Translate Word Problems for Area and Perimeter
This Grade 4 Eureka Math skill teaches students to translate multiplicative comparison word problems involving area and perimeter. Students must first identify whether the problem requires measuring a surface (area) or the distance around an edge (perimeter), then translate phrases like three times its width into algebraic expressions. For a field whose length is 3 times its width, students write l = 3w and apply the perimeter formula P = 2(l + w) or the area formula A = l times w accordingly. This skill from Chapter 9 of Eureka Math Grade 4 connects language, algebra, and geometry.
Key Concepts
To solve word problems, first identify whether the context requires area (covering a surface) or perimeter (distance around an edge). Then, translate multiplicative comparison phrases into algebraic expressions to define the dimensions. For example, if a rectangle's length ($l$) is described as '$n$ times its width ($w$)', the relationship is written as $l = n \times w$.
Common Questions
How do you decide whether a word problem requires area or perimeter?
Look for context clues: fencing or border around a shape requires perimeter (distance around the edge). Covering a surface, such as carpet or tiles, requires area (space inside the boundary).
How do you translate the phrase length is 3 times its width into math?
Write l = 3w, where l represents length and w represents width. This is a multiplicative comparison algebraic expression.
How do you find perimeter if length is 3 times width and width is 5 meters?
Length = 3 times 5 = 15 m. Perimeter P = 2(l + w) = 2(15 + 5) = 2(20) = 40 meters.
How do you find area if length is 3 times width and width is 5 meters?
Length = 3 times 5 = 15 m. Area A = l times w = 15 times 5 = 75 square meters.
What is the perimeter formula for a rectangle?
P = 2 times (l + w), where l is the length and w is the width. Add the two dimensions and multiply by 2.
What is the area formula for a rectangle?
A = l times w. Multiply the length by the width. The result is measured in square units.