Ditch the Drill: Prime Climb
Learning Math with Games Series
Ditch the Drill is my new math series on learning math with games. I'm only reviewing math games that I like and ones that we use - this post is about Prime Climb.
My criteria for purchasing a math game is that math must actually be the game, not something tacked on. I'm not using math games to trick my student into doing math drill. Bonus points if I can adapt the game for other learning opportunities.
After playing a well designed math game, students should have a better understanding of math concepts and their relationship to other math concepts. Dan Finkel, creator of Prime Climb, referred to it as math being the engine of the game. It's not an afterthought. Thus, I want to invite you to play one of our current favorite math games.
Prime Climb is easily the most beautiful representation of number I've ever seen. The game board is stunning to look at. But the game has more than just a pretty face. It is a way of seeing and understanding numbers that allows students to discover: how numbers are built; the relationship between multiplication and division; explore exponents; and make sense of fractions. With a little creativity (not very much really), this game can be expanded to study algebraic notation and order of operations.
Here's the short and sweet of the game:
AGES: 7 - Adult
DESCRIPTION: Prime Climb is an easy-to-learn roll and move game, similar in concept to the game SORRY! Roll the dice and move your two pawns from 1 - 101, knocking your opponents back to start as you go. Players use addition, subtraction, multiplication and division to get the center of the board to land exactly on 101. There is just enough chance and strategy to make this game fun and interesting.
CONSTRUCTION: This is a well-made game. The new dice are large and feel good in the hand. The board is solid and has taken a bit of abuse from us. It folds nicely into a square size box. The only issue I have is that the pawns in the new edition are pretty flimsy. We haven't broken them yet, but given the quality of the other components, this was a bit disappointing. I'd spend the extra money to get decent pawns.
It's one of the best games on the market for visualizing numbers, multiplication and division.
The game's brilliant design creates an abundance of opportunity for extention activities that include algebra, exponents, fractions, and more.
This game is a on the higher end as far as board games go. But totally worth it .
Note: Dan Finkel said that the pawn is designed so that you can easily see the number. I still don't like them, but ours are still going strong.
Overall rating : 4.7 / 5
Our In-Depth Review of Prime Climb
Once upon a time, I was really concerned about memorizing math facts. I drilled and drilled. There were tears but we got it done. The problem with drill is that it is mind numbing, ineffective, and not particularly useful when it comes to understanding how numbers work.
You want the truth -- it makes kids hate math. "I went into math because I was really fast on timed tests in 4th grade," said no mathematician ever.
It's been my experience that knowing isolated factor pairs doesn't assist students' understanding of how numbers are built nor how they function in connection with other numbers.
Another problem with drill is that it gives students the idea that math is about speed and accuracy instead of thinking deeply and reflecting on ideas involving quantity.
How Does The Prime Climb Number Representation Work? In the above image we see that 2 is orange. Whenever you see an orange, you know it represents one factor of 2. Nine is made up of two 3's -- there are 2 green sections in the circle. Green is the color of the prime 3. Nine has two prime factors of 3 in it. When we multiply, the factors are combined into the new product 18. We see the two 3's from the nine and the 2 in 18. Easy. Done. Are you sure?
One of the complaints that I've heard from multiple people is that Prime Climb is boring. I'm pretty sure this is an indication of our poor math backgrounds. You couldn't say that if you understood what you are looking at, it's potential or how beautiful it really is.
Do you see the beauty of 18? Does it remind you of six and the one-thirdness of it?
If I remove a three (the one with the arrow), and multiply the other two factors ( 2 x 3), I have a six. One third of what I started with. There are three 6's in 18, and one more would make 4, which means that 1/3 of 18 = 1/4 of 24.
Quick tell me: 1/3 x 18 = 1/4 x 24 = 1/5 x __?__ . We are just counting numbers with a factor of six. It's stunning how you can see this visually.
It's a beautiful display. But perhaps you don't see it yet or I've lost you. Which is exactly the reason you need to play Prime Climb. You need to get in on all this mathy goodness with me.
Before You Play Prime Climb - Just Look
Before you play the game - just spend some time looking. What do you see? Find the first two, then the second, then the third. What do you notice about the colors in three of the 2's? Do the same with 3's. What do you notice?
Count by 2's all the way to 100. Can you predict the primes for each new number?
Count by 3's to 100. Did you find it easier to count to 100 by 3's after counting by 2's? Attend to the primes and make predications. What did you learn about the properties of numbers?
