Measurement & Data
Area, Perimeter, and Scaled Graphs
Grade 3
- ✓By the end of this lesson students will be able to understand area as the number of unit squares needed to cover a shape.
- ✓By the end of this lesson students will be able to find the area of a rectangle by tiling it with unit squares and counting.
- ✓By the end of this lesson students will be able to find the perimeter of a polygon by adding the lengths of all its sides.
- ✓By the end of this lesson students will be able to interpret and solve problems using information presented in scaled picture graphs and scaled bar graphs.
Key concepts
Area is the amount of surface a two-dimensional shape covers. We measure area in square units. To find the area of a shape by tiling, you cover the shape completely with unit squares, without any gaps or overlaps, and then count how many unit squares you used. A unit square has sides of 1 unit length, so its area is 1 square unit.
Perimeter is the total distance around the outside edge of a two-dimensional shape. To find the perimeter of any polygon, you add the lengths of all its sides. The units for perimeter are linear units, like inches, feet, or meters.
Scaled graphs help us show a lot of data in a clear way. \n* A **scaled picture graph** uses pictures or symbols, where each picture stands for more than one item. The 'key' tells you how many items each picture represents. For example, one apple symbol might represent 5 students.\n* A **scaled bar graph** uses bars of different lengths to show data. The 'scale' on the axis (usually the vertical axis) tells you how many items each unit on the bar represents. For example, the scale might count by 2s, 5s, or 10s.\nTo read a scaled graph, always look at the key or the scale first to understand what each picture or bar unit means before counting or comparing data.
Key facts to remember
- 1Area is the space inside a 2D shape and is measured in square units.
- 2Perimeter is the distance around the outside of a 2D shape and is measured in linear units.
- 3To find the perimeter, add the lengths of all sides of the shape.
- 4To find the area by tiling, count the number of unit squares that completely cover the shape.
- 5Scaled graphs use a key or scale where one symbol or unit represents more than one item.
- 6Always check the key or scale on a scaled graph before interpreting the data or making calculations.
Worked examples
Example 1
A rectangular placemat is 5 units long and 3 units wide. What is its area? Show your work by imagining tiling it with unit squares.
Answer
The area of the placemat is 15 square units.
Area is always measured in square units.
Example 2
A square sandbox has sides that each measure 7 feet. What is the perimeter of the sandbox?
Answer
The perimeter of the sandbox is 28 feet.
Remember to include all sides when calculating perimeter, even if only one side length is given for a square.
Example 3
Look at the scaled picture graph below showing the number of books read by students in a month.\n\n**Books Read in October**\n* Maria: 📚📚📚\n* David: 📚📚📚📚📚\n* Sarah: 📚📚\n\nKey: 📚 = 3 books\n\nHow many more books did David read than Sarah?
Answer
David read 9 more books than Sarah.
Always multiply the number of symbols by the value in the key to get the actual quantity.
Common mistakes
- ✗Confusing area (the space inside) with perimeter (the distance around the outside).
- ✗Forgetting to add all sides when calculating perimeter, especially for rectangles (only adding the two given sides instead of all four).
- ✗Not using the key or scale correctly when reading scaled graphs (e.g., counting symbols directly instead of multiplying by the key value).
- ✗Using linear units (like feet) instead of square units (like square feet) for area measurements.
Exam tips
- ★Read each problem carefully to determine if you need to find the area or the perimeter.
- ★For perimeter problems, draw the shape and label all side lengths before adding them to ensure you don't miss any sides.
- ★For area by tiling, visualize or draw the unit squares to help count them accurately.
- ★When working with scaled graphs, circle or highlight the key or scale first to make sure you use it correctly for all calculations and comparisons.
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