Problem Solving With Number Tiles in Middle School

Math Activities for Grades 5-8

I prefer using hands-on activities when teaching math. One of the most successful items I have used is number tiles. Because number tiles can be moved around without the need to erase or cross out an answer, I have discovered that students are more at ease and more willing to try challenging activities. There is something about not having a permanent answer on the page that allows the student to explore, investigate, problem solve, and yes, even guess.

I have created several number tile booklets, but the one I will feature today is for grades 5-8. It is a booklet that contains 15 different math problem solving activities that range from addition and multiplication, to primes and composites, to exponent problems, to using the divisibility rules. Since the students do not write in the book, the pages can be copied and laminated so that they can be used from year to year. These activities may be placed at a table for math practice or as a center activity. They are also a perfect resource for those students who finish an assignment or test early. Use these activities to reteach a concept to a small group as well as to introduce a new mathematical concept to the whole class.

Students solve the Number Tile Math Activities by arranging ten number tiles, numbered 0-9. Most of the number tile activities require that the students use each tile only once. The number tiles can be made from construction paper, cardboard, or square colored tiles that are purchased.  (How to make the number tiles as well as storage ideas is included in the handout.) Each problem is given on a single page, and each activity varies in difficulty which is suitable for any diverse classroom. Since the students have the freedom to move the tiles around, they are more engaged and more willing to try multiple methods to find the solution. Some of the problems will have just one solution while others have several solutions. These activities are very suitable for the visual and/or kinesthetic learner.

A free version for each of my number tile resources is also available in my TPT store.  While visiting my store, take time to check out these additional Number Tile activities.

• The A, B, C's of Number Tiles - 26 Problem Solving Math Puzzles
• Geometric Math Puzzles –Using Number Tiles Learning to Learn About Plane Geometry
• Number Tiles – Hands On Math Activities for the Primary Grades

Using the Book, Anno's Mysterious Multiplying Jar, to Learn About Factorials

Let's look at one more book in this series of books that link literature and math. This book is more for those taking algebra as it as to do with factorials.  Factorial is a word that mathematicians use to describe a special kind of numerical relationship. Factorials are very simple things. They are just products, indicated by the symbol of an exclamation mark. The factorial function (symbol: !) means to multiply a series of descending natural numbers. For instance, "five factorial" is written as "5!" (a shorthand method) and means 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in determining the numbers of combinations and permutations and in finding probability.

A Few Are Available
on Amazon

Now all of that may seem above your mathematical head, but let me introduce you to the book Anno's Mysterious Multiplying Jar by Masaichir and Mitsumasa Anno.  It is a story about one jar and what is inside it. Anno begins with the jar, which contains one island, that has two countries, each of which has three mountains. The story continues like this until 10 is reached.  The colorful pictures are arranged within borders on the page as many times as the number of objects being discussed. For instance when four walled kingdoms are introduced, four kingdoms are on the page.

The explanation of 10! in the back of the book is also very helpful. Even if children do not understand the concept being taught, they will certainly appreciate the detailed colored drawings and imaginative story! The book is best for kids who have been introduced to at least basic multiplication facts, but younger kids will enjoy counting and looking at the pictures even if the rest of it is over their heads; so, this book helps with multiplying skills as well as the mathematical concept of factorials.

You might give the students a worksheet to keep track of how many islands, rooms, etc. there are. The final question is how many jars are there. Hopefully there will some students who catch on to the factorial concept, find the pattern and discover the answer! 

Here is an example of how you might use factorials in solving a word problem.  How many different arrangements can be made with the letters from the word MOVE?  Because there are four different letters and four different spaces, this is how you would solve the problem.

____   ____   ____   ____ 

Four Possible Spaces

All four letters could be placed in the first space. Once the first space is filled, only three letters remain to fit in the second space. Once the second space is filled with a letter, two letters remain to write in the third space. Finally, only one letter is left to take the fourth and final space. Hence, the answer is a factorial (4!) = 4 × 3 × 2 × 1 = 24 arrangements.

Try some problems in your classroom. Start with an imaginary character, Cal Q. Late, who is working at an Ice Cream Store called Flavors. A hungry customer orders a triple scoop ice cream cone with Berry, Vanilla, and Bubble Gum ice cream. How many different ways could Cal Q. Late stack the ice cream flavors on top of each other?

You could answer the question by listing all of the possible orders of the three ice cream flavors from top to bottom. (Students could have colored circles of construction paper to physically rearrange.)

• 
  Bubble Gum - Berry - Vanilla
• Bubble Gum - Vanilla - Berry

• Berry - Vanilla - Bubble Gum
• Berry - Bubble Gum - Vanilla

• Vanilla - Berry - Bubble Gum
• Vanilla - Bubble Gum - Strawberry

Or, if we use factorials, we arrive at the answer much faster: 3! = 3 × 2 × 1 = 6

Learning about patterns and the use of factorials will stretch a students' mathematical mind. Why not try a few problems in your classroom? And by all means, check out Anno's Mysterious Multiplying Jar.

Taking A Brief Break from Technology

For three weeks, I am setting aside all technology and work related items so I can spend some time to relax with my husband, my grandchildren and friends. In the meantime, if you really want something to read, choose one of my older posts. 

 

My blog posts will return on Wednesday, July 23, 2025.

A Day With No Math - Another Book that Links Math and Literature

Who wants to read about math? Who even likes it? Many, many times I have heard a parent of one of my students say, "I understand why my child cannot do math. I was never very good at math, either." Right! So you weren't good at reading; so, your child should be illiterate? So you don't like to play sports; so, PE should be optional? I don't think so.
 

My goal in life is to make people, students, adults, children, comfortable with math; to see its value; to learn to at least like it. After all, there isn't a day that goes by that you don't use math in some form. Did you read a clock today? Did you buy something with money? Did you go to the home improvement store to buy paint? Did you cook or keep score while you played a game? That is all math. Useful - right?


Ask yourself or your students, "What would happen if suddenly there were no numbers?" To find out, read A Day with No Math by Marilyn Kaye, published by Harcourt Brace Jaovanovich, Inc. in 1992. It is a great read aloud book. It's one I have used in workshops and in my own classroom with children, college students and adults. The book demonstrates how mathematics plays an important role in our daily lives and shows the reader how time, measurement, money and other mathematics are used everyday. The story helps kids to understand that math is a part of all aspects of our every day life and without it, our life would be such a mess. Try reading this if you hate math or even if you love it, and you will be surprised at how much math you really know. It will give you a different appreciation for math 

This is a book teachers will treasure to have in your classroom library. Currently, it's difficult to find, but Amazon seems to have a few copies