6th Grade Mathematics

Sixth Grade Benchmarks - Numbers & Operations

Math Olympics - Answer 20 multiple choice questions correctly to win the Math Olympics. Topics range from basic computation and general math knowledge to word problems with percentages, ratios, and fractions.

Rainforest Maths - tons of great math resources for grades K-6. The interface of the whole site is also colorful, inviting and age-appropriate. Also, many of the activities/exercises include assorted visuals, and there is a good variety of questions within each topic.

6.1.spi.1.

Identify the place value of a given digit;

  
6.1.spi.2. Solve one-step real-world problems involving whole numbers and decimals.  
6.1.spi.3.

Represent numbers using a variety of models and equivalent forms (i.e., whole numbers, mixed numbers, fractions, decimals, and percents);

 Rename Fractions - Activities to practice changing fractions to mixed numbers, higher terms, lowest terms, etc.
6.1.spi.4.
Connect whole numbers, mixed numbers, fractions, and decimals to locations on the number line;
  
6.1.spi.5. Compare and order whole numbers, fractions, decimals, and percents using the appropriate symbol (<, >, =); Compare Fractions - Activities to practice comparing fractions - shows examples on number lines and circles.
6.1.spi.6. identify prime and composite numbers up to 50;  
6.1.spi.7. Apply order of operations when computing with whole numbers (no parentheses or exponents);  
6.1.spi.8. Use estimation to select a reasonable solution to a computation involving whole numbers, fractions, and/or decimals;  
6.1.spi.9. Compute efficiently and accurately with whole numbers, fractions, and decimals .

Math at the Mall - Navigate the virtual mall - calculate correct change, interest earned, the correct tip to leave, etc.

Word Problems with Katie & Arlo - Choose from Level 1 (addition/subtraction) or Level 2 (multiplication/division) and solve the word problems.

Math Millionaire - Questions cover a variety of topics including fractions, geometry, decimals, percentages, averages, and more. There are both word problems and computation problems.

Balloon Invaders II - Can you find the percentage of a number before the invaders take over the planet?

Speedy Sums -Develop mental math skills with this simple addition game. The object is to click on numbers that add to the target sum. The more numbers you use, the higher your score will be.

Add Fractions - Students can practice adding fractions with like and unlike denominators, mixed numbers, etc.

6.1.spi.10.

Connect ratios to a variety of models, real-world situations, and symbolic representations;

 Thinking Blocks - Scroll to the bottom of the page - Ratio Word Problems - to solve problems dealing with ratio and proportion. The Math Tutor works you through solving the problems.
6.1.spi.11. Select a reasonable solution to a real-world division problem in which the remainder must be considered.  

 

Sixth Grade Benchmarks - Algebra

6.2.spi.1.

Extend geometric and numerical patterns.

 
6.2.spi.2.

Generalize patterns in data represented in tables;

  
6.2.spi.3.

Apply function rules;

  
6.2.spi.4.

Find missing addends or factors represented as variables in simple equations;

  
6.2.spi.5. Extend rate charts to solve real-world problems;  
6.2.spi.6. Select an equation that represents a given mathematical relationship.  
6.2.spi.7.

Evaluate algebraic expressions for a given value of the variable.

 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.

Sixth Grade Benchmarks - Geometry

6.3.spi.1.

Identify parallel, perpendicular, and intersecting lines;

  
6.3.spi.2.

use ordered pairs to describe given points in Quadrant I of a coordinate system.

 Alien Find - Type in the coordinates to show where the aliens are. 4 quadrants.
6.3.spi.3.

Classify two-dimensional geometric figures using properties;

  
6.3.spi.4. Identify the results of transformations of two-dimensional figures (i.e.., rotations/turns, flips/reflections, slides/translations);  
6.3.spi.5.

Use spatial reasoning to identify the three-dimensional figure created from a two-dimensional representation (net) of that figure (i.e., cube, rectangular prism, pyramid, cone, or cylinder);

  
6.3.spi.6. Classify angles as acute, obtuse, right, or straight.  
6.3.spi.7.

Classify quadrilaterals using their defining properties.

  

 

Sixth Grade Benchmarks - Measurement

6.4.spi.1.

Use strategies to estimate perimeter and area of rectangles ;

Perimeter Explorer - Students are shown shapes on a grid after setting the area and asked to calculate perimeters of the shapes.

Perimeter of a Square - Calculate the perimeter of a square with given dimensions.

Perimeter of a Rectangle - Calculate the perimeter of a rectangle with given dimensions.
6.4.spi.2.

Solve real-world problems involving elapsed time.

Bedtime Bandits - (students try to stay up as late as possible by blasting killer clocks that drop from the ceiling) After each stage, identifying the correct clock gets harder and harder.

Clockworks - Try to set the time on the clock. (select the challenge level)

6.4.spi.3.

Convert from one unit to another within the same system

Measure it - practice using a ruler [inches and centimeters]

Measurement Equivalents - Match game with standard equivalent measurements, such as pounds, ounces, pints, cups, etc.

