## 7th Grade Number Sense

**Tested on the CAHSEE**Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.

Exploring Exponents and Scientific Notation – **Junior High Interactive resource**. Includes a video that illustrates how math is used by paleotologists in the study of dinosaurs. An interactive activity allows students to sort and then order numbers that are expressed in scientific notation. A print activity about exponents can be downloaded.

Scientific Notation – For fee **Brainpop video** explains how to write scientific notation using planet distances as an example. It walks students through the process of converting positive and negative numbers into scientific notation. Can be paused or replayed. Includes an interactive quiz.

Converting Numbers to Scientific Notation – **Video 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.

Quick Math Scientific Notation – Very cool **JavaScript tool** from Quick Math that lets you plug in numbers and then it walks the user through steps that it took to arrive at the conversion to scientific notation. Eight types of problems are covered.

Scientific Notation Conversions – Write a whole number in scientific notation and vice versa. Follow the directions to **learn how to convert from scientific notation** to whole numbers using an online scientific calculator, then make your own examples. Uses Macromedia flash.

Scientific Notation Problem Generator – **JavaScript program** that lets you convert basic numbers to scientific notation.

Scientific Notation – From Argyll Math. **Explore** the components of scientific notation. Includes interactive exercises on converting between forms. Uses Macromedia flash.

**Key Standard**Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

MathStar New Media Project: Integers — **Complete lessons** on adding, subtracting and multiplying integers. Includes videos best practices and actual classroom footage as well as downloadable worksheets, matboard activities and links to other sites that enhance the lessons.

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

Math Star Lesson Links: Algebraic thinking for Middle School Students. Comprehensive **exploration of integers **through paper & pencil exercises, flash tutorials and games. Includes downloadable journals and options for pre-and post assessment quizzes. Each lesson is divided into four or five sub-topics with at least four activities in each.

Late Delivery – **Shockwave game**: Students learn about variable expression in this game of postman. Letters are used to represent numbers and students must do the math to deliver the right mail. Three levels of difficulty, onscreen help and printable prizes motivate them to learn.

Interactive Integers – From Learning Wave Online. **Learn interactively** about the number line, comparing and ordering, absolute value, addition, subtraction, multiplication & division of integers. Includes printable worksheets, puzzles of the week,skill builder problems and highly motivating, interactive challenges from basic to advanced.

Integer Operations (Addition) – This **activity from the National Library of Virtual Manipulatives** uses plus-minus chips to demonstrate adding positive and negative values. Students learn that a pair consisting of one positive and one negative has a value of zero and that they effectively cancel one another.

Integer Operations (Subtraction) – This **activity from the National Library of Virtual Manipulatives** uses plus-minus chips to demonstrate subtracting positive and negative values and helps conceptualize the combination of positive and negative numbers.

Integers – **PowerPoint Jeopardy Game** -Need to review Integers with your students? Let Alex Trabeck show the way with this ready-made Power Point that has built-in categories for addition, subtraction, multiplication and division, plus integer word problems.

Illustrating Integers – **PowerPoint Download** – This colorful Powerpoint presentation is a helpful introduction to addition, subtraction, multiplication and division of integers and is ideal for whole group instruction or a tutorial for students needing one-on-one help.

Circle 0, Circle 21, Circle 99 – **Puzzle activities** **from the National Library of Virtual Manipulatives** that involve adding positive and negative integers to reach specific sums.

Multiplying Integers/Quest for a Cubicle – **Clever interactive game** that has students work with positive and negative integers as they calculate answers to multi-step word problems, collect passwords and earn their way to their own cubicle. Three other integer games are available at this same site (Learning Wave).

**Factoring Numbers – tutorials** from PurpleMath.com with examples and practice problems.

Tutorial 1 Tutorial 2

**Tested on the CAHSEE**Convert fractions to decimals and percents and use these representations in estimations, computations and applications.

