EngageNY
The Angle-Angle (AA) Criterion for Two Triangles to Be Similar
What do you need to prove triangles are similar? Learners answer this question through a construction exploration. Once they establish the criteria, they use the congruence and proportionality properties of similar objects to find...
EngageNY
Properties of Similarity Transformations
You can explain it, but can you do it? After learners view a sequence of transformations, the next logical step is creating the transformation. Challenge your classes to construct a composition of transformations and verify the...
EngageNY
Dilations from Different Centers
Can you follow a composition of transformations, or better yet construct them? Young mathematicians analyze the composition of dilations, examining both the scale factor and centers of dilations. They discover relationships for both and...
EngageNY
How Do Dilations Map Lines, Rays, and Circles?
Applying a learned technique to a new type of problem is an important skill in mathematics. The lesson asks scholars to apply their understanding to analyze dilations of different figures. They make conjectures and conclusions to...
EngageNY
Scale Factors
Is it bigger, or is it smaller—or maybe it's the same size? Individuals learn to describe enlargements and reductions and quantify the result. Lesson five in the series connects the creation of a dilated image to the result. Pupils...
EngageNY
Making Scale Drawings Using the Ratio Method
Is that drawn to scale? Capture the artistry of geometry using the ratio method to create dilations. Mathematicians use a center and ratio to create a scaled drawing. They then use a ruler and protractor to verify measurements.
Math Drills
Classifying Prisms and Pyramids
Young geometers identify prisms and pyramids based on the number of edges they have. Answers vary from hexagonal and rectangular prisms to pentagonal and octagonal pyramids.
Math in English
3-D Shapes
Young mathematicians look at five 3-D shapes and name them based on the accompanying image. For each shape, learners state the number of faces, vertices, and edges.
EngageNY
How Do 3D Printers Work?
If we stack up all the cross sections of a figure, does it create the figure? Pupils make the connection between the complete set of cross sections and the solid. They then view videos in order to see how 3D printers use Cavalerie's...
EngageNY
The Volume of Prisms and Cylinders and Cavalieri’s Principle
Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two figures do not...
EngageNY
General Prisms and Cylinders and Their Cross-Sections
So a cylinder does not have to look like a can? By expanding upon the precise definition of a rectangular prism, the lesson develops the definition of a general cylinder. Scholars continue on to develop a graphical organizer for the...
EngageNY
The Scaling Principle for Area
As they investigate scaling figures and calculate the resulting areas, groups determine the area of similar figures. They continue to investigate the results when the vertical and horizontal scales are not equal.
Kentucky Educational Television
The Road to Proportional Reasoning
Just how big would it really be? Young mathematicians determine if different toys are proportional and if their scale is accurate. They solve problems relating scale along with volume and surface area using manipulatives. The last day of...
Techbridge Curriculum
Calculating Rainwater Runoff
Thirsty plants soak up every bit of a rainfall, but what happens to the rain that hits the roof? Calculate the amount of rainwater from your school's roof with an Earth science activity, which brings measurement skills, observation...
EngageNY
Solving Problems Using Sine and Cosine
Concepts are only valuable if they are applicable. An informative resource uses concepts developed in lessons 26 and 27 in a 36-part series. Scholars write equations and solve for missing side lengths for given right triangles. When...
EngageNY
Incredibly Useful Ratios
Start the exploration of trigonometry off right! Pupils build on their understanding of similarity in this lesson that introduces the three trigonometric ratios. They first learn to identify opposite and adjacent sides before exploring...
EngageNY
Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles
Why are right triangles so special? Pupils begin their study of right triangles by examining similar right triangles. Verifying through proofs, scholars recognize the three similar right triangles formed by drawing the altitude. Once...
EngageNY
Similarity and the Angle Bisector Theorem
Identifying and verifying reproducible patterns in mathematics is an essential skill. Mathematicians identify the relationship of sides when an angle is bisected in a triangle. Once the pupils determine the relationship, they prove it to...
EngageNY
What Are Similarity Transformations, and Why Do We Need Them?
It's time for your young artists to shine! Learners examine images to determine possible similarity transformations. They then provide a sequence of transformations that map one image to the next, or give an explanation why it is not...
EngageNY
Dividing the King’s Foot into 12 Equal Pieces
Apply, apply, apply! A measurement lesson plan applies a number of concepts to help learn a new construction. Scholars learn to divide a segment into n equal parts using a method that uses the Side Splitter Theorem and a method that...
EngageNY
How Do Dilations Map Segments?
Do you view proofs as an essential geometric skill? The resource builds on an understanding of dilations by proving the Dilation Theorem of Segments. Pupils learn to question and verify rather than make assumptions.
EngageNY
Comparing the Ratio Method with the Parallel Method
Can you prove it? Lead your class through the development of the Side Splitter Theorem through proofs. Individuals connect the ratio and parallel method of dilation through an exploration of two proofs. After completing the proofs,...
Scholastic
Study Jams! Congruent Figures
There is more to congruency than just looking similar. Learn the difference and calculate the matching angles and sides to prove the congruence between figures. Lesson has step-by-step slides and follows with an assessment.
Scholastic
Study Jams! Edges, Faces, Vertices
Before determining the classification of a three-dimensional shape, you need to know about the characteristics of a vertex, edge, and face. Go step-by-step using a prism, and discover what each aspect refers to and how it applies to...