Ditch the Drill: Multi Board Game
Learning Math with Games Series
Ditch the Drill is my ongoing series on learning math with well-designed games. In this blog post, I'm reviewing the Multi Board Game, a multiplication game created by Joyful Mathematics.
Just so you know, I don't get paid to review games. I only review games that I like, I purchased and that we use. There are too many great games out there to waste time on bad ones.
In addition, I do a bit of research before I puchase a game. We don't use games to trick kids into doing math drill. I want my kids to be excited about math - so math must be the engine of the game.
After playing a well-designed math game, students should have a better understanding of math concepts and how they are related to other math concepts. I want to introduce you to our newest and my son's favorite math game: Multi Board Game created by Federico Chialvo at Joyful Mathematics.
If you were only going to get two math games to help your student work on multiplication, I'd say get Prime Climb and Multi. These two games go together like peanut butter and chocolate. Who doesn't like peanut butter and chocolate?
Prime Climb is, hands down, my favorite math game for multiplication. But that game is going to be hard to beat. While I love it, I don't think the game play is as fun for students as Multi Board Game is. My 10 year old didn't want to stop playing because this game is addictive.
Here's the short and sweet of Multi Board Game:
GAME: Multi Board Game
AGES: 7 - Adult
DESCRIPTION: Multi is a multidimensional version of Tic Tac Toe created by the folks at Joyful Mathematics. Two players play nine simultaneous games of Tic Tac Toe hoping to capture 3 of those in a row to win the whole board. It takes just a few minutes to learn. This game relies heavily on strategy.
CONSTRUCTION: Multi is a well-made game that comes with one large board and a smaller factor board. Both boards store neatly in a square box. In addition to the boards, there are multiple cardboard x's and o's in two sizes. I really appreciated that they included way more board pieces than you'll need. We have a tendency, in our house, to misplace parts.
It is very effective for developing fluency with multiplication facts, factors and multiples without drill. Super rich in critical and strategic thinking skills.
The game offers lots of notice and wonder opportunties, and we did some extension activities, but it's not as easily adaptable as other games on the market.
Multi is very reasonably priced compared to other games in it's class. There is a print and play game version on Joyful Mathematics that is super reasonable.
Overall rating : 4.5 / 5
Our In-Depth Review of the Multi Board Game
There was a time when I insisted on drilling the multiplication facts. Why? Because everyone was doing it. It was how I learned my multiplication facts. It's how my friends learned theirs. It's what you do.
Drilling multiplication facts is mind numbing and does not lead to understanding the relationships between multiples and factors. Drilling doesn't even lead to the knowledge that 4 x 6 is the same as 6 x 4 because we treat them as different math facts.
Beyond problems of understanding, students (and even some teachers and parents) get the idea that math is about speed and accuracy instead of thinking about ideas involving quantity. Students with poor memories are labeled "poor" or "not mathy" and the timed tests lead to math anxiety. We don't drill math facts - ever.
Before You Play the Multi Math Game - Just Look
How Does The Multi Board Game Work? The board is set-up as a traditional Tic Tac Toe board. But inside each square is smaller Tic Tac Toe board. Players must win three in a row on the small squares to claim the large square as theirs.
Before you play the game - just spend some time looking. What do you see?
Find all the multiples of 5. Is there a way to know if a number is a multiple of 5? Where are they located on the board?
Find all the multiples of 9? Where are those located? What does this tell you about how the board is set up?
There is a number that is in the top left corner of each square. What does that number represent?
Are there any numbers that occupy only one square? What do you notice about those numbers? Why do you think some numbers that occupy a single square have prime factors and others do not? What would change if the game board included more factors?
This simple exploring develops players awareness of what is and is not on the board. In Prime Climb, every counting number is on the board from 1-101. While 4 x 12 is 48, 12 is not a factor on the Multi board. Sometimes it's as important to know what isn't included as it is to know what is.
How to Play the Multi Board Game
The game is simple to play. Play begins when player one places a single token on the factor board. We will be using 4, and then she places an X on all squares that have a product of 4.
Player two places his token on the factor board, we will be using 6, and then he places an O on all squares that have a product of 6.
From this point in the game, each player moves only one of the two markers and claims the squares that correspond to the product of the two factors under the markers.
For instance, player one moves the marker from 6 and places it on 3. The product of 4 and 3 is 12. Player one claims all squares with a product of 12, even if the image of the square shows 2 x 6 and not 3 x 4.
Once a player wins three in a row, they place their large X or O to claim that square. Play continues until someone has claimed three large squares in a row.
