Topic 15: Equal Shares of Circles and Rectangles

Pacing (Duration of Unit): 4 Lessons

Desired Results

Transfer:
1. Makes sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Established Goals:
  • 1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Student "I Can" Statements:

  • I can understand that "halves" means two equal parts and "fourths" or "quarters" means four equal parts.
  • I can break circles and rectangles into equal parts and use the words whole, halves, fourths, and quarters to talk about them.
  • I can understand that breaking circles or rectangles into more equal parts means that the parts will be smaller.

Prerequisite Standards:
  • K.G.1: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
  • K.G.2: Correctly name shapes regardless of their orientations or overall size
  • K.G.3: Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
  • K.G.4: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).
Big Ideas:

Comparison and Relationships
Numbers, expressions, measures, and objects can be compared and related to other numbers, expressions, measures, and objects in different ways.


Geometric Figures

Two- and three-dimensional objects with or without curved surfaces can be described, classified, and analyzed by their attributes. An object's location in space can be described quantitatively.

Practices, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • What are some different names for equal shapes?
Students will know...

  • A region can be divided into equal sized shares in different ways. Equal sized shares of a region have the same area but not necessarily the same shape.
  • Shapes can be divided into equal parts called halves and quarters, or fourths.
  • When dividing a whole into fractions, the smaller the fractional piece, the greater the number of pieces; the larger the piece, the fewer the number of pieces.
  • Mathematicians use math they know to show and solve problems.


Vocabulary:

equal shares, halves, fourths, quarters
Students will be skilled at...

  • Determining whether shapes are divided into equal shares,
  • Dividing shaped into 2 and 4 equal shares and use words to describe those shares.
  • Understanding that more equal shares of the same whole creates smaller shares.
  • Understanding how to make a drawing to show a problem about equal shares.

Assessment Evidence

Performance Assessment:
Other Evidence:

Formative Assessments:

Learning Plan

Learning Activities:

15-1 A region can be divided into equal sized shares in different ways. Equal sized shares of a region have the same area but not necessarily the same shape.
15-2 Shapes can be divided into equal parts called halves and quarters, or fourths.
15-3 When dividing a whole into fractions, the smaller the fractional piece, the greater the number of pieces; the larger the piece, the fewer the number of pieces.
15-4 Mathematicians use math they know to show and solve problems.
Resources:

Problem of the Month:


Centers:



SmartBoard Resources/Games:

*