- This is a sample lesson using by design curriculum.
|Unit||Ratio and Proportion using Similarity|
|Assessment||Allow 40 minutes for assessment|
(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.
Many 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.
Mathematical Problem solving and Communication:
Identify and/or use proportional relationships in problem solving settings.
Use properties of congruence, correspondence and similarity in problem-solving 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…”
ratio, proportion, similarity, and triangle similarity
What arguable, recurring, and thought-provoking 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?