17 7.G.1 7.G.1 Math.7.G.1 7.G.1 7.G.1 7.G.1 CC.2.7.A.2 M07.C-G.1.1 MA.7.1.5 7.PAR.6

Scale Drawings 7th Grade

Alabama Course of Study Standards: 17
Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.
Arkansas Academic Standards: 7.G.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale Note: This concept ties into ratio and proportion.
Arizona - K-12 Academic Standards: 7.G.1
Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Common Core State Standards: Math.7.G.1 or 7.G.1 Ohio's Learning Standards: 7.G.1
Solve problems involving similar figures with right triangles, other triangles, and special quadrilaterals. Compute actual lengths and areas from a scale drawing and reproduce a scale drawing at a different scale. Represent proportional relationships within and between similar figures.
North Carolina - Standard Course of Study: 7.G.1
Solve problems involving scale drawings of geometric figures by: Building an understanding that angle measures remain the same and side lengths are proportional. Using a scale factor to compute actual lengths and areas from a scale drawing. Creating a scale drawing.
Pennsylvania Core Standards: CC.2.7.A.2
Visualize and represent geometric figures and describe the relationships between them.
Pennsylvania Core Standards: M07.C-G.1.1
Solve problems involving scale drawings of geometric figures, including finding length and area.
Florida - Benchmarks for Excellent Student Thinking: MA.7.1.5
Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.
Georgia Standards of Excellence (GSE): 7.PAR.6
Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Similar figures are the same shape, but not necessarily the same size.

Scale factor is the ratio of corresponding side lengths
(new image to old image) of similar figures.

\begin{array}{rcl} scale factor & = & \frac{new length}{old length} \\ = & \frac{12 ft}{4 ft} \\ = & 3 \end{array}

If the scale factor from figure A to figure B is k,
then the area of figure B is k^² times the area of figure A.

Figure 1 has side lengths: a, b, and c.
A scale factor of k has been applied to figure 1 to produce figure 2.
So, figure 2 has side lengths: k times a, k times b, and k times c.

The area of a triangle is one-half times the base times the height.
Examine the areas of both figures.

Area_{_{figure 1}}	=	$\frac{1}{2}$ ab
Area_{_{figure 2}}	=	$\frac{1}{2}$ (ka)(kb)
	=	kk( $\frac{1}{2}$ ab)
	=	k^²(Area_{_{figure 1}})

So, the area of figure 2 is k^² times the area of figure 1.

A scale drawing (or scale model) is a proportional representation of an object.

A scale drawing's scale indicates the relationship between the
representation's measurements and the actual measurements.

\begin{array}{rcl} \frac{1 in.}{14.4 ft} & = & \frac{5 in.}{x} \\ 1 in. (x) & = & 5 in. (14.4 ft) \\ 1 in. (x) & = & 72 in. ft \\ 1 in. (x) \div 1 in. & = & 72 in. ft \div 1 in. \\ x & = & 72 ft \end{array}

Area	=	base × height
	=	$\frac{5}{8}$ in. × $1 \frac{1}{4}$ in.
	=	$\frac{5}{8}$ in. × $\frac{5}{4}$ in.
	=	$\frac{25}{32}$ sq in.

The scale for area is the scale for length squared.
So, the scale for area is 1 square inch to (14.4)^² square feet, which is 1 square inch to 207.36 square feet.
To find the area in square feet, multiply

\frac{25}{32}

square inch by 207.36 sq ft/sq in.

207.36 sq ft/sq in. ×

\frac{25}{32}

sq in. = 162 sq ft

Scale Drawings

Alabama Course of Study Standards: 17

Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.

Arkansas Academic Standards: 7.G.1

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale

Note: This concept ties into ratio and proportion.

Arizona - K-12 Academic Standards: 7.G.1

Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Common Core State Standards: Math.7.G.1 or 7.G.1

Ohio's Learning Standards: 7.G.1

Solve problems involving similar figures with right triangles, other triangles, and special quadrilaterals.
Compute actual lengths and areas from a scale drawing and reproduce a scale drawing at a different scale.
Represent proportional relationships within and between similar figures.

North Carolina - Standard Course of Study: 7.G.1

Solve problems involving scale drawings of geometric figures by:
Building an understanding that angle measures remain the same and side lengths are proportional.
Using a scale factor to compute actual lengths and areas from a scale drawing.
Creating a scale drawing.

Pennsylvania Core Standards: CC.2.7.A.2

Visualize and represent geometric figures and describe the relationships between them.

Pennsylvania Core Standards: M07.C-G.1.1

Solve problems involving scale drawings of geometric figures, including finding length and area.

Florida - Benchmarks for Excellent Student Thinking: MA.7.1.5

Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.

Georgia Standards of Excellence (GSE): 7.PAR.6

Solve everyday problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

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