Middle School Math Resources

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This secton of the MSM is an extensive collection of resources for math teaching and learning and testing review:

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Math Test Prep Resources

Wednesday, 10 March 2010 11:31 | Written by Micheline LeBlanc |

CAHSEE and Middle School Math CST Resources

	Blueprints	Practice/Released Test Questions	Other Resources
6th	Blueprint Grades 2 - 7	Released Test Questions for 2003, 2004, 2005 CST Review Jeopardy PowerPoints, created with the CST released test questions: Algebra & Functions Game Number Sense Game MG & SDP Game	CAHSEE practice CAHSEE released questions 2004 (PDF) CAHSEE released questions 2005 (PDF) CAHSEE teacher guide CAHSEE study guide CAHSEE in the Classroom Series California Mathematics Content Standards CAHSEE Math Reasoning (PDF) Math Standard matrix at the SCORE math site
7th	Blueprint Grades 2 - 7	Released Test Questions for 2003, 2004, 2005 CST Review Jeopardy PowerPoints, created with the CST released test questions: Algebra & Functions Game Number Sense Game MG & SDP Game
Algebra	CAHSEE Blueprint CST Algebra Blueprint	Released Test Questions for 2003, 2004, 2005 CST Review Jeopardy PowerPoints, created with the CST released test questions: Linear Equations Exponents Game System of Equations, Rational Exp, Factoring, & Polynomials Game Quadratics, Rate/work problems, Misc. Game

Last Updated (Monday, 05 April 2010 15:45)

7th Grade Algebra and Functions

Wednesday, 10 March 2010 10:20 | Written by Micheline LeBlanc |

Number Sense | Algebra & Functions | Measurement & Geometry | Statistics, Data, Probability

AF 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:

AF 1.1 Tested on the CAHSEE Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).

Writing Algebraic Equations - Tutorial and practice

Balance Beam Activity - Solve simple linear equations using a balance beam representation.

Balance Beam Solving equations - Interactive text (itext) from Prentice Hall. Includes a teacher QuickTime video explaining the process of balancing equations. Could be used with previous activity.

The Language of Algebra - The user can practice their understanding of algebraic terms, the correct order of operations, and how to write equations and inequalities as they take an online interactive quiz. (Math.com)

Writing Inequalities - Students learn how to write inequalities from sentences. After viewing examples, users can interactively match sentences to the equivalent inequality. (Math.com)

Using Algebraic Equations – Explore Learning gizmo, for fee. Students translate equations into English sentences and translate English sentences into equations. Read the equation or sentence and select word tiles or symbol tiles to form the corresponding sentence or equation.guided practice and exploration.

AF 1.2 Tested on the CAHSEE Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)

Expression Maze - Practice evaluating expressions with this printable and fun maze game from Harcourt.

Lesson on Order of Operations - Tutorial on the Order of Operations followed by a set of problems.

Order of Operations - The user reviews the rules for the order of operations for a given expression. After viewing examples, users can interactively practice evaluating expressions following the rules for the order of operations.

Order of Operations - Mathcasts by students simplying expressions using the correct order of operations.

Order of Operations - Exploration guide, interactive applets and assessment questions.

Order of Operations - Brainpop Movie and Interactive Quiz, for fee.

Order of Operations - 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.

AF 1.3 Key Standard Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.

Interactive Number Theory - From Learning Wave Online. Learn about order of operations, commutative and associative properties of addition and multiplication, distributive property, and additive property of zero. Practice Problems. Numerous interactive challenges provide motivation and give students a rigorous workout.

Associative Property – BrainPop movie and interactive quiz, for fee.

Commutative Property – BrainPop movie and interactive quiz, for fee.

Distributive Property – BrainPop movie and interactive quiz, for fee.

Properties Drill - use this Powerpoint properties drill to assess student understanding of additive, commutative, associative and distributive properties.

Multiplication Properties - Students can test their knowledge of properties with this AAAmath.com practice game. Provides instant feedback and scroring.

