## 6th Grade Number Sense

**Note: the type of resource is bolded in the descriptive text.**

NS 1.1 ** Key Standard** – Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

Visual Fractions – An **online tutorial** that offers instruction and practice in identifying, renaming, and operating on fractions. All examples are modeled with number lines or circles.

Factor Trees – **PowerPoint slideshow** that could be used for direct instruction or small group instruction entitled Growing a Factor Tree – Click on Factor Trees to download the slideshow.

Fraction Tracks – From Annenberg/PBS Learning Channel. Learn how to play **a game **of “Fraction Tracks” with your students to encourage mathematical discourse and to enhance the players’ understanding of fractions. Sample plays and possible moves are given. There is an option for watching a video of the game in a classroom setting.

Comparing and Ordering Decimals can be good for your health. “Mathnavox” **interactive video **(Alberta CA Dept of Education) allows users to compare fat content of grocery products to find the most nutritious items. Students drag and drop decimal numbers onto a number line. Assessment tools are provided as a downloadable file.

Integer Arithmetic – **Interactive online math lesson** from the National Library of Virtual Manipulatives site. Includes ideas and examples to help teachers introduce their pre algebra students to the concepts, applications, and skills associated with integer operations. Students can manipulative onscreen tools, write mathematical sentences and explore mathematical patterns. Teacher section gives research-based strategies and suggestions for application of the lesson.

Comparing and Ordering Decimals. Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. Five minutes of free activity with this **gizmo from Explore Learning.**

Equivalent Fraction Circles – **Interactive exercise** in equivalent fractions from Visual Math Learning web site. Students find fractions on the left and right sides of the page that are equivalent to the fraction in the center and drag them to the interior of the large circle, where they get immediate feedback and visually see the representation. There are 16 choices and 4 right answers in every grouping.

Spy Guys: Understanding Integers Select Lesson 6 **video**. Covers positive and negative integers and the number line. These video and auditory tutorials from LearnAlberta.CA allow teachers and students to explore math concepts, pause and replay. Includes interactive exercises that provide immediate feedback. Printable worksheets, parent notes, and a glossary are included for each lesson. In addition to the lessons, there are sections on problem-solving strategies.

Spy Guys: Decimals – Select Lesson 1 **video**. Spy Guys Interactive 6th Grade Math Lessons (Alberta CA). Colorful tutorials with narration on decimal basics, interactive quizzes (that check for understanding and provide immediate feedback), printable student activities to reinforce the lesson, helpful notes for parents on what students are expected to know. Pause & Replay is available for each screen.

Spy Guys: Solving Problems with Decimals – Select Lesson 5 **video**. Spy Guys Interactive 6th Grade Math Lessons (Alberta CA). Colorful tutorials with narration on solving problems with decimals, interactive quizzes (that check for understanding and provide immediate feedback), printable student activities to reinforce the lesson, helpful notes for parents on what students are expected to know. Pause & Replay is available for each screen.

Learning Wave INTEGERS: Concepts & Applications – **Interactive Mathematics** by LearningWave.com Covers number line, pairing and ordering, absolute value, addition, subtraction, multiplication, division, equations, and an interactive skills review. There is a pre-test, post-test and clever **interactive games and exercises** that allow students to apply what they have learned. Includes printable worksheets, puzzles of the week,skill builder problems and highly motivating, interactive challenges from basic to advanced.

Learning Wave DECIMALS: Concepts & Applications – Interactive Mathematics by LearningWave.com Covers converting and comparing fractions to decimals, rounding decimals, estimating decimal operations, addition, subtraction, multiplication and division of decimals and an interactive skills review. There is a pre-test, post-test and clever **interactive games and exercises** that allow students to apply what they have learned. Includes printable worksheets, puzzles of the week,skill builder problems and highly motivating, interactive challenges from basic to advanced.

Learning Wave FRACTIONS: Concepts & Applications – Interactive Mathematics by LearningWave.com Covers fraction facts, fractions and ratios, equivalent fractions, converting fractions, addition & subtraction with like and unlike denominators, subtraction with borrowing, multiplying fractions reciprocals, dividing fractions. and and an interactive skills review. There is a pre-test, post-test and clever **interactive games and exercises** that allow students to apply what they have learned. Includes printable worksheets, puzzles of the week,skill builder problems and highly motivating, interactive challenges from basic to advanced.

