Grade 4 · Mathematics
Quarter 3 · Week 2 · TEKS
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This lesson helps Grade 4 students understand how to use visual models to find formulas for the perimeter of rectangles and squares, as well as the area of rectangles. Students will explore the formulas l + w + l + w, 2l + 2w for perimeter, the special case 4s for squares, and the area formula l × w. They will then apply these formulas to solve problems with whole number dimensions, building algebraic reasoning skills aligned with TEKS standards.
Students should understand the concepts of length and width as dimensions of rectangles and squares, be familiar with addition and multiplication of whole numbers, and have experience with basic geometric shapes.
Perimeter is the total distance around a shape. For rectangles, the perimeter is the sum of all four sides. Since opposite sides of a rectangle are equal in length, the perimeter can be found by adding length and width twice: l + w + l + w. This can be simplified to 2l + 2w. For squares, all four sides are equal, so the perimeter is 4 times the length of one side, written as 4s.
Visual models such as drawings on grid paper or physical cut-outs help students see that a rectangle has two lengths and two widths. By counting units along the sides, students can add the sides to find perimeter. Grouping the two lengths and two widths shows why 2l + 2w works. For squares, counting all four equal sides shows why 4s is the formula.
Area measures the amount of space inside a shape. For rectangles, area is found by multiplying length by width (l × w). Using grid paper, students can count the number of square units inside a rectangle to see that area equals the number of length units times the number of width units.
By drawing rectangles on grid paper and counting the total squares inside, students observe that area equals the number of squares along the length times the number along the width. This concrete counting helps students understand why the formula for area is l × w.
Students apply the perimeter and area formulas to solve real-world problems where length and width are whole numbers. Problems can involve finding missing dimensions, calculating total fencing needed (perimeter), or determining the amount of flooring needed (area). This practice reinforces understanding and connects math to everyday life.
A rectangle has length 5 units and width 3 units. Use a model or drawing to find its perimeter using both addition and the formula 2l + 2w.
First, add all sides: 5 + 3 + 5 + 3 = 16 units. Using the formula: 2 × 5 + 2 × 3 = 10 + 6 = 16 units. Both methods give the same perimeter, confirming the formula works.
The perimeter is 16 units by both addition and the formula.
A square has side length 4 units. Find its perimeter using the formula 4s.
Since all sides of a square are equal, multiply the side length by 4: 4 × 4 = 16 units. This is the total perimeter.
The perimeter of the square is 16 units.
A rectangle has length 6 units and width 2 units. Use a model to find its area.
Draw a 6 by 2 grid and count the squares inside. There are 12 squares, so the area is 6 × 2 = 12 square units.
The area of the rectangle is 12 square units.
Show students a rectangle drawn on grid paper and ask them to count the units around the edge to find the perimeter.
Students count the units along each side of the rectangle and add them to find the total perimeter.
Counting the units around the rectangle helps students understand that perimeter is the total distance around the shape.
Provide students with paper rectangles and squares and ask them to measure sides and calculate perimeter using addition and then using formulas.
Students measure sides, add all sides to find perimeter, then use formulas to check their answers.
Hands-on measuring and calculating helps students connect concrete measurements to abstract formulas.
Demonstrate on the board how the perimeter formulas for rectangles and squares are derived from adding sides. Show the area formula by counting squares inside a rectangle on grid paper.
Students follow the demonstration and take notes on how formulas relate to the shape's sides and area units.
Explicit explanation connects the visual and numeric representations of perimeter and area formulas.
Present word problems involving perimeter and area of rectangles and squares with whole number dimensions for students to solve in pairs.
Students solve problems using formulas and explain their reasoning to partners.
Applying formulas to real problems deepens understanding and builds problem-solving skills.
Ask students to complete a short quiz where they calculate perimeter and area from given dimensions and explain how the formulas are used.
Students complete the quiz independently and explain their reasoning in writing or orally.
Assessment confirms students can use and explain perimeter and area formulas correctly.
Students measure sides, add all sides to find perimeter, then use formulas to check their answers.
What is the perimeter of a rectangle with length 7 units and width 2 units if you add all sides?
Add all sides: 7 + 2 + 7 + 2 = 18 units.
Use the formula 2l + 2w to find the perimeter of a rectangle with length 8 units and width 3 units.
Calculate 2 × 8 + 2 × 3 = 16 + 6 = 22 units.
A square has a side length of 5 units. What is its perimeter using the formula 4s?
Perimeter = 4 × 5 = 20 units.
Explain why the perimeter formula for a rectangle can be written as 2l + 2w instead of l + w + l + w.
Because a rectangle has two lengths and two widths, adding l + w + l + w is the same as 2 times length plus 2 times width, which is 2l + 2w. This simplifies the addition.
A rectangle has a perimeter of 24 units. If the length is 7 units, what is the width? Use the formula 2l + 2w = perimeter to solve.
Substitute: 2 × 7 + 2w = 24 → 14 + 2w = 24 → 2w = 10 → w = 5 units.
Use physical models and grid paper to visualize sides and area. Provide step-by-step guided practice with measuring and adding sides. Use color coding to distinguish length and width sides.
Use simple language and visuals to explain perimeter and area. Label sides clearly with length and width. Use gestures and drawings to support vocabulary.
Challenge students to create their own word problems involving perimeter and area. Explore perimeter and area of irregular shapes. Introduce variables for length and width to write algebraic expressions.
Ask students to find the perimeter and area of rectangular objects at home, such as a book or a table, by measuring and applying the formulas learned in class.
Students learned to use models to understand and derive formulas for the perimeter of rectangles and squares and the area of rectangles. They practiced calculating perimeter and area using these formulas and solved problems involving whole number dimensions. This lesson builds foundational algebraic reasoning skills by connecting visual models to mathematical expressions and problem solving.
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