AF 1.5 Tested on the CAHSEE Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

Identifying qualitative graphs - This activity is a downloadable file in PDF format with a series of graphs. Students choose the graph that best describes the situation presented.

Create A Graph – interactive site allows students to communicate information visually through construction of area, bar, line and pie charts with single or multiple data sets.

Bar & Line Graphs - Video tutorial on creating bar & line graphs 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.

Using Tables, Rules and Graphs – Explore Learning guided practice and exploration. Students compare the graph of a linear function to its rule and to a table of its values.

Make a Rule - This interactive activity from PBSTeacherLine Interactives demonstrates the relationship between a real-life situation, the values it presents and the mathematical equation that generates those values. This activity could be used in combination with a graphing activity.

Slope and Y Intercept - Tutorial on graphing equations and inequalities, followed by examples and practice problems. Student gets immediate feedback if they answer incorrectly.

Math Forum Web Unit on Graphs - Unit on graphs with everything you need to know about bar graphs, pie charts, pictographs and graphing linear, polynomial and exponential functions.

AF 2.0 Students interpret and evaluate expressions involving integer powers and simple roots:

AF 2.1 Tested on the CAHSEE Interpret positive whole number powers as repeated multiplication and negative whole number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.

Explore the Multiplication of Integers - Videotape Project: The concept of multiplication of positive and negative integers is cleverly presented using backward & forward motion of students walking and forward/reverse actions of a video camera to encourage understanding, not simply rote memorization of facts. Complete lesson plan and worksheets are included.

Arithmetic Four - Practice with positive & negative whole number and integer addition, subtraction, multiplication and division. Two-player timed game with three levels of difficulty. Exploration questions are also offered as an extension of the activity.

Rational Exponents - Rules for working with fractional (rational) exponents.

Order of Operations with Exponents - Mrs. Glosser’s Lesson on order of operations with exponents. Gives a helpful mnemonic for remembering the order of operations. Includes examples and practice problems for this skill.

Multiplying Exponential Expressions - Practice simplifying expressions with assessment questions.

Dividing Exponential Expressions – guided practice simplifying expressions.

AF 2.2 Tested on the CAHSEE Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer component.

Rules of Exponents - Students learn the rules of exponents and solve easy, difficult or random problems.

Multiplying Exponential Expressions - Students use tiles to simplify expressions. They are given expressions and asked to rewrite them with a single exponent. Tips are offered to further understanding. Multiple-choice questions follow for assessment.

Dividing Exponential Expressions - Students must simplify exponential expressions as described above.

AF 3.0 Students graph and interpret linear and some nonlinear functions.

AF 3.1 Tested on the CAHSEE Graph functions of the form y = nx and y = nx and use in solving problems.

Understanding linear equations - Tutorial: one-step, single-variable, first-degree linear equation, using a variety of methods.

Quadratic and Absolute Value Functions - Exploration and guided practice.

AF 3.3 Key Standard tested on the CAHSEE Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a graph.

Point-Slope Form of a Line – exploration and guided practice.

Rate of Change in Linear Functions Using Interactive Graphs - Interactive applet from NCTM.

Slope Slider - online manipultive to experiment with slope and y-intercept, from Interactivate.

AF 3.4 Key Standard tested on the CAHSEE Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

Exploring Linear Data - Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students can work alone or in small groups to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.

Zona Land - Experiment with changing the values for the slope and y-intercept and visualize how it affects the graph of the equation y=mx+b.

AF 4.0 Students solve simple linear equations and inequalities over the rational numbers:

AF 4.1 Key Standard tested on the CAHSEE Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

Algebra Four Game - This activity is similar to Connect Four, and is designed for two players. The goal is to have four pieces of the same color connected either horizontally, vertically, or diagonally. To earn a piece, you need to correctly solve an algebraic equation. Solving an algebraic equation means finding the value of an unknown value in an equation that makes that equation true. For equations in the Algebra Four activity, you will be asked to find solutions to single variable equations.

