Topic Fourteen: Area

Pacing (Duration of Unit):

Desired Results

Transfer:
Standards for Mathematical Practices
1. Make 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:

3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.5.a A square with side length 1 unit, called a "unit square," is said to have "one square unit" of area, and can be used to measure area.

3.MD.6 Measure area by counting unit squares.

3.MD.7.a Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

3.MD.7.b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

3.MD.7.c Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b+c is the sum of axb and axc. Use area models to represent the distributive property in mathematical reasoning.

3.MD.7.d Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real word problems.

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fractions of the whole.

Student I Can Statements:
  • I can define a unit square.
  • I can define area as the measure of space within a plane figure and explain why area is measured in square units.
  • I can measure the area of a shape or flat surface by covering it with unit square - with no gaps or overlaps - and counting the number of unit squares used.
  • I can use tiles to find the area of rectangles.
  • I can explain the relationship between tiling and multiplying side lengths to find the area of rectangles.
  • I can multiply adjacent side lengths of rectangles to solve word problems.
  • I can use area models to explain the distributive property.
  • I can decompose an irregular figure into non-overlapping rectangles.
  • I can explain area as additive and use this understanding to solve word problems.
  • I can partition shapes into equal parts.
  • I can explain any unit fraction as one part of a whole divided into equal parts.

Prerequisite Standards
2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Big Ideas:

Measurement
Some attributes of objects are measureable and can be quantified using unit amounts.

Practices, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • What does area mean?
  • What are different ways to find the area of a shape?
  • How can I partition a shape to make equal parts or areas?
  • Why does "what" we measure influence "how" we measure?
Students will know...
  • The amount of space inside a shape is its area, and area can be estimated or found using square units.
  • Square units can be used to create shapes with given areas.
  • Standard measurement units are used for consistency in finding and communicating measurements.
  • The amount of space inside a shape is its area and area can be estimated or found using square units. Formulas exist for finding the area of a polygon.
  • The area of rectangles can be used to model the distributive property.
  • The area of some irregular shapes can be found by breaking apart the original shape into other shapes for which the areas can be found.
  • There are relationships between the perimeter and the area of a polygon.
  • Equal-area parts of a figure can be used to model unit fractions.
  • Some problems can be solved by breaking apart or changing the problem into simpler ones, solving the simpler one, and using those solutions to solve the original problem.
  • In a given measurement situation, the type of measuring tool and the measurement units it contains determine the appropriateness of the tool.

Vocabulary:
area
square unit

Students will be skilled at...
  • measuring the area of a shape by counting the number of square units that cover a region.
  • creating figures with given areas using square units.
  • counting to measure the area of a shape using standard units of area.
  • measuring the area of rectangles by counting squares or by using a formula.
  • modeling the distributive property using the areas of rectangles.
  • solving complex problems asking for the area of irregular shapes.
  • calculate the area of irregular shapes.
  • comparing different rectangles with the same area to discover the change in perimeter.
  • modeling unit fractions using equal areas of parts of figures.
  • selecting appropriate units and tools for measuring the area of given items.

Assessment Evidence

Performance Assessment:


Other Evidence:

Exit Tickets:




Formative Assessment Task:


Learning Plan

Learning Activities:

14-1 The amount of space inside a shape is its area, and area can be estimated or found using square units.

14-2 Square units can be used to create shapes with given areas.

14-3 Standard measurement units are used for consistency in finding and communicating measurements.

14-4 The amount of space inside a shape is its area and area can be estimated or found using square units. Formulas exist for finding the area of a polygon.

14-5 The area of rectangles can be used to model the distributive property.

14-6 Some problems can be solved by breaking apart or changing the problem into simpler ones, solving the simpler one, and using those solutions to solve the original problem.

14-7 The area of some irregular shapes can be found by breaking apart the original shape into other shapes for which the areas can be found.

14-8 There are relationships between the perimeter and the area of a polygon.

14-9 Equal-area parts of a figure can be used to model unit fractions.

14-10 In a given measurement situation, the type of measuring tool and the measurement units it contains determine the appropriateness of the tool.
Resources:

Home School Connection:


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Student Online Videos:
Learn Zillions Video on Multiplication and Area
Learn Zillion Video Relating Multiplication and Area

Teacher Resources: