Unit Overview: The Chinese Zodiac and the Division Algorithm

Aim: How can the Chinese zodiac help us examine important relationships in the division of numbers?

Objectives: Students build on their intuitive understanding of equivalence in everyday situations and apply that practical knowledge to exploring the cycles and equivalence classes within the Chinese zodiac. Students move from the physical event of winding around chairs to employing a formula or general rule for finding the zodiac sign for any year: Year = 12 x Number of winds + Remainder. In the form for the division algorithm, this becomes d = nq + r, where d is the dividend, n is a whole number, q is the quotient, and r is the remainder. Grade Level: Third-fourth

Number of 60-Minute Periods: Two periods for this lesson; 12-15 days for the unit Source: Algebra Project Transition Curriculum

NCTM Teaching Principles: Access and Equity, Curriculum, Tools and Technology, Assessment

NCTM Standards

• Algebra: Understand patterns, relations, and functions; represent and analyze mathematical situations and structures; use mathematical models to represent and understand

quantitative relationships

• Number and Operations: Understand meanings of operations and how they relate to one

another; compute fluently and make reasonable estimates

CCSSM Standards

  • 3.OA.A.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
  • 3.OA.C.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.
  • 3.OA.B.5. Apply properties of operations as strategies to multiply and divide.
  • 3.OA.D.8. 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.OA.D.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.
  • 4.OA.A.1. Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.
  • 4.OA.A.2. Multiply or divide to solve word problems involving multiplicative comparison,
  • 4.OA.A.3. 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.

NCTM Processes/CCSSM Mathematical Practices

• Problem Solving

SMP1: Make sense of problems and persevere in solving them.

• Reasoning and Proof

SMP2: Reason abstractly and quantitatively.

SMP8: Look for and express regularity in repeated reasoning.

• Communication

SMP3: Construct viable arguments.

SMP6: Attend to precision.

• Representation

SMP4: Model with mathematics.

Prerequisites

  • • Previous experience with equivalence, equality, and "making-do"
  • • Knowledge of the Chinese zodiac

Mathematical Concepts

  • • Equivalence and division/multiplication relationships
  • • Division algorithm

Materials and Tools

  • • Table of years of the Chinese zodiac
  • • Drawing paper and art supplies
  • • Worksheets from the Algebra Project Transition Curriculum (See figures in this lesson.)
  • • Twelve chairs arranged in a circle

Management Procedures

  • • Arrange 12 chairs in a circle for the Winding Game portion of the lesson.
  • • Divide students into groups for the purpose of designing the zodiac sign posters in order to complete the equivalence charts and to play the Winding Game.

Assessment: The completed worksheets become part of each student's portfolio compiled throughout the Algebra Project units. There is no formal test covering these topics. The primary goal of the Algebra Project units is to strengthen the confidence of the students in their study of mathematics.

 
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