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Color By Divisor

Arts Integrated Small Group for Grade 4 Divisibility

Tags: Division Small Group Divisibility Divisors Prime Numbers

Color By Divisor

Pairs with Reveal Math Lessons 4th Grade: 7-2, 5-3

Students use their understanding of divisibility and prime numbers to complete a color-by-number artwork. For each number, students determine which divisors apply and use the corresponding colors to fill in the picture. When a number is divisible by multiple divisors, students layer colors to visually represent these overlapping mathematical relationships.

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MARYLAND STATE STANDARDS

MD Math Standards:

  • 4.NOS.B.6a – Divide whole numbers with up to four-digit dividends and one-digit divisors with and without remainders. Apply estimation strategies to estimate quotients
  • 4.NOS.A.1b – Apply and extend place value understanding to multi-digit whole numbers within 1,000,000. Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rounding to any place.

In the 4th Grade MD Companion Guide it is emphasized that estimation should be taught through conceptual understanding of number relationships instead of using mnemonic tricks. When students practice recognizing multiples of 10, 100, and 1,000 that are divisible by their divisor, they are developing an understanding of the relationships between their dividend and compatible numbers that can help them estimate. This is essential because rounding 101 ÷ 3 as 90 ÷ 3 or 120 ÷ 3 cannot be done by using mnemonic tricks, as the student may round to 100 ÷ 3 and stop.

MD Arts Standards:

  • VA.AS1.E:3-5:1 – Collaboratively combine ideas to generate an innovative theme, concept, or idea for art-making
  • VA.AS2.I:3-5:1 – Develop and experiment in the creation and design of artworks.

These standards focus on how students create art. What is the stimulus? Instead of traditional sources of inspiration like an existing art piece, the inspiration will be math. Their artistic choices will be guided by their number sense to create a visually appealing image.

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.
  • 4.NBT.A.3: Use place value understanding to round multi-digit whole numbers to any place.
National Arts Standards:

  • VA:Cr2.1.4a Explore and invent art-making techniques and approaches. 
  • VA:Re.7.2.4a Analyze components in visual imagery that convey messages.

ARTS INTERATED LEARNING OBJECTIVE

Students will be able to create color-by-number artwork by determining divisors for a wide range of one to four digit numbers.

MATH DOMAIN

  • Number and Operation Sense → Use place value understanding and properties of operations to perform multi-digit arithmetic. → Divide whole numbers with up to four-digit dividends and one-digit divisors with and without remainders.
    • Number and Operation Sense → Generalize place value understanding for multi-digit whole numbers. → Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rounding to any place.

    COHERENCE

    • Before: Students recalled basic division facts (Grade 3). Students estimated products of multi-digit numbers (Unit 6). 
    • After: Students use partial quotients to divide (Unit 7). Students use partial quotients to divide by two-digit divisors (Grade 5).

    MATH & ART SKILLS

    • Math: Determine what numbers are divisible by a chosen number.
    • Art: Recognize what colors are created by mixing primary colors together.

    MATERIALS

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    1. INTRODUCE THE WORKSHEET & COLOR KEY

      • Explain that each color represents a divisor (2, 3, 5, or 7) or the category of prime numbers. Review what it means for a number to be divisible by another number and remind students that prime numbers have exactly two factors: 1 and themselves.
      • Note that we’ll start with the primary colors of red, yellow, and blue. Some numbers have multiple divisors, so these primary colors may be combined to make the secondary colors of green, orange, and purple.
        • It is important for students not to color too hard in this case, because the colors will not blend together.

      2. MODEL HOW TO DETERMINE WHICH COLORS TO USE

      Choose a number from the worksheet and identify which divisors divide it evenly. For example, 900 is divisible by 2, 3, and 5, so it would receive all three corresponding colors. Students can use a whiteboard or scrap paper to check their thinking.

      3. COLOR THE PICTURE

      Students determine which divisors apply to each number and color each section using the corresponding colors. Some numbers may be divisible by multiple divisors, so students should layer the appropriate colors lightly to show these overlapping relationships.

      4. REFLECT ON THE MATH & ARTWORK

      • Ask students:
        • What numbers could be divided by multiple divisors?
          • It should be a secondary color.
        • Pick one of the numbers that now has a secondary color: What color did you make when you colored it in? What primary colors did you use to make this color?
        • What emotion do you feel when you look at the art you made? What colors make you feel this way?

      ASSESSMENT & REFLECTION

      This activity is easy to assess since the teacher will know what the final product will look like. If the sheet is colored correctly, the student understands the content. You may need to encourage students to revisit the sections with multiple divisors represented to make sure they are using all the applicable colors.

      For the reflection, students need to notice which numbers could be divided by different divisors. This is an essential aspect of the arts integration, because the numbers that have multiple divisors will create new colors with the primary colors.

      Making emotional connections to the art is another crucial point of the reflection. If 5 is one of the divisors and is given the color blue, how would an art piece that has mostly numbers divisible by 5 make the artist feel? What if 2 is a divisor and is given the color red, and all of the numbers are even? How would that piece of art make the artist feel?

      DIFFERENTIATION

      The coloring sheet can be edited to focus on whatever math skill you may need.

      • If your focus is multiplication, change the sheet to reflect factors instead of divisors.
      • If your focus is on fractions, swap the numbers for fractions.
      • By changing the colors used, you can create different moods or themes.
      • By changing the numbers, you can focus on not only division, but any of the four operations they may be working on in a particular unit. You can easily scale up by using more digits or down by using fewer.

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      Materials Google Folder

      BRAIN TARGETED TEACHING IN THE CLASSROOM

      This activity requires students to put their knowledge of factors and divisors to create a piece of art. By assigning certain numbers with certain colors, students can see the physical representation of that number’s value with swatches of color. If 2 is yellow and 5 is blue, students can color in the 10 area with green to show this relationship (both 2 and 5 are divisors of 10). This worksheet is also editable so it can be used across units for artful repetition.

      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 are known to engage students positively in learning. Using coloring as a vehicle for practicing a frustrating skill for students, estimation, may make positive emotional connections to the skill that will support long term retention.

      The Physical Space:

      This activity requires very little in terms of physical space, but it is important that students have a whiteboard or scratch paper to work out their thinking before they color something they can’t erase. Students are also being presented with skills that they have practiced before, determining multiples and factors, in a different context than before.

      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.

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