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Grade 3 Mathematics Module 4, Topic D: Applications of Area Using Side Lengths of Figures

  Classroom Resource Information  

Title:

 Grade 3 Mathematics Module 4, Topic D: Applications of Area Using Side Lengths of Figures

URL:

 https://www.engageny.org/resource/grade-3-mathematics-module-4-topic-d-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

Module 4, Topic D creates an opportunity for students to solve problems involving area (3.MD.7b). Students decompose and/or compose composite regions into non-overlapping rectangles, find the area of each region, and add or subtract to determine the total area of the original shape. This leads students to design a simple floor plan that conforms to given area specifications (3.MD.7d).

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 3
21. Count unit squares (square cm, square m, square in, square ft, and improvised or non-standard units) to determine area.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Accurately measure area by counting standard unit squares (square cm, square m, square in, and square ft) and non-standard unit squares (e.g., orange pattern blocks or floor tiles).
Teacher Vocabulary:
  • Unit square
  • Length
  • Plane figure
  • Square cm
  • Square m
  • Square in
  • Square ft
  • Improvised
  • Non-standard unit
Knowledge:
Students know:
  • area is a measurable attribute of two-dimensional figures.
Skills:
Students are able to:
  • Determine area of a rectangle by counting unit squares.
Understanding:
Students understand that:
  • A unit square is a square with a side length of 1 unit, and that such a square represents a unit of measurement.
  • The area of a plane figure is measured by counting the number of same-size squares (unit squares) that exactly cover the interior space of the figure.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.3.21.1: Recognize that unit squares are equal.
M.3.21.2: Define the units of measurement (cm, m, in, ft).
M.3.21.3: Express the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

Prior Knowledge Skills:
  • Identify units of measurement for length.
  • Order three objects by length.
  • Compare the lengths of two objects indirectly by using a third object.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.

Mathematics
MA2019 (2019)
Grade: 3
22. Relate area to the operations of multiplication using real-world problems, concrete materials, mathematical reasoning, and the distributive property.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use arrays and area models to represent the distributive property in mathematical reasoning.
  • Given the side lengths of a rectangle, use a multiplication expression to determine the area of the rectangle.
  • Solve real-world problems involving areas of rectangles using concrete materials, reasoning, multiplication, and distributive property.
Teacher Vocabulary:
  • Area
  • Multiplication
  • Distributive property
  • Mathematical reasoning
  • Expression
  • Square unit
  • Multiplicative
Knowledge:
Students know:
  • The area measurement of rectangular regions has a multiplicative relationship of the number of square units in a row and the number of rows.
  • The area of a rectangle with whole number side lengths is the same as the product of multiplying side lengths.
  • How to use an area model to illustrate the distributive property.
Skills:
Students are able to:
  • Relate the area of a rectangle with whole number side lengths and show that the area is the same as would be found by multiplying side lengths.
  • Use concrete materials, arrays and area models to illustrate the distributive property.
  • Solve real-world problems involving areas of rectangles using concrete materials, reasoning, multiplication, and distributive property.
Understanding:
Students understand that:
  • side lengths with unit squares produces rows and columns and that multiplying the number of rows by the number of columns is equivalent to the total number of squares just like arrays.
  • The side length of a rectangle can be rewritten as the sum of two numbers and that when the other side is multiplied by each of those two numbers, then the sum of the products is equal to the area of the rectangle.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.3.22.1: Recognize arrays as multiplication or repeated addition.
M.3.22.2: Recall basic addition and multiplication facts.
M.3.22.3: Build and draw shapes to possess defining attributes.
M.3.22.4: Compose simple shapes to form larger shapes.

Prior Knowledge Skills:
  • Recall doubles addition facts with sums to 20.
  • Apply signs + and = to actions of joining sets.
  • Model written method for composing equations.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.

Mathematics
MA2019 (2019)
Grade: 3
23. Decompose rectilinear figures into smaller rectangles to find the area, using concrete materials.
Unpacked Content
Evidence Of Student Attainment:
Students:
Will use concrete materials to find areas of rectilinear figures by
  • Decomposing the figure into non overlapping rectangles, finding the area of each, and then finding the sum of the areas.
  • Composing rectilinear figures by joining two rectangles (without overlapping) and determine the area of the composed rectilinear figure is the sum of the areas of the two joined rectangles.
Teacher Vocabulary:
  • Compose
  • Decompose
  • Area
  • Additive
  • Rectilinear figure
  • Equivalent
  • Non-overlapping
  • Overlapping
Knowledge:
Students know:
  • Area is a measurable attribute of two-dimensional figures.
  • The area measurement of rectangular regions has a multiplicative relationship of the number of square units in a row and the number of rows.
Skills:
Students are able to:
  • Decompose rectilinear figures as non-overlapping rectangles using concrete materials.
  • Find the area of two rectangles, and create a rectilinear figure by joining the two rectangles (without overlapping), and determine the area of the created rectilinear figure as the sum of the two rectangles.
Understanding:
Students understand that:
  • rectilinear shapes can be decomposed into non overlapping rectangles, and the sum of the areas of the nonverlapping rectangles is equivalent to the area of the original rectilinear shape.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.3.23.1: Label pre-made arrays.
M.3.23.2: Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them.
M.3.23.3: Recall basic addition and multiplication facts.
M.3.23.4: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles).
M.3.23.5: Identify a rectangle.

Prior Knowledge Skills:
  • Define side, angle, face, closed, and open.
  • Use vocabulary related to shape attributes.
    Examples: sides, angles, face, closed, open.
  • Trace shapes.
  • Sort triangles, quadrilaterals, pentagons, hexagons, and cubes.
  • Explore triangles, quadrilaterals, pentagons, hexagons, and cubes.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.3.20 Find the area of a given shape using arrays (unit cubes and tiles) in relationship to multiplication. Limit units to 25.

Tags: area, decompose, length, measurement, rectangles, unit squares
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There are five lessons in this topic.

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Author: Hannah Bradley
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