I. Patterns, Relationships, and Functions

1. Patterns
2. Variability and Change

Additional Links to General Mathematics Sites

• Mathematics Games and Student Activities
• Mathematics Lessons Plans
• Interactive Learning and Problem Solving Activities
• Word Searches and Puzzles in Mathematics
• Miscellaneous Sites

Middle School

1. Benchmark 1. "Describe, analyze and generalize patterns arising in a variety of contexts and express them in general terms."
   1. Easier Fibonacci Puzzles - Patterns (I.1.MS.1)
      Easier Fibonacci Number puzzles appropriate for Middle School level students offers a variety of exercises, all simply related to the Fibonacci numbers. Uses many other types of patterning. Goes beyond, using pictures and diagrams to completely cover the patterning.
   2. Find a Missing Number in a Sequence - Patterns  (I.1.MS.1&3)
      Students have to find the missing number in a pattern of numbers.  It correctly keeps track of percentage.  Good for introduction to patterns or a review of patterns.
   3. Number Cracker -  Patterns (I.1.MS.1)
      This is a game which gives students three numbers in a pattern and they need to find the fourth.  The "missing" number can be in any of the four spots.  There are several levels of difficulty.  Try "super brain!"
   4. The Golden Rule - Patterns (I.1.MS.1,3&5)
      This a series of interactive lessons about the Fibonnacci Sequence and the Golden Rule. The lessons include explanations and exact instructions. However, the teacher may need to get students started at each new stage. Many opportunities for measuring, gathering data, and making predictions are included throughout the lesson as well as good questions. Hyerlinks to connected sites are included.
   5. Themepark-Utah Education Network - Patterns  (I.1.MS.1)
      This site has a lot of links to other "pattern" sites.  Sites are available for patterns in algebra, geometry, calculus,  statistics, fractals, fractions, and tesselations.   Helps students and teachers to realize that patterns can be found everywhere. Must put in the word "Pattern" in the "Search UEN" box at the top.
2. Benchmark 2. "Represent and record patterns in a variety of ways including tables, charts and graphs, and translate between various representations."
   1. Rectangle Pattern Challenges - Patterns (I.1.MS.2&4)
      This site explores patterns in rectangles and then has students organizing the data they find into a table.  Also has discussion questions at the end. Use as whole class instruction or print off for inividual use.
   2. The Hand Shake - Patterns (I.1.MS.2)
      A data collection and analysis class experiment. Use a table to show the number of handshakes when every person in the room shakes hands with everyone else.
3. Benchmark 3. "Use patterns and their generalizations to make and justify inferences and predictions."
   1. Attribute Trains  - Patterns  (I.1.MS.3)
      Interactive site to practice completing patterns.
   2. Doubling Pennies - Patterns (I.1.MS.3,4&5)
      This site poses a question relating to the doubling of pennies as opposed to receiving a set amount of money. It then goes through the solution using charts and a formula. This site also contains links to similar problems. This is a student activity.
   3. Find a Missing Number in a Sequence - Patterns (I.1.MS.1&3)
      Students have to find the missing number in a pattern of numbers.  It correctly keeps track of percentage.  Good for introduction to patterns or a review of patterns.
   4. No Matter What Shape Your Fractions are In - Patterns  (I.1.MS.3)
      This site is a great site to have students find patterns in the shapes and then make predictions about future shapes.  There is a online interactive link or you can print it off and go!!
   5. Patterns in Mathematics: Number Patterns- Patterns (I.1.MS.3)
      Math is especially helpful when it helps you predict, and number patterns are all about predictions.  Through everyday situations students use number patterns to solve a variety of problems.  The site helps the student walk through the problem step by step and analyze their thinking process.  It gives them hints along the way as they work towards the final answer.  It allows student to give a written response to how they think through the problem.
   6. Play Pool on Different Sized Pool Tables -  Patterns (I.1.MS.3&4)
      In this interactive activity students will predict which pocket the pool ball will go into as well as the number of hits needed to sink the ball. By changing variables they will see patterns and generalizations to aide them in their predictions. Data will be represented by a model as well as a spreadsheet and a graph.
   7. The Golden Rule - Patterns (I.1.MS.1,3&5)
      This a series of interactive lessons about the Fibonnacci Sequence and the Golden Rule. The lessons include explanations and exact instructions. However, the teacher may need to get students started at each new stage. Many opportunities for measuring, gathering data, and making predictions are included throughout the lesson as well as good questions. Hyerlinks to connected sites are included.