Compare and order decimals, fractions, percents – Figure This! Math Challenge #14 :Batting Averages. One of a series of **NCTM standards-aligned math challenges** designed for students to work out with their families. Available in English and Spanish. Figure out who has the highest batting average between two players.

Compare and order decimals, fractions, percents – Figure This! Math Challenge #25 : Grape Juice Jungle . One of a series of **NCTM standards-aligned math challenges** designed for students to work out with their families. Available in English and Spanish. Compare two or more quantities to find out which grape juice recipe is juicier.

Compare and Order Numbers – **Shockwave audio and visual tutoria**l from Harcourt Publishers. Each screen includes a replay button.

Comparing Fractions – **NCTM/Illuminations Fraction Model applet **explores several models for representing fractions with adjustable numerators and denominators. You may also download an interactive Excel file.

Addition & Subtraction of Fractions using a TI Calculator and number line – Download instructions for using **the number line application** for a dynamic, visual representation of the number line that will help students build skills in comparing decimals, fractions and percents. Add and subtract integers with vector and arithmetic updates of the expression.

A Gigabyte of Music: How Much is That? Students gain experience in converting equations to fractions and converting one unit of measure to another as they solve the problem “How many CD’s does it take to download 5 gb of music?”** The activity** is provided by PBS.org and is tied into a news article from Jim Leher on illegal downloading of music by students. This activity can also be done on a TI calculator.

Decimals: Concepts & Computation – **PowerPoint presentation.**

Display Fractions in an Excel Spreadsheets – **Student acitivty** with Microsoft Excel, which can display fractions using numerators and denominators, rather than as decimals. When students need to see real fractions in cells, let Excel take care of the formatting for you. This special way of formatting numbers will especially come in handy when you need to add, subtract, multiply, or divide fractions.

Jenn’s Fish Tank: Difference of Two Fractions – **Math TV problem solving video**. Students must calculate the volume of water that a fish tank can hold. They know how much water Jen has added and how full the tank currently is. Onscreen audio and visual help is provided in setting up the problem and solving it. Once it is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

NS 1.2 ** Key Standard **– Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations ( a / b, a to b , a : b ).

Thinking blocks – Students learn how to solve challenging word problems dealing with ratio and proportion using **Thinking Blocks.** Thinking Blocks is an engaging, interactive math tool developed by classroom teachers to help students learn how to solve multi step word problems. Using brightly colored blocks, students model the relationships among the components of each word problem.

Brain POP Videos – **Video for fee** – choose Ratios

Brain POP – **Video for fee** – choose Proportions

Ratio & Proportion – **Video and auditory tutorial** from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. (You may need to set up a free user account to access this site and see all topics). Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the videos as needed. Requires Flash 6.

Exploring Rate/Ratio/Proportion – **this multimedia resource** from Junior High Interactives (learnalberta.ca) examines rate, ratio and proportion and shows how they play a role in photography. Using the interactive components, students explore ratio equivalencies by enlarging and reducing images to compare an original ratio and a target ratio. A print activity is included.

PBS Mathline: the Math of Bicycles– **Lesson plan/offline activity**. Students explore ratios by comparing bicycles to tricycles. They describe the ratio of the relationship between one turn of the pedal and one turn of the wheel, and define the ratio between number of teeth to sizes of the gears.

Spy Guys: Percents. **Video** – Select Lesson 4. These video and auditory tutorials from LearnAlberta.CA allow teachers and students to explore math concepts, pause and replay. Includes interactive exercises that provide immediate feedback. Printable worksheets, parent notes, and a glossary are included for each lesson. In addition to the lessons, there are sections on problem-solving strategies.

Spy Guys: Ratio. **Video** – Select Lesson 3. These video and auditory tutorials from LearnAlberta.CA allow teachers and students to explore math concepts, pause and replay. Includes interactive exercises that provide immediate feedback. Printable worksheets, parent notes, and a glossary are included for each lesson. In addition to the lessons, there are sections on problem-solving strategies.

Body Ratios – Modeling Middle School Mathematics project (MMSM) is a professional development program using **video lessons and Web-based Internet materials **to examine mathematical concepts. Video clips and full transcripts are provided of actual classroom situations in which the lesson is taught. In this lesson on ratios and scaled drawings, educators use the story of Gulliver’s Travels to pose the problem: how to make a shirt for someone who is much bigger.

Ratios and Equivalent Ratios – From Math.com. **In-depth tutorial** with java applets, visuals, examples and workouts. Could be used at home or in class for review or reteaching.

