The boards can be printed on card stock or if you will be making "file-folder" games, print on heavy paper and glue inside of a file folder.

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Primary Resources: Maths: Calculations: Addition and Subtraction

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Primary Resources: Maths: Calculations: Addition and Subtraction

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Primary Resources: Maths: Calculations: Addition and Subtraction

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Primary Resources - free worksheets, lesson plans and teaching ideas for primary and elementary teachers.

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Primary Resources: Maths: Calculations: Addition and Subtraction

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Primary Resources: Maths: Calculations: Addition and Subtraction

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Primary Resources: Maths: Calculations: Addition and Subtraction

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Primary Resources - free worksheets, lesson plans and teaching ideas for primary and elementary teachers.

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Comparison Concept....Teach Kids Math Using The Model Method From Singapore Math

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Comparison Concept....Teach Kids Math Using The Model Method From Singapore Math

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The Comparison Concept is one of the three main concepts in the Model Method which all math models are derived from, the other two being the

Part-Whole Concept and the Change Concept . The Singapore Math Primary Curriculum adopts a concrete-pictorial-abstract progressive approach to help pupils tackle seemingly difficult and challenging word problems. Mathematics Teachers in Singapore usually make use of concrete objects to allow students to make sense of the comparison concept by comparing two or more quantities. Once the pupils can visualize how much one quantity is greater than or smaller than another quantity, they will then move on to put these relationships in rectangular bars as pictorial representations of the math models concerned.

To illustrate the comparison concept, take a look at the following problem:

Peter has 5 pencils and 3 erasers. How many more pencils than erasers does he have?

We can first give the child concrete objects, like 5 pencils and 3 erasers, and let the child put the two groups of objects side-by-side to match the 2 types of items, i.e., 1 pencils match with 1 eraser. Then, he will be able to see that there are 2 more pencils which cannot be matched with any erasers because he has run out of erasers to do that.

When they are comfortable with comparing concrete objects, we can then proceed to teach them to draw pictures of the concrete objects within boxes to illustrate the equation 5 - 3 = 2

After that, we can teach the kids to go on to draw the boxes without the objects.

Eventually, the equation can be visualised as a comparison between the 2 quantities given in the question and the pupils can easily see that to find the difference, they just need to subtract the smaller quantity from the larger quantity.

Therefore, Peter has 2 more pencils than erasers.

Hence, we can see that the relationship among the larger quantity, the smaller quantity and the difference can be summarised as follows:

To find the difference given two unequal quantities, just subtract the smaller quantity from the larger quantity:

Larger Quantity - Smaller Quantity = Difference

To find the larger quantity given the difference and the smaller quantity, just add the smaller quantity to the difference:

Smaller Quantity + Difference = Larger Quantity

To find the smaller quantity given the difference and the larger quantity, just subtract the Difference from the larger quantity:

Larger Quantity - Difference = Smaller Quantity

Go To Top - Comparison Concept

If you want us to send you our future Modelmatics eZine that would inform you on the latest article in Teach Kids Math By Model Method, do an easy sign-up below. Subscription is FREE!

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Comparison Concept....Teach Kids Math Using The Model Method From Singapore Math

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The Comparison Concept is one of the three main concepts in the Model Method which all math models are derived from, the other two being the Part-Whole Concept and the Change Concept .

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Number Bonds to 10 Activities and Teaching Resources - SparkleBox

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Number Bonds to 10 Activities and Teaching Resources - SparkleBox

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Number Bonds to 10 Activities and Teaching Resources - SparkleBox

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FREE printable teaching resources for number bonds to 10.

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Ladybird Spots Number Bonds Interactive Activity (SBi5) - SparkleBox

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Ladybird Spots Number Bonds Interactive Activity (SBi5) - SparkleBox

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Ladybird Spots Number Bonds Interactive Activity (SBi5) - SparkleBox

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A simple click-and-drag interactive activity where children move the spots on the ladybird wings to make different combinations that total 10.

