Math Playground, is a dynamic, for-all-ages, arena filled with engaging math game, introduced by YPP at the 2024 National Tournament in Cambridge, MA.  Playgrounds are organized by four “lands”: Number Discovery, Flagway, Algebra, and Fractions/Ratio.  Each of the four lands reflect YPP's pedagogical approach of using games, activities, and a focus on multiple representations to develop conceptual understanding and build procedural fluency with mathematical concepts. Activities draw on YPP's catalog of games and activities developed over the years; are developed by math literacy workers in response to noticing a particular conceptual challenge their younger students are having; are developed in collaboration with mathematicians to make higher level math concepts accessible to elementary students.

Number Discovery Land

Number Discovery Land helps 2nd - 6th graders develop skills across the following strands: Operations and Algebraic Thinking, Number and Operations in Base 10, and Geometry. Concepts include fluency with addition, subtraction, multiplication, and division; categorization and fluency with odd/even, and prime/composite numbers; and analyzing shapes.

• Factorization Puzzles. Build a factor tree using prime and composite numbers that may or may not belong. Players place the largest number at the top and continue to break that number down leaving only prime numbers at the bottom, to complete a puzzle.
• Prime Hunt. Sort a deck of number cards into two groups, one being prime, and the other composite. Players usually play multiple 30 second rounds against an opponent to work on speed and accuracy.
• Prime Factor Card (PFC) Match Up. Place number cards on the correct PFC. Players see a displayed deck of PFCs either in order from least to greatest or randomized. They use the prime factors to multiply together and place the number card they are holding on that same spot.
• Math Ladder. Solve equation cards and place them along the ladder. Players see two displayed decks of equation cards to solve.
  Connect Four. With a random assortment of equations for age and grades, students will solve math problems. Once solved, they must compete in a game of connect four.
• Math Race. Use operations to solve equations to build fluency with math seen in the classroom to advance their understanding and accuracy of math problems while competing with other students.
• Find The Path. Students from grades 2-5, answer addition and subtraction with fraction questions while on a grid of 12-16 poly spots starting from one end and trying to end at the opposite side.
• Geometry Character Creation. Use all of the pre-selected shapes to create a body, head, face, and hair. Once drawn in pencil kids are free to color in their character. This helps with understanding shapes/basic geometry
• Rock Paper Scissors Multiply Challenge. Competitive form of rock paper scissors using their fingers (2-5). When two students face off, if one player has 3 fingers up and the other 5, they will multiply the fingers to find the product.
• Wind and Talk. Place numbers in a winding game structure and notice similarities between the number you have, and the numbers already placed. The structure is 12 cones in a circle like a clock, and students go clockwise starting from 12.
• Making Jewelry with Beads. With a given amount of beads, participants will create a bracelet using a pattern. For example: for every 2 green beads, 1 black bead, or for every 4 blue beads, follows 2 red beads. At the end of this activity, participants will get to learn about the ratio they used and go home with a bracelet. Younger students can represent the pattern by drawing a picture, older students can represent the pattern in a table and on a graph.

Fraction Land

Fraction Land helps 3rd - 6th graders understand fractions. Concepts include working with unit fractions with a numerator of 1, adding and subtracting fractions, fraction equivalence, and adding/subtracting and multiplying and dividing fractions by whole numbers.

• Fraction Finding Relay. Students find a fraction on a number line using dice determining the numerator and denominator
• Piece of Pi*. Played with cards, where players take turns matching fraction cards with pictorial representations of fractions.
• Roll that Fraction*. Using a pair of dice, students will label one die the numerator and the other denominator. Playing against an opponent, whomever rolls the larger fraction gets to place their fraction on a number line. They continue for 5 rounds and the player with the biggest fractions wins.
  
  * Piece of Pi and Roll that Fraction are games developed by the YPP Math Playbook team in partnership with the Cambridge Design Lab.

Flagway Land

Flagway Land helps 4th - 7th graders deepen and apply their number sense to a study of the Mobius Function, which categorizes the natural numbers into three mutually exclusive groups according to the prime factorization of the number. Students use algebraic representations of numbers to support categorization and multiplicative fluency skills. Flagway builds number sense and helps students apply algebraic expressions to solve a math problem. 

• Factor Tree. The facilitator will give them a number and the first person to complete a factor tree correctly wins that round. A correct factor tree must include the prime factors listed from least to greatest, and all prime numbers on the factor tree must be circled.
• Flagway Tic Tac Toe. To get three Xs or Os in a row, diagonal, horizontal, and vertical. Players must solve a problem from the Flagway Game, in order to earn Xs and Os, and then place them on the Tic Tac Toe board. 
• Walk The Structure OGP. Develop your own rules to categorize a set of numbers into three mutually exclusive groups. Assign each group a color (e.g., orange, green, or purple) and walk a flagway structure 
• Math Escape Room. Players solve a sequence of increasingly difficult problems based on the Flagway Game to make it through the Math Escape Room. 
• Algebra Form Layout. Timed relay race where players race against the clock and other players place the correct prime factor card with its corresponding algebra form.

Algebra Land

Algebra Land helps 6th - 8th graders develop skills in the following strands: Ratio and Proportional Relationships, Expressions and Equations, and Statistics and Probability. Concepts focus on representations of ratio relationships, trip lines and the idea of a movement number, probability and random walks on mathematical objects, and introduction to functions. 

• The Algebra Project Trip Card Game. Players take turns making books of three cards, such that each book represents a valid trip on a trip line. Each book of three cards must have two location cards, representing the start and finish of the trip, and a movement number card, representing the displacement comparing the finish to the start of the trip. Trips represent linear equations in one dimension. 
• Random Walks. A “random walk” can be thought of as a trip that is controlled by a coin flip. Building on the Trip Line model, if someone starts on the Trip Line at the “benchmark” (the point labeled “0”) and then flips a coin and if “heads” you take one step to the right and “tails” you take one step to the left, the path you take is called a random walk. Random walks will provide students an early experience of probability. In addition, having the class produce many “sample paths” will generate data sets that will be the source of an introduction to statistics. Students can “bet” on what the most likely landing spot would be after some number of coin flips and how probable it would be for a person to end up at a place after a certain number of coin flips. YPP has created random walk activities that are played on different mathematical objects: tree diagrams, circles with a discrete number of points on them, trip lines, and directed graphs.
• Human Programming. Write a set of instructions, with fewer than 10 lines or "steps," that navigate across an obstacle course from start to the. Players are placed in a specific location that contains random objects they need to cross, bypass, or turn away from. As coding requires you to be specific in your code this teaches the same discipline to be intentional and precise a key mathematical practice standard. 
• Hula Hoop Race. Team stand in a circle and hold hands. They place a hula hoop over two people's hands. How many people can go through the hoop in 10 seconds without anyone breaking hands? Continue this process but increase the time to 15 seconds, 20 seconds, and then 30 seconds. What is the ratio of the number of people through the hoop to the number of seconds for each round? Represent these ratios in a table and on a graph. Discuss the data: which round was the fastest? what would the table or graph look like if players played at a constant rate from round to round?