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Fantastic Fractions

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Summary

Students will develop an understanding of fractions as parts of a whole.

Coin Type(s)

  • Cent
  • Nickel
  • Dime
  • Quarter

Coin Program(s)

  • 50 State Quarters

Objectives

Students will develop an understanding of fractions as parts of a whole.

Major Subject Area Connections

  • Language Arts
  • Math

Grades

  • Second grade
  • Third grade

Class Time

Sessions: One
Session Length: 30-45 minutes
Total Length: 0-45 minutes

Groupings

  • Whole group

Terms and Concepts

  • Fraction
  • Whole
  • Denominator
  • Numerator

Materials

  • Coins: assortment of cent, nickel, dime, eagle quarter, and ten new quarters (paper coins, copied from the "Reproducible Coin Sheets," on pages 31 and 32)
  • Copies of the "Fantastic Fractions" worksheet (page 23), one per student
  • Scissors
  • Bag

Preparations

  • Prepare one bag of coins.
  • Write four categories on the board, labeled: Cents; Nickels; Dimes; and Quarters.
  • Read over lesson.

Worksheets and Files

Lesson plan, worksheet(s), and rubric (if any) at www.usmint.gov/kids/teachers/lessonPlans/300-305.pdf.

  1. Taking turns, have 10 students choose a coin out of the bag and place a tally mark on the chart under the coin they chose.
  2. Under each category, write as a fraction the number of coins students select out of 10 (example: 5/10 cents, 2/10 nickels, 1/10 dimes, 2/10 quarters).
  3. Draw attention to each of the fractions written. Note that each denominator is the same. Explain that the denominator is the total number of objects that belong to a group. The top number is the numerator, and it stands for only part of the whole.
  4. Hand out copies of the 10 new quarters and have students cut them out.
  5. Collect all the quarter cutouts in a bag and mix them up. Each child should choose 10 quarters from the bag. Each child will have a different collection of quarters.
  6. Pass out the "Fantastic Fractions" worksheet (page 23). Review directions and have students write as fractions the number of each quarter they have out of the total number of quarters they have chosen (10).
  7. Students will be assessed based on their ability to correctly answer the questions about the characteristics of the 10 quarters on the "Fantastic Fractions" worksheet (page 23).

Enrichments/Extensions

  • Students can create their own fraction questions using the quarters.
  • Students can use fractions to create an information poster about their class, displaying information, such as how many students like certain foods, how many are wearing a certain color of shoes, etc.
  • Have students create their own quarter design using a fraction.

Use the worksheets and class participation to assess whether the students have met the lesson objectives.

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: Math
Domain: 2.OA Operations and Algebraic Thinking
Grade(s): Grade 2
Cluster: Represent and solve problems involving addition and subtraction.
Standards:

  • 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, eg, by using 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.

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.

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

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.

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.

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.

Discipline: Language Arts
Domain: All Language Arts Standards
Cluster: Use of Spoken, Written, and Visual Language
Grade(s): Grades K–2
Standards:

  • Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

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.

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.   

Discipline: Language Arts
Domain: All Language Arts Standards
Cluster: Effective Communication
Grade(s): Grades K–2
Standards:

  • Students adjust their use of spoken, written, and visual language (e.g., conventions, style, vocabulary) to communicate effectively with a variety of audiences and for different purposes.

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