3.MD.7d: Area of Rectilinear Figures

Visual Models to Use

• Grid Paper - Draw rectilinear shapes on grid paper and show how to decompose them into rectangles using different colors
• Tangram Puzzles - Use tangram pieces to create rectilinear shapes, then find the total area
• Floor Plans - Use simple floor plans to show how rooms in a house can be broken into rectangles to find total area
• Decomposition Diagrams - Draw lines showing different ways to break the same shape into rectangles

Everyday Activities

1. Home Designer

Draw a simple floor plan of your home (or just a few rooms) on grid paper. Have your child decompose the L-shaped or T-shaped rooms into rectangles, find the area of each rectangle, and then add them together to find the total area.

2. Garden Planning

Design an L-shaped or T-shaped garden on grid paper. If each square represents 1 square foot, have your child determine how many plants they can fit if each plant needs 1 square foot of space. They'll need to break the garden into rectangles, find each area, and add them together.

3. Playground Measurer

At a playground or park, find an L-shaped or irregularly shaped area. Help your child measure the dimensions and draw it on grid paper. Then have them decompose it into rectangles to find the total area.

4. Area Puzzle Challenge

Cut out several small rectangles of different sizes from grid paper. Challenge your child to arrange them to form different rectilinear shapes, then find the total area by adding the areas of each rectangle.

Strategies When Your Child Struggles

1. Start with Simple Shapes

Begin with L-shapes before moving to more complex rectilinear figures. L-shapes are easiest to decompose into two rectangles.

2. Use Color-Coding

Have your child color each rectangle a different color after decomposing the shape. This helps them visualize the separate rectangles and avoid counting areas twice.

3. Label All Dimensions

Encourage your child to label all dimensions on their decomposed rectangles. This helps ensure they have all the information needed to find each area.

4. Try Different Decompositions

Show your child that there are often multiple ways to decompose the same shape. If one approach seems confusing, try a different way of breaking up the shape.

5-Minute Practice Activities

1. Quick Decompose

Draw a simple rectilinear figure on grid paper. Time your child for 1 minute as they draw lines to decompose it into rectangles. Then give them 2 minutes to find the total area.

2. Missing Dimension

Draw a rectilinear figure on grid paper with some dimensions labeled. Tell your child the total area and have them figure out a missing dimension.

3. Area Comparison

Draw two different rectilinear figures on grid paper. Have your child determine which has the larger area by decomposing each into rectangles.

4. Create Your Own

Challenge your child to create a rectilinear figure with a specific area (e.g., "Draw a rectilinear figure with an area of 24 square units"). They'll need to plan the dimensions of each rectangle to achieve the target area.

Mid-Year Expectations

By the middle of third grade, your child should be able to:

• Understand what a rectilinear figure is (a shape with only right angles)
• Recognize that rectilinear figures can be decomposed into rectangles
• Find the area of simple L-shaped figures by breaking them into two rectangles
• Calculate the area of each rectangle using length × width
• Add the areas of the rectangles to find the total area

End-of-Year Expectations

By the end of third grade, your child should be able to:

• Decompose various rectilinear figures into non-overlapping rectangles
• Find the area of each rectangle efficiently using multiplication
• Add the areas correctly to find the total area
• Solve real-world problems involving the area of rectilinear figures
• Recognize that there may be multiple ways to decompose the same figure

Mastery Signs

Your child has mastered this standard when they can:

• Independently decompose complex rectilinear figures into rectangles
• Accurately find the area of each rectangle and the total area
• Explain their decomposition strategy and why it works
• Find efficient ways to decompose figures to minimize calculations
• Apply this skill to solve real-world problems involving irregular shapes
• Create their own rectilinear figures with specific areas

Below Grade Level

For students who need additional support with basic area concepts and decomposing shapes.

Download Practice Worksheet

At Grade Level

For students who are working at the expected level for this standard.

Download Grade Level Worksheet

Above Grade Level

For students who are ready for more challenging area problems with complex shapes.

Download Challenge Worksheet