8th Grade -  Math

8th Grade Math Skills

SB-You may need to download the smart board program to use some of the following links.  This may be done by clicking on the following download version 9.5 .  Once you have done this you will be able to view and use the smart board activity.    Every Smart Board activity has the letters SB  for Smart Board next to it. SB
 

= a site for teachers | = a PowerPoint show | This is an Adobe Acrobat document= Adobe Acrobat document | Word document  = Video

Math
Worksheet Generator - This web site will allow you to create printable math worksheets from your browser.  (addition, subtraction, multiplication, division, mixed problems, fractions, measurement, fractions, graphing, telling time, and a one-hundred chart)

Measurement Standard

Geometry and Spatial Sense Standard Patterns, Functions and Algebra Standard Data Analysis and Probability Standard

  Number, Number Sense and Operations Standard 

(Based on Ohio State
Curriculum Standards)

 

1.   Use scientific notation to express large numbers and small numbers between 0 and 1.

  1. Mathematics in the Movies -  This is a collection of movie clips in which Mathematics appears in movies.   Interesting idea!!
  2. Math Dictionary animation for kids  This is an outstanding website allowing you to explore a comprehensive view of math with many examples  4 Star
  3. Composite and Prime numbers
  4. Prime Numbers - Prime Number Sieve: "Remove all proper multiples of the next remaining number." Start with the number 2.When all proper multiples of all numbers in the first row are deleted, the table will contain only primes.
  5. Kids Port.  Great site to assist in all areas
  6. Scientific Notation  This is a Smart Board activity that is very well put together.  SB
  7. Origin of Zero  How would math be different without zero?  You may download a quite detailed power point illustrating this point.   The author for this presentation is Michelle Yee SB

  8. Scientific Notation   Smart board Assignment.   SB

Gizmos are fun, easy to use, and flexible enough to support many different teaching styles and contexts. 

You will present to your students a visual animated manipulative allowing for an easier and faster teaching pedagogy.

You will discover this tool strategically located throughout the website.

 

2.      Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system.

  1. You want to be a Math Millionaire.   All students will enjoy this site as well as teachers.  It is fun to do and see if you can make it to the Millionaire spot.  This is an outstanding website.
  2. The Learning Equation Math   Explanation of the Real Number System & Number Munchers Game (scroll down to Number System Descriptions)

  3. All the rational and irrational numbers   Examples of the subsets of the Real Number System

  4.  The Math forum      Explanation of Integers, Rational, & Irrational

  5.  The Number System      Explanation of Natural Numbers, Integers, Rational, & Real

3. Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals.

 

  1. Simplifying Multiplication  This web site teaches about simplifying expressions by multiplying algebraic terms with exponents, and then has an interactive quiz to test what was learned.
  2. Polynomial Exponents  This web site teaches about simplifying polynomial expressions involving exponents, and then has an interactive quiz to test what was learned.
  3. Simplifying Negative Exponents  This web site teaches about simplifying integer expressions with negative exponents, and then has an interactive quiz to test what was learned.
  4. Simplifying Fractions With Negative Exponents  This web site teaches about simplifying algebraic fractions involving exponents, and then has a quiz to test what was learned.
  5. Lesson on Order of Operations This is a collection of online lesson that students can read through with good examples and explanations of order of operations. Each finishes with an interactive quiz the student can take right on the web page to see if they understand the material.
  6.  Order of operations    Lesson on Order of Operations with exponents and practice
  7. Smart Board Lesson Created by:  Elaine Tsoumas  SB

     

4.   Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations.
 

  5.  Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than.

 
  1. Math Continuum    This web page will take you and your students to new heights in learning about math.  You only need to click on the hyperlink to explore another dimension.
6.   Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.
  1. Mathway This a step by step math solver for General Math, Geometry, Algebra, Pre Algebra, Trigonometry, Pre-calculus, Calculus.  A great program to show students step by step directions and also allow a teacher to create a presentation to be used on their LSD projector.  This is a great tool for facilitating and allowing at teacher to better present their instruction.   4 Star

  7.  Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g.,  is between 11 and 12.

 

  1. Relationship between Squares and Square Root     Squares, Square Roots, Approximating, & Calculator (scroll down to “Estimate the Square Root” for an explanation)
  2.  Table of Squares and Square Roots  Using a square root table to approximate square roots
  3. Square root flashcards

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  8.  Add, subtract, multiply, divide and compare numbers written in scientific notation.