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This is like our game, Twins, but we put numbers on the balls. You have to match up numbers (like in our game Shisen) to make the correct sums.

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Math games and more at MathPlayground.com! Problem solving, games, and puzzles the entire family will enjoy.

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I am always looking for new ideas to keep my students motivated when we review our math skills. These addition cards are a great way for students to practice adding numbers to 10. The best part is, they have a quirky robot theme!

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1.OA.A.1 - About the Math, Learning Targets, and Increasing Rigor: Grade 1 Mathematics

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1.OA.A.1 - About the Math, Learning Targets, and Increasing Rigor: Grade 1 Mathematics

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1.OA.A.1 - About the Math, Learning Targets, and Increasing Rigor: Grade 1 Mathematics

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Browse all the free Your Therapy Source special education, occupational and physical therapy printables, forms, worksheets, and activity ideas. We have finally reorganized these pages so it will be easier for you to navigate. If you were used to the old page and knew where everything was just scroll down.

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Browse all the free Your Therapy Source special education, occupational and physical therapy printables, forms, worksheets, and activity ideas.

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Teaching multiplication of fractions is, in one way, simple-the rule of multiplying across the numerators and the denominators is easy for teachers to teach and for students to learn. However, teaching so that students also develop understanding is more demanding, and Marilyn Burns tackles this in her new book Teaching Arithmetic: Lessons for Multiplying and Dividing Fractions, Grades 5-6 (Math Solutions Publications, 2003). In the following excerpt from Chapter 2, Marilyn builds on what students know about multiplying whole numbers to begin developing understanding of what occurs when we multiply fractions.

I began the lesson by posting the chart of "true" statements about multiplying whole numbers that I had previously generated with the class:

1. Multiplication is the same as repeated addition when you add the same number again and again.

2. Times means "groups of."

3. A multiplication problem can be shown as a rectangle.

4. You can reverse the order of the factors and the product stays the same.

5. You can break numbers apart to make multiplying easier.

6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one.

I planned to use these statements as a base for helping the students think about multiplying fractions. To begin, I pointed to the first statement:
1. Multiplication is the same as repeated addition when you add the same number again and again.
"Do you think this is true when we think about fractions?" I asked. I wrote on the board:

"Talk with your neighbor about how you might make sense of this problem with repeated addition," I continued.

After a few minutes, I called on Juanita. She said, "I think you can do it by adding one-half over and over again. I did one-half plus one-half, like that, six times. I think the answer is three." I wrote on the board:

"How did you get the answer of three?" I asked.

Juanita responded, "One-half plus one-half is one whole, and you can do that three times, and you get three." I wrote:

Eddie added, "It's like if you had six times something else, you could add the something else six times, and that's what Juanita did with the one-halves."

"So, does this first statement work for multiplying with a fraction?" I asked. The students nodded their agreement, and I wrote OK next to the first statement.

I then pointed to the second statement:
2. Times means "groups of."
"Does it make sense to read 'six times one-half' as 'six groups of one-half'?" Most of the students nodded.

Saul added, "The answer is still three." I wrote OK next to the second statement and then pointed to the third statement:
3. A multiplication problem can be shown as a rectangle.
I asked, "Can we draw a rectangle to show six times one-half?" The students weren't sure.

"Suppose the problem were six times one," I said, writing 6 x 1 on the board. The students were familiar with using rectangles for whole number multiplication. I sketched a rectangle, saying as I did so, "One side of the rectangle is six units long and the other side of the rectangle is one unit long." I labeled the sides 6 and 1 and then divided the rectangle into six small squares.

"See if this rectangle helps you think about how I might draw a rectangle to show six times one-half," I said.

Kayla said, "Just cut it in half."

"Which way should I cut the rectangle?" I asked.

