SCHUYLERVILLE PREPARATORY HIGH SCHOOL
Jeanette Del Valle, Principal
3000 East Tremont Avenue
Bronx, NY 10461
Tel: 718-904-5080 Fax: 718-904-5089
Marta Colon, Administrator
Zulay Martinez, Assistant Principal
Bienvenido Hernandez, Assistant Principal
Unit 5: Solids - Further Solids: Cross Sections
Lesson 38B
Standard: Geometric Measurement & Dimension - CCSS.MATH.CONTENT.HSG.GMD.A - solids, volume formulas and arguments rela ng
dissec on to form solids.
STANDARDS FOR MATHEMATICAL PRACTICE developed in the lesson:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quan ta vely.
CCSS.MATH.PRACTICE.MP4 Model with mathema cs.
Success Goal I see 2D shapes created by slicing 3D shapes, demonstra
Tiered POU Performance of Understanding
ng my visualiza on of solids
On-level students will be able to explain different solids and the concept of three dimensions with a slice through - and how this this
cut produces different 2D shapes depending on the angle and loca on of the cut.
Checks for
Understanding
Worksheet interac ve handout
Exit Slip
Pathway to
Learning
Discussion Questions and Techniques
Group Discussion on concepts of slicing.
Class discussion a erwards
Do we begin to see the rela onship between volume and area mul plied by a height/length?
Do Now: show do now on board, and provide the interac ve handout which has same for students.
This Do Now allows students to consider applying the concept of nets (per prior lesson) with the idea of thinking about solids in more
than one way.
Lesson Success Goal: Ask a student to read out the lesson success goal, and then discuss what this means.
→ prompt students what is meant by 2D and 3D shapes. Prompt: can you name some 2D and 3D shapes?
Vocabulary Building: have students complete their vocabulary building - fill in the blanks - on their sheet.
READ OUT (shown on board): a cross-sec on is a two-dimensional shape that shows what the inside of a three-dimensional solid looks
like a er a cut or slice has been made across it.
Intro to New Concept: show the idea of a cross-sec on of a donut (Torus), and discuss with students how this would be in real life
cu ng a slice (of bread, donut, sausage, cheese etc.)
INTRO TO NEW CONCEPT ACTIVITY: In this ac vity, pick two students to be actors - playing the parts of Euclid and Plato.
Have them read from the script (provide a copy each) but have the class help them with the missing words - the example is shown on
the board to help connect the visual to the words.
DIGITAL ACTIVITY Group Work: assemble students in groups, and then begin further Student explora on / DIGITAL ACTIVITY: link
provided in Google Classroom & prompts on sheet to complete.
The digital ac vity is a “Cross Sec on” tool that allows students to visualize different cross-sec ons.
Once complete, Conceptual Knowledge → Procedural Knowledge: have students complete the back page of the handout, where they
iden fy the type of cross-sec on created by the slice.
⇒ provide loose leaf / pa y paper / scissors if students want to visualize in 3D with their own modeling.
Circulate among students as they review - have backup slides on board to show as needed.
Wrap-Up - show wrap-up slide.
PROMPT: Do we begin to see the rela onship between volume and area mul plied by a height/length, even for solids such as spheres
which are a mul plica on of radius×radius×radius?
Misconceptions
Exit Ticket - Hand out exit cket.
Students may get confused by the new vocabulary introduced.
Students may struggle to think about the symbol PI.
Students may struggle to perform the various math (division, mul plica on) - so be prepared to assist as needed.
Materials
Whiteboard / Handout / Laptops / Looseleaf / Pa y Paper
Additional:
Accomodation:
ELLs / SWDs
Vocabulary
Printouts of 3D shapes for students.
3D shape manipula ves.
Coordinates
Congruence
Median
Distance formula
Corresponding
Perpendicular
Midpoint
Midpoint formula
Bisector
Statement/Reason
Orthocenter
Eleva on
Hypotenuse
Square root
Square of a number
Proof
Hypothesis
Image Pre-Image
Depression Cone Pyramid