Piggy+Bank-+Quarter+Version

= = = Continuing the Investigation = As you play **Quarter Piggy Bank**, reflect on the following:

Mathematics Involved:
1.) What is the mathematical reasoning that is possible as the game is being played? 2.) What standards are being addressed? 3.) What are some strategies or mathematical models I can promote through thinking aloud?

Pedagogical Issues:
1.) What are effective ways to introduce the game? 2.) Who could benefit from playing this game? 3.) How can I facilitate student autonomy in playing the game? 4.) How can I get students to share their thinking with their peers while playing the game?

Ways to Improve the game:
1.) Appearance 2.) Wording of rules 3.) Changing of rules

NCTM Standards:

Number and Operations
=== 1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems=== ==== Pre-K–2 Expectations: In pre-K through grade 2 all students should–====

• count with understanding and recognize "how many" in sets of objects; • use multiple models to develop initial understandings of place value and the base-ten number system; • develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections; • develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers; • connect number words and numerals to the quantities they represent, using various physical models and representations; • understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. ==== Grades 3–5 Expectations: In grades 3–5 all students should–====

• understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals; • recognize equivalent representations for the same number and generate them by decomposing and composing numbers; • develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers; • use models, benchmarks, and equivalent forms to judge the size of fractions; • recognize and generate equivalent forms of commonly used fractions, decimals, and percents; • explore numbers less than 0 by extending the number line and through familiar applications; • describe classes of numbers according to characteristics such as the nature of their factors. === 2. Understand meanings of operations and how they relate to one another=== ==== Pre-K–2 Expectations: In pre-K through grade 2 all students should–====

• understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations; • understand the effects of adding and subtracting whole numbers; • understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally. ==== Grades 3–5 Expectations: In grades 3–5 all students should–====

• understand various meanings of multiplication and division; • understand the effects of multiplying and dividing whole numbers; • identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems; • understand and use properties of operations, such as the distributivity of multiplication over addition. === 3. Compute fluently and make reasonable estimates=== ==== Pre-K–2 Expectations: In pre-K through grade 2 all students should–====

• develop and use strategies for whole-number computations, with a focus on addition and subtraction; • develop fluency with basic number combinations for addition and subtraction; • use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. ==== Grades 3–5 Expectations: In grades 3–5 all students should–====

• develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50; • develop fluency in adding, subtracting, multiplying, and dividing whole numbers; • develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results; • develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience; • use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; • select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.