Concept of Congruency, Similarity, and Equivalency Manual with Lesson Plans

Prove the concepts of congruency, similarity, and equivalency sensorially and numerically.

Save yourself HOURS of work.

This is Unit 1: The Concept of Congruency, Similarity, and Equivalency

This resource is relevant to ANY child, regardless of whether they have been in a Montessori environment or not. It is suitable for parents and/or teachers and perfect for homeschooling. 12 concept lessons/presentations featuring background information, detailed instructions, photographs, and illustrations.

These presentations are used to prove the concepts of congruency, similarity, and equivalency and prepare the child's mind for further work in area.

This resource includes:

Constructive Triangles, Set 2A: The Triangular Box of Coloured Triangles Materials Analysis
Constructive Triangles, Set 2B: The Large Hexagonal Box of Coloured Triangles Materials Analysis
Constructive Triangles, Set 2C: The Small Hexagonal Box of Coloured Triangles Materials Analysis
Presentation 1: Triangular Box (T1) – Equivalency
Presentation 2: Triangular Box (T1) – Relationship of Figures According to Parts
Presentation 1: Large Hexagonal Box (H1) – Forming New Figures
Presentation 2: Large Hexagonal Box (H1) – Relationship of Figures According to Parts
Presentation 3: Large Hexagonal Box (H1) – Relationship of Figures According to Lines
Presentation 1: Relationship between the Hexagon and the Triangle/Quadrilaterals – According to Sides
Presentation 2: Relationship between the Hexagon and the Triangle/Quadrilaterals – According to Lines
Presentation 1: Small Hexagonal Box (H2) – First Level
Presentation 2: Small Hexagonal Box (H2) – Relationship According to Parts
Presentation 2: Small Hexagonal Box (H2) – Relationship According to Lines
Presentation 2: Small Hexagonal Box (H2) – Second Level
Presentation 2: Small Hexagonal Box (H2) – Relating the Figures from (H2) and (T1)
This bundle is useful for children from ages 10-12 years of age and up.

This resource is the 1st unit of the AMS Montessori Geometry Curriculum for 9-12 year olds.

Please note that these lesson plans are written and illustrated by hand.

CCSS 6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
CCSS 6.EE.A.2a
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract 𝘺 from 5” as 5 - 𝘺.
CCSS 6.EE.A.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions 𝘺 + 𝘺 + 𝘺 and 3𝘺 are equivalent because they name the same number regardless of which number 𝘺 stands for.
CCSS 6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations of the form 𝘹 + 𝘱 = 𝘲 and 𝘱𝘹 = 𝘲 for cases in which 𝘱, 𝘲 and 𝘹 are all nonnegative rational numbers.
CCSS MP2
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.