Fantastic Fractions

Discipline: Math Domain: 2.OA Operations and Algebraic Thinking Grade(s): Grade 2 Cluster: Add and subtract within 20 Standards:

• 2.OA.2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, eg, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Discipline: Mathematics Domain: K-2 Number and Operations Cluster: Compute fluently and make reasonable estimates. Grade(s): Grades K–2 Standards: In 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; and
• use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

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Discipline: Mathematics Domain: K-2 Number and Operations Cluster: Understand meanings of operations and how they relate to one another. Grade(s): Grades K–2 Standards: In 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; and
• understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

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Discipline: Mathematics Domain: All Problem Solving Cluster: Instructional programs from kindergarten through grade 12 should enable all students to Grade(s): Grades K–2 Standards:

• Build new mathematical knowledge through problem solving
• Solve problems that arise in mathematics and in other contexts
• Apply and adapt a variety of appropriate strategies to solve problems
• Monitor and reflect on the process of mathematical problem solving

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Discipline: Mathematics Domain: 3-5 Number and Operations Cluster: Compute fluently and make reasonable estimates. Grade(s): Grades K–2 Standards: 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; and
• 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.

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Discipline: Mathematics Domain: 3-5 Number and Operations Cluster: Understand meanings of operations and how they relate to one another. Grade(s): Grades K–2 Standards: 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; and
• understand and use properties of operations, such as the distributivity of multiplication over addition.

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Discipline: Mathematics Domain: 3-5 Number and Operations Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Grade(s): Grades K–2 Standards: 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; and
• describe classes of numbers according to characteristics such as the nature of their factors.

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Discipline: Mathematics Domain: K-2 Number and Operations Cluster: Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Grade(s): Grades K–2 Standards: In 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; and
• understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.

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Discipline: Mathematics Domain: All Communication Cluster: Instructional programs from kindergarten through grade 12 should enable all students to Grade(s): Grades K–2 Standards:

• organize and consolidate their mathematical thinking through communication
• communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
• analyze and evaluate the mathematical thinking and strategies of others; and
• use the language of mathematics to express mathematical ideas precisely.