Middleschool Math and Pre-Algebra
As a final step before Algebra, children are taught fractions, percents, decimals and ratios while perfecting their grasp of the four operations, addition, subtraction, multiplication and division. This mastery of the four operations is what makes the higher levels of math turn into fun puzzles and intriguing patterns of numbers that can explain the universe.
This article will give you an overview of math taught in K-8 as preparation for High School Algebra with an emphasis on games and activities that will help children in 4-8 grades solidify their understanding of pre-algebra concepts while playing fun and challenging games. Come roll the dice and shuffle the cards. It's time for pre-algebra fun...
Alternatives to Math Textbooks
Of course you could use textbooks. There are many out there and you will be assured of covering all of the subjects thoroughly. However, if you are brave and have confidence in yourself and you child, there are many more exciting ways to learn all the math skills to prepare for algebra lessons.
We homeschooled our oldest until she started 7th grade. When she entered public school for the first time she was beginning Algebra II. The following are materials that we used and found most helpful for learning pre-Algebra.
Number Sense - What do those number really mean?
Number Sense is understanding what numbers mean. From beginning levels where the number 5 represents five fingers to fractions where 1/4 means that there is one out of four and on to understanding that 2-5=3 does not make sense. This is the beginning of number sense. It is also understanding that 56 is a smaller amount than 65 and that 1/2 is the same as .5. All of these concepts are needed in order to begin to study algebra and there are games that you can play with your child to learn each one of these concepts.
Teaching Number Sense
Play finger games with your child
Despite all that you have learned up until now, counting on fingers is a good thing.
- Ask your child to hold up two fingers.
- Now take away five of them.
- It can't be done! It is time to go back and look at the problem again. Was the problem really 5-2 rather than 2-5?
- That is a difficult concept for 6 and 7 year olds but with repetition they certainly get it by the time they are ready for algebra.
Most textbooks stop there but I have found that it makes more sense to continue on and explain negative numbers to your child.
- Ask your child how many people will be eating at your table for the next meal. (Let's say 5)
- Hand him or her items to be placed on the table.
- 4 plates. You need 5. I gave you 4. How many more do you need? One!
- You have negative one plates.
- Hand your child 3 forks.
- Once they have placed those three forks they can be taught the terms that they now have negative 2 forks or that 2 more forks are needed.
Your child is learning the terms that will prepare them to understand algebra.
We started playing finger games when the kids were young. Wherever we were we counted, added, multiplied and figured out problems. It was always fun and it wasn't long before the kids were making up their own problems.
Hi Ho a Cherry O
Games that teach Number Sense - Number Sense builds skills needed for learning Algebra
Board games are great for teaching number sense. Counting backward and forward, moving spaces, skipping ten, going back two on the board helps children understand the relationship between numbers.
Snakes and Ladders, Rack-O, Go to the Head of the Class, Hi Ho a Cherry O and Monopoly are just a few of the games that teach children number sense while having lots of fun and family time.
A good sense of just what numbers mean is vital when beginning algebra.
Snakes and Ladders
At first it might seem that Mancala is just a simple counting game. Very young children can quickly begin to play successfully.
But as with many good games the more you play the more math is involved, the more patterns you notice and you start applying strategies to your game.
Usually we begin with three beans in each pod.
- What happens when you begin in different places?
- Does it matter who begins the game?
- How does your strategy change when you start with 4, 5 or more beans in each pod?
Mancala can involve strategy and complex higher math, putting it on par with chess and similar strategy board games.
Four Operations on the Hundreds Board
Learn the Four Operations with this variation on the Hundreds Board. Tom DeRosa from the I Want to Teach Forever Blog tells us that The Sequence Numbers Game allows students to practice addition and subtraction number facts in the context of an easy to learn game.
- The game goes like this: each player/team has a handful of these number facts cards.
- The game board, as you can see in the picture, has color-coded numbers that match the cards.
- Each turn, you can put one of your chips on the answer to one of the cards in your hand.
- The object is to get five chips in a row..
This game would be a wonderful addition to any classroom or homeschool family's game closet.
Adding and Subtracting with Parcheese
Board Games teach Arithmetic
One of our favorite board games is Parcheesi.
- Roll the dice and count the dots (One to one correspondence)
- Add the two numbers together (Addition)
- Move your playing piece that number of spaces. (Counting)
- Notice how many more spaces are needed to get around the board. (Subtraction)
- You have to get the correct number to get into the home space. (Addition and Subtraction)
As the kids get more and more proficient with the board it is fun to look for more and more math.
- How many spaces are there between circles?
- How many spaces are there to get all around the board?
- Each person needs to move all four of their pawns around the board. Multiply to see how many spaces to get all four around the board.
- How many different geometric shapes can you find on the board?
Add, Subtract, Multiply and Divide - You must know the Four Operations before beginning Algebra!
Unless you can answer this question with yes, quickly and easily, your child should be playing more games.
