Learning Well at Home

Category: Math Games

  • Review of Charlotte Mason a Living Math

    Review of Charlotte Mason a Living Math

    Eight years ago, a conversation about Charlotte Mason, Gattegno, and mathematics landed in my Facebook group, Learning Math with Base Ten Blocks. My friend and my sidekick, Lacy, was engaging the Charlotte Mason community and introduced many families to Cuisenaire rods. The conversation quickly turned to whether Cuisenaire rods fit within a Charlotte Mason education. I thought we were discussing beans and rods. I wrote my response to that conversation. Looking back, we were asking a much larger question. Denise Gaskins participated in those discussions and wrote several essays exploring the relationship between Charlotte Mason’s philosophy and mathematics. Eight years later, she has written Charlotte Mason’s Living Math. I’ve been waiting for this book for eight years. I just didn’t know it until she wrote it.

    Denise Gaskins is the founder of Tabletop Academy Press and the author of Let’s Play Math, the Math You Can Play series, and now Charlotte Mason’s Living Math. Through her website, Let’s Play Math, she has spent years writing about mathematical play, games, puzzles, investigations, and

    learning. She also runs the Math Teachers at Play (later Playful Math) Blog Carnival, a monthly collection of articles from classroom teachers, homeschool educators, mathematicians, and recreational math enthusiasts. I hosted several editions of the carnival over the years, and its archives remain one of my favorite collections of mathematics resources.

    Denise and I have known each other for nearly a decade. She has always been generous with her time and careful with her words. Because she remains my fairy math mother, I’m not pretending to be neutral. 

    Underlying Assumptions About Math and Charlotte Mason

    Before I can review Denise’s book, I need to answer an underlying question.

    Denise is asking what it means to teach mathematics in a way that is faithful to Charlotte Mason’s educational philosophy. Charlotte Mason described education as the science of relations. 

    Calling something “Charlotte Mason friendly” isn’t enough. Many educational methods are compatible with Charlotte Mason. That doesn’t mean they arise naturally from her philosophy. I want to answer this question: If we truly taught mathematics as a science of relations, what would it look like? That is the measure by which I read Denise’s book. Not can you use it if you are a careful reader of Charlotte Mason, but if you are a careful reader of Charlotte Mason, how does her philosophy intersect with math. 

    I come to that question with my own assumptions. You should know what they are. I know many of my readers are highly inclined toward Charlotte Mason. It helps to know where my potential biases are.

    One of them is that numbers are not objects. You can’t point to something and say, “This is a ten.” The orange Cuisenaire rod isn’t ten. It is a colored rod made of plastic or wood. In our lessons, we don’t mark the rods, and we don’t encourage children to call them by number. Only after establishing that the white rod represents one do we name the rod ten. We use “white = 1” as the unit by which other rods are measured. The same orange rod can represent one, and then white would be 1/10. One hundred and white would be ten. The relationship provides context and meaning. The rod is the object. 

    You cannot know ten on its own. We know it through the infinite relationships that point to ten and give it its meaning. Ten is two fives and five twos. Ten is half of twenty. Ten is one more than nine, but one less than eleven. It is the same length as two light green rods and a purple when white is the unit. None of these relationships is ten. Each one enriches the child’s understanding of what ten refers to.

    If education, including math, is truly a science of relations, then I would expect children to come to know numbers through richer networks of relationships rather than through isolated facts or procedures. New ideas would grow naturally from earlier relationships. Learners would develop fluency because each new relationship gives the child another way of knowing the same referent. Most of all, I would expect mathematics to become more coherent as children learn, not more fragmented.

    That is the lens I bring to Denise’s book. It isn’t the only possible lens, but it is the one I find most faithful to Charlotte Mason’s phrase, the science of relations. 

    Part One: The Philosophical Foundation

    Before Denise tells us how to teach mathematics, she asks a more important question: What is mathematics for?