Fractions Pairs Game – **Shockwave skills game** from the BBC. Match fractions, decimals or percentage pairs and learn which are equal to each other. Three levels of difficulty, immediate feedback, onscreen help. Records how many tries it took to match all site.

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

Equivalent Fractions Pointer – In this **Interactivate activity,** students practice simplifying fractions, compare fractions and order them on a number line.

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.

Interactive Decimals – From Learning Wave Online. **Learn **about converting and comparing fractions to decimals, rounding decimals, estimating decimal operations and addition, subtraction, multiplication and division of decimals. 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.

Percent Tricks – Teach your student how to calculate percentages using the Percent Tricks method with **handout and lesson plan**.

Finding Percents – For fee, **Brainpop video** and interactive quiz on how parts of the day are spent.

Practice Using Percent Proportion – **Tutorial** for three types of questions and practice problems.

Proportions – This Web-Based Math Education (WBE) site offers colorful, **interactive tutorials** in 9 topic areas of 7th & 8th grade math. Each is divided into 10 or more sub-topics. The Proportions topic area offers a visual look at adjusting proportions and scale in five activities: Serving Apples, Visualizing Proportions, Another Look at Serving Apples, Making Lemonade and Building Model Airplanes.

Solving Equations with Fractions – Use this **PowerPoint** from Chipman Middle School teachers (Alameda, CA) to teach your students how to solve equations with fractions.

Percent III – PowerPoint Tutorial This highly visual **PowerPoint tutorial** by Monica Yuskaitis teaches students equivalent percents and the process for changing fractions to percents.

Percentages – **Virtual Manipulative:** Discover relationships between fractions, percents, and decimals by specifying two of the three quantities (part, whole or percent) and computing results.

Percentage Converter – **Virtual manipulative** that lends itself to a discussion of relations among fractions, decimals, ratios and percentages.

How students spend parts of their day. – A **spreadsheet activity**

How Do You Manage Your Time? – **Similar activity** with extensive handouts, activities and web resources.

Fractions In The Kitchen – Following the study of the addition, subtraction, multiplication, and division of fractions, the students **use the Internet to locate recipes that contain fractions. **This hands-on learning experience helps students recognize that fractions are used in everyday life. Students apply the rules for multiplication of fractions and for finding the least common denominator for a group of fractions. Lesson Plan includes downloadable student handouts and assessment.

Fraction Pie – **Discover relationships** between fractions, percents, and decimals with a fraction model applet using sliders to change values. Experiment with circles, rectangles and sets.

Fraction conversions – This **Interactivate activity** uses online manipulatives and allows the user to explore converting decimals to fractions and fractions to decimals. Includes assessment questions.

Fractions Four – **Another Interactivate online manipulative**. Practice converting fractions, percentages and decimals in a two-person competitive game.

Converting Fractions to Decimals – From AAAmath.com. **Learn-Practice-Play-Explore** venue for converting fractions to decimals and percents and reverse.

A Conceptual Model for Solving Percent Problems – Students use a 10 x 10 grid to represent given information and solve various percentage problems. **Lesson plan from Illuminations/nctm.org is included.**

Fractions & Decimals – **Streaming video** segments from Annenberg/PBS Learning Math series. Learn how to teach unit fractions and decimals, predicting remainders, converting decimals to fractions and watch a video on use of numbers in ancient Babylonia.

**Key Standard**Differentiate between rational and irrational numbers.

Rational and irrational numbers – For fee **Brainpop movie and interactive quiz** – Quick and simple explanations of rational numbers with examples. Built-in assessment with questions. Feedback given if questions are incorrectly answered more than once. Web of related topics included. Venn Diagram model used to show classification of types of numbers. Examples of repeating and non-repeating decimals are visually represented.

Introduction to rational and irrational numbers – **Lesson, student practice and teacher resources** for working with rational and irrational numbers.

Rational and irrational numbers – A **PowerPoint** introduction to rational and irrational numbers suitable for teacher presentation, review by students or for absent students.

