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Drawing Algebraic Curves

Arts Integrated Small Group for Algebra I Graphing Exponential Functions

Tags: Algebra I Small Group Algebraic Curves Exponential Curves Graphing The Walters Art Museum

Drawing Algebraic Curves

Pairs with Reveal Math Lessons Algebra I: 9-1, 9-2

In this two-part series of differentiated small-group activities, students will practice drawing smooth curves using techniques demonstrated by line artists. They will then incorporate intervals of exponential curves into original 2D and 3D designs.

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MARYLAND STATE STANDARDS

MD Math Standards:

  • Algebra I: F.IF.C.7 – Graph functions expressed symbolically and show key features of the graph
  • Integrated Algebra I: IA1.AT.D.14 – Represent functions using tables and graphs

This activity supports enduring understanding of exponential curves because it gives students an opportunity to focus on physically feeling a curve while graphing it. This helps to support them with understanding the continuity of these curves, and be able to more easily make sense of how the slope continues to change in whichever direction they are drawing.

MD Arts Standards:

  • VA.AS1.I:9-12:1 – Act on creative ideas within the context of a given or chosen art problem.

Students are being asked to use an exponential curve to create a drawing or sketch of a larger art piece, which requires them to think about how to incorporate that element into something they want to create. They are solving a given art problem using multiple solutions.

OUTSIDE OF MD?

Common Core State Standards:

  • HSF.IF.C.7.e – Graph exponential and logarithmic functions
National Arts Standards:

  • VA:Cr1.1.Ia – Use multiple approaches to begin creative endeavors.

ARTS INTERATED LEARNING OBJECTIVE

SWBAT incorporate exponential curves into 2-dimensional and 3-dimensional designs in order to more confidently draw smooth curves.

MATH DOMAIN

  • Functions (HS) → Interpreting Functions → Graphing exponential functions
  • Algebraic Thinking (Integrated Algebra I) → Model with Functions→ Graphing exponential functions

COHERENCE

  • Before: Graphing linear functions
  • After: Transformations of exponential functions

MATH & ART SKILLS

  • Math: Graphing exponential functions
  • Art: Drawing, creative thinking with pre-existing lines, idea generation, real world application

MATERIALS

  • Slides
  • Graph paper
  • Pencils and other drawing implements
  • Access to technology (for watching the video – linked in slides)
  • Exponential Growth Worksheet 1 & 2
  • Exponential Decay Worksheet 1 & 2

Printable Version

Video Playlist

Slides

Concept Map

SMALL GROUP SESSION ONE

    1. Watch the video (Slide 2)

    • Students watch the video independently or in groups and take notes on key ideas. It will give them tips on improving the smoothness and accuracy of their curves in tattoo design, ink drawing, and sign/banner painting.

    2. Graph an exponential (growth) function

    • Students choose an exponential function and graph it, showing their work as necessary. For growth functions, this should be in the bottom-right quadrant of the page so that the curve fits well into an outline. For decay functions, this should be in the bottom-left quadrant, but if that doesn’t happen, it just requires a little bit of extra creativity on the part of the student!

    3. Incorporate part of the curve into a design

    • Students use an interval of the curve in their graph and use it as part of a tattoo/drawing/sign design.

    4. Repeat steps 2-3 (if time)

    SMALL GROUP SESSION TWO

    1. Explore the Walters Art Museum collection on slide 3.

    • Students look closely at 3-dimensional art that uses curves, either independently or as a group, taking notes on important connections to curves. This will give them ideas of how to incorporate curves in the context of pottery and sculpture.

    2. Learn more about these featured pieces in the Walters collection!

    • Stemmed Kylix with Cuttlefish
      • Mycenaean (Artist), 14th century BCE
      • Ceramics
      • Acquired by Henry Walters, 1924, 48.211
    • Pair of Mulberry Earrings
      • Syrian (Artist), 11th–10th century BCE
      • Gold
      • Acquired by Henry Walters, VO.70.
    • Wak’a del Agua
      • Kukli Velarde (Peruvian), 2022-2023
      • Clay, underglaze, casein and enamel paint
      • Museum purchase, 2024, 48.2903
      • © Kukuli Velarde

    3. Graph an exponential (decay) function

    • Students choose an exponential function and graph it, showing their work as necessary. For growth functions, this should be in the bottom-right quadrant of the page so that the curve fits well into an outline. For decay functions, this should be in the bottom-left quadrant, but if that doesn’t happen, it just requires a little bit of extra creativity on the part of the student!

