Opto Math

This exploration has proved to be an investigative, scaffolded introduction to the idea of triangle congruence. Over the years I have tried investigating this topic by use of patty paper, and that was good, but I felt there were too many moving parts for a 40 minute class period and learners who needed a bit more scaffolding. I like this exploration because it clearly defines the "parts" of the triangle needed to investigate each triangle shortcut. Students are working tangibly for this invest

This resource is an exploration lesson where students use Desmos Geometry Tools to create constructions. Essentially, this is an activity sheet with questions to complete after completing the constructions on Desmos Geometry Tools. Here is the free link to the Desmos activity that corresponds with this exploration sheet. In this activity, students create the following constructions: copy a segmentcopy an angleperpendicular bisectorparallel linesAfter each construction, students answer question

OverviewThis symmetry exploration guides learners to investigate the reflectional and rotational symmetry of various shapes. What's includedWith this resource, you are supplied with a "cut-out and companion" page and the exploration activity page. How to useThe way I like to use this product is as an introduction to symmetry, followed by direct instruction, guided practice, and then individual practice. Be on the lookout for Symmetry Notes and Symmetry Practice from my store. The "cut-out and

Enjoy this bundle of resources about Tessellations, including the Exploration, Notes, and Practice. It would usually take me 2-3 40 minute class periods to work through these 3 resources, and I used them in succession. Exploration, then notes, then practice. Sometimes notes and practice can work on the same day.

This product includes all of the vocabulary terms from Unit 2: Congruence in Geometry: CongruenceSequence of Rigid TransformationsReflectional SymmetryRotational SymmetryOrder of Rotational SymmetryEquilateral TriangleIsosceles Triangle TheoremConverse to the Isosceles Triangle TheoremAngle Side Angle CongruenceSide Angle Side CongruenceSide Side Side CongruenceAngle Angle Side CongruenceHypotenuse Leg CongruenceCPCTC (Corresponding Parts of Congruent Triangles are Congruent)I give this sheet to

Tessellations Notes is a great way to follow Tessellations Exploration and precede Tessellations Practice. In a 40-minute class period, I might could do the notes and the practice. This is a great way to give students some context with the interior angle sum of polygons and the measure of one interior angle in a regular polygon. I usually do these notes the day after I do the Tessellations Exploration, which takes a whole class period for me. It could be fun to start class by showing some pictu

This tessellations practice includes 6 questions about tessellations on one-page. There are two of each level of question, with each section getting progressively more challenging: shrimp, kiwi bird, dragon. This practice works well with my Tessellations Exploration and Tessellations Notes. I like to use my notes pages as a guided practice where we work one of each level together then I allow students to work on the other question of that level individually or in small groups/pairs.

This vocabulary sheet is a handout including all vocabulary terms from Unit 4: Trigonometry in Geometry: TrigonometryReference AngleOpposite SideAdjacent SideHypotenuseSineCosineTangentInverse SineInverse CosineInverse TangentCofunction IdentityAngle of ElevationAngle of DepressionUnit CircleThis is a great tool to give to students at the beginning of the unit so they can use it as a reference sheet throughout the unit. This can also be a great reference sheet for students with IEPs on assessmen

This vocabulary sheet includes all of the vocabulary terms from Unit 1: Constructions & Rigid Transformations in Geometry. This handout can be given to students at the beginning of the unit for reference throughout. A great use of this product throughout the unit is to have students star vocabulary terms once students have learned the term. This is also a great resource for open-note quizzes and a great resource for students with IEPs.

This formula sheet includes all 11 formulas from Unit 1: Constructions & Rigid Transformations in Geometry: Pythagorean Theorem90° or -270° Rotation About the Origin180° Rotation About the Origin270° or -90° Rotation About the OriginX-Axis ReflectionY-Axis ReflectionReflection Over y=xTranslation UpTranslation DownTranslation LeftTranslation RightInterior Angle Sum of a PolygonOne Interior Angle in a Regular PolygonOne Central Angle or Exterior Angle in a Regular PolygonI print this for my

Use these bundled Bisectors (segment and angle) products over 1-2 days to have students explore bisectors then solidify their understanding through notes and practice. In my classroom I start with the exploration one day and then the next day I provide direct instruction through the notes then allow students to practice the concepts.

These sets of notes are a great way to provide direct instruction over the topics of segment and angle bisectors. In my classroom, I use these set of notes the day after the " Bisectors Exploration" lesson, and followed by the " Bisectors Practice." The key is included.

This product includes all of the vocabulary terms from Unit 3: Similarity in Geometry: SimilaritySimilar FiguresDilationReduction DilationEnlargement DilationCenter of DilationScale Factor (k)Angle Angle SimilaritySide Angle Side SimilaritySide Side Side SimilarityI give this sheet to students at the beginning of the unit so they can use as a reference throughout the unit. Another great use of this product is to have students star the vocabulary term once they have learned it, so they can refer

This exploration sheet is a great way to get students to explore the definition of a tessellation and whether or not certain polygons have the ability to tessellate. The activity is designed to work with polygon tiles, as pictured in the thumbnail. This exploration is best followed by direct instruction, using my Tessellations Notes.

In these notes, students learn about the three rigid transformations: translations, reflections, and rotations. The following components of transformations are included: transformations definitionsnotation for each transformationgraphical examples of each transformationquestions about the properties of each transformationcoordinate rules for each transformation as transformations as functionsThis notes page is great to follow my Rigid Transformations Exploration.

This notes page is best used as a follow up to my Constructions Compass & Straightedge Exploration and my Constructions Desmos Geometry Tools Exploration. This notes page includes a fill-in-the-blank proof of the triangle interior angle sum theorem.

This practice page includes 6 questions of three different levels on logic statements and proofs. The first two questions are the lowest level of difficulty, the "shrimp" questions. Questions 3 and 4 are medium level questions, the "kiwi bird" questions. Questions 5 and 6 are the most difficult level questions, the "dragon" questions. These questions involve these skills: Identifying the hypothesis and conclusion of a conditional statementWriting the converse, contrapositive, and inverse of a

This notes page is great to use as a follow-up to the logic & proofs exploration activity that you can find in my store. In my classroom, I use these notes the day after using the exploration and then on the same day, I follow up with my logic & proofs practice page. These notes are mostly a reference page for students, with a few fill-in-the-blanks. These notes are a great way to synthesize logic statements and proofs, which are introduced in my logic & proofs exploration.

MaterialsThis exploration activity includes a 2-page activity sheet for students along with the corresponding print and cut card matchings. TopicsLogic statements (conditional, converse, inverse, contrapositive)Truth values of statementsLogical equivalenceVertical anglesLinear pairsVertical angles theorem 2-column proofTriangle exterior angle theorem 2-column proofHow to use this resourceWhen I use this is my classroom I print the student activity sheets front-to-back to fit on one page. I prin

Purchase the Bisectors Notes & Bisectors Practice to use together! In my classroom I use these two resources in one class period.