 

 

Measurement Standard

1.  Compare and order the relative size of common U.S. customary units and metric units; e.g., mile and kilometer, gallon and liter, pound and kilogram.  

2.  Use proportional relationships and formulas to convert units from one  measurement system to another; e.g., degrees Fahrenheit to degrees Celsius.

 

  1. Practice converting from one metric unit to another with this java applet (length, area, volume, mass, or time units)

 

3.   Use appropriate levels of precision when calculating with measurements.  

  4.  Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find:
       a.    the surface area of a cylinder as a function of its height and radius;
       b.    that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height.

  1. Triangle Explorer  In this online activity students learn about areas of triangles and about the Cartesian coordinate system through experimenting with triangles drawn on a grid.
  2. Area of a Circle   Know and apply measurement formulas to solve real-world problems that include area of squares, rectangles, triangles parallelograms, and circles; and area of two-dimensional composite figures of circles, squares, rectangles and triangles. SB
  3. Area of a Triangle  know and apply measurement formulas to solve real-world problems that include area of squares, rectangles, triangles parallelograms, and circles; and area of two-dimensional composite figures of circles, squares, rectangles and triangles.  SB
  4. Determining Areas of shapes  You will find a smart board lesson to help you in this area of learning  SB
  5. Determining Areas  You will find a smart board lesson to help you in this area of learning  ou will find a smart board lesson to help you in this area of learning  SB
  6. Determining area of a triangle.  This Lesson will give you an outstanding presentation of using Smart Board to determine area  ou will find a smart board lesson to help you in this area of learning  SB
  7. Volume Calculate the volume of various shapes.  SB
  8. The area of a trapezoid  Learn the formula for finding the area of a trapezoid, and practice, using examples created for visual and kinesthetic learners   SB
  9. Area of a parallelogram   Learn the formula for finding the area of a parallelogram, and practice, using examples created for visual and kinesthetic learners.  SB
  10. Area of a Square  Learn the formula for finding the area of a square, and practice, using examples created for visual and kinesthetic learners   SB
 

  5.  Determine surface area for pyramids by analyzing their parts.

 

6. Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs.

 

 

7. Apply proportional reasoning to solve problems involving indirect measurements or rates.

 

 

  8.  Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor.

 

  1. Angle Activates  This is an online collection of virtual interactive angle activities covering such topics as the sum of interior and exterior angles in polygons, supplementary angles, angles created by a transversal, vertical angles, and more

  9.  Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.)

 

  1. Prisms and Cylinders - Activity B   Vary the height and base‑edge or radius length of a prism or cylinder and examine how its three‑dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew prism or cylinder to the volume of a right prism or cylinder.
  2. Pyramids and Cones - Activity B     Vary the height and base‑edge or radius length of a pyramid or cone and examine how its three‑dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone
  3. Circle: Circumference and Area 
    Resize a circle and compare its radius, circumference, and area.

10.  Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision.

 

 

Geometry and Spatial Sense Standard

1.  Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.
  1. Platonic Solids - Virtual Manipulative  This online activity allows you to experiment with five platonic solids, counting their faces, edges, and vertices.
  2. Platonic Solids - Duals  The dual of a Platonic solid is another solid inside the first. The vertices of the inner (dual) Platonic solid are the center points of each of the surfaces of the outer Platonic solid.


     

2.   Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal.
  1. 20 Angle Activities
    This is an online collection of virtual interactive angle activities covering such topics as the sum of interior and exterior angles in polygons, supplementary angles, angles created by a transversal, vertical angles, and more. 

  2. Angles
    In this online activity students are shown two parallel lines cut by one or two transversals. Then two angles are selected which the student must identify as acute, right, or obtuse, and then identify the relationship between them.

  3. Turtle Geometry Using this virtual manipulative you may:  Make a plan for the turtle to travel using different angles. 
3.             Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures).
  1. Math Continuum    This web page will take you and your students to new heights in learning about math.  You only need to click on the hyperlink to explore another dimension.
 

  4.  Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex.

 

  1. Shapes   This website will allow your students to learn all about shapes and have fun at the same time.
 

  5.  Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations.

