An Introduction to Basic Math Quads Puzzles and Games
Accelerated Math Practice Using Puzzles (AMP-UP) - AMP-UP is a math practicing program which uses specially designed equation based puzzles and games to challenge students to use their mental math skills in an interactive game play environment. This puzzle concept effectively addresses the following Common Core Math Standards for Grades 3-8 and reinforces these standards with students in Grades 9-16: reference the Common Core Standards initiative, www.corestandards.org:
3rd Grade - Operations and Algebraic Thinking
“Represent and solve problems involving multiplication and division.
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.
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 x ? = 48, 5 =_ ÷ 3, 6 x 6 = ?
Understand properties of multiplication and the relationship between multiplication and division.
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.
Multiply and divide within 100.
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.”
4th Grade - Operations and Algebraic Thinking
“Use the four operations with whole numbers to solve problems.
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.”
4th Grade - Number and Operations in Base Ten
“Generalize place value understanding for multi-digit whole numbers.
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.”
5th Grade - Operation and Algebraic Thinking
“Write and interpret numerical expressions.
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.”
6th Grade - Expressions and Equations
“Apply and extend previous understandings of arithmetic to algebraic expressions.
Write and evaluate numerical expressions involving whole-number exponents.
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
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.”
7th Grade - Expressions and Equations
“Use properties of operations to generate equivalent expressions.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."”
8th Grade - Expressions and Equations
“Work with radicals and integer exponents.
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.”
AMP-UP contains four titled skill levels of puzzles, Elementary Math Quads, Basic Math Quads, Advance Math Quads and Binary Quads Puzzles and Games. These instructional strategies helps teachers and parents teach their students deductive and inductive reasoning techniques, which will be invaluable and applicable in any profession they may choose in the future.
Quads Puzzles - These are equation puzzles with a format similar to traditional crossword puzzles. The equations in the first three puzzle formats follow a traditional decimal number structure and the rules set forth in The Order of Operation. Each equation is then rotated up to 360 degrees on its traditional left axis to form vertical, horizontal and diagonally orientated and crisscrossed equations to increase the levels of difficulty.
Binary Quads Puzzles represents a more advance formats based on a unique equation configuration I called Binary Mixed Equations. Each equation may contain a mixture of traditional decimal numbers such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and binary number sequences of ones (1s) and zeros (0s), which must be converted to decimal numbers to solve the equation.
I create this format to begin teaching my students about a basic and central mathematical concept, which has been essential to the creation of our computer base society, Binary Numbers. A tutorial of the binary to decimal conversion process called Binary Coded Decimal is included in this packet.
- Thirty sets of four Basic Math Quads Puzzles and Games (120 puzzles). Note: These puzzles were designed to be used for multiple lessons over many years. All puzzles are UV Coated and individually contained in a protective plastic sleeve to fulfill this expectation. Only Dry or Wet Makers should be used on the sleeved puzzles to protect the surface. However, it is recommended that plastic document protectors be used to allow the puzzle set to be stored within a binder.
- Support Materials - Five sheets containing introductions, strategies, Answer Keys and game play instructions. Note: The sheet containing the game instruction is copy ready. I authorize any Classroom Teachers purchasing this packet to maintain 30 copies of this sheet in their inventory for their students use.
- Binary to Decimal conversion Tutorial
More information about these and other products and support materials can be found on my website at www.coygonarts.com. Thank you for considering my lesson materials.
Coygon Robinson Jr.