With over a dozen teacher presentations and a few videos demonstrating how Polyup can be used for a number of concepts, you would think Polyup is the calculator of the future, but sadly it may lead to more frustration than calculation for students. Calculators are designed to "crunch numbers" and help students quickly come up with answers to various operations, and Polyup does that very well. But by limiting which numbers and operations can be substituted or reordered to "fix" the modules Polyup provides, students have very little freedom to explore alternative answers in the preset activities; they have to follow the exact instructions that Poly wants. This could be good if you're teaching students programming concepts and they have to follow very exact rules and roles, but for exploring and teaching math, it could lead to significant frustrations. The RPN (Reverse Polish Notation) method could also lead to confusion transferring information from Polyup to regular classroom instruction. However, for students that really "get it," many machines are available to challenge and inspire them to learn new ideas, as well as a sandbox mode where all numbers and operations are available for experimentation.Continue reading Show less
Polyup is a web-based platform (and iOS and Android app) that provides students with gamified math challenges. Using a cute guide (Poly) and calculation challenges called Poly Machines, students can explore anything from simple operations (add, subtract, multiply, and divide) to more complex sequences and series (like the Fibonacci sequence and solving the Birthday Problem). Polyup walks students through problems that get progressively harder and, on the higher level machines, students are provided with a wide range of operations and functions to choose from.
Polyup also has a freeform sandbox mode and a place for users to submit their own Poly Machines, as well as over a dozen presentations available for teachers that outline how to use Polyup to teach a wide variety of concepts. Students have the choice to create an account that tracks their progress or use a guest account that seems to keep track of progress if they're using the same computer/web browser.
Polyup uses a top-down model, or Reverse Polish Notation (RPN), to do calculations -- which could be very confusing for students. While it works very well for Polyup, this method is counterintuitive for students who have been taught PEMDAS or BEDMAS. Students could easily get confused about which operation is being performed on which set of numbers and how these calculations are being put together to come up with the answer.
The calculations also run extremely fast (unless students can quickly navigate to the "slow down" button, which then runs very slowly), and once an answer has been reached, there are no indications of what went wrong -- simply a statement from Poly of "That is not what I am looking for." This could quickly frustrate students who may not be able to determine where they went wrong. The app addresses some of these issues by providing a variable speed bar and hints when students get stuck, but this feature doesn't seem to be available on the web browser version. For students who are struggling or just being introduced to these concepts, Polyup may be more frustrating than insightful. For students who have a strong grasp of the concepts or want a challenge, then Polyup may be just the game for them.
Key Standards Supported
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Expressions And Equations
Write and evaluate numerical expressions involving whole-number exponents.
Write, read, and evaluate expressions in which letters stand for numbers.
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.
Apply the properties of operations to generate equivalent expressions.
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Operations And Algebraic Thinking
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?.
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.