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

6.4.spi.4. Select units of appropriate size and type to measure angles, perimeter, area, capacity, volume, and weight;

Alien Angles - estimate angles, without a protractor, ranging from 1-180 by dragging a movable line

Banana Hunt - This game helps students practice the degrees of an angle

Measuring Angles - Investigating angles and the use of a protractor

6.4.spi.5.

Apply formulas to determine the area of rectangles and triangles;

Pythagorean Explorer - find the length of a side of a right triangle by using the Pythagorean Theorem, and then check answers

Shape Explorer - calculate areas and perimeters of the shapes

Squaring the Triangle - learn about how the Pythagorean Theorem works, through investigating the standard geometric proof. Parameters: Sizes of the legs of the triangle.

6.4.spi.6. Use scales to read maps;

Latitude and Longitude quiz - online quiz that checks answers

Map Reading Activities - practice reading maps using compasses, latitude, longitude and more

Mathematics of Cartography - several map activity from Cynthia Lanius

6.4.tpi.7. Solve real-world problems involving perimeter and area of rectangles; Shape Surveyor - you never know what you'll find if you dig geometry
6.4.spi.8.

Determine the distance between two points on the x- or the y-axis in Quadrant I.

  
6.4.spi.9.

Solve problems involving ratios and proportions.

Thinking Blocks - Scroll to the bottom of the page - Ratio Word Problems - to solve problems dealing with ratio and proportion. The Math Tutor works you through solving the problems.

All About Ratios: (Problem Solving) - A famous Texas chef has a secret recipe for her chili. When people ask her for it, she hands them a card with the complete recipe except for 1 detail. For the missing detail, she gives them a clue. Use ratios to discover the missing ingredient.

Comparing Ratios and Rates - online quiz

Determine the number based on the ratio - instruction and review, practice, and a quiz

Determining the Ratio - instruction and review, practice, and a quiz

 

 

Sixth Grade Benchmarks - Data Analysis & Probability

6.5.spi.1.

Determine the mode of a data set.

All That Data & All That Data 2 - Activities that use range, mean, median, and mode (Author - Kristy Rousseau)

Basketball Debate - An activity that explores the meaning of average (or mean) and relates these concepts to real world experiences (Author - Michael Naylor)

Handling Data - Calculate mode, median and mode of a set of buildings, then repeat the activity with a different set - (metric measurements)

6.5.spi.2.

Interpret bar and line graphs to answer questions and solve real-world problems;

Fun and Sun Rent-a-Car - students use tables, graphs, linear functions to solve a real-world problem

Heads I Win - predict the likelihood of tossing heads or tails and graphs the results of coin tosses (Author - Michaél Dunnivant)

The Hot Tub - This is a fun activity where students tell the story behind a graph and relate slope to rate of change.

6.5.spi.3.

Determine the mean of a data set;

  
6.5.spi.4. Determine the median from a stem-and-leaf-plot;

Long Distance Airplanes - a stem-and-leaf plot lesson from Iluminations

Organizing Data in Stem & Leaf Plot - A three part lesson from Annenburg CPB including interactive activities

Stem & Leaf Plots - lesson from Purple Math

Stem & Leaf Plotter - An "Interactivate" activity that allows students to input data. Java-based - Worksheet to accompany this lesson.

6.5.spi.5. Determine if a sample is biased; Biased Sample - also known as: Biased Statistics, Loaded Sample, Prejudiced Statistics, Prejudiced Sample, Loaded Statistics, Biased Induction, Biased Generalization (3 good examples at the bottom of the page)
6.5.spi.6. Represent the likelihood of an event using a number from 0 – 1. The Random Ball-Picking Machine - experiment with a random generator at a BBC site to collect data to make decisions about probability. After you finish working through the ball-picking activity, take a ten-question quiz
6.5.spi.7.

Connect data sets and their graphical representations (i.e., bar graphs, circle, graphs, and stem-and-leaf plots);

Data Interpretation Games - Numerous activities on using and interpreting data - Activities include bar, pie and line graphs, data collecting, etc.

Piece Of Pie - display data using a circle graph (Author - Sandi King)

Push Ups - collect data to put on a line graph (Author - Sandi King)

 
6.5.spi.8. Make conjectures and predictions based on data.

Exploring Baby Weight - A baby's weight changes dramatically in the first weeks of life. For example, students will look at data for Baby Kevin and Baby David.

Interpreting Chart Data - students practice by answering questions about what can be found in a grid chart

Pin the Tail - use probability to predict and conduct experiments to test predictions. (Author - Michaél Dunnivant)

Marbles - from Interactivate - learn about sampling with and without replacement by modeling drawing marbles from a bag - [Parameters: Number and color of marbles in the bag, replacement rule]

6.5.spi.9.

Use a tree diagram or organized list to determine all possible outcomes of a simple compound event.

Leap Frog - design an experiment to answer a question, collect information, and interpret the results using charts (Author - Michaél Dunnivant)

Me Too Probability - use a tree diagram to display possible outcomes of who will come to the party (Author - Michaél Dunnivant)

Chances - A dice game that allows you to see how increasing or decreasing the number of dice rolls effects an outcome.