Equation of Mystery Game - Solve extraterrestrial math equations in the Cargo Bay with this shockwave version of Astro Algebra from Harcourt Brace and Edmark. Click and drag tiles to complete hidden equations.

Equation Match - Shockwave game from the BBC. Students match pairs by working out the values in each equation. Includes help file of “key ideas” in solving an expression.

Modeling and Solving two-step equations – interactive math applet.

Solve two-step equations - BrainPop movie and interactive quiz, for fee.

Solving Inequalities – BrainPop movie and interactive quiz, for fee.

Solving Linear Equations - Tutorial & Practice

Solving Inequalities - Students can read the tutorial, see examples and interactively practice solving equations and inequalities for the variables with a quiz.

Two-Step Equations and Inequalities - Students learn to solve equations that have more than one operation, see examples and interactively practice solving equations.

AF 4.2 Key Standard tested on the CAHSEE Solve multi-step problems involving rate, average speed, distance, and time or a direct variation.

Distance, Rate & Time: For fee, BrainPop video and quiz: Tim & Moby discuss the formulas for problems involving distance, rate & time and solve a traveling train problem.

Rate/Time/Distance Problem : Math TV Problem solving video. How long will it take a cyclist to catch up with her friend on her bike? Infinity Quick (IQ) leads students through word problems with step-by-step solutions, followed by an interactive word problem similar to the one in the video. Includes practice area, online calculator and notepad.

Understanding Distance, Speed, and Time Relationships - Using Simulation Software: students control the speeds and starting points of runners, watch a simulated race, and examine a graph of the time-versus-distance. They analyze change that occurs as they manipulate the environment.

Learn about Rate of Change in Linear Functions - Using Interactive Graphs: Constant Cost per Minute.

Distance, Time and Speed Graphs – guided practice and exploration with two runners.

Distance-Time Graphs – guided practice and exploration with two runners.

Distance, Rate, Time Word Problems – teacher lesson plan with suggestions for guided and independent practic

Distance, Rate, Time - Prentice Hall tutorial with checks for understanding.

Distance, Rate & Time - Practice Word Problems that involve distance, rate and time. Hints for up to five steps in the process are given.

Last Updated (Wednesday, 10 March 2010 11:18)

7th Grade Statistics, Data Analysis, and Probability

Tuesday, 09 March 2010 11:08 | Written by Micheline LeBlanc |

Number Sense | Algebra & Functions | Measurement & Geometry | Statistics, Data, Probability

SDP 1.0 Students collect, organize and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet program.

SDP 1.1 Tested on the CAHSEE Know various forms of display for datasets including stem-and-leaf plot, box-and-whisker plot; use the forms to display a single set of data or compare two sets of data.

Exploring Data - Curriculum support materials for teachers of introductory statistics. From Boxplots and datasets to linear regression and probability, find everything you could possibly need. Many topics contain worksheets and downloadable files.

Olympic Records Through Time – Graphing activity that shows trends in performance over time.

Create A Graph – Interactive site allows students to communicate information visually through construction of area, bar, line and pie charts with single or multiple data sets.

Growing, Growing, Graphing! - Population Growth lesson plan from WNET Thirteen Ed Online. Nicely detailed lesson plan with teacher resources, student activities, and tips for doing this activity as a one-computer classroom, with multiple computers or in a computer lab.

Line Plots – Guided practice and exploration with comparison data.

Trashketball - Modeling Middle School Mathematics site uses QuickTime video lessons to model best practices. In this game of "trashketball," students take their best shots with their left hand and right hand, then compare data sets. They learn about stem-and-leaf plots and analyze the data to find the mean, median, mode, cluster etc. Includes discussion and reflection.

SDP 1.2 Tested on the CAHSEE Represent two numerical variables on a scatter plot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).

Scatter Plots, Activity A – Guided practice and exploration with scatter plots in relating two sets of data.

Scatter Plots - Students collect data about two different characteristics within a population and plot data using virtual manipulatives to investigate whether there is a relationship between two variables.

Correlation – Explore correlation coefficients and estimation of line of best fit.