Proportions – From Math.com. **In-depth tutorial** with java applets, visuals, examples and workouts. Could be used at home or in class for review or reteaching

Using Scale Drawings – Floorplan Your Classroom – The** activities** presented here allow students to study mathematics by doing real-life architecture to walk through the floor plan design process. Look for measurement and drawing tips as you create a scale drawing on graph paper or using a computer drawing program.

Scale Factors – Figure This! Math Challenge #61 : Statue of Liberty. One of a series of **NCTM standards-aligned math challenges** designed for students to work out with their families. Available in English and Spanish. Learn about similarity and scaling by measuring the length of your nose and your arm in the same units. Then apply this knowledge to find out if the Statue of Liberty’s nose is too long.

Ratio & Proportions – Figure This! Math Challenge #47 : VCR Recording Tape . One of a series of **NCTM standards-aligned math challenges** designed for students to work out with their families. Available in English and Spanish. Develop proportional reasoning by solving this problem related to VCR Tape recording settings.

Great Cartoon Blow-up Activity **Students practice **drawing to scale and create blow-ups of their favorite Flintstone characters while learning about similarity

Proportional Reasoning: The Mixture Blues – Session 4, Part B. **Annenberg Media Lesson for teachers** to improve their own teaching practices. Includes **excellent teacher training videos** at the beginning of each session. In “Mixture Blues,” teachers compare mixtures of blue liquid and clear water and predict which set would be bluer. The video includes reflection on what has been learned.

Proportional Reasoning: QuadPerson – Session 4, Part C. **Annenberg Media Lesson for teachers **to improve their own teaching practices. Includes excellent teacher training videos at the beginning of each session. The lesson includes a scaling exercise with “Quadperson” that could be used with students and the video shows teachers using it in a learning situation. Participants learn the significance of relative vs. absolute change.

Proportioner – A **free resource** from the Concord Consortium’s “Seeing Math” Project. Proportioner allows students to specify image dimensions graphically, numerically or using a scale factor. They can duplicate images and modify comparisons or use one image to “paint” another. Interactives can be downloaded for offline use. There is a user’s guide, warm-up and sample activities.

The Right Ratio of Rest: Proportional Reasoning – In **NASA CONNECT™**: The Right Ratio of Rest: Proportional Reasoning, students learn about the human circadian clock and how it affects peoples’ daily lives. Students see how NASA scientists are studying the circadian timing system to improve astronaut’s physical and mental tasks while working in space. Conducting research to help astronauts sleep better in space also helps people on Earth with similar problems. The hands-on activity in this guide allows students to demonstrate how fractions, decimals, and percents are related and further develop their proportional reasoning skills. **Includes a 28-minute video** that can be paused at appropriate intervals.

NS 1.3 Key Standard – Use proportions to solve problems (e.g., determine the value of N if 4/7 = N /21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

Ratio and Proportion Game – Find out how to use ratio and proportion in everyday life. Students can view **tutorials on 6 related topic areas or play a shockwave game** from the BBC to practice writing ratios.

Understanding Rational Numbers and Proportions – **students use real-world models** to develop an understanding of fractions, decimals, unit rates, proportions, and problem solving. Illuminations/NCTM classroom activities.

Population Ratios – An **interdisciplinary project** (mathematics, social studies) where students choose a county in the United States and using ratios convert the statistics into meaningful numbers. Illuminations/NCTM classroom activity.

Proportions – BrainPop **video**. Students will write proportions to solve real problems.

Rags To Riches –**“Millionaire” style game** from Quia that quizzes students on proportions.

Solving Proportions – Glencoe **Online Study Tool **with hints for solving proportion problems.

Solve Proportions – Harcourt School Publishers **tutorial** on solving proportions. Includes auditory reinforcement and the ability to replay screens.

Scales, Ratio & Proportion – **Video and auditory tutorial** on working with scale drawings from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. (You may need to set up a free user account to access this site and see all topics). Designed as a homework help tutorial, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the video. Flash 6 required.

Scales, Ratio, Proportion Jeopardy Game – Use this ready-made** PowerPoint Jeopardy game** from Taft Middle School teachers to test student knowledge on ratios and unit rates, proportions, similar figures,scale drawings and probability.

NS 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

Election Night with Percent **– **A **graphing calculator activity** in which the students will work primarily with the concept of % of a number. They will calculate the number of people expected to vote when given the population and % of registered voters along with historical data on percentage of voter turnout. They will then use polls to graph predictions.