    That choice sets the tone for the entire book. Rather than beginning with curriculum, manipulatives, or lesson plans, Denise begins with Charlotte Mason herself. She argues that if we want a genuinely Charlotte Mason mathematics education, we must first understand Charlotte Mason’s educational philosophy. Only then can we ask how mathematics fits within it.

    Denise takes Mason’s insistence on relations seriously. Instead of asking which manipulatives or textbooks Charlotte Mason might have approved of, she asks how Mason’s principles should shape the way we think about mathematics itself. Throughout these opening chapters, she returns to familiar Mason themes: children are born persons, education is an atmosphere, a discipline, and a life, the cultivation of good habits, living ideas, narration, and the training of reason. Her point is that mathematics should not stand outside this philosophy. We should teach mathematics according to the same principles that govern every other subject.

    Part Two: From Philosophy to Practice

    Once Denise has established the philosophical foundation, she shows readers what those principles look like in practice. Rather than presenting a prescribed curriculum, she offers a way of thinking about mathematics lessons. The emphasis remains on reasoning, conversation, investigation, and the habits of mind that Charlotte Mason believed education should cultivate. Mathematics is treated as something children actively engage with rather than passively receive. Gattegno said somewhere, “We give children things to do and stuff to talk about.” Mason was doing the same thing. Denise shows you how to do it with math. 

    One strength of this section is that Denise draws from a wide range of mathematicians and mathematics educators. She does not recreate a nineteenth-century classroom. Instead, she asks which modern practices embody Charlotte Mason’s philosophy. The result is a book that is both historically grounded and educationally current. Readers will encounter mathematical games, investigations, conversations, puzzles, and rich problems, all chosen because they encourage children to reason and make connections rather than simply produce correct answers.

    I was pleased to see the Substitution Game included among the mathematical conversations. Substitution is one of the most important mathematical ideas children encounter. It teaches them that different expressions can refer to the same mathematical reality. That habit of recognizing equivalence reaches far beyond arithmetic and becomes foundational for algebra, functions, and higher mathematics. Its inclusion here illustrates Denise’s larger point: mathematics grows through relationships between ideas, not through the accumulation of isolated facts.

    Is Denise Faithful to Charlotte Mason’s Philosophy?

    I believe the answer is yes.

    One of the strengths of Charlotte Mason’s Living Math is that Denise refuses to reduce Charlotte Mason to a collection of educational techniques. She does not ask whether Charlotte Mason would have approved of Cuisenaire rods, games, or a particular curriculum. Instead, she begins where Charlotte Mason herself began: with a philosophy of education.

    The opening chapters establish that philosophy before discussing mathematics. Denise returns repeatedly to Charlotte Mason’s central ideas about children and education. Rather than treating mathematics as an exception, Denise shows you how to enter the arena of mathematical relationships instead of learning about them. She does this by showing you how to apply Mason’s ideas to math. That was the premise of the response I wrote eight years ago.

    That argument isn’t window dressing. It changes the conversation from “Which math curriculum would Charlotte Mason have used?” to the much more interesting question, “What would mathematics look like if it were taught according to Charlotte Mason’s philosophy?”  Those are not the same questions. There is no equal sign between them. The first looks for historical approval. The second asks whether a way of teaching grows naturally from Charlotte Mason’s understanding of education.

    By beginning with philosophy rather than methods, Denise gives readers a coherent framework for evaluating mathematics instruction. Whether or not one agrees with every application, the argument grows naturally from Charlotte Mason’s educational principles rather than from a collection of isolated quotations. For me, that is the book’s greatest strength. It also is the approach that has shaped my own work for the past eight years.

    Finally, Is the Book Helpful?

    That depends.

    Helpful for what? Here we encounter those referents again. Like the number 10, helpful needs to refer to something. 

    If you’re looking for a guide to navigating a national park, probably not.

    If you’re looking for a complete mathematics curriculum, again, no.

    If you’re looking for a scripted lesson to teach tomorrow morning, only in the broadest sense.

