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Middle School
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Middle School: Mathematical Patterns
In grades 68, students continue to explore patterns as a means of
developing algebraic thinking and logic skills. The study of patterns
and relationships in the middle grades focuses on patterns that relate
to linear functions, which arise when there is a constant rate of change.
Students use tables, graphs, words, and symbolic expressions to solve
problems involving functions and patterns of change, and learn to look
for formulas to express the patterns they discover. In addition, a goal
at this level is to develop a facility with using patterns and functions
to represent, model, and analyze phenomena in the real world.
The problems listed below require students to investigate patterns in
order to find an answer or reach a solution. They may address the NCTM Grades 68
Algebra
Standard,
Problem
Solving Standard, or
Connections
Standard.
To find relevant sites on the Web, browse and search
Patterns/Relationships
in our Internet Mathematics Library; to find middleschool sites, go to the
bottom of the page, set the searcher for middle school (68), and press the
Search button.
Access to these problems requires a Membership.

Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
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A Day at the Arcade
 Judy Ann Brown

Middle School, difficulty level 2. The 25cent token dispensing machine only accepts quarters and half dollars one at a time. How many different combinations of coins, using quarters (q) and half dollars (h), are there to purchase the desired number of tokens?
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Fall Festival Frolic
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different types of candy are needed to make at least 50 different treat bags?
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Gearing Up
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Think about and explain the relationship between three differentsized gears.
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Grandmother's Birthday Party
 Judy Ann Brown

Middle School, difficulty level 1. Alice and Jessica are writing invitations for a surprise birthday party for their grandmother. Determine how many invitations they have written?
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I Know a Secret!
 Judy Ann Brown

Middle School, difficulty level 2. On the first day I told two friends my secret.They each told two friends. How long until 100 people know the secret?
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The Magic of Number 6174
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Have fun exploring this number magic.
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Making Money
 Alice Miller

PreAlgebra, difficulty level 3. How much money would you have by December 31, 1999, if you put 10 cents in the special "math" bank on January 1, 1999?
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The Math Club Holiday Party
 Judy Ann Brown

Middle School, difficulty level 2. The Math Club is having a holiday party. If the presents are opened in 5 minute intervals starting at 1:00 p.m. the last gift will be opened starting at 5:35 p.m. How many club members are there?
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Milk Madness
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes.
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Mr. Carmel's Party Plan
 Judy Ann Brown

PreAlgebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes.
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The Name Game
 Judy Ann Brown

PreAlgebra, difficulty level 3. The first student says his/her own name; the second student repeats the first student's name and adds his/her own name... How many names are said if the numbers of students in my math classes on the first day are 27, 28, 32, 31, and 30?
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Rampaging Reindeer
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different ways can Santa's reindeer be arranged?
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Runsums, Part 1
 Ron Knott

PreAlgebra, difficulty level 3. By spotting the pattern, tell me the smallest number that is a sum of a run of one hundred consecutive numbers.
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Runsums, Part 2
 Ron Knott

PreAlgebra, difficulty level 3. Explore number patterns and report on what you have learned.
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Santa's Little Helpers
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves.
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Seating Dilemma
 Judy Ann Brown

PreAlgebra, difficulty level 2. Count the number of ways to seat people, if some are math teachers who cannot be next to each other.
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Seesaw
 Suzanne Alejandre

PreAlgebra, difficulty level 3. How did the four friends balance on the seesaw?
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Sequence of Exercise
 Judy Ann Brown

Middle School, difficulty level 2. Each day Chris and Jody jog three blocks farther than they did the day before. How many days have Chris and Jody been jogging?
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Shapes Rock
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides.
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Snow Day Phone Chain
 Judy Ann Brown

PreAlgebra, difficulty level 4. Use the given information to find out how many phone calls were made.
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Super Bowl XXXII
 Judy Ann Brown

Middle School, difficulty level 2. The Super Bowl committee has decided to create a plaque to hang in the NFL Hall of Fame. Your job is to determine how many of each letter or symbol must be made in gold.
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Tiling Triangles
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it.
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