    Incorporate part of the curve into a design

    • Students use an interval of the curve in their graph and use it as part of a sculpture/pottery design.

    4. Repeat steps 2-3 (if time)

    ASSESSMENT & REFLECTION

    Teachers will check for understanding based on the accuracy and smoothness of the curves, as well as their logical and creative incorporation into a larger design.

    DIFFERENTIATION

    This can also be used for quadratic functions, as well as other curved graphs in higher-level math.

    For students with fine motor difficulties, it might be easier for them to use modeling clay or something similar to “draw” the graph with. This will allow them to make easy adjustments without sacrificing the ability to feel the curve.

    Calculators are a helpful support for all students.

    Students who are able to independently plot points when provided with a visual model or other accommodations (like color coding, flow charts, provided tables, etc.) during the lesson should also be provided with the same supports when completing this activity independently.

    Return to Topic

    Materials Google Folder

    BRAIN TARGETED TEACHING IN THE CLASSROOM

    This activity is designed to give students repeated practice with drawing smooth and accurate curves in a focused and artful way, and to be thinking of other contexts for them, which is a more engaging and meaningful way to work on this skill than simply graphing over and over again.

    Artful Repetition for Long Term Memory – Engaging Repetition:

    Repeated rehearsal is the process of revisiting information, or repeating it, to strengthen memory.

    Arts integration naturally supports repeated, varied rehearsal by engaging students in creative, meaningful ways. Each artistic iteration reinforces learning while maintaining engagement.

    Ex: Students create a song about the states of matter (solids, liquids, & gas) using lyrical substitution, then demonstrate the molecular structure of each state through tableau. The song can be used at the start of every class period throughout the unit for more repeated rehearsal (science)

    The Emotional Climate:

    Students should feel safe and comfortable to work independently and rely on other students in their group for support. Students should feel confident in their ability to accurately choose and plot points from a function on a coordinate plane based on teacher feedback.

    The Physical Space:

    There should be enough desk space for each student to turn their worksheet in different directions when creating designs. Students should have easy access to drawing materials (including colored pencils/pens/markers).

    Learn More:

    Learn more about Brain Targeted Teaching via Dr. Mariale Hardiman’s site.

    FIELD TRIP OPPORTUNITIES

    Want to see these objects in person? Book a free field trip to the Walters Art Museum! Visit the Walters website to learn more about field trips and bus reimbursements or contact tours@thewalters.org directly.

    ROOT BRANCH MEDIA GROUP – BRING ROOT BRANCH TO YOUR SCHOOL!

    All video content made in partnership with Baltimore’s Root Branch Media Group.

    STEVII MARSHALL

    Stevii is a special educator who has worked with students in 5th to 8th grade across content areas, often teaching an honors Algebra I class and coaching her school’s chess team as well. As someone who didn’t learn to love math until she was 16, one of her biggest goals is to never hear the phrase “not a math person” in a school ever again, and believes that creativity and playfulness in math are key to achieving this. She has lived in 7 countries on 4 different continents, but has made Baltimore her home since 2021. She has 3 cats, and enjoys fiber arts, baking, and riding bikes. Beginning in the fall of 2026, she will be spending the her evenings attending law school at the University of Maryland in pursuit of fighting for a public educational system that works for all.

    SAM TROILO

    Sam is a Visual Art teacher in Baltimore City who loves supporting students (and educators!) in learning through the arts. With a background in photography, music composition, and one million craft hobbies, Sam loves to merge mediums to create interesting and impactful experiences. She is a strong believer in arts integration and feels that it is the true future of education.

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