Teaching Plus One & Minus One Within 10
Rusty Bresser
Engaging Experiences for Transitional Kindergarten
Recently, I sat in on a professional development session in which Math Transformations consultant Elba Ozakcay shared some of her favorite lessons with a group of transitional kindergarten teachers.
Watching Elba share her wisdom with the TK teachers was really inspiring. All her advice about what to teach and ways to teach it are firmly grounded in her many years as a bilingual early childhood instructor. What struck me about Elba’s presentation, even more than the lessons that she shared, was her approach to teaching. She sees teaching as an opportunity to be surprised at what her students can do, and she is constantly excited to witness their brilliance as they make sense of numbers, quantities, and counting.
The ‘favorite lessons’ she shared are ones that teachers can use to help young children understand that adding one or taking away one changes the number in a small group of objects by exactly one. The lessons give students experience being producers of counting. For example, the lessons require students to roll a die and count out a certain number of objects. As they count, children have to keep the target number in mind at all times and stop themselves when they reach it. Producing a set of numbers is typically more difficult than counting a collection of items.
Elba’s lessons also engage children with the important counting concepts and skills listed below.
- Subitizing: the ability to know ‘how many’ without having to count.
- One-to-one Correspondence: saying number words in correspondence with the objects counted.
- Number Sequence: the names and the ordered list of number words.
- Cardinality: the last number word said when counting tells how many objects have been counted
Experience #1: Fish Friends
The first experience Elba shared is called Fish Friends. With children, she begins the lesson by reading a book by Lois Ehlert called Fish Eyes.
This colorfully illustrated book follows a pattern that students can quickly catch onto.
“1 green fish plus me makes 2.”
“2 jumping fish plus me makes 3.”
“3 smiling fish plus me makes 4.”
“4 striped fish plus me makes 5.”
The book continues the pattern up to “10 darting fish plus me makes 11.” Fish Eyes is full of interesting fish described using a variety of adjectives. Plus, it models for young children what happens to a small group of fish when you add exactly one more.
The Fish Friends Plus One/Minus One Game
Following is a game that Elba created for children to play after listening to Fish Eyes. Here’s a link to the Fish Friends Game Board.
Directions:
- Each player places five counters/fish on a ten frame to start the game.
- Partners take turns rolling a +1/-1/+0/-0 die and changing the amount of counters/fish on their board. Players end their turn by saying the sentence frame that matches with their roll:
- There were ___ fish, plus 1 fish, now there are ___ fish.
- There were ___ fish, minus 1 fish, now there are ___ fish.
- There were ___ fish, plus 0 fish, now there are ___ fish.
- There were ___ fish, minus 0 fish, now there are ___ fish.
What to watch for as children play the game:
- Do students count the cubes with one-to-one correspondence?
- When they add or take away a cube, do students automatically know the result, or do they have to count all the cubes?
- Do students know the counting sequence?
- When asked how many cubes are on their ten-frame, do they automatically know, or do they have to count? Or do they ‘count on’ from an amount?
- How do students respond when they roll a +0 or -0?
Teaching Young Children How to Work with a Partner
Playing a game with a partner can be difficult for young children. Teaching them how to take turns, follow directions, and be kind to their partner takes time and explicit instruction and modeling.
When Elba plays partner games with young children, she starts by playing with a small group of six. When introducing the Fish Friends Game, Elba has all six students place five counters on their ten-frame. She then has a student roll the die and everyone uses that roll to play. As they play, Elba emphasizes and models taking turns rolling the die and following directions. Only when she feels that students are ready does she gradually release them to play with a partner.
A Follow up Activity
When students have had many opportunities to play the game, Elba suggests that teachers ask students to select how many fish they want to draw (between 1 and 10). Have them draw that number of fish plus one more and then finish illustrating their picture. For those who are ready, have them write an equation that matches their picture.
Experience #2: Buttons Come and Buttons Go
The second experience Elba shared with the TK teachers is called Buttons Come and Buttons Go. With students, Elba begins the lesson by reading Pete The Cat and His Four Groovy Buttons by Eric Litwin. Use the following link to access the book in Spanish Pete The Cat and His Four Groovy Buttons.
The book tells the story of Pete the Cat and his four groovy buttons. Students invariably join in as Pete sings,
“My buttons, my buttons, my four groovy buttons.
My buttons, my buttons, my four groovy buttons!”
And then, “Oh No!” One button falls off and rolls away. Now Pete has three groovy buttons and continues with his song, but this time he now has three groovy buttons. The story continues as Pete loses one button after another, modeling for young children what happens to a small group of buttons when you subtract exactly one.
After reading the story, Elba shows the children an image of some buttons and asks, “What do you notice? What do you wonder? Do you have buttons on today? If so, how many?”
Pete’s Button Game
Finally, Elba shares a game (see directions below) she created for children called Pete’s Button Game. Here’s a link to the Button Game Board:
Directions:
- 2 players take turns rolling a 1-6 die.
- On their first turn, Player 1 rolls the die to count how many buttons they will add to their shirt.
- Next, the player takes away one button and tells their partner their math story of how many buttons they now have. For example: “I had 4 buttons, one popped off and rolled away. Now I have 3 buttons left. 4 minus 1 is 3.”
- Player 2 takes their turn.
- On their next turn, Player 1 rolls the 1-6 die again. They make their shirt show the number of buttons that matches the number on the die. For example, if their shirt had 3 buttons and they roll a 6, they must make their shirt have 6 buttons.
- Player 1 then takes away one button (now they have 5) and tells their partner their math story.
- The game keeps going until the teacher says, “Stop!”
What to watch for as children play the game:
- Do students count using one-to-one correspondence?
- When students must make their shirt have the number of buttons that corresponds with the number on the die, do they have to take off all the counters and start over? Or do they use the counters they already have on their shirt (for example, if they have 3 buttons on their shirt and they roll a 4, do they just add one more button to their shirt?).
- When asked how many buttons are on their shirt, do students automatically know or do they have to count?
Let the Kids Surprise You!
Elba shared with the teachers the surprises she experienced while playing the button game with students. For example, Elba recalled a boy who had 5 buttons on his shirt, and he rolled a 4 on the die. He immediately took one button off his shirt to make four. Elba was surprised that this four-year old didn’t have to take off all the buttons and count out 5. He knew that there were 4 ‘inside’ 5 and made quick use of this knowledge.
Experience #3: Math Flips
The last experience Elba shared is a slideshow called Math Flips from MathVisuals.wordpress.com. Teachers can use this routine to help students think about the concepts of one more and one less and much more! Each slide begins with a “Side A” showing a ten-frame filled with a certain number of dots. The teacher asks, “How many? How do you know? Next, the teacher shows side B and asks, “How many NOW? How do you know? See two examples below.
After using Math Flips for a while, ask generalizing and extending questions, like:
- How does side A help you with side B?
- What is the same and different about side A and side B?
- If I told you a number (1-9) could you tell me what one more is? What about one less?
Here’s another example:
Progression of Early Number and Counting
Elba’s lessons are examples of rich experiences that help children move through the progression of early number and counting that Graham Fletchy so expertly illustrates in his video linked here. By engaging in these games and routines, children learn and practice important counting skills and concepts, and they become producers of counting. They learn about numbers and quantities in engaging ways and in interesting contexts. And you get a chance to watch and be surprised at the brilliance of transitional kindergartners!
