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The Art of Division
Arts Integrated Activity for Grades 3-4 Division with Arrays and Area Models
The Art of Division
Pairs with Reveal Math Launch 4th Grade: 7-1, 7-2, 7-3, 7-4, 7-5, 7-6, 7-7, 7-8 3rd Grade: 9-1, 9-2, 9-3, 9-4, 9-5, 9-6, 9-7, 9-8, 9-9
In this 5-7 minute low-stakes, low-materials entry point to the lesson, students will engage in visual thinking routines to analyze a variety of visual art images that feature arrays, developing multiplication and division equations that capture the artwork’s design. Rather than thinking about the artwork through additive equations, students will move towards analyzing the artwork multiplicatively, recognizing math concepts such as division, arrays, area models, and symmetry.
Standards
Getting Ready
Downloads
TEACH!
Brain Connections
Creators
MARYLAND STATE STANDARDS
MD Math Standards:
- 4.NOS.B.6c – Students apply their understanding of multiplication and division as inverse operations to think of a division problem as a multiplication problem with a missing factor.
- 4.NOS.B.6d – Students can explain how their representation or strategy accurately represents division.
This activity supports enduring understanding by providing students with the opportunity to engage in number talks. The dividends will extend closer to 100 towards the end of the series, but every array/grid will allow opportunities for flexible thinking as students create multiple equations to describe each piece of art. Students can connect pieces of art to arrays, area models, and all four operations to deepen their understanding of the strategies required to solve multi digit division problems.
MD Arts Standards:
- VA.AS7.I:3-5:1 – Analyze similarities and differences between the elements of art in observed form.
- VA.AS8.E:3-5:2 – Interpret art through contextual information.
These standards focus on analysis and interpretation of existing artwork. In this routine, students are asked to view artwork not only as admirers, but also as mathematicians that can identify core math principles and how they might present themselves in a piece of visual art.
OUTSIDE OF MD?
Common Core State Standards:
- 4.NBT.B.6 – Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models
National Arts Standards:
- VA:Re.7.2.4a – Analyze components in visual imagery that convey messages.
ARTS INTERATED LEARNING OBJECTIVE
- Students will be able to identify core division concepts such as arrays, partitive and quotative division, and factors by analyzing pieces of visual art.
MATH DOMAIN
- Number and Operation Sense / Number and Operations in Base Ten
- Use place value understanding and properties of operations to perform multi-digit arithmetic.
- Divide whole numbers with up to four-digit divisors with and without remainders
- Use place value understanding and properties of operations to perform multi-digit arithmetic.
COHERENCE
- Before: Recall or quickly derive multiplication and division facts within 100 (3.NOS.E.9)
- After: Divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors.
MATH & ART SKILLS
- Math: Writing multiplication and division equations that describe an array / area model.
- Art: Analysis of visual art pieces
MATERIALS
- Slides
TEACHER BACKGROUND
While these instructions follow the general outline of the strategy, there are individual instructions and questioning strategies in the speaker notes section of the attached slides.
For each art piece, it should be presented in 3 stages lasting no longer than 10-12 minutes.
STAGE 1
See-think-wonder (5 minutes – 3 for students to write, 2 for discussion)
Students use the see-think-wonder routine to make observations about the image that is presented.
STAGE 2
Looking 5×2 (6 minutes – 2 minutes for each set of equations, 1 minute for recording the equation with the student explanation)
- After the see-think-wonder routine, we will move into 5×2.
- Looking 5×2 is modeled off of “looking 10 x 2”, where students come up with 10 descriptive words for a piece of art, discuss their choices, and then come up with 10 more descriptive words.
- In looking 5×2, students will work together to quickly come up with 5 equations that match the piece of visual art they see. After the first round, the teacher should guide students to share their equations with an explanation of why the equation describes the visual art. The teacher’s job is to record the equations somewhere visible and to assess reasonableness, not correctness.
- After recording 5 equations, if students cannot come up with 5 on their own they must fill in from the board, teachers have a moment to point out alternative ways of viewing the visual art.
- For pieces like Warhol’s Campbell’s Soup Cans, you may be unable to do the second round, but that is also an opportunity for questioning. For pieces like Kandinsky’s Color Study, the volume of each square allows a depth of questioning that takes the equation from 4 x 3 = 12 and 12 / 3 = 4 to 5 circles x 4 columns x 3 rows = 60, or 60 circles / 5 circles per square = 12 squares. This creates an opportunity to take student thinking further.
