8.3

8.3 is a knowledge and skills statement. These are the student expectations under it.

• 8.3.A

  generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

• 8.3.B

  compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

• 8.3.C

  use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with th...

01

What Students Need to Do

Students identify corresponding sides in similar figures and show that their lengths share one constant ratio. They dilate figures from the origin by multiplying each coordinate by a positive rational scale factor. They compare lengths, angles, orientation, parallel sides, and area.

02

What Mastery Looks Like

A student can match corresponding sides and show that all side-length ratios equal the scale factor. The student can use (x, y) → (kx, ky) and explain which attributes change or stay fixed.

03

Common Misconceptions

Students may add the scale factor to coordinates instead of multiplying both coordinates. They may think side lengths and area use the same scale factor, or that a dilation changes angle measures.

04

How to Assess It

Give triangle A(2, 0), B(0, 4), and C(2, 4) with scale factor 3/2 centered at the origin. Ask for the image coordinates, one side-length ratio, and two preserved attributes.

1. 01

   Place a figure on grid paper, multiply each vertex coordinate by a scale factor, then trace and compare the two figures.

2. 02

   Write a response to: Why does multiplying every coordinate by the same number preserve angle measures but change side lengths?

3. 03

   Use a card sort to match original figures, scale factors, image coordinates, and corresponding side-length ratios.

4. 04

   Enlarge a small logo for a poster, calculate the new dimensions, and explain why its shape and angles remain unchanged.

• 7.4

  The student applies mathematical process standards to represent and solve problems involving proportional relationships

• 7.5

  The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships

• 6.5

  The student applies mathematical process standards to solve problems involving proportional relationships

• 6.4

  The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations