7th Grade Math

7th Grade Math  

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 9.7 .  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
 

 

Measurement Standard

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

Number, Number Sense and Operations

(Based on the State
of Ohio Standards)

1. Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation.
  1. Math Dictionary animation for kids  This is an outstanding website allowing you to explore a comprehensive view of math with many examples  4 Star
  2. Quiz  Created by:  Allison Green
  3. 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.
  4. Scientific Notation  This is a Smart Board activity that is very well put together.  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. Explain the meaning of exponents that are negative or 0.
  1. Exponents  This web site teaches about simplifying exponents and then has an interactive quiz to test what was learned
  2. 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.
3. Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and others (irrational) as non-terminating and non-repeating decimals.
  1. One line explanation   This is a valued website that will explain various concepts of rational, national numbers and Integers plus more
 
4. Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals.
  1. Order of Operations This web site teaches about simplifying expressions using order of operations, and then has an interactive quiz to test what was learned.
  2. 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
  3. Effects of Parentheses  This is an Excel spreadsheet activity for a whole class or individual students.   
5. Explain the meaning and effect of adding, subtracting, multiplying and dividing integers; e.g., how adding two integers can result in a lesser value.  
6. Simplify numerical expressions involving integers and use integers to solve real-life problems.
  1. Mrs. Glosser's Math Goodies - Lesson on Integers  This site provides online lessons for adding, subtracting, multiplying, and dividing integers. It also offers exercises for the student to do and get immediate feedback.
  2. Amby's Math Resources - Integers  This site gives explanations of the rules for integers with sample exercises.
7. Solve problems using the appropriate form of a rational number (fraction, decimal or percent).  
8. Develop and analyze algorithms for computing with percents and integers, and demonstrate fluency in their use.
  1. Lesson on Surface Area and Volume
    This site offers a lesson on surface area and volume, along with an interactive 3-D model that the students can manipulate to learn more about these concepts
9. Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares).  

Measurement

1. Select appropriate units for measuring derived measurements; e.g., miles per hour, revolutions per minute.
  1. Composite Math Site       This site is outstanding as it will offer you and your students many lessons that normally would be difficult for you to create in class.
2. Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters.  
3. Estimate a measurement to a greater degree of precision than the tool provides.
  1. Exploring Pi This is an Excel spreadsheet activity for the whole class. As students report measurements on circumference and diameter of objects, the spreadsheet calculates their ratio and averages them together to approximate pi.
  2. Estimator  This online activity has the student estimate length, quantity, or area. They can control how close they need to be to the true answer, how difficult the problem is, and if a grid is given to help with the estimate.
 
4. Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system.  
5. Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems.  
6. Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms.
  1. Volume Calculate the volume of various shapes.  SB
  2. 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
  3. 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
  4. 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
 
7. Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors.
  1. Plotting to find the area   This is a smart board lesson  SB
8. Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas.
  1. Lesson on Surface Area and Volume  This site offers a lesson on surface area and volume, along with an interactive 3-D model that the students can manipulate to learn more about these concepts.
  2. Smart Board
9. Describe what happens to the surface area and volume of a three- dimensional object when the measurements of the object are changed; e.g., length of sides are doubled.
  1. Surface Area and Volume In this online activity students manipulate dimensions of rectangular or triangular prisms, and watch how the surface area and volume change.

Geometry and Spatial Sense

1. Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures.
  1. Composite Math Site       This site is outstanding as it will offer you and your students many lessons that normally would be difficult for you to create in class.
  2.  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
 
2. Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example:
a. Determine when one set of figures is a subset of another; e.g., all squares are rectangles.
b. Develop a set of properties that eliminates all but the desired figure; e.g., only squares are quadrilaterals with all sides congruent and all angles congruent.
  1. Shapes   This website will allow your students to learn all about shapes and have fun at the same time.
 
3. Use and demonstrate understanding of the properties of triangles. For example:
a. Use Pythagorean Theorem to solve problems involving right triangles.
b. Use triangle angle sum relationships to solve problems.
  1. Pythagorean Theorem - Virtual Manipulative  This online activity allows you to demonstrate the proof of the Pythagorean Theorem using area models that can be manipulated.
4. Determine necessary conditions for congruence of triangles.
  1. Congruent Triangles - Virtual Manipulative  This online activity allows you to manipulate virtual angles and segments to learn what does and does not guarantee congruent triangles. The methods covered include SSS, SAS, ASA, and SSA
5. Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures.
  1. Properties of congruent or similar triangles  this is a worksheet format to allow you step by step to solve a problem
6. Determine and use scale factors for similar figures to solve problems using proportional reasoning.
  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. Identify the line and rotation symmetries of two-dimensional figures to solve problems.  
8. Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).
  1. Math Manipulatives - Flips, Slides, and Turns
    This online activity from Encyclopedia Britanica 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. TransmoGrapher
    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.
  7. Transformation Game
    In this interactive online game you try to move colored shapes into their matching holes by using reflections, rotations, and translations. The challenge is to use the least number of moves. You can even move the line of symmetry and point of rotation.
9. Draw representations of three-dimensional geometric objects from different views.  