"Sideways," Kayla said. I split the rectangle as Kayla suggested, then erased the 1 and replaced it with 1 written twice. Also, I shaded in the bottom half to indicate that it wasn't part of the problem.

"The top half of the rectangle is six units by one-half unit and shows the problem six times one-half. The bottom shaded half shows the same problem again, but we don't need to consider both. How many squares are there in the unshaded rectangle? Does this still give an answer of three?"

Damien explained, "Two halves make a whole, and you do that three times, so the six halves make three whole squares. Three is still the answer."

"But what about if both the numbers are fractions?" Julio challenged.

"Let's try one," I said. I wrote on the board:

I decided to show the students a way to think about representing the problem with a rectangle. "When I draw a rectangle for a multiplication problem with fractions, I find it easier first to draw a rectangle with whole number sides. So, for this problem, I think about a rectangle that is one by one," I said. I drew a square on the board, labeled each side with a 1, and continued, "This rectangle is a square because both factors are the same. It shows that one times one is one. Now watch as I draw a rectangle inside this one with sides that each measure one-half." I divided the square, shaded in the part we didn't need to consider to show the 1/2-by-1/2 portion in the upper left corner, and labeled each side 1/2.

I said, "The part that isn't shaded has sides that are each one-half of a unit. How much of the one-by-one square isn't shaded?"

"One-fourth," several students responded.

Saul was skeptical. He asked, "You mean that one-half times one-half is one-fourth?" I nodded.

"I don't get it," he said.

"But do you agree that the unshaded rectangle has sides that are each one-half?" I asked. Saul nodded.

"But you're not sure that the answer of one-fourth is correct?" I asked. Again, Saul nodded.

"Let's see if the other statements can help you see why," I said. I knew that if the students thought of the problem as "one-half of one-half," they would agree with the answer of one-fourth. I planned to develop this idea, and I used the next statement to do so.

I pointed to the next statement:
4. You can reverse the order of the factors and the product stays the same.
Craig commented, "That should work." Others agreed.

"But it doesn't matter for one-half times one-half," Brendan said. "If you switch them, you still have the same problem."

I said, "Right, so let's think about this statement for the first problem we solved-six times one-half. What about if we think about the problem as one-half times six?" I wrote on the board:

I continued, "If we think about the times sign as 'groups of,' then one-half times six should be 'one-half groups of six.' But that doesn't sound right. It does make sense, however, to say 'one half of a group of six,' or 'one-half of six,' and leave off the 'groups' part. Both sound better, and they're still the same idea. What do you think 'one-half of six' could mean?"

"It's the same," Sabrina said. "One-half of six is three, so one-half times six is three, and that's the same as six times one-half."

I said, "Let's think about one-half times one-half the same way. What is one-half of one-half?"

I heard several answers. "A fourth." "A quarter." "One-fourth."

"So what do you think about reversing the order of the factors when the factors are fractions?" I asked.

The students agreed that it would work, so I wrote OK next to Statements 3 and 4.

"Let's look at the fifth statement," I said, pointing to it:
5. You can break numbers apart to make multiplying easier.
"Talk with your neighbor about how you could apply this statement to the problem six times one-half."

After a few moments, I called on Brendan. He said, "It works. You could break the six into twos, and then you do two times one-half three times. Two times one-half is one. One plus one plus one is three. So it works." I wrote on the board:

Anita said, "We split the six into four and two. Half of four is two and half of two is one and two plus one is three. It works." I recorded:

I wrote OK next to the statement. "We have one statement left," I said, pointing to it:
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one.
I asked, "Does this statement hold true for six times one-half?"

"It doesn't work," Sachi said. "Three is smaller than six, so it doesn't work."

"Could we change the statement so that it does work?" I asked.