SDP 1.3 Key Standard Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.

Mean, Median, and Mode - A video - At the bottom of this page is a catchy tune that your students will enjoy to review the concepts of mode, mean, and median.

Box Plots - Students explore maximum, minimum, median, upper quartile, lower quartile and outliers while learning how to draw box plots.

The Pizza Palace - Students (in groups of 3) design a pizza and use a calculator to find out its cost. They record the mean, median and mode for the prices of three pizzas and demonstrate positions on a box plot.

Box Plot/Histogram - Students record data from a data set and use a box plot or histogram to represent their data.

Box and whisker plots – Explore the relationship between data points and box-and-whisker plots.

Stem & Leaf Plotter - This activity generates a stem and leaf plot from data that the user enters. Users must have data to enter in order to effectively use the applet. This activity would work well in groups of two to four. Includes exploration questions and discussion.

If A Tree Fell In the Woods, Would It Be Part of A Stem-And-Leaf Plot? - Students will learn about stem-and-leaf plots and compare the visual display of these plots with those of bar, line, and pie charts in order to determine when stem-and-leaf plots offer the best option for displaying a data set.

Last Updated (Wednesday, 10 March 2010 11:20)

7th Grade Measurement and Geometry

Tuesday, 09 March 2010 11:22 | Written by Micheline LeBlanc |

Number Sense | Algebra & Functions | Measurement & Geometry | Statistics, Data, Probability

MG 1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:

MG 1.1 Tested on the CAHSEE Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).

Velocity & Acceleration: Sea World Physics

Measuring Speed with iMovie - Using a digital camcorder, iMovie, and a spreadsheet program, students measure the speed of a variety of objects (running, walking, throwing a ball). They use a spreadsheet and the number of video frames per second to compute the speed in miles per hour. iMovie and spreadsheet activity.

The Race - This math applet from PBS Teachers Online provides a visual and a graphical comparison of actual speed and average speed over an entire race. Within the problem there is a link to an interactive that relates a visual image of a race with its graphical representation.

Comparing Mixtures: Mixing Orange Juice - From PBS Teachers Online. Students use a java applet to “mix orange juice” concentrates with cans of water as they solve problems on ratio and proportion and explore “orangeyness” of their mixtures. Addresses the misconception that proportionality is based on additive relationships.

Units of Measurement - Powerpoint jeopardy game.

Ratio and Earned Dollars - Math Playground Word Problem. How much money did each of two web site designers make? Onscreen audio and visual help is provided in setting up the problem and solving it. Once the problem is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

Quick Landscaping - Math Playground Word Problem. (Area and proportional reasoning). How long will it take Jamie to mow a square lawn if we know the time it takes him to mow a smaller lawn? Onscreen audio and visual help is provided in setting up the problem and solving it. Once the problem is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

MG 1.2 Tested on the CAHSEE Construct and read drawings and models made to scale.

Great Cartoon Blow-Up Activity. Students practice drawing to scale and create blow-ups of their favorite Flinestone characters while learning about ratio of simultude.

Scales, Ratio & Proportion - Video 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.

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.

Ratio & Proportion - Tutorial/Practice from the Math League.

Introduction to Ratios - Math.com interactive tutoring and practice.

Estimator - Interactivate activity. Solve problems involving scale factors, using ratio and proportion; Students practice estimation skills by determining the number of objects, length, or area.

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. (English/Spanish).

MG 1.3 Key Standard tested on the CAHSEE Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.

Distance, Rate & Time - For fee, Brainpop movie and interactive quiz.

Going Nowhere Fast - Math Playground video word problems. Students must solve a swimming pool problem fill and draining problem that involves work, rate and time. Onscreen audio and visual help is provided in setting up the problem and solving it. Once the problem is solved, students are given another problem to solve and can make use of the practice video, a scratch pad and calculator.

Rate of Work Problems - How long does it take Bart vs Homer to wash the family car? Colorful PowerPoint covering rate-of-work math problems that involve the entire Simpson family.