Only with a quick, fluent sense of numbers and how to add, subtract, multiply and divide will your child be ready for learning algebra. But this is where the fun begins.
Learning to Multiply with Yahtzee
Roll the Dice and Multiply
We always have a pair of dice on the dining room table. If we are in a hurry we might just each take a turn rolling the dice, multiplying the two and cheering the one with the highest number.
Sometimes we will add the two dice, subtract the higher from the lower number, or see if we can roll doubles.
When we have more time, we like to play Yahtzee. Yahtzee involves addition, subtraction and multiplication.
Once the kids were getting proficient we started playing 24 Game. We first learned the game as a board game but one day we decided to try playing it with just 4 dice. Of course, sometimes you can't get to 24 but that just makes the game more fun.
Add, Subtract, Multiply and Divide with the 24 Game
Use the four numbers around the card to add, subtract, multiply and divide to get to 24. The first one to get to 24 wins that card.
Playing this game is not only fun, but helps your children master the four operations of addition, subtraction, multiplication and division. It is a game that can be played by children and adults. You might be surprised at how much fun it is playing games like 24 and not even realize that you are preparing to learn Algebra.
Fraction Balance Scale
Practice adding and subtracting fractions in a fun, hands-on way that will help children truly understand what all those numbers actually mean.
Hands-on Fraction Activities
- Fractions for Hands-on Learners
Hands-on activities for understanding fractions | See more about fractions, equivalent fractions and pattern blocks.
What's My Rule?
What's My Rule? - Using Problem Soving Strategies (Grades 6-12)
If one number goes into the tiger's head and another number comes out, what did the tiger have to do to the first number to get the second number.
The problems in this book get progressively harder. I have never found a child that didn't enjoy the challenge of trying to figure out this tiger's mind.
The Game of Sprouts
- Sprouts Game
Sprouts is a pencil-and-paper game with interesting mathematical properties. It was invented by mathematicians John Horton Conway and Michael S. Paterson at Cambridge University in 1967. A 2-spot game of Sprouts The game is played by two players, s
Algebra in the Concrete
Mary Laycock found a way to show algebra in a fun and exciting, hands-on way that excites kids to play with first year algebra. My 10 year old homeschooler loved using the Cuisenaire Rods to work out the problems while discovering the relationships between the different parts of equations. She quickly learned to make up her own problems. I wish I knew of a good sequel.
This book was enacted by a group of upper elementary school children as they built the sequences, algebraic expressions, rectangular arrays, and equations of elementary algebra.
Pictures of their work are included so you and your students can see how many different types of manipulatives can be used in constructing some of the fundamental concepts of algebra. Added activities include factoring trinomials to solving quadratics.
- Cuisenaire Rods
Activities and centers using Cuisenaire Rods to help children learn mathematical concepts.
The Mathematics of the Spirograph - Symmetry
- The Mathematics of the Spirograph (Any Excuse to Play)
Symmetry Each Spirograph pattern displays two kinds of symmetry: - Rotation - Mirror (Reflection)
- Spirograph Math
Can a child really learn math from doing spirographs? This page explains some of the math that an elementary school child might learn from doing spirograph patterns.
- Roman Glassmakers Board Games Page
Ludus Latrunculorum: and Merils, or Nine Men's Morris were games of chance.
Hexagram to square hinged dissection - Mathematics of Puzzles
- To make the above puzzle, just tape together the green triangles from your set of Pattern Blocks.
- Can you construct other puzzles?
- Can you make other transformations?
- Can you understand mathematically why these puzzles work?
Mathematical Puzzles and Hinged Dissections
- Mathematics Learning: Jigsaw Mathematical puzzles
You can make your own online Jigsaw puzzle. Why not challenge the kids to make Jigsaw puzzles of mathematical concepts? It's hard to get kids to do the repetition needed to memorize but when given the opportunity to do it in a creative way that repet
- Hinged Dissections: Swinging & Twisting
A wide variety of twist-hinged dissections with mathematical proofs.
Books of Puzzles - Puzzles use Pre-Algebra and Algebra skills without kids knowing it.
Cross Sums were one of my first forays into using puzzle books to teach pre-algebra. You don't realize how much practice you are getting in the four operations until suddenly realize that the puzzles are getting easier and easier.
What's My Rule? gently leads students from pre-algebra into the logical formulas of algebra. This book is so much fun it's too bad there aren't more volumes.
Sing the Quadratic Equation Song
Sing along and learn the Quadratic Equation in preparation for learning algebra. You will be surprised how much this will help you. I love the way that the formula is sung over and over. The tune is catchy and sticks in your head.
Coffee Table Quality Rush Hour
Learning Strategy and Logical Reasoning
ThinkFun Rush Hour is one of our favorite strategy and logic games. The object of the game is to get the red car out of traffic gridlock.
The game comes with a bunch of little cars and trucks that are placed, puzzle-fashion at an intersection. Your job is to get the red car out.
Sounds simple enough doesn't it?
Start with card one and you think, "This is a breeze!" but the cards get progressively harder.
