6th 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
 


Updated 10/2010

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)
(Based on the State of Ohio Standards)
1. Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 25 ), and explain why “squared” means “second power” and “cubed” means “third power.”
  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. Math Glossary   Click on this link to illustrate and teach.  This link will present a Visual illustration.  4 star
  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. Spy Guys Interactive - Ratio - Click Skip Intro, then select Lessons, and then click on Lesson  
  5. Exponents  This web site teaches about simplifying exponents and then has an interactive quiz to test what was learned
  6. Lesson on Exponents  This is an online lesson that students can read through with good examples and explanations of exponents, rules about them, and terms such as factor, base, exponent, squared, and cubed. It finishes with an interactive quiz the student can take right on the web page to see if they understand the material.
  7. Factorize 2  Learn about factors through building rectangular arrays on a grid.
  8. Exponents  This web site uses pictures and clear explanations to teach about exponential form, expanded form, and standard form, and how to convert between them. When done with the lesson, students can take an interactive quiz over what they learned.

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. Find and use the prime factorization of composite numbers. For example:
a. Use the prime factorization to recognize the greatest common factor (GCF).
b. Use the prime factorization to recognize the least common multiple (LCM).
c. Apply the prime factorization to solve problems and explain solutions.
  1. Amby's Math Instruction  The section titled "Properties of Numbers" has lessons on prime factorization and using it to find GCF and LCM. After each lesson, there are exercises for the student to try online.
  2. Spy Guys Interactive - Ratio - Click Skip Intro, then select Lessons, and then click on Lesson 3
3. Explain why a number is referred to as being “rational,” and recognize that the expression a/b can mean ‘a’ parts of size 1/b each, a divided by b, or the ratio of a to b.
  1. One line explanation   This is a valued website that will explain various concepts of rational, national numbers and Integers plus more
4. Describe what it means to find a specific percent of a number, using real-life examples.
  1. Spy Guys Interactive - Ratio - Click Skip Intro, then select Lessons, and then click on Lesson  
5. Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.
  1. All About Ratios  This site has many pictoral examples of ratios as well as exercises for students to try.
6. Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions.
  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.                                                                                         There is an equation set in cell B3. (=3*5+5*4+2-8-2*6/8*2)  The user inputs a parentheses, and then alters it to see how many different answers can be generated. Great for order of operations.
  4. Rational Numbers Triangle – Explore a triangular array that contains every positive rational number exactly once.
     
  5. Spy Guys Interactive - Ratio - Click Skip Intro, then select Lessons, and then click on Lesson  
7. Use simple expressions involving integers to represent and solve problems; e.g., if a running back loses 15 yards on the first carry but gains 8 yards on the second carry, what is the net gain/loss?
  1. Mrs. Glosser's Math Goodies - Lesson on Introduction to Integers  This online lesson explains what integers are, gives examples in real life, and offers exercises for the student to do and get immediate feedback.
8. Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take 2 2/3 ÷ 1/6.
  1. Visual Fractions   This site covers many operations with fractions by showing visual representations and having students do exercises with them.
  2. Visual Fractions  This is a virtual Manipulative site that will allow the student's to create their own graphics.
  3. Fractions Adding Illustrates what it means to find a common denominator and combine.
  4. Fractions - Rectangle Multiplication  Visualize and practice multiplying fractions using an area representation.