Using Percentages – Use this** tutorial **to calculate discounts and sale prices and work with percents to understand demographics.

Grid & Percent It – **Students use a 10×10 grid** to solve percent problems (Illuminations/NCTM activity).

Brain POP Videos – **Video for fee** – choose Finding Percents

Moneyopolis – This site offers some suggestions for middle schoolers on saving and budgeting money. There is a money management spreadsheet for kids you can print off, a set of financial planning steps and other useful resources to help you plan your earning and spending habits. The teacher section has lesson plans based on NCTM standards. The Moneyopolis game requires a student login but also complies with COPPA online privacy requirements.

The Discount is Right – **Web activity** from Mississippi Regional Educators for calculating original price, sales price and rate of discount. Includes student handouts and rubric.

Let’s Go Shopping – **Lesson plan and worksheets** from Beacon Lesson Plan Library. Students spend $500, determine discounts, convert percents and fractions to decimals, and calculate 7.5% tax amounts on purchases. They use ads from newspapers, catalogues and magazines to locate sale items. Could also be done as a spreadsheet activity

Calculating Discounts – **Math TV Problem Solving Videos**. Students follow along as their TV host (IQ) works through step-by-step solutions of a word problem; then they are invited to solve an interactive word problem of their own. They can replay the video as needed. The practice area is equipped with a notepad and calculator. Whole numbers, fractions, percentages, ratios, probability, algebra and geometry topics are explored.

Percentages –** **Figure This! Math Challenge #17 : Perplexing Percentages. One of a series of ∫ designed for students to work out with their families. Available in English and Spanish. Calculate the effect of consecutive discounts and determine which sale price is a better deal. Discover the relationship between fractions and percentages and when percentages might be more useful than fractions.

Markup Tutorial – AAAmath.com **math lesson**. Learn, practice, play, explore.

Discounts Tutorial – AAAmath.com **math lesson**. Learn, practice, play, explore.

Simple and Compound Interest – An overview of interest. After reviewing some basic facts about interest and the way it is calculated, students link to other sites on the Internet to try out a variety of financial calculators to experiment with the concepts introduced here. Through this **activity**, students will look at the basic concepts of savings and investing, and see how money can actually make more money.

Simple and Compound Interest –** Interactive gizmo for fee**, exploration guide and assessment questions. Great resource to accompany investment simulation project. Good follow-up activity to direct instruction. Real world application of math. Could be used with overhead to provide visual representation of key concepts. Subscription-based site. Explore Learning provides five free minutes of usage of any gizmo in their library.

**Middle School Lessons & Materials for Teachers – Fractions** – The **lessons and materials** available here come from a variety of sites and organizations. Some include offers for video or software, and some are lesson plans

**Math TV Problem Solving Videos**– to find an interactive **video lesson** on fractions – click on Roll’Em (the archive) and then select Fractions button. Click on Episode 1-differnce of two fractions

**Explore Learning Gizmo – Fractions with Unlike Denominators – Gizmo for fee – **In guided exploration, users find the sum or difference of two fractions with unlike denominators using graphic models. Find the least common denominator graphically. Subscription-based site but five minutes of free usage are allowed on each gizmo.

Visual Fraction – An **online tutorial** that offers instruction and practice in identifying, renaming, and operating on fractions. All examples are modeled with number lines or circles.

Adding and Subtracting Rational Fractions – **online review or homework help **from regentsprep.org

Saloon Snap –** Shockwave game** from the BBC. Students match fractions with decimals and percentages in a race to beat “Fast Fingers Malcolm.” Three levels of difficulty. Students lose points for guessing. Includes a tutorial of “key ideas” for converting fractions, decimals and percents. Colorful graphics that do not interfere with learning and onscreen tips make this an engaging choice for students in need of practice.

Interactive Fractions – From Learning Wave Online. Learn about fractions and ratios, equivalent fractions, addition and subtraction with like and unlike denominators, multiplying fractions, reciprocals and dividing fractions. **Includes printable worksheets**, puzzles of the week, skill builder problems and highly motivating, interactive challenges from basic to advanced.

Exploring Fractions – **Junior High Interactives video** illustrates how math is used every day in hotels and restaurants. In an interactive activity, students explore improper, mixed and equivalent fractions by using measuring cups to obtain a target fraction. Includes printable activity.