- After pointing out areas for more math to take place, students will have time to come up with 5 more equations. Students may be unable to come up with 5 equations on their own, this productive struggle is an important part of the learning process!
- After students have their second set of 5 equations (or as many as they can come up with) the teacher will record their new equations as they explain.
STAGE 3
Art background and description (1 minute)
- The teacher shares background information on the piece. Given the information on the slides (Artist name, medium, date, etc.), ask students what the artist was trying to convey. What colors, shapes, etc. makes you say that? Do you think the artist intentionally or unintentionally incorporated math into their art?
- Each slide will have more specific questions included in the presenter notes.
Note:
It is essential that the teacher spends time with the piece of art to write their own equations and engage with the questioning process they will go through with students.
- The goal of this lesson is to think about arrays multiplicatively, not additively. Students will be able to describe some of the visual art examples using additive equations, but the goal should be for the teacher to drive questioning towards thinking about how equal groups show up in each piece.
- Every example will have questioning guides included in the teacher notes to support teachers in guiding discussion towards analyzing the visual art multiplicatively.
ASSESSMENT & REFLECTION
Connect, Extend, Challenge
Due to the open-ended nature of a Reveal Math Launch, or for teachers who use this at the beginning of their math lesson, there is no need for a formal assessment of this activity. Instead, teachers can follow the Connect, Extend, Challenge protocol.
- Connect: How do the ideas and information in this image connect to what you already know about division?
- Extend: How does this image extend or broaden your thinking about division?
- Challenge: Does this image complicate your understanding of division? What new questions do you have?
DIFFERENTIATION
Grade Level:
While aimed at 4th grade, this activity can be easily scaled for adjacent grades (3rd or 5th). Math is an iterative process and the concepts are revisited each year.
Extension:
Each of these pieces has a mathematical structure. As an optional extension, students can create their own version of the art mirroring the concepts gleaned from the launch
BRAIN TARGETED TEACHING IN THE CLASSROOM
This activity series combines a visual art example with an artful thinking routine to get students consistently analyzing art pieces through a mathematics lens.
Using Visuals to Build Thinking Habits – Visual Thinking Routines:
Visuals enhance memory more effectively than words alone (the picture superiority effect “a picture is worth a thousand words”).
Images are processed both visually and verbally, leading to deeper encoding and retention. Visual art also supports building strong thinking habits, including observation and interpretation, conceptual understanding, perspective-taking, and questioning
Using images helps make student thinking visible and promotes deeper cognitive processing. This is because it aligns with how the brain naturally learns: requiring students to slow down, make connections, and engage curiosity. In doing so, habits of thinking are reinforced.
Harvard’s Project Zero Thinking Routines are an excellent resource.
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:
Visual arts tap into positive learning systems and support students in applying their knowledge and skills in a non-traditional, open ended manner. It is essential that as many answers as possible are accepted. Any observations and equations students come up with to describe the art should be celebrated and encouraged.
The Physical Space:
The art present in this series will add novelty to the beginning of division lessons, and can also add to the classroom environment if teachers choose to print out pictures of them to use as decorations.
Learn More:
Learn more about Brain Targeted Teaching via Dr. Mariale Hardiman’s site.
ROOT BRANCH MEDIA GROUP – BRING ROOT BRANCH TO YOUR SCHOOL!
All video content made in partnership with Baltimore’s Root Branch Media Group.
MITCH HARRIS – BRING MITCH TO YOUR SCHOOL!
Mitch Harris is an actor, writer, and educator based in Baltimore. He believes in the power of the arts to tell meaningful stories, uplift communities, and enhance student learning. His work has taken him from Texas to India to Chicago and everywhere in between. From directing a creative writing program, to teaching elementary art, to performing in theatre for young audiences. Mitch believes that when students can connect both their brains and their bodies to big ideas, artistic and academic magic are sure to follow.
SAM SHELDON
Sam is a 4th grade Math and Science teacher at North Bend Elementary/Middle School. He has taught in Baltimore City Public Schools for 5 years. Sam’s journey with Arts Integration started with a summer spent working for SALA, and it has been an interest of his since. Arts were a large part of Sam’s educational journey, and his concert band conductor was Sam’s inspiration to become a teacher. Sam thinks that every student should be able to have intentionally designed lessons that meet all of their needs and interests.