MG 2.0 Students compute the perimeter, area and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area and volume are affected by changes of scale.

MG 2.1 Tested on the CAHSEE Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

What on Earth is Greater Than? – Lesson Plan

Surface Area and Volume – Manipulate a three-dimensional polyhedron to experiment with surface area and volume.

Circle: Perimeter, Circumference and Area – Resize a rectangle, circle, or square and find its perimeter or circumference and area. Superimpose a grid on the figure to estimate its area.

Find the Area of a Shape - Investigate area of parallelograms, triangles, trapezoids and circles with colorful manipulatives and answer questions to test understanding.

Designing Packages - Modeling Middle School Mathematics lesson and activity uses QuickTime video of actual teacher, group and student work to model best practices in teaching mathematics. A full transcript of the video is provided. In this activity, students learn what surface area and volume mean mathematically by designing packages that will house 24 blocks (representing toys) and calculating the surface area of prisms.

Shape Explorer - Students test their skills at calculating the area and perimeter of a given figure. Includes exploration questions and teacher coaching materials. (Shodor.org)

Learn about Length, Perimeter, Area, and Volume of Similar Objects by Using Interactive Figures - This interactive activity allows users to explore the relationship between volume and surface area of a given shape.

Using Spreadsheets to find area and perimeter – Classroom spreadsheet exercises, activities and instructions for teachers.

Length, Perimeter, Area & Volume - NCTM Illuminations Interactive. Students experiment with rectangles of different shapes and scale factors relative to side lengths and observe and interpret changes in perimeter and area. In Part II, they also learn about side length, volume, and surface are of similar solids.

Automatic Circle, Sphere & Cylinder Calculator (Includes Formulas)

Classify Polygons - Annenberg Media/Learning.org activity. Tutorial and practice in grouping polygons according to certain properties.

MG 2.2 Tested on the CAHSEE Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.

Pyramids - Tutorial, examples and workout problems for calculating the volume of a pyramid.

Area of a Trapezoid - The 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 Area & Perimeter of a Trapezoid activity allows students to move the four vertices of a figure to make their own trapezoid and creates awareness that the area of a trapezoid can be calculated by adding the areas of the two triangles together. There are diagram exercises to complete, questions to answer (immediate feedback is given), and a summary writing activity, complete with writing tablet.

MG 2.3 Tested on the CAHSEE Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.

Surface Area of a Tetrahedron - Using a digital camcorder and iMovie, students practice reciprocal teaching by making a 3-minute movie on a real world application of math.

Volume of a Cube - NCTM Illuminations Interactive. Students determine the volume of a box by manipulating unit cubes.

Surface Area and Volume - Students manipulate three-dimensional polyhedra to experiment with surface area and volume. Includes worksheets and discussion.(Shodor.org)

Similar Solids - A PowerPoint presentation explaining the scale factor and other properties of similar solids.

Covering the Plane with Rep-Tiles - In this activity, students discover and explore a special kind of tiling of the plane. Rep-tiles are geometric figures such that n copies can fit together to form a larger, similar figure.

Linking Length, Perimeter, Area, and Volume - Five lessons: The first is an online pre-activity to build students’ understanding of ratio, proportion and similarity. Another online pre-activity follows with similarity and scale factor. The third lesson involves students comparing perimeter and area ratios of similar rectangles with various scale factors using an e-manipultive which is the basis for the fourth and fifth lessons. The fourth lesson focuses on the relationship between scale factor and volume. The final lesson highlights the surface area for rectangular prisms in relationship to scale factor.

Surface Area and Volume - This lesson is designed to introduce students to surface area and volume.

Student-made videos - These movies were made by students to teach a math concept.

MG 2.4 Tested on the CAHSEE Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft] = [144 in], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in] = [16.38 cm].

Side Length, Volume, and Surface Area of Similar Solids - Java Applet that lets the user manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships among edge lengths, surface areas, and volumes.

Comparison of volumes with Similar Solids - Lesson, practice and teacher resources for determining volumes of similar solids (Regents Exam Prep).