  5.  
9. Give examples of how ratios are used to represent comparisons; e.g., part-to-part, part-to-whole, whole-to-part.
  1. Fibonacci Sequence – Explore the Fibonacci sequence and the golden ratio.
10.Recognize that a quotient may be larger than the dividend when the divisor is a fraction; e.g., 6 ÷ 1/2 = 12.
  1. Lessons in Division   This site has video and sounds  Covers division in detail and does a nice job.  At the bottom left of the screen make sure you hit lessons.
11. Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning.
  1. Virtual Manipulate for determining percents.  You will find this extremely helpful for students.   4 Star
  2. AAA Math - Fractions  This site has lessons and exercises on many topics concerning fractions
  3. AAA Math - Decimals  This site has lessons and exercises for many decimal topics.
  4. Fishy Fractions - Adding and Subtracting Fractions  In this collection of games you help Ulani the pelican catch fish by adding and subtracting fractions and mixed numbers, with common and unlike denominators. Simply choose the game you want to play.
  5. Virtual Base Blocks - Adding and Subtracting Decimals  This online virtual manipulative lets the student use base blocks to add and subtract decimals, by splitting and combining blocks. This is also a great way to visualize the concepts of decimal place value
  6. Virtual Manipulative - Adding Fractions   This interactive web site helps students learn to add fractions. Two randomly generated fractions are shown along with a visual representation, which can be manipulated by the student. They have to rename the fractions to have the same denominator and then add them.
  7. Spy Guys Interactive - Ratio - Click Skip Intro, then select Lessons, and then click on Lesson  
12. Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use.
  1. Website for fractions has both a video and also an interactive website.  Click on Fractions at the top.  You will notice this website will work for quite a few various math concepts.
13. Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 is about equal to 2 and 4.23 x 5.8 is about equal to 25.
  1. On Line Quiz   Estimation  Created by:   Larry Solomon
14. Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.
  1. How Percentage works  This is basic stuff with some great examples explaining how percentage works. Very nicely done.
15. Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100.
  1. ReviseWise - Percents  This web site uses colorful animation and great explanations to teach about percents, visualizing percents, and percent of a number. After the instruction, the students can take an online quiz to assess their understanding. The only drawback is the use of English pounds instead of American dollars.

Measurement
1. Understand and describe the difference between surface area and volume.
  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
2. Use strategies to develop formulas for finding circumference and area of circles, and to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/4 circle.
  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. 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. Circumference Discover the relationship between circumference and diameter (pi), and use it to calculate unknown measurements of any circle.  SB
  4. Plotting to find the area   This is a smart board lesson  SB
     
3. Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by:
a. estimating lengths using string or links, areas using tiles or grid, and volumes using cubes;
b. measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.
  1. Mrs. Glosser's Math Goodies - Lesson on Circumference of a Circle  This online lesson explains the different parts of a circle and how to find the circumference. Several examples are given and exercises are provided for the students to do online and get immediate feedback
  2. Mrs. Glosser's Math Goodies - Lesson on Area of a Circle  This online lesson explains the different parts of a circle and how to find the area. Several examples are given and exercises are provided for the students to do online and get immediate feedback.
  3. 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.
  4. 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.
  5. 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.
  6. 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
  7. 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
  8. Determining Areas of shapes  You will find a smart board lesson to help you in this area of learning  SB
  9. 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
  10. 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
  11. Volume Calculate the volume of various shapes.  SB
  12. 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
  13. 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
  14. 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
4. Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation; e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room.
  1. The website.   This website will allow you to explore perimeter, area and surface area.  Visually scroll down the screen and look for area and perimeter.
  2. How High? – Try your hand at the classic Piagetian conservation of volume test.

  3. Virtual Manipulative  Converting Units of different areas

  4. Geoboard – Use geoboards to illustrate area, perimeter, and rational number concepts.

  5. Geoboard - Circular – Use circular geoboards to illustrate angles and degrees.

  6. Great Circle – Use a 3D globe to visualize and measure the shortest path between cities.

  7. How High? – Try your hand at the classic Piagetian conservation of volume test.

     
5. Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.
  1. Shape Explorer  In this online activity students are shown shapes on a grid and asked to calculate areas and perimeters of the shapes.
     
6. Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape are changed; e.g. length of sides are doubled.
  1. The website.   This website will allow you to explore perimeter, area and surface area.  Visually scroll down the screen and look for area and perimeter.
  2. Determining Angles of a triangle   You will find a lesson allowing you to learn about angles. You will find a smart board lesson to help you in this area of learning  SB
 

Geometry and Spatial Sense
1. Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides.
  1. Platonic Solids - Virtual Manipulative  This online activity allows you to experiment with five platonic solids, counting their faces, edges, and vertices.
  2. Shapes   This website will allow your students to learn all about shapes and have fun at the same time.
2. Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse and other vocabulary as appropriate.
  1. Sorting Triangles  This interactive website begins with an animated review of scalene, isosceles, and equilateral triangles. Then students get to sort the triangles using Venn diagrams based upon single and multiple characteristics. Very good
3. Use multiple classification criteria to classify triangles; e.g., right scalene triangle.
  1. Sorting Triangles  This interactive website begins with an animated review of scalene, isosceles, and equilateral triangles. Then students get to sort the triangles using Venn diagrams based upon single and multiple characteristics. Very good
4. Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting.
  1. Super Maths World   This is a highly visual game.  Students will be totally engaged.  4 Star
5. Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations.
  1. Dam Jammer Game - Flips and Turns  In this online game you help Bucky the Beaver to plug holes in the dam by flipping and rotating basic shapes, and then placing them on the congruent holes in the dam. Great Game!!
  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.
6. Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other.  
7. Build three-dimensional objects with cubes, and sketch the two-dimensional representations of each side; i.e., projection sets.
  1. Geoboard - Isometric – Use geoboard to illustrate three-dimensional shapes.

