Zero and Infinity: Sparking Kids Imagination in Math Class
For many kids, math class is boring! It is a class where rules and procedures are the focus, and there is no room for the imagination. Yet, higher-level mathematics is the opposite of this. It’s about beauty. It’s about discovering the language and secrets of the universe. Yet many possible mathematicians are turned off by the subject before high school and never think about pursuing a career in STEM.
Do you want to spark your students’ imagination? Do you want to create a sense of wonder and awe in your students? But are too afraid from straying from the standards because of testing? Then studying zero and infinity are perfect way to get your kids interested in mathematics.
I’ve developed several cross-curricular units from Pre-K through high school that are aligned to the Common Core standards.
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STEM & STEAM
STEM and STEAM units focused on zero and infinity is a great way to incorporate STEM ideas into the classroom. The topics around zero and infinity even at a young age point people to Calculus setting the stage to get students interested in STEM careers.
Cross-Curricular Learning
The more connections the brain makes, the greater the depth of learning. That is why cross-curricular lessons are so important. Additionally, they hook students who may not enjoy math with another subject that they love. Keep reading for some great cross-curricular lesson ideas!
Homeschool
Many of these lessons are great for home school where students can dive into deep concepts at their own pace.
Christian School
Zero and infinity naturally lead to conversations about God, the creator of the universe. Many of the mathematicians who discovered these concepts in Western culture were Christians who were also interested in theology. For Christian school teachers, it would be nice to pair this unit with a Bible unit on Genesis 1 or the characteristics of God.
Unit Ideas
Kindergarten
Zero Zebras: A Counting Book About What’s Not There by Bruce Goldstone
Zero is a different type of concept than counting numbers. To explore zero, students can read Zero Zebras: A Counting Book About What’s Not There by Bruce Goldstone. Students explore the concept of 0 and infinity by using a mystery box which is laid out in my lesson Engaging Math Lesson: Zero Zebras and Infinity. Additionally, music is incorporated into the lesson with the integration of Seph Schleuter’s “Counting My Blessings” songs. This lesson hits kindergarten various ELA standards and K.CC.3 for math: K.CC.3 Write numerals from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
Zero is the Leaves on the Trees by Betsy Franco
Another book for younger grades to expand the zero theme is Zero is the Leaves on the Trees by Betsy Franco which can be found in Math Picture Books: Teaching the Number Zero through Stories my post.
Black Holes
Integrating black holes into a unit about zero is a great way to add science to the thematic unit. For kindergarten I would recommend the book Black Hole: My Guide to the Solar System by Czeena Devara. It is a great informational text for kindergarteners and first graders who want to learn about black holes. More information about books about black holes can be found on my 11 Engaging Books About Black Holes post.
Counting Your Blessings
Counting Your Blessings is the perfect activity for the Holidays. Students count their blessings using counting skills. They can extend this lesson to talk about infinity. This lesson fits nicely with Zero Zebras.
Grade 1
Counting Your Blessings
Counting Your Blessings is the perfect activity for the Holidays. Students count their blessings by using their counting on skills. They can extend this lesson to talk about infinity. This lesson fits nicely with Zero Zebras that was discussed under Kindergarten.
Grades 4
Pointillism
Pointillism is a great way to incorporate infinity and art. To align with the standards, you can focus on 4.G.1, (4.G.1 Draw points, lines, line segments, rays, angles (right, acute, and obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.). But you can also talk about how a number line is dense and there is an infinite amount of numbers between any two numbers on a number line. Find the lesson here: Pointillism and Density of Numbers | A Great STEAM Lesson for International Dot Day
Black Holes
NASA/Dana Berry/SkyWorks Digital
Another fun way to incorporate zero and infinity is with the study of black holes. If you want to expand your zero unit to include science connections around black holes you can find some good books in this post: 11 Engaging Books About Black Holes.
A great literary text about black holes is The Care and Feeding of a Pet Black Hole by Michelle Cuevas. Although, this lesson plan is written for Grade 7, the reading level is low and the humor is right on par for 4th grade. So if your students are mature enough to handle the themes of depression and death, it’s a great book that incorporates zero and infinity. You can modify the lesson I’ve written here for your grade level: The Care and Feeding of a Pet Black Hole by Michelle Cuevas: Heartfelt Cross-Curricular Teaching Resource – Word & Numbers
Picture Books About Zero
There are also some great pictures books for elementary students about zero that can be found in my post Math Picture Books: Teaching the Number Zero through Stories.
Grades 6 and 7 (maybe 5)
Zero Zebras and a Mystery Box
If you can find something that excites them, middle schoolers are curious and love to learn. Use my lesson plan from A Mathematical Journey through Zero & Infinity-Part 1: A Mystery Box, Some Books, and a Contest. It’s a great lesson about zero and infinity, but it also addresses equivalence and properties of operations (6.EE.3, 7.NS.1, 7.EE.1). Find other books about zero for middle schoolers in my Math Picture Books: Teaching the Number Zero through Stories post.
Pointillism
To integrate art and infinity and the density of rational numbers use my lesson Pointillism and Density of Numbers | A Great STEAM Lesson for International Dot Day. It is written to specifically address 6.NS.6 (6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes.), but it could be modified to be used in both a 5th grade and 7th grade classroom to talk about rational numbers and the density of a number line.