Approximations of Irrational Numbers – **Lesson, student practice and teacher resources** for approximations of irrational numbers and discovering Pi.

Fact Monster Rational & Irrational Numbers – quick **tutorial**.

Rational Numbers – **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.

**Key Standard**Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.

Terminating & Repeating Decimals – Students learn to convert from terminating decimals to fractions and convert from single-digit repeating decimals to fractions using patterns. **Problems are solved using an onscreen calculator.**

Turn Repeating Decimals into Fractions– **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.

Repeating Decimals. **Annenberg Media multimedia resources** to help teachers increase their expertise and improve their teaching methods.

Repeating or Terminating? – **Check** to see if a fraction becomes a terminating or repeating decimal.

Terminating & Repeating Decimals – From Houghton Mifflin, **online coaching for teachers** on introducing the concept of terminating and repeating decimals.

**Tested on the CAHSEE**Calculate the percentage of increases and decreases of a quantity.

“Percent of” Word Problems – **PurpleMath tutorials** and practice problems on markup and markdown.

Percent of Increase & Decrease –** Learningwave.com tutorials** and colorfully illustrated interactive math challenges help students learn how to use formulas to solve percent problems.

Word Problems: Percent Increase & Decrease – **Excellent tutorial** from Algebra Lab on solving problems that deal with increase or decrease. Includes practice problems and the ability to check your answers.

Word Problems involving Percents – WebMath.com resource lets students find a **word problem** below that resembles the one they need help with, fill in the blanks, then click “Solve” to find the answer. Some coaching help is offered, based on input.

Glencoe Online Self-Check – **Quiz on Percent of Change**

Percentage of Increase Calculator – **Simple javascript tool** that lets students calculate the percentage of increase between two units. input.

Percent increase or decrease tutorial – “Out of” problems and “difference”** tutorial **and problems from “The Math Page” web site. Choose Lesson 30.

Then and Now – 7th Grade **Lesson Plan** from the Department of Education/National D-Day Museum.

**Key Standard tested on the CAHSEE**Solve problems that involve discounts, markups, commissions and profit and compute single and compound interest.

Perplexing Percentages – **Everyday real-world math challenge** from Figure This! site for the classroom or for families to do together. Students must determine if multiple successive discounts on clothing yield a lower price than one larger discount. They are given hints, things to think about and additional problems. Bilingual web site, indexed according to challenges and math strands. Each problem also contains bonus “interesting facts” related to the topic.

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

Let’s Go Shopping – **Lesson plan and worksheets** from Technology Innovation Challenge Grant site. 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 Playground. 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.

Calculating Simple Interest – **Learningwave tutorials and practice** on calculating simple interest, calculating sales tax and tipping.

Markup Tutorial – Triple A **Math tutorial and practice samples**.

Discounts Tutorial – Triple A Math **tutorial and practice samples**.

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 – For fee,** Interactive gizmo**, 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.

Compound Interest and Exponential Growth – Math.com **tutorial**

**Tested on the CAHSEE**Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.

Negative Exponents – PurpleMath.com **tutorial**.

Exponents – For fee, **Brainpop video** and adventure with Tim and Moby. Students discover how far it is to Mexico as they learn to convert numbers between standard and exponent form. Includes video and interactive quiz.

Working With Exponents – **Flash Video 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.

Working With Negative Exponents – **Flash Video 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.

Exponents (Multiplication, Division, Negative Exponents) – The user reviews the basic rules of working with exponents in algebra. After viewing examples of the rules, users can **interactively practice** solving problems with exponents.

Multiplying Exponential Expressions – **Explore Learning guided practice** in simplifying expressions using multiplication. Students choose the correct steps to multiply exponential expressions and use the feedback to diagnose incorrect steps.

Dividing Exponential Expressions – **Explore Learning guided practice** in simplifying expressions using division. Students choose the correct steps to divide exponential expressions and use the feedback to diagnose incorrect steps.