Patterns, Functions and Algebra
1. Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.
  1. 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
  2. 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
  3. 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
  4. 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.  Very good
  5. 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.
  6. Whole 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.
  7. Make a Table  This web site uses pictures and clear explanations to teach about solving a problem by making a table. When done with the lesson, students can take an interactive quiz over what they learned.
  8. Smart Board Algebra Lesson  This lesson has examples and videos.  Smart board manipulative  SB
  9. Algebra Tiles icon Algebra Tiles – Visualize multiplying and factoring algebraic expressions using tiles.
  10. Algebraic Tiles   -  This website will allow you to show students how this works.
  12. Algebraic Skills: Signed Numbers -  This website will assist you in teaching this concept.
  13. Algebra Balance Scales icon Algebra Balance Scales – Solve simple linear equations using a balance beam representation.
  14. Algebra Balance Scales - Negatives icon Algebra Balance Scales - Negatives – Solve simple linear equations using a balance beam representation.
  15. Student Resources for Algebra -  Outstanding web site for teachers and students.
     
2. Use words and symbols to describe numerical and geometric patterns, rules and functions.
  1. Function Machine  Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs.
  2. 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.
  3. Whole 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.
3. Recognize and generate equivalent forms of algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(l + w) or 2l + 2w.
  1. 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.
  2. Distributive problem flashcards  Interactive flashcards to practice the distributive property
4. Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.
  1. Equations  This web site teaches about solving simple equations and then has an interactive quiz to test what was learned.
5. Produce and interpret graphs that represent the relationship between two variables.  
6. Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations.
  1. Using algebraic methods to solve systems of equations  Power Point  Interactive, power point- like notes that show the steps of solving an equation. Interesting and easy to understand.
7. Identify and describe situations with constant or varying rates of change, and compare them.  
8. Use technology to analyze change; e.g., use computer applications or graphing calculators to display and interpret rate of change.
  1. 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.

Data Analysis and Probability
1. Read, construct and interpret line graphs, circle graphs and histograms.
  1. Pie Chart (8 items)  This is an Excel spreadsheet activity for the whole class or individual students. A generic 8 item pie chart can be dynamically altered with custom data and labels.
  2. Pie Chart - Virtual Manipulative  This online manipulative allows the user to create a colorful pie chart with up to eight different categories. Suggested activities are included on the site.
  3. Box Plot and Histogram - Virtual Manipulative  This online interactive activity generates a box plot and a histogram for data provided. You can choose from several pre-made sets of topical data, or you can enter new data or change the data there. Several measures of the data are given as well.
  4. 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.
  5. Histograms  Interactive example
  6. Histograms  The purpose of a histogram (Chambers) is to graphically summarize the distribution of a univariate data set.
  7. Circle Graphs  This web site uses clear explanations and diagrams to teach how to read and create circle graphs. After the review, students can take an interactive quiz on the material.
  8. Line Graphs   This web site uses clear explanations and diagrams to teach how to read and create line graphs. After the review, students can take an interactive quiz on the material.
  9. Using Line Graphs  This web site explains the advantages and disadvantages of line graphs, and provides an interactive quiz.

     
2. Select, create and use graphical representations that are appropriate for the type of data collected.  
3. Compare representations of the same data in different types of graphs, such as a bar graph and circle graph.
  1. Comparing Graphs - Excel Activity  This is an Excel spreadsheet activity. In it three different sets of data (earnings, votes, heights) are shown with three different types of graphs (line, bar, circle). The student is to compare the different graphs to determine which is the best representation
4. Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range).
  1. Lessons on Statistics  This site has a collection of lessons on stats including range, mean, median, and mode. Each lesson also has an interactive quiz.
  2. ReviseWise - Mode, median, mean  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.
     
5. Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers.  
6. Make logical inferences from statistical data.  
7. Design an experiment to test a theoretical probability and explain how the results may vary.
  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.