Caleb Gattegno And Prime Climb Extension Activities
Math For Love is not the first to represent numbers with color. Nor are they the first to visualize numbers in this fashion. Cuisenaire came up colored rods a long time ago. Caleb Gattegno popularized Cuisenaire Rods and came up with the product chart for Cuisenaire Rods in 1963.
As soon as I saw prime climb, I knew what I was looking at. I am a giant fan of Gattegno. Our Math Academy is based almost entirely off his work.
This is the Gattegno Wall Chart. Each colored circle on the chart represents a rod - opposite sides are factor pairs. Successive products in each row are double the previous product.
We ditched the Wall Chart for the Prime Climb representation almost immediately.
The Prime Climb representation allows us to see the big picture. They resemble what those of us who use Cuisenaire Rods call towers.
You can watch a free towers training I did here.
I took the Prime Climb circle and colored it according to the Cuisenaire Rods. Maybe you'll begin to see the absolute brilliance of this number representation. Red rods = 2 if white is one. And light green rods = 3 if white is one.
Towers represent multiplication. Each rod in the tower is a factor. By removing a rod, I divide (or multiply by a fraction). When going from 12 to 24, I multiply by two. One more two gets added to the circle and another two is added to our tower. Going from 24 to 12, I remove a rod from the tower, in the same way I remove a red from the circle. Going backward I divided by two or multiplied by 1/2.
If I remove two of the red rods from twelve (2 x 2), what is left is 3. I have divided by 4 or multiplied by 1/4. One fourth of 12 is the rod that's left after removing the two reds.
Prime factoring in color allows students to easily visualize how exponents work.
In the above image, we see that there are there are two factors of two in twelve. That's two squared times three.
And in twenty four, three factors of two. That's 3 to the power of 3 times three.
Multiplying and dividing exponents starts to make sense and becomes accessible to students as young as 6 and 7. Student's further develop an awareness of how this works by coloring the blank Prime Climb 100 chart.
If you have base ten blocks, I'd color the sheet according to your base ten blocks colors (Cuisenaire, Math-U-See, Mortensen) and build the towers to match. There is something about physically manipulating the rods that drives concepts home.
Order of Operations and Notation:
Every time a player lands on a prime number they collect Prime cards. Prime cards come in two types. The first type must be played immediately, the second type is called Keeper Card. Keeper Cards cannot be played immediately and therefore must be kept. Some keeper cards are played on opponents but others allow a player to add or subtract a number. Let's take a look at a possible round for Player 1.
Let's say that Player 1 starts on the number 7 and has two keeper cards. The Keeper Cards are add or subtract 3 and add or subtract 4. Our player then rolls a 9 and 2. Player 2 has pawns on 63 and 4.
It is important to note that the Prime Cards and the dice are operations on "n". The card and dice do not operate on each other. This means that Player 1 cannot multiply 9 and 2 together and add 18 to 7. The cards and dice are always operating on "n" where "n" is the location of the pawn on the board, in this case 7.
Let's look at the options a player has depending on how they order the operations:
Possible Game Plays
(n x 9) - 2
Given that Player 2 has a pawn on 63, Player 1 can multiply 7 x 9 and to land on 63 and send Player 2 home. Player 1 then subtracts 2 to land on a prime number and collect another card. End turn.
9(n + 4) + 2
Player 1 can ignore natural instincts to knock a player out of the game. Instead, adds 4 to his 7 pawn. 11 is a prime number, so Player 1 collects another Prime Keeper Card. Player 1 then multiplies 11 x 9, adds 99 + 2, which takes the pawn home. Player 1 has two keeper cards left. End turn.
9((n - 3) + 4 + 2)
By subtracting 3 from 7, Player 1 lands on 4 and sends Player 2 back to start. Adding first 4 and then 2 puts Player 1's pawn on 10. Player 1 can then multiply 10 x 9 and which puts the pawn on 90. End turn.
One of the problems people have with math is notation. They find it scary. That's because we spoon feed notation to students in the form of worksheets and written problems. They don't have experience taking what is in their head and putting it on paper. Extending plays to include notation would go a long way to solving this problem.
Any player that is able to use notation to express what they are doing draws an extra Prime Card or is allowed an extra roll. Five notations in a row and you skip homeschool math for today (or tomorrow if Prime Climb is math today) - because honestly, 5 well thought out notations in elementary and middle school are far more valuable than 30 problems on a page.
Things to wonder about: How does the order in which cards and dice are played change both the outcome and the notation?
Because I've been trained well by Caleb Gattegno, everything is about the symbols and manipulating them. If the teacher minds the symbols, the numbers (number sense) will take care of themselves.
Leave us a comment about how you are using Prime Climb.