**Classroom Activity** – Company is Coming students will be able to multiply fractions & convert fractions in a **pancake recipe.**

Interactive Fractions – From Learning Wave Online. Learn about fractions and ratios, equivalent fractions, addition and subtraction with like and unlike denominators, multiplying fractions, reciprocals and dividing fractions. Includes printable worksheets, puzzles of the week, skill builder problems and highly motivating, interactive challenges from basic to advanced

Spy Guys Improper Fractions and Mixed Numbers. **Click on Lesson 2**. This video and auditory tutorial from LearnAlberta.ca allows teachers and students to explore math concepts, pause and replay. Learn how to show fractions and mixed numbers on a number line. Includes interactive exercises that provide immediate feedback.** Printable worksheets, parent notes**, and a glossary are included for each lesson. In addition to the lessons, there are sections on problem-solving strategies.

Multiplying Fractions and Mixed Numbers – **Step-by-step tutorial** from math.com. Includes practice and examples.

Fractions, Percents & Ratios: Multiplication and Division of Fractions – Session 9, Part A. **Annenberg Media Lesson for teachers to improve their own teaching practices.** Includes teacher training videos at the beginning of each session. Some of the applets could be used with students

Fractions, Percents & Ratios: Decimals & Percents – Session 9, Part B. **Annenberg Media Lesson for teachers to improve their own teaching practices**. Includes teacher training videos at the beginning of each session. Some of the applets could be used with students.

**– Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations that use positive and negative integers and combinations of these operations.**

*Key Standard*Adding and Subtracting Integers – using a **BrainPop video for fee.**

Integer Multiplication – using a **United Streaming video for fee**, Multiplying Signed Numbers The selected videos provide a concise explanation, with examples, for multiplying both positive and negative integers. Students will have an understanding of the multiplication of integers, both positive and negative, and be familiar with the rules governing integer multiplication.

Multiplying Integers – using MathStar New Media Project, Integers 3 **Following video modeling, students will complete lessons on adding, subtracting and multiplying integers.**

MathTutor: Integers A local San Francisco Bay Area middle school math teacher has created this website in support of integer teaching and learning. ** **e**There are videos, games, practice, and more**.

**Virtual Manipulatives** – Number Line Bounce

Everyday Math **Homework Help** – Adding and Subtracting Integers

Integers: Concepts & Applications – Interactive Mathematics by LearningWave.com Covers number line, pairing and ordering, absolute value, addition, subtraction, multiplication, division, equations, and an interactive skills review. **There is a pre-test, post-test and clever interactive games and exercises that allow students to apply what they have learned.**

Math League – This **reference guide** covers the basics of adding, subtracting, multiplying, and dividing integers. Also includes absolute value, integer coordinates, and comparing integers.

NS 2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

Middle School Lessons & Materials for Teachers Fractions – **The lessons and materials** available here come from a variety of sites and organizations. Some include offers for video or software, and some are lesson plans

** Visual Fraction** – An **online tutorial** that offers instruction and practice in identifying, renaming, and operating on fractions. All examples are modeled with number lines or circles.

Fraction Frenzy **– ****Equivalent Fractions Game** – Fun factor, motivational, engaging, clear objectives. Energizing, competitive element. Could be set up as team challenges. Good mental exercise for simplifying fractions. Immediate feedback. Challenging for GATE students. Performance is rewarded with more challenging problems and greater quantities of problems. Good review; use for minimum day, assembly day, fun Fridays activity.

Least Common Multiple – **Tutorial and math workout.**

Simplify Fractions – Harcourt Shockwave **audio and visual tutorial** that takes students through the process of finding the GCF

GCF & LCM – **Video and auditory tutorial** from the Tampa Educational Channel. One of over 30 topics specifically covering problem areas of middle school math. (You may need to set up a free user account to access this site and see all topics). Designed as a homework help site, this makes an excellent link for teachers to include on their own web pages. Students can pause and replay the videos as needed. Requires Flash 6. line.

Reducing Fractions –** Animated tutorial**, guided practice and assessment problems.

Equivalent fractions pointer –** Experiment** with the relationship between the values of equivalent fractions and areas within a square or a circle. (Shodor.org)

Fresh Baked Fractions – **Game of equivalent fractions** – Four levels of difficulty. Student selects entry level. Goal-oriented (24 correct answers needed for reward). Meter monitors progress toward goal. Multiple forms of immediate feedback. Clear, concise directions are readily accessible make it good for independent work. Opener or closing activity. Good for review before a test. Hones in on skill of selecting “wrong” answer, comparable to some CST questions.

Last Updated (Tuesday, 02 March 2010 16:48)