4. Benchmark 4. "Explore and describe visual and numeric patterns, including linear expressions, near-linear patterns and symmetric and spatial patterns."
   1. Discovering Growth Patterns - Patterns (I.1.MS.4)
      A web activity comparing linear and exponential growth.
   2. Dot Patterns and Sierpinski Gasket - Patterns  (I.1.MS.4)
      This site allows you to generate the Sierpanski Triangle.  You can enlarge the triangle one row at a time allowing you to see the changes at each stage of the triangle.
   3. Doubling Pennies - Patterns (I.1.MS.3,4&5)
      This site poses a question relating to the doubling of pennies as opposed to receiving a set amount of money. It then goes through the solution using charts and a formula. This site also contains links to similar problems. This is a student activity.
   4. Pattern Blocks - Patterns (I.1.MS.4)
      This site allows the students to create their own patterns by manipulating the pattern block shapes onto the graph. It also gives a definition of each shape if the student needs the reference. Teachers can choose what type of pattern they want students to create. Also a possibility of using it for fractions.
   5. Play Pool on Different Sized Pool Tables -  Patterns (I.1.MS.3&4)
      In this interactive activity students will predict which pocket the pool ball will go into as well as the number of hits needed to sink the ball. By changing variables they will see patterns and generalizations to aide them in their predictions. Data will be represented by a model as well as a spreadsheet and a graph.
   6. Rectangle Pattern Challenges - Patterns (I.1.MS.2&4)
      This site explores patterns in rectangles and then has students organizing the data they find into a table.  Also has discussion questions at the end. Use as whole class instruction or print off for inividual use.
   7. Using Graphs to Convey Information - Patterns (I.1.MS.4)
      This site contains eight problems in which students must explore and graph data, including graphing independent and dependent variables. In the first four problems, one factor changes over time; students are asked to sketch the graphs of the information and then analyze their graphs. In the second four problems, students need to decide what in the problem could be illustrated with a graph and then create that graph. Although this isn't an interactive activity for students, it is a good problem-solving resource for teachers to incorporate into their classrooms. Students may be able to use the web site: http://nces.ed.gov/nceskids/graphing/index.asp to helpgraph this information.
   8. Waldo's Interactive Math - Patterns (I.1.MS.4)
      This interactive site allows students to manipulate triangles on a coordinate graph in order to explore their relationship. The site relies on Java applets.
5. Benchmark 5. "Use patterns and generalizations to solve problems and explore new content."
   1. A Thousand Lockers - Patterns (I.1.MS.5)
      There are 1000 lockers numbered 1 to 1000. Suppose you open all of the lockers, then close every other locker. Then, for every third locker, you close each opened locker and open each closed locker. You follow the same pattern for every fourth locker, every fifth locker, and so on up to every thousandth locker. Which locker doors will be open when the process is complete? This site wants the students to solve the problem by solving it with the use of patterns.
   2. Doubling Pennies - Patterns (I.1.MS.3,4&5)
      This site poses a question relating to the doubling of pennies as opposed to receiving a set amount of money. It then goes through the solution using charts and a formula. This site also contains links to similar problems. This is a student activity.
   3. From Corner to Corner - Patterns (I.1.MS.5)
      Students are supplied with an on-line ruler and must use it to measure the side of a square and a diagonal. Students then need to analyze the data to develop a rule for estimating the length of the diagonal given the length of the side without actually measuring the length. Students then need to consider if the rule would work for other shapes. They also need to reflect on their rule and submit a short explanation of why it works. (This could also be extended to include the Pythagorean Theorem. This activity also hits benchmarks II.3.MS.1,5,6)
   4. The Golden Rule - Patterns (I.1.MS.1,3&5)
      This a series of interactive lessons about the Fibonnacci Sequence and the Golden Rule. The lessons include explanations and exact instructions. However, the teacher may need to get students started at each new stage. Many opportunities for measuring, gathering data, and making predictions are included throughout the lesson as well as good questions. Hyerlinks to connected sites are included.