MG 3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:

MG 3.2 Tested on the CAHSEE Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

Points in the Coordinated Plane – plot order pairs, x and y values and work within quadrants. Guided practice and exploration.

Coordinates Game - Java Activity allows the user to plot points on the coordinate plane and to read the coordinates of a point plotted by the computer.

Maze Game - Users practice their point plotting skills by moving a robot through a minefield to a target location. Moves are accomplished by specifying the coordinates of the new location. In order to win, the path must not cross a mine.

Mathsnet: Interactive Rotations, Reflections and Translations - Students observe reflected shapes, answer quiz questions on reflection, practice creating reflections and mirror lines. Includes sections for investigating rotations and translations.

MG 3.3 Key standard tested on the CAHSEE Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.

Pythagorean Theorem - Video tutorial on understanding the Pythagorean theorem. 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.

Geoboard: Pythagorean Theorem – guided practice and exploration using and interactive geoboard.

Pythagorean Explorer – Find the length of a triangle and check answers.

Walk through a visual proof of the Pythagorean theorem

Figure out the Pythagorean Theorem - This lesson is intended for students to work on their own and provides java applets for them to figure out the theorem on their own and understand it. It includes, tips, practice problems using onscreen manipulatives and history about Pythagoras.

Animated Proof

Explore Learning: Pythagorean theorem – Interactive guided exploration.

Pythagorean theorem – What is it and how does it work? PowerPoint presentation walkthrough suitiable for teacher presentation or student review.

Squaring the Triangle - learn how the Pythagorean Theorem works through investigating the standard geometric proof.

MG 3.4 Key Standard tested on the CAHSEE Demonstrate an understanding of conditions that indicate two geometric figures are congruent and what congruence means about relationships between the sides and angles of two figures.

Congruence Tutorial and Math Applet - Students manipulate shapes to show that they can be fitted exactly over each other by rotation, translation and reflection. Shows multiple examples of congruence (side-angle-side, angle-side-angle, side-side-side.

Congruence Theorems - Explore the conditions that guarantee uniqueness of a triangle, quadrilateral, or pentagon regardless of location or orientation. Each set of conditions results in a new congruence theorem.

Explore Learning: Congruence in Right Triangles - Exploration: Apply constraints to right triangles, drag their vertices and determine conditions of congruence.

Proving Triangles Congruent – guided practice and exploration.

Congruent triangles - This virtual manipulative allows students to construct two triangles from various combinations of sides and angles. You can choose to work with any one of four different cases.

MG 3.6 Key Standard Identify elements of the three dimensional geometric objects (e.g. diagonals of rectangular solids) and describe how two or more objects are related in space (e.g. skew lines, the possible ways three planes might intersect).

Investigating Parallel Lines and Planes – exploration and guided practice with parallel, intersecting and skew lines.

Points, Lines & Intersections - Definitions, explanations and examples for lines, points, intersections, line segments, rays, endpoints and parallel lines.

Geometry in Tessellations - Students examine tessellations and their geometric properties. The activity and discussion may be used to develop students' understanding of lines, planes, angles, and polygons.

A Math Dictionary: Skewed Lines - Description of skew lines along with a visual representation. Use the links to related terms, everyday examples, more information, and the interactive checkpoint involving skew lines located in the left-hand column.

Last Updated (Wednesday, 10 March 2010 11:19)

7th Grade Number Sense

Tuesday, 09 March 2010 10:06 | Written by Micheline LeBlanc |

Number Sense | Algebra & Functions | Measurement & Geometry | Statistics, Data, Probability

NS 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:

NS 1.1 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.

NS 1.2 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

NS 1.3 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.

NS 1.4 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.

NS 1.5 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 Decimal Rings

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.

NS 1.6 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.

NS 1.7 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.
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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

NS 2.0 Students use exponents, powers, and roots and use exponents in working with fractions:

NS 2.1 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.

NS 2.2 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.

NS 2.3 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.

NS 2.4 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.

NS 2.5 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)

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