Children and adults love playing this game. They won't even know they are learning math.
Donald Duck in Mathemagic Land - Introduce Children to Exciting concepts in Mathematics
This is a video that can be watched and enjoyed by children from pre-school through high school ages. Each age will gain more understanding of mathematical concepts in a fun and entertaining way. Visual images of mathematical concepts will help when preparing children for algebra.
Donald Duck in Mathmagicland
Donald Duck is surprised to discover how fascinating math can be. He discovers how wonderful, fun and exciting math can be.
- He goes to Ancient Greece to learn about Pythagoras.
- He learns how fractions relate to music.
- He learns the relationship between pentagrams, the golden ratio, and how it can be found in nature.
My children loved watching this video over and over again. Each time we watch it we discover more avenues to understanding math.
Roman Board Games can help pre-algebra students work on strategies that develop an understanding of mathematical concepts. The more times you play the game the more patterns and strategies you see. Play with another person and suddenly you start to see new ways to play.
How do you teach your children Pre-Algebra?
mathkplus on April 25, 2014:
I think the answer is two parts: (1) the learning material must be easy and fun to read, and (2) the student must have a means of dynamic practice of the material to complete the learning process.
cleansweeping on February 10, 2014:
Nice lens! Very complete!
LearnKidstoRead on November 17, 2013:
Even saying the word 'Algebra' grosses me out! Great lens thanks for the info. Will try these games out with my son who is struggling with math. Sue
Bill Armstrong from Valencia, California on February 27, 2013:
No kids but love your games ;)
kuldeeppal on January 24, 2013:
Your lens looks really great it for my friends.
rudhushudu on December 17, 2012:
i love your lens
Evelyn Saenz (author) from Royalton on September 02, 2012:
@anonymous: Yes! You are right. 6 is indeed a triangular number.
anonymous on September 02, 2012:
Wouldn't 6 also be a triangular number?
DMVAgent on August 05, 2012:
Got new info! Thanks for lens, you made a great job. Learning can be done in any way, in easy way. :)
OrganicMom247 on June 15, 2012:
Learning is easier when you do it though games or songs.
KandH on December 20, 2011:
Love this lens: maths and puzzles - these are a two of my favorite things!!
EMangl on October 29, 2011:
by making games for her, i think i showed you :-)
Rankography on July 30, 2011:
if you have not checked out KhanAcademy yet you should. It is the coolest most revolutionary site I have seen in education and 100% free.
tandemonimom lm on July 25, 2011:
FABULOUS page, Evelyn! I think the only game I could possibly add to this list would be Muggins. I'll be coming back here to remember the ones I don't have yet!
AngelDey on July 24, 2011:
This is wonderful. Thank you.
akumar46 lm on May 19, 2011:
Great method of teaching Pre-Algebra to children.Nice lens.
akumar46 lm on May 19, 2011:
Great algebra lessons for kids.Thanks for such useful lens.
JanieceTobey on February 07, 2011:
I love your lens on pre-algebra games and activities!!! Can I bless it about twenty times?! Thanks so much for creating this page of fun ways to do math!
TeacherCaren on December 24, 2010:
Balancing, not Balencing.
I find that using food, not games, is an even bigger motivator for people :D.
SofiaMann on December 02, 2010:
You do the math so much fun. Congratulations.
VSP on November 30, 2010:
I loved spirograph as a child. I'd probably like it today too. Am posting this on my fb Homeschool Preschool Through High School page.
Canela Ajena from Houston on September 17, 2010:
great lens. wish someone had played math games with me when i needed help. when it's time for my daughter to learn pre-algebra games will be on my list for ways to help. thanks
Evelyn Saenz (author) from Royalton on March 05, 2010:
@julieannbrady: You certainly put an exciting twist on the subject! I wonder what you are plotting?
julieannbrady on March 01, 2010:
Ah, this sounds so "sexy" my dear ... "Plotting in all Four Quadrants ... Plotting Coordinates on a Cartesian Plane." Don't you think?
Evelyn Saenz (author) from Royalton on January 06, 2010:
@RhondaAlbom: Thank you so much SquidAngel, for featuring this lens. ,
Rhonda Albom from New Zealand on December 31, 2009:
Fantastic! Perfect for our upcoming term. I have made this Link of the month for Jan 2010 on Math Resources for homeschoolers and it is Blessed by this Squidoo Angel.
TrishH LM on November 05, 2009:
This is a great lens. My son is starting to learn some of this and school now and it is a great help for him.
Thanks. going to check out some of your other lenses now.
JoyfulPamela2 from Pennsylvania, USA on October 03, 2009:
Again, great hands-on ideas ~ I love it 5*!
anonymous on April 07, 2009:
Thanks Evelyn for visiting my lens and lens rolling it. I am honoured.
Ialmost forgot - a 5* for this lens. For all the information in here.
Jimmie Quick from Memphis, TN, USA on March 27, 2009:
My daughter will be in 5th grade this fall, so this is helpful!