 

  1. Math Manipulative - Flips, Slides, and Turns
    This online activity from Encyclopedia Britannica allows the user to place geometric figures and then apply reflections, rotations, and translations to them. 

  2. Translation Transformation - Virtual Manipulative
    This online activity allows you to place pattern blocks on a grid and apply a translation to them. You can do this on your own, or go through three pre-made activities. 

  3. Rotation Transformation - Virtual Manipulative
    This online activity allows you to place pattern blocks on a grid and apply a rotation to them. You can do this on your own, or go through three pre-made activities. 

  4. Reflection Transformation - Virtual Manipulative
    This online activity allows you to place pattern blocks on a grid and apply a reflection to them. You can do this on your own, or go through three pre-made activities. 

  5. Dilation Transformation - Virtual Manipulative
    This online activity allows you to place pattern blocks on a grid and apply a dilation to them. You can do this on your own, or go through two pre-made activities. 

  6. Transmo Grapher
    Students explore the world of translations, reflections, and rotations in the Cartesian coordinate system by transforming squares, triangles and parallelograms. Parameters: Shape, x or y translation, x or y reflection, angle of rotation.

  6.  Draw nets for a variety of prisms, pyramids, cylinders and cones.

 

 

Patterns, Functions and Algebra Standard

1.  Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form.

 

  1. Super Maths World   This is a highly visual game.  Students will be totally engaged.  4 Star
  2. Algebraic Reasoning   Learn how to think algebraically with these clever weighing scales. Levels 1 and 2 contain two scales. Level 3 is more difficult and has three scales. Your goal is to determine the weight of one or more of the objects  4 Star
  3. Algebra Puzzle Find the value of each of the three objects presented in the puzzle. The numbers given represent the sum of the objects in each row or column. Sometimes, only one object will appear in a row or column. That makes the puzzle easier to solve. Other times, you will have to look for relationships among the objects.  4 Star
  4. Weigh the Wangdoodles  Your job is to find the weight of each Wangdoodle using the information provided by the scales. To be successful, you will have to make sure that the weight you assign to each Wangdoodle works on each scale. This activity is a fun but challenging introduction to multiple algebraic equations.  4 Star
  5.  Mathway This a step by step math solver for General Math, Geometry, Algebra, Pre Algebra, Trigonometry, Pre-calculus, Calculus.  A great program to show students step by step directions and also allow a teacher to create a presentation to be used on their LSD projector.  This is a great tool for facilitating and allowing at teacher to better present their instruction.   4 Star
  6. Smart Board Algebra Lesson  This lesson has examples and videos.  Smart board manipulative  SB
  7. Algebra Tiles icon Algebra Tiles – Visualize multiplying and factoring algebraic expressions using tiles.
  8. Algebraic Tiles   -  This website will allow you to show students how this works.
  9. Algebraic Skills: Signed Numbers -  This website will assist you in teaching this concept.
  10. Algebra Balance Scales icon Algebra Balance Scales Solve simple linear equations using a balance beam representation.
  11. Algebra Balance Scales - Negatives icon Algebra Balance Scales - NegativesSolve simple linear equations using a balance beam representation.
  12. Student Resources for Algebra Outstanding web site for teachers and students.
  13. Simplifying Algebraic expressions
 
2. Generalize patterns and sequences by describing how to find the nth term.
  1. Math Continuum    This web page will take you and your students to new heights in learning about math.  You only need to click on the hyperlink to explore another dimension.
  2.  Math Sequences        Explanation of sequences (also click on “Key Points” for additional information)
  3.  The nth Term     Explanation and examples of n-th term
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  3.  Identify functions as linear or nonlinear based on information given in a table, graph or equation.

 

 

  4.  Extend the uses of variables to include covariants where y depends on x.

 

 

  5.  Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial.

 

  1. Virtual Manipulatives - Algebra Tiles
    This site lets you work with online algebra tiles, and includes sample activities for you to complete.

     

  6.  Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems.

 

  7.  Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.

 

 

  8.  Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.

 

  1. Combining like terms
    This web site teaches about combining like terms to simplify expressions and equations, and then has an interactive quiz to test what was learned.

  2. Simplifying Multiplication
    This web site teaches about simplifying expressions by multiplying algebraic terms with exponents, and then has an interactive quiz to test what was learned.

