Example of an Understanding By Design Curriculum
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Unit: Unit w/No Topics  Ratio and Proportion using Similarity
Subject: Mathematics
Minutes for Assessments: 40
Brief Summary of Unit
(Describe the context for this unit within the curriculum, and the curricular aims of the unit.)
Ratio and proportion are key concepts in mathematics and are essential to understanding scale drawings and the relationships between many geometric figures. Similarity is the first step in determining lengths, perimeter, and area when doing a comparison between shapes. Triangle similarity is essential to the understanding of congruence and vice versa.
Students will not struggle so much with the mathematics of ratio and proportion but more so the implications and applications of it. For instance determining when to use indirect measurement and getting the proportions set up correctly is very difficult for most students. After the proportion is set up, the math is simple. The uncoverage refers to the application of ratio, proportion, and similarity. Understanding why a proportions works will help students understand how to use one more effectively.
Math of the lesson in math lack student engagement and therefore students never really develop an enduring understanding of the content. Similarity is an area of mathematics where student engagement can be limitless. Students can learn indirect measurement by using mirrors to determine the height of immeasurable objects. Cartoons or pictures can be used to scale up or down according to a certain ratio. Students can determine the consistency of a “Hot Wheels” car to that of a real version of the car using measurement and proportion. Similarity can be used to “guess” the number of Skittles in a jar. This content has a wealth of opportunities to make the material meaningful and engaging to students.
Stage One  Desired Results
Mathematical Problem solving and Communication:
A. Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving nonroutine and multistep problems.
B. Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results.
C. Present mathematical procedures and results clearly, systematically, succinctly and correctly.
Numbers and Operations:
Identify and/or use proportional relationships in problem solving settings.
Geometry:
Use properties of congruence, correspondence and similarity in problemsolving settings involving two and three dimensional figures.
What will students understand (about what big ideas) as a result of the unit? “Students will understand that…” Big Ideas: ratio, proportion, similarity, and triangle similarity Understandings:

What arguable, recurring, and thoughtprovoking questions will guide inquiry and point toward the big ideas of the unit?

What key knowledge and skills are needed to develop the desired understandings and meet the goals of the unit? What knowledge and skill relate to the content standards on which the unit is focused?
Students will know:
 Key terms – ratio, proportion, scale, perimeter, area, hypotenuse, leg, altitude, right triangle, geometric mean, similar triangles, similar figures, indirect measurement, scale drawing, similarity ratio
 Similarity theorems – AA Similarity, SAS Similarity, SSS Similarity, Sidesplitter Theorem, Altitude to Hypotenuse Similarity Theorem, Triangle – Angle Bisector, Perimeters & Areas of Similar Figures
 Mathematical calculations with the cross product property
 Mathematical rules for multiplying monomials and binomial
Students will be able to:
 Ratio and proportion – write ratios and solve proportions
 Similar polygons – identify and apply similar polygons
 Proving triangles similar – use and apply AA, SAS, and SSS similarity statements
 Proportions in triangles – find and use relationships in similar right triangles
 Perimeter and areas of similar figures – use the side – splitter theorem and the triangle angle bisector theorem