This resource was created as a supplement for the Language Builder: ARIS® Academic Readiness Intervention System complete early autism curriculum, Lesson #175, Receptive Numbers 11+. Download a free copy of the lesson and learn more about ARIS here.
Teaching concepts to autistic children—be it phonics, tooth brushing, or greeting people—typically requires high repetition and explicit, concrete instruction. So how can we teach the concept of zero to autistic students where there is literally nothing to represent the amount!?
Using tens-frames and counters, activities, and story-based resources helps get across the complex concept of zero for autistic children. Real life also offers some excellent “teachable moments” for autistic children who tend to be concrete thinkers.
Introducing the Concept
Number Representation
When children first learn to count, they tend to use what’s available: their fingers. To make zero more concrete, have students use a fist to represent when they are counting zero. This can also be a helpful way to prompt and cue students to remember the numeric representation of 0 as they learn to write, label, and expressively identify the number.
Tens-Frames and Counters
A template such as a tens-frame can help make “nothing” more apparent to students with autism. The struggle with zero is that it is often an absence of something, like an empty space, which can deter understanding the concept for black-and-white thinkers.
- When you have students take away or label “how many,” have students use counters (such as coins, blocks, etc.) and place them in the tens-frame.
- As they remove counters from the tens-frame, have them label how many counters are left in the frame. Seeing the space empty can help quantify the concept of zero.
Activities to Reinforce the Concept
Hi-Ho Cherry-Oh!
If it’s been a while since you’ve played, check out this quick rule refresher. You’ll find a fantastic game for working on subtraction, addition, and the concept of zero. The ultimate goal is to win by having zero apples left on your tree. Likewise, one of the spinner options is a spilled bucket, when the player must empty all cherries from their bucket and put them back on the tree, leaving zero cherries in the bucket. This is a fantastic way to reinforce the concept, and as referred to later, the spinner could be adapted and simplified if needed.
Playing I Spy with or without a picture book
One way to help children understand the absence of something when there is zero is to have them look for examples of items. If you’re looking at a picture book, you can say “I spy 3 apples, can you find them?” and likewise ask “How many bananas do you see on the page?” If they struggle, you can offer the prompt—“There are zero bananas because there are none on this page!” The same principles could work at a store or even in your living room—"I spy 2 laptops, can you find them?” Or “How many rocking chairs are in the room?”
Make your own spinner
One of the reasons zero can be such a challenging concept is that we typically start counting with 1, and the same goes with spinners and dice included in board or card games. To help practice and apply the concept of zero, make your own spinner to use during a game. All you need is a brad (paper fastener), a paper clip, and some paper to designate 0, 1, 2, 3, etc. You can use this spinner when you’re playing other board games like Sorry! This will give the student a chance to see what moving zero spaces looks like.
Building (and destroying) towers
Building towers out of blocks can be a great way to reinforce math concepts for addition and subtraction—and what is the best part about a tower? Why, knocking it down of course! This is a fun and easy way to help generalize the concept of zero to their play.—“There are zero cubes left in our tower!”
Supporting Literature
Just as research continues to suggest the use of social narratives, having a story-based resource can be a powerful tool for autistic students. It is a constant reference material that can be accessed again and again as they continue to learn new ideas. Here are a few books specifically related to teaching the concept of zero in straightforward terms.
Zero is the Leaves on the Trees by Betsy Franco
Typical audience: Kindergarten to 2nd grade
This book applies the concept of zero to different observable phenomena in nature such as when all of the leaves fall off the trees in autumn or the number of balls left in a bin at recess time.
The Hueys in None the Number by Oliver Jeffers
Typical audience: Kindergarten to 3rd grade
This book teaches the concept of zero through subtraction. One of the Hueys works to explain “none” by having a number of items, 1 through 10, and then taking those away to give an example of what it looks like to go from something to nothing.
Zero: Is it Something? Is it Nothing? by Claudia Zaslavksy
Typical audience: 1st to 4th grade
This book goes beyond showing zero as a “none” and goes into what zero can mean in different mathematical positions such as 501 or 20. The book distinguishes the number zero from the letter “O” and includes riddles and word games.
There are plenty of other books out there about the concept of zero, but these picture books are specifically identified for autistic students due to the concrete and real-life application used in introducing this mathematical process.
Big Take-away: Real-life Application
Our autistic students are concrete thinkers who need opportunities to generalize their learning across settings. When someone eats all of the cookies, this is a good opportunity to prompt and reinforce the concept in a real way—and maybe make more cookies! Likewise, if students are struggling with contextualizing zero as a placeholder number, using those visual cues and tools can help students see that zero can mean something in larger numbers. This could even look like setting up the oranges in a ten-frame format so they can connect the visuals they’ve used to real life.
What are some other ways that you have introduced, reinforced, and generalized the concept of zero? Are there any supporting texts that have been successful in teaching your autistic student?
This resource was created as a supplement for the Language Builder: ARIS complete early autism curriculum, Lesson #175, Receptive Numbers 11+. Download a free copy of the lesson and learn more about ARIS here.