  3. Simplifying Using Distribution
    This web site teaches about using the distributive property to simplify algebraic expressions, and then has an interactive quiz to test what was learned.

  4. FOIL Method
    This web site teaches about using the FOIL method to multiply two binomials, and then has an interactive quiz to test what was learned.

  5. Variables of Exponents
    This web site teaches about simplifying exponential expressions involving variables, and then has an interactive quiz to test what was learned.

  6. Polynomial Exponents
    This web site teaches about simplifying polynomial expressions involving exponents, and then has an interactive quiz to test what was learned.

  7. Simplifying Fractions With Negative Exponents
    This web site teaches about simplifying algebraic fractions involving exponents, and then has a quiz to test what was learned.

9. Solve linear equations and inequalities graphically, symbolically and using technology.

 

  1. Equations
    This web site teaches about solving simple equations and then has an interactive quiz to test what was learned

10.  Solve 2 by 2 systems of linear equations graphically and by simple substitution.

 

 

11.  Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution.

 

 

12.  Solve simple quadratic equations graphically; e.g., y = x2 – 16.

 

 

13.  Compute and interpret slope, midpoint and distance given a set of ordered pairs.

 

  1. Slope activity
    This web page allows you to manipulate the slope of a line, or the location of the points on the line to get a better understanding of slope. 

  2. Slopes of Lines
    This page from OJK's Pre calculus Site covers a review of slope, how to find it, diagrams of lines with different slopes, and some exercises to try.

  3. Slope Slider
    This activity allows the manipulation of a linear function of the form f(x)=mx+b and encourages the user to explore the relationship between slope and intercept in the Cartesian coordinate system.

14.   Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. non-continuous, direct variation vs. inverse variation.

 

  1. Function Flyer
    A more advanced version of Slope Slider, this activity allows the manipulation of the constants and coefficients in any function thereby encouraging the user to explore the effects on the graph of the function by changing those numbers.

  2. Slope Slider
    This activity allows the manipulation of a linear function of the form f(x)=mx+b and encourages the user to explore the relationship between slope and intercept in the Cartesian coordinate system.

     

     

     

15.  Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts.

 

 
16. Use graphing calculators or computers to analyze change; e.g., interest   compounded over time as a nonlinear growth pattern.  

Data Analysis and Probability Standard

1. Use, create and interpret scatter plots and other types of graphs as appropriate.

 

  1. Scatterplot - Virtual Manipulative
    This online activity allows the user to create scatter plot by adding points to a grid, and then calculates and displays the line of best fit. The grid size can be changed fit any activity, and one suggested activity is explained on the site.

  2. Histograms
    This web site uses clear explanations and diagrams to explain how to read and create histograms. After the review, the student can take an interactive quiz over the material

  2.  Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants.

 

 

  3.  Differentiate between discrete and continuous data and appropriate ways to represent each.

 

 

4.  Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, inter-quartile range, percentiles).

 

  1. Statistics - Deviation from the Mean
    This study guide from Encyclopedia Britannica covers several lessons on stats such as range, inter quartile range, box and whisker plots, and more 

     

  5.  Explain the mean's sensitivity to extremes and its use in comparison with the median and mode.

 

  1. Intro to Stats - Mean, Median, Mode
    This site has a lesson on statistical analysis of data and includes an interactive activity where students can manipulate data to see the effect on mean, media, mode, range, and such.

     

  6.  Make conjectures about possible relationship in a scatter plot and approximate line of best fit.

 

  1. Data Flyer
    Similar to Function Flyer, but with the capability of plotting data points as well as a function. Then you can tweak the function to fit the data.

7.   Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample.

 

8.  Describe how the relative size of a sample compared to the target population affects the validity of predictions.

 

  1. Box Model - Virtual Manipulative
    This online activity models a probability experiment of pulling numbers from a box. First, the user decides which numbers, and how many of each, are in a box. Then the computer begins randomly drawing numbers and keeping totals. Superimposed can be a graph of the expected theoretical probabilities. This is excellent to show real v. theoretical probability, and the effect of the number of trials on the results.

  9.  Construct convincing arguments based on analysis of data and interpretation of graphs.

 

 
10.   Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important.  

11.  Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities.