Math Forum - Problems Library - Middle School, Mathematical Patterns

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Middle School: Mathematical Patterns

In grades 6-8, 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 6-8 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 middle-school sites, go to the bottom of the page, set the searcher for middle school (6-8), and press the Search button.


Access to these problems requires a Membership.

Balancing Mobiles - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile. ... more>>

A Day at the Arcade - Judy Ann Brown
Middle School, difficulty level 2. The 25-cent 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? ... more>>

Fall Festival Frolic - Judy Ann Brown
Pre-Algebra, difficulty level 3. How many different types of candy are needed to make at least 50 different treat bags? ... more>>

Gearing Up - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears. ... more>>

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? ... more>>

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? ... more>>

The Magic of Number 6174 - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Have fun exploring this number magic. ... more>>

Making Money - Alice Miller
Pre-Algebra, 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? ... more>>

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? ... more>>

Milk Madness - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes. ... more>>

Mr. Carmel's Party Plan - Judy Ann Brown
Pre-Algebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes. ... more>>

The Name Game - Judy Ann Brown
Pre-Algebra, 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? ... more>>

Rampaging Reindeer - Judy Ann Brown
Pre-Algebra, difficulty level 3. How many different ways can Santa's reindeer be arranged? ... more>>

Runsums, Part 1 - Ron Knott
Pre-Algebra, difficulty level 3. By spotting the pattern, tell me the smallest number that is a sum of a run of one hundred consecutive numbers. ... more>>

Runsums, Part 2 - Ron Knott
Pre-Algebra, difficulty level 3. Explore number patterns and report on what you have learned. ... more>>

Santa's Little Helpers - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves. ... more>>

Seating Dilemma - Judy Ann Brown
Pre-Algebra, difficulty level 2. Count the number of ways to seat people, if some are math teachers who cannot be next to each other. ... more>>

Seesaw - Suzanne Alejandre
Pre-Algebra, difficulty level 3. How did the four friends balance on the seesaw? ... more>>

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? ... more>>

Shapes Rock - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides. ... more>>

Snow Day Phone Chain - Judy Ann Brown
Pre-Algebra, difficulty level 4. Use the given information to find out how many phone calls were made. ... more>>

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. ... more>>

Tiling Triangles - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it. ... more>>

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