A focused Grade 3 learning session for Area as Additive using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can break apart a figure and add partial areas.
Area as Additive means measuring how much flat space a figure covers by using equal-sized square units.
Question: An L-shaped garden is divided into two rectangles. The top rectangle has length \(5\) m and width \(3\) m. The bottom rectangle has length \(4\) m and width \(2\) m. What is the total area of the garden?
Why it works: Find each rectangle: top is \(5 \times 3 = 15\) sq m; bottom is \(4 \times 2 = 8\) sq m. Total: \(15+8=23\) sq m.
Answer: \(23\) sq m
Question: A floor plan shows an L-shaped room. One part is \(4\) units long and \(3\) units wide. The other part is \(6\) units long and \(2\) units wide. What is the total floor area?
Answer: \(24\) sq units
Question: A composite shape has areas of \(18\) sq units and \(11\) sq units. Find the total area.
Answer: \(29\) sq units
Question: A classroom floor is T-shaped. The top part is \(6\) units by \(2\) units. The bottom part is \(4\) units by \(3\) units. What is the total floor area?
Why it works: Top rectangle: \(6 \times 2 = 12\) sq units. Bottom rectangle: \(4 \times 3 = 12\) sq units. Total: \(12+12=24\) sq units.
Answer: \(24\) sq units
Area as Additive becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Area means every square unit inside the figure.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
A shape is made of two rectangles. Rectangle 1 has area \(12\) sq units, and Rectangle 2 has area \(15\) sq units. What is the total area?
Answer C: \(27\) sq units
When a composite shape is divided into non-overlapping rectangles, the total area equals the sum of the individual rectangle areas. Here: \(12+15=27\) square units.
An L-shaped garden is divided into two rectangles. The top rectangle has length \(5\) m and width \(3\) m. The bottom rectangle has length \(4\) m and width \(2\) m. What is the total area of the garden?
Answer B: \(23\) sq m
Find each rectangle: top is \(5 \times 3 = 15\) sq m; bottom is \(4 \times 2 = 8\) sq m. Total: \(15+8=23\) sq m.
A composite shape is made by joining two rectangles. What is the total area?
Answer B: \(9\) sq units
Left rectangle: \(3 \times 2 = 6\) sq units. Right rectangle: \(3 \times 1 = 3\) sq units. Total: \(6+3=9\) sq units.
A floor plan shows an L-shaped room. One part is \(4\) units long and \(3\) units wide. The other part is \(6\) units long and \(2\) units wide. What is the total floor area?
Answer A: \(24\) sq units
Part 1: \(4 \times 3 = 12\) sq units. Part 2: \(6 \times 2 = 12\) sq units. Total: \(12+12=24\) sq units.
A composite shape has areas of \(18\) sq units and \(11\) sq units. Find the total area.
Answer A: \(29\) sq units
Add the areas: \(18+11=29\) square units. Choice B (only one part) and C (subtraction) are common errors.
An L-shaped patio is shown with dashed lines dividing it into two rectangles. The first rectangle is \(5\) ft by \(4\) ft. The second is \(3\) ft by \(2\) ft. What is the total area of the patio?
Answer A: \(26\) sq ft
Top rectangle: \(5 \times 4 = 20\) sq ft. Bottom rectangle: \(3 \times 2 = 6\) sq ft. Total: \(20+6=26\) sq ft.
Which shows a correct way to find the total area of an L-shaped figure?
Answer B: Break it into rectangles and add their areas
Composite shapes are found by dividing them into non-overlapping rectangles, finding each area, and adding them together. Choice A fails because an L-shape is not a single rectangle. Choices C and D are incorrect methods.
A classroom floor is T-shaped. The top part is \(6\) units by \(2\) units. The bottom part is \(4\) units by \(3\) units. What is the total floor area?
Answer A: \(24\) sq units
Top rectangle: \(6 \times 2 = 12\) sq units. Bottom rectangle: \(4 \times 3 = 12\) sq units. Total: \(12+12=24\) sq units.
An L-shaped garden with dashed decomposition lines shows: The bottom part is \(5\) units by \(2\) units. The top part is \(2\) units by \(2\) units. What is the total area?
Answer B: \(14\) sq units
Bottom: \(5 \times 2 = 10\) sq units. Top: \(2 \times 2 = 4\) sq units. Total: \(10+4=14\) sq units.
Sam's bedroom is shaped like an L. One part is \(3\) m long and \(4\) m wide. The other part is \(5\) m long and \(2\) m wide. What is the total area of his bedroom?
Answer C: \(22\) sq m
Part 1: \(3 \times 4 = 12\) sq m. Part 2: \(5 \times 2 = 10\) sq m. Total: \(12+10=22\) sq m.
A composite shape is divided by dashed lines. Part A has area \(7\) sq units. Part B has area \(9\) sq units. What is the total?
Answer B: \(16\) sq units
Add the parts: \(7+9=16\) square units. Choice A (forgot Part A) and C (multiply instead of add) are common errors.
