The Size of the Scale Factor

Student Summary

The size of the scale factor affects the size of the copy. When a figure is scaled by a scale factor greater than 1, the copy is larger than the original. When the scale factor is less than 1, the copy is smaller. When the scale factor is exactly 1, the copy is the same size as the original.

Triangle DEFDEF is a larger scaled copy of triangle ABCABC, because the scale factor from ABCABC to DEFDEF is 32\frac32. Triangle ABCABC is a smaller scaled copy of triangle DEFDEF, because the scale factor from DEFDEF to ABCABC is 23\frac23.

Two triangles; one labeled A B C with horizontal A B and the other D E F with horizontal D E. 
Two triangles; one labeled A B C with horizontal A B and the other D E F with horizontal D E. The length of A B is labeled 4. The length of B C is labeled 3. The length of C A is labeled 5. The length of D E is labeled 6. The length of E F is labeled 4.5. The length of F D is labeled 7.5. An arrow from triangle A B C pointing to triangle D E F is labeled, times 3 halves. An arrow from triangle D E F pointing to triangle A B C is labeled times 2 thirds.

This means that triangles ABCABC and DEFDEF are scaled copies of each other. It also shows that scaling can be reversed using reciprocal scale factors, such as 23\frac23 and 32\frac32.

In other words, if we scale Figure A using a scale factor of 4 to create Figure B, we can scale Figure B using the reciprocal scale factor, 14\frac14, to create Figure A.

Visual / Anchor Chart

Standards

Building On
5.NBT.6

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

5.NF.4

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction.

5.NF.5

Interpret multiplication as scaling (resizing).

6.NS.1

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

Addressing
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.

Building Toward
7.RP.2

Recognize and represent proportional relationships between quantities.