In order to play this game well, players will need to develop awareness of numbers and their factors; and how to use that information to develop a strategy for winning . This is where the game gets really fun. Because each square is set-up as an array, players don't have to have all the facts memorized to enjoy the game.
I'm a pretty competitive person. I don't "let" my children win. I lost the first two games to my 10 year old.
Multi Board Game: Extension Exercises
Multi doesn't easily lend itself to extention activities. You can calculate game states, but for most homeschooling moms, elementary math teachers and tutors, that's way beyond anything they'll want to get into.
But, if you combine the Multi Board Game with Prime Climb and throw in a some Cuisenaire Rods or other graduated base-ten block and you have a lot of material to use to help student's master the Multiplication Tables without resorting to memorization and drill.
Halving and Doubling: Multi Board Game and the Gattegno Chart
Each square on the Multi board is an array. An array means the factors are organized by rows and columns.
A 6 by 4 array is six units long and four units wide. The total units in the array are 24. There are other arrays that can be made with those 24 units.
This image is part of the Gattegno wall chart. The colors represent Cuisenaire Rods. Colors that are opposite are factors of that number. For instance, 24 has the opposite factors of brown and light green vertically plus purple and dark green horizontally. In this case, brown is 8 and light green is 3. Purple is 4 and dark green is 6.
You'll notice that each successive product is twice the previous product. What do you notice about the factors?
If you make a similar chart using the colors of your base ten blocks, you'll begin to notice patterns that will help student's both play Multi and also make sense of the multiplication table and factors.
For example: factors of six are 2 x 3. Six doubled is twelve. Factors of twelve are 2 x 6 and 4 x 3. When we doubled 6, what stayed the same? What changed? Is that always true? What about when we halve 24 to get 12? What happens to the factors? What changes and what stays the same? How would this knowledge help you play Multi?
Twenty has four factors on the Gattegno chart. Why is there only one 20 on the Multi game board?
Prime Factors: Multi Board Game and Prime Climb
If aren't familar with Prime Climb, I highly recommend that you remedy that situation fairly soon. Prime Climb is the most beautiful representation of number that I've ever seen. The Prime Climb 100 chart is incredibly useful.
Instead of coloring the whole chart, just color the products in the multiplication table 1-9. You can use the Prime Climb color code if you don't have base ten blocks, but because we use Cuisenaire Rods, we colored ours using the Cuisenaire Color system.
Then, we built crosses with the factors. A cross is like a shorthand version of an array made with Cuisenaire Rods. So instead of laying out 6 of the 4 rods or 4 of the 6 rods, we just make a cross with a 4 and a 6.
Physically building the crosses is much better than just looking at an image. Students who don't recognize the symmetry of the board will have no trouble after having built it.
After we built crosses, with our Prime Climb 100 chart in hand, we explored where these factors came from. How do we get from the prime factors to composite factors?
The next thing we did is built towers. Towers are interesting because they are an excellent visual of both multiplication and division. You can manipulate primes and see with your eyes what happens. You can access a free webinar I did on towers here.
If we take the product 48 and explore the factors with the rods, the Multi Game Board, and the Prime Climb chart, we'll soon discover that the factors of 48 are 2 x 24, 4 x 12, 8 x 6, and 3 x 16 and they're going to figure out how they are made. In the hands of a good teacher, students with poor memories will learn how to manipulate those factors to turn multiplication problems they don't like into multiplication problems that do like. Having this ability is way more valuable than memorizing.
Bringing It All Back to the Game Board
After doing some basic exploration of factors and how we get them, we can now use that information to inform our strategy when playing Multi.
Reasoning from one factor pair to another.
Player X wants to claim a 3 x 3 array. The markers on the factor board are on 1 and 7. Is there a way to claim the 9 by moving only one of the factor markers?
Opening Move Strategies
In the opening round, players may only place one marker on the factor board. Players claim those squares whose produce is the same as that factor? Does it make more sense to place a marker on 2 or on 6? Why?
Strategic and Critical Thinking
This is the game board. The 2, 4 and 6 tables were not won by either player. There are 4 squares left. On the 3 table, 3 and 15 are open, on the 5 table 5 and 15 are open. Factor markers are on 1 and 9.
Given that either player can claim tables that have an X and an O, if they need it, what is the best strategy for if it is Player X's turn? What if it is Player O's? How do you know?
Conclusion: Multi Board Game is a Hit
Hit or miss? Well, we only review hits on this blog. So you know it's a hit. How much of a hit? This game is number two on my list for teaching multiplication but number one on my son's. Multi Board Game can be purchased directly from the Joyful Mathematics shop. It comes in a tabletop version and a print yourself version for a mere $5 that can be laminated and used with dry erase markers.