Julio said, "It should say at the end 'unless the factors are zero or one or a fraction.'" I edited the statement as Julio suggested:
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one or a fraction.
I thought about how to respond. If one of the factors is a fraction less than one, then Julio's idea works. But if the fraction is more than one, Julio's idea might not work. I wanted to acknowledge Julio's idea but also give him the chance to refine it. I posed a problem that had a fraction as one of the factors for which the answer was greater than both of the factors. I said, "That's a good idea, but I think it needs a little more information. Think about this problem-six times three-halves. That's the same as six groups of three-halves." I wrote on the board:

"Talk with your neighbor about what the answer would be to this problem," I said. After a couple of minutes, I called on Craig.

"We got nine," he said. "We knew that three-halves is the same as one and a half, and one and a half plus one and a half is three, and three plus three plus three is nine, so the answer is nine." I recorded Craig's idea on the board:

Craig continued, "And nine is bigger than six or three-halves. So the statement doesn't work. It works the way it used to be, but it doesn't work the way you changed it."

"I think I can fix what I said," Julio said. "The fraction has to be smaller than one. So any number that is zero or one or in between makes an answer that is smaller than the factors."

"So what should I write to change the statement?" I asked.

Julio said, "At the end, write 'zero or one or a fraction that's smaller than one.'" I wrote on the board:
6. When you multiply two numbers, the product is larger than the factors unless one of the factors is zero or one or a fraction smaller than one.
Julio and others nodded. I wrote OK next to the revised statement.

This was just the first lesson I planned to teach about multiplying fractions. In later lessons, I further developed the students' understanding and skills.

From Online Newsletter Issue Number 12, Winter 2003-2004

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Teaching multiplication of fractions is, in one way, simple-the rule of multiplying across the numerators and the denominators is easy for teachers to teach and for students to learn. However, teaching so that students also develop understanding is more demanding, and Marilyn Burns tackles this in her new book Teaching Arithmetic: Lessons for Multiplying and Dividing Fractions, Grades 5-6 (Math Solutions Publications, 2003).

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Common Core Resources | Inside Mathematics

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Inside Mathematics illuminates the mathematical practice standards with video excerpts of mathematics lessons.

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Please note: Although we have taken care to create all files so that they are as accurate as possible, some files may not print accurately. Computer and printer settings may affect the accuracy of items such as rulers and protractors.

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Module 2 serves as a bridge from students' prior work with problem solving within 10 to work within 100 as students begin to solve addition and subtraction problems involving teen numbers. Students go beyond the Level 2 strategies of counting on and counting back as they learn Level 3 strategies informally called "make ten" or "take from ten."

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Free Learning Printables 4 Kids | Pre-K to 2

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Free Learning Printables 4 Kids | Pre-K to 2

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Teacher Mama School | Free Printables for Kids | Literacy & Numeracy

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Free Learning Printables 4 Kids | Pre-K to 2

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Free printables and other resources to teach kids literacy and numeracy. For kids in levels Pre-K to 2.

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26 Addition Games for 1st Graders (Educational Fun Activities for Kids Online)

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26 Addition Games for 1st Graders (Educational Fun Activities for Kids Online)

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Addition with Sums Up to 18 - Grade 1 - Practice with Math Games

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Addition with Sums Up to 18 - Grade 1 - Practice with Math Games

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Looking for math centers for your 1st Grade classroom? Grab some FREE 1st Grade Number centers here!

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Thinking Blocks Junior | MathPlayground.com

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Model and solve word problems using interactive tape diagrams.

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Thinking Blocks | Model and Solve Math Word Problems

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Thinking Blocks | Model and Solve Math Word Problems

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NLVM Pre-K - 2 - Number & Operations Manipulatives

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NLVM Pre-K - 2 - Number & Operations Manipulatives

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NLVM Pre-K - 2 - Number & Operations Manipulatives

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NLVM manipulatives for Pre-K - 2 - Number & Operations

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K-5 Math Teaching Resources This site provides an extensive collection of free resources, math games, and hands-on math activities aligned with the Common Core State Standards for Mathematics. Printables are suitable for use in math centers, small group or whole class settings.