    But those aren’t the questions this book is trying to answer. If you’re looking for help rethinking your relationship to mathematics, then I believe the answer is yes.

    If you’re a Charlotte Mason parent trying to understand what it means to teach mathematics according to Charlotte Mason’s educational philosophy, then I believe the answer is absolutely yes.

    Denise is not trying to hand parents another curriculum. She is offering a vision. Like Let’s Play Math, this book gives parents permission to believe that mathematics is something children can reason about, wonder about, discuss, investigate, and enjoy. It invites parents to treat children as people who have mathematical ideas worth listening to.

    For many parents, that shift in orientation will be far more valuable than another collection of lesson plans.

  • Ditch the Drill: Multi Board Game Review

    Ditch the Drill: Multi Board Game Review

    Ditch the Drill: Multi Board GameLearning 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:

    Ditch the Drill · Game Review

    Multi Board Game

    Game

    Multi Board Game

    Ages

    7–Adult

    Players

    2

    Description

    Multi is a multidimensional version of Tic Tac Toe created by Joyful Mathematics. Two players play nine simultaneous games of Tic Tac Toe, hoping to capture three of those in a row to win the whole board. It takes only a few minutes to learn and relies heavily on strategy.

    Construction

    Multi is a well-made game with one large board and a smaller factor board. Both boards store neatly in a square box. The game includes cardboard Xs and Os in two sizes, with plenty of extra pieces.

    Effectiveness

    Very effective for developing fluency with multiplication facts, factors, and multiples while building critical and strategic thinking.

    Adaptability

    The game offers many opportunities to notice and wonder, although its basic gameplay is less adaptable than some other math games.

    Price

    Very reasonably priced compared with similar games. Joyful Mathematics also offers an inexpensive print-and-play version.

    What Works Well

    • Develops fluency with the 1–9 multiplication tables.
    • Builds attention, focus, and strategic thinking.
    • It is a blast to play.

    Things to Consider

    • Gameplay is limited to multiplication.
    • It is less adaptable than some other games.

    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. 

    The Problem:

    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. 

    The Solution:

    The creators of Multi Board Game have created a game that allows students to interact with the structure of the multiplication tables 1-9 and easily understand the relationships between factors and multiples. This alone makes mastering the 1-9 times tables simpler and more efficient.  Not only that, students develop the ability to use those connections to strategically play the game. 

    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?

    How many squares have a product of 9? How many squares have a product of 18? What about 16?

    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. 

    Happy Mathing!

  • Ditch the Drill: Prime Climb Review

    Ditch the Drill: Prime Climb Review

    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:

    Ditch the Drill · Game Review

    Multi Board Game

    Game

    Prime Clime

    Ages

    7–Adult

    Players

    2 – 4

    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. Note: Dan Finkel said that the pawn is designed so that you can easily see the number.  Edit August 2026: I’ve grown used to them and ours are still going strong.

    Effectiveness

    Very effective for developing fluency with multiplication facts, factors, and multiples while building critical and strategic thinking.

    Adaptability

    The game offers many opportunities to notice and wonder, although its basic gameplay is less adaptable than some other math games.

    Price

    Very reasonably priced compared with similar games. Joyful Mathematics also offers an inexpensive print-and-play version.

    What Works Well

    • Develops fluency with the 1–9 multiplication tables.
    • Builds attention, focus, and strategic thinking.
    • It is a blast to play.

    Things to Consider

    • Gameplay is limited to multiplication.
    • It is less adaptable than some other games.

    Overall Rating

    4.5 / 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.

    The Problem:

    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.

    The Solution:

    The creators of Prime Climb have created a visual representation of number based on primes by attaching a corresponding color for prime numbers between 1-10 and one additional color for primes over 10. This allows students to visualize numbers and see what is happening with the math.

    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. 

    Exponents:

    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 2 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

     1. (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. 

     2. 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.

     3. 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.

    All Prime Climb Images courtesy of Math for Love. You can get Prime Climb here. 

    Leave us a comment about how you are using Prime Climb.