One-Point Perspective
Another way to incorporate a STEAM lesson around zero and infinity is with the topic of one-point perspective. The 7th grade aspect of this lesson focuses on similarity, scale factor, and vanishing points aligning to Common Core standards 7.G.1 and 7.RP.2. You can find the post about this lesson here: A Mathematical Journey Through Zero and Infinity Part 2: The Zeroth Dimension and Vanishing Points | a STEAM Lesson
Black Holes
Black holes are another fascinating topic that discusses infinity and zero. For ELA connections use my lesson on The Care and Feeding of a Pet Black Hole by Michelle Cuevas: Heartfelt Cross-Curricular Teaching Resource – Word & Numbers as a literary text. It is a book that is humorous and deep with a lot of literary language elements. Both you and your students will fall in love with it.
You can find informational texts about black holes in my 11 Engaging Books About Black Holes post.
Counting Your Blessings
Counting Your Blessings is the perfect activity for the Holidays. Students connect infinity with the number line and use statistics to count the blessings for all the kids in the school. There is a service-learning opportunity.
Grade 8
One-Point Perspective
Carnival on the Via del Corso, Frederic Edwin Church, Gift of Louis P. Church, https://www.si.edu/Many students who dislike math love art! So integrating a STEAM lesson featuring both math and art can draw in many students who might feel side-lined during a typical math lesson. A vanishing point is a great real-world example of a dilation that integrates art. My lesson for 8th grade on one-point perspective and vanishing points aligns to Common Core’s 8.G.3 and 8.G.4. The blog post that features this lesson can be found here: A Mathematical Journey Through Zero and Infinity Part 2: The Zeroth Dimension and Vanishing Points | a STEAM Lesson
Counting Your Blessings
Counting Your Blessings is the perfect activity for the Holidays. Students count their blessings by using their counting on skills. This lesson follows nicely with the activity about a Mystery Box. It has a service-learning connection.
Algebra 1
Infinity and a Mystery Box
Who isn’t fascinated by zero and infinity? My lesson A Mathematical Journey through Zero & Infinity-Part 1: A Mystery Box, Some Books, and a Contest has Algebra 1 connections. Students can explore concepts of zero and infinity while addressing standards N.Q.1, A.SSE.3, and A.REI.1. The lesson integrates equivalence and properties of operations.
Counting Your Blessings
Counting Your Blessings is the perfect activity for the Holidays. Students count their blessings by using their counting on skills. This lesson follows nicely with the activity about a Mystery Box. It has a service-learning connection.
ELA Connections
I would love to find a great ELA text or short story about zero and/or infinity for 9th graders to add to my thematic unit about zero and infinity. So if anyone knows of any texts, please leave a note in the comments 😊🙂.
Black Holes
If you want to integrate the idea of black holes into your discussion about zero and infinity, check out my post 11 Engaging Books About Black Holes for good resources.
Geometry
Pointillism
Pointillism and Density of Numbers | A Great STEAM Lesson for International Dot Day is fun lesson that celebrates International Dot Day and Pointillism. Pair up with an art teacher as you explore the definitions of a point, line, and a plane reinforcing the idea that a number line (and a plane) are dense. The lesson aligns to G.CO.1: Know precise definitions of ray, angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and arc length.
One-Point Perspective
Many Geometry teachers are familiar with Flatland where A. Square goes on a journey to visit other dimensions. One step farther into the 0th dimension allows artists to create more life-like paintings using a vanishing point. Geometry students can study real-life applications of similar figures, scale factor and dilations using art. A Mathematical Journey Through Zero and Infinity Part 2: The Zeroth Dimension and Vanishing Points | a STEAM Lesson describes how to apply these concepts in a high school Geometry class. It will cover Common Core standards N.Q.1, G.SRT.1, G.SRT., and G.SRT.3.
Black Holes
If you want to integrate the idea of black holes into your discussion about zero and infinity, pair up with a science teacher and check out my post 11 Engaging Books About Black Holes for good resources.
Pre-Calculus and Calculus
As Flatland is to Geometry, so Zero: The Biography of a Dangerous Idea by Charles Seife should be to Pre-Calculus and Calculus. It’s a must-read for students on a STEM pathway! I loved this book! It helps you understand the background and significance and controversy of zero and infinity and will broaden your mathematical horizons. There is a lot for discussion that will pique students’ interest. Although non-fiction it’s an entertaining read You can find a review for the book and my discussion guide here: Zero: The Biography of a Dangerous Idea | Book Review.
Counting Your Blessings
Counting Your Blessings is the perfect activity for the Holidays. Students count an infinite number of blessings and discuss the concept of infinity. There is a service-learning component as well.
High School Statistics & Probability
What if you could change reality? How would you change it? Do your students like science fiction? The End of Eternity by Isaac Asimov is a fun way to get students to think about statistics and probability incorporating the idea of time travel and reality changes. Here is my post that includes a discussion guide: Exploring Asimov’s ‘The End of Eternity’ in High School Curriculum |A Cross Curricular ELA & High School Statistics Lesson
Conclusion
Zero and infinity are fascinating subjects to all kinds of people. Finding an interesting topic helps engage kids in mathematics. Incorporating the imagination and the “what-ifs?” is a way to hook kids that might not be interested in a classroom that is primarily procedure based. What if a unit on zero and infinity could change a student’s life trajectory forever?
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Comment
Let me know if you have any other ideas to incorporate 0 or infinity into your classroom!