**Key Standard**Add and subtract fractions by using factoring to find common denominators

How to Add & Subtract Fractions – **Tutorial and examples **on adding and subtraction fractions with same and different denominators. Includes a practice game.

Primes, Factors & Divisibility – **Adventure into the world of numbers and their properties.**(Mathsyear2000.org)

Grid Game – **Shockwave game** from BBC Education. Find the factors, multiples, powers, prime and triangular numbers from the selection shown on the grid and see Pythagoras and Hypatia jump for joy. Key ideas and three levels of difficulty are available. The higher level also covers squares and cubes.

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** from Math.com

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

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

Multiplying and Dividing Fractions – Flash-based** animated fraction tutorial, guided practice and assessment** from kidsOLR.com. Includes improper fractions and mixed numbers.

Math Splat – **Shockwave game** from the Family Education Network with three levels of increasing difficulty. Students swat bugs from a windshield by correctly solving equivalent fraction problems. Some problems can be challenging. Would be good for work with partners. Limited number of problems available.

Equivalent fractions pointer – **Interactivate 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** – FunBrain activity with 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.

Fractions with unlike denominators – **Exploration and guided practice**

Fraction Sorter – **Practice** fractions and get a better understanding of them with two different aspects of fractions: making them and putting them in order from least to greatest.

GCF and LCM – **Flash Video 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.

**Key Standard tested on the CAHSEE**Multiply, divide, and simplify rational numbers by using exponent rules.

Adding and Multiplying Integers – **Series of lessons and quick time videos** from the MathStar New Media Project that model how to teach addition and subtraction of integers. Teacher PD Lessons include video clips, worksheets, flash activities, web resources, user guides, standards, discussions etc.

Simplifying with Exponents – **Tutorial** from PurpleMath.com

Exponents and Power Rules – **This for fee Gizmo®** generates problems involving exponents; includes assessment questions. Pay-for-use site with five minutes of free usage per gizmo.

Multiplying Exponential Expressions – **Interactive gizmo** for fee. Students drag tiles with correct answers into a problem area to simplify expressions. They choose the correct steps to multiply exponential expressions and use the feedback loop to diagnose incorrect steps. Pay-for-use site with five minutes of daily free usage per gizmo.

**Tested on the CAHSEE**Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.

Square Roots – **Explore Learning Activity**. Students explore the meaning of square roots using an area model. They use the side length of a square to find the square root of a decimal number or a whole number.

Square Roots – Tim & Moby explain square roots and find the area of a baseball diamond. **BrainPop movie and interactive quiz**. For fee.

Square Roots **Matching Game/Concentration** – Find the square root of a perfect square number by matching squares or through a game of concentration (Quia).Game 1 Game 2

Ordering and Approximating Square Roots – **Explore Learning module.** Students order square roots on a number line. They approximate the square roots using the side lengths of square regions in a grid.

Looking for Squares – **Best Practices video streaming lesson** for teachers from the Modeling Middle School Math Project. Students find the area of a square and look at its dimensions. They complete exercises that help them determine the relationship between area and side length. The class investigates estimation strategies for finding square roots.

**Key Standard tested on the CAHSEE**Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.

Absolute Value – For fee, **BrainPop video** to learn about the absolute value of positive and negative integers with Tim & Moby.

Absolute Value – **A student tutorial and practice** of the absolute value concept at the MathStar website.

Absolute Value – “Mathulator” is an **online tool** that can help students understand the concept of absolute value by explaining sample problems and by evaluating whether statements are true or false. The graphing component is simple to use and can plot simple functions.

Absolute Value – **Explore Learning online simulation** that allows students to manipulate a number line to compare the opposites and real values of numbers.

Are You Absolutely Sure of the Value? – **Group Activity**. Students develop an understanding of absolute value through real world situations by participating in tasks that represent a situation where absolute value is appropriate. They use symbolic algebra to represent and explain mathematical relationships.

Comparing and ordering integers – **guided practice and exploration**.

Last Updated (Wednesday, 10 March 2010 11:21)