Patterns, Functions and Algebra

1. Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.
  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
    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
  5. Function Machine
    Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs.
  6. Function Machine
    This online tool has you put in a number, and then it spits out a result. Your goal is to determine what the function machine is doing to the number. You can choose the type of function it uses or let it be random.
  7. Mystery Functions
    This is an Excel spreadsheet activity for the whole class or individual student use. There are 20 different mystery formulas in this spreadsheet. For each one the student enters several numbers for the "Input" and examines what comes out for the "Result", trying to determine each function by looking for patterns.
  8. Number Cruncher
    Similar to the original "Function Machine" but lists input and output in a table and will not let the user attempt to guess the rule on without at least having two data points.
  9. 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
  10. Smart Board Algebra Lesson  This lesson has examples and videos.  Smart board manipulativeSB
  11. Algebra Tiles icon   Algebra Tiles Visualize multiplying and factoring algebraic expressions using tiles.   Algebra Tile manipulative
  12. Algebraic Skills: Signed Numbers -  This website will assist you in teaching this concept.
2. Generalize patterns by describing in words how to find the next term.
  1. Composite Math Site       This site is outstanding as it will offer you and your students many lessons that normally would be difficult for you to create in class.
 
3. Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1, 3, 5, 7... is linear and 1, 3, 4, 8, 16... is nonlinear.  
4. Create visual representations of equation-solving processes that model the use of inverse operations.  
5. Represent linear equations by plotting points in the coordinate plane.
  1. Simple Plot
    http://www.shodor.org/interactivate/activities/simpleplot/index.html
    Students can plot ordered pairs of numbers, either as a scatter plot or with the dots connected.
6. Represent inequalities on a number line or a coordinate plane.  
7. Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified; e.g., 4m = m + m + m + m or a 5 + 4 = 5a + 4.
  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 alegraic expressions, and then has an interactive quiz to test what was learned.
8. Use formulas in problem-solving situations.
  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
9. Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula.
  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
10. Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another.  
11. Use graphing calculators or computers to analyze change; e.g., distance-time relationships.
  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
    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.

Data Analysis and Probability

1. Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate.
  1. Data Analysis   You will find a number of activates using smart board technology that will allow the student to better learn this indicator.  SB  Created by Michelle Yee
  2. Data Analysis 2    You should find activates that will help you with this lesson.  SB  Created by Tracy Rulison
2. Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph.  
3. Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, inter-quartile range), and describe how the inclusion or exclusion of outliers affects those measures.  
  1. Intro to Stats - Mean, Median, Mode
    http://www.shodor.org/interactivate/lessons/sm1.html
    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.
  2. ReviseWise - Mode, median, mean
    http://www.bbc.co.uk/schools/revisewise/maths/data/12_act.shtml
    This web site uses colorful animation and great explanations to teach about mean, median, and mode. After the instruction, the students can take an online quiz to assess their understanding.
  3. Comparing Data - Excel Activity
    This is an Excel spreadsheet activity in which the student enters data and then the spreadsheet generates several measures of that data such as mean, median, mode, quartiles, and range. The student can then investigate the measures to compare the different sets of data.
4. Construct opposing arguments based on analysis of the same data, using different graphical representations.
  1. Misleading Graphs
    This is an Excel spreadsheet activity for the whole class or individual student use. Two different bar graphs are made from the same survey of favorite foods. The students need to determine which graph is more fair and why, by studying the graphs and altering the data.
5. Compare data from two or more samples to determine how sample selection can influence results.  
6. Identify misuses of statistical data in articles, advertisements, and other media.
  1. Misleading Graphs
    This is an Excel spreadsheet activity for the whole class or individual student use. Two different bar graphs are made from the same survey of favorite foods. The students need to determine which graph is more fair and why, by studying the graphs and altering the data.
7. Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models.  
8. Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences.
  1. Box Model - Virtual Manipulative
    http://matti.usu.edu/nlvm/nav/frames_asid_146_g_4_t_5.html?open=instructions
    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. thoeretical probability, and the effect of the number of trials on the results.