Tiny Human Perspectives: What About 0?

What is up with 0? It is nothing, nada, zilch. So why spend time thinking about nothing?

While playing a game with dice (labeled 0-5 each), pre-schoolers had no trouble thinking about zero as nothing.

Student (rolls a 0 and 5): 0 and 5 is still 5!

Me: Why is it 5?

Student (now rolling eyes): Because you added nothing to 5, so it stays 5. You didn’t do anything to it! (Duh…Mrs. M!)

Playing the same game in Kindergarten. Out of 20 students, only 2 (one being my son, since he already struggled with it at home and had made some headway with clarifying what happens when you add 0) students were okay not changing the value of the addend when added to 0. The others added at least one more to their addend, or just sat there and said they lost a turn because they got a 0. ????

Why the struggle?

Students use their instincts when learning. While playing (without formal teaching), the preschoolers made sense of the zero. When you add nothing to a number, it stays the same (AKA Additive Identity Property). However, this ‘sense-making’ was left behind once (I will use my son as the example) Chris started learning addition. He figured out that when you add numbers, the value changes. Every problem he did resulted in a larger value than the two addends. Mama, it gets bigger as you add. When he rolled a 0, he couldn’t make sense of that with his understanding of what addition IS. We had to roll LOTS of 0’s before he finally clicked that adding nothing doesn’t change the other addend.

What Can You Do?

Allow you child to play with a die that has a 0. Allow them to make sense of this new phenomena and open their eyes to new learnings about addition. This will help them later, when adding different kinds of numbers (like negatives) results in smaller sums.

Remember, Zero really is a Hero!

Tiny Human Perspectives: What About 0?

Race to the Top: Kinder Observations

Last week I posted a game called “Race to the Top”. I was able to play the game with all of the students in my son’s kindergarten class. I was one of the stations during center time, and had between 4-6 students each rotation. We kept them 15 min per station, which seemed enough time for their engagement. (One group ran at 20 min and it was too long.) Each person at my station had their game card (see links below for options) and each pair had one number cube (labeled either 0-5, 1-6, or 5-10) and one dot die (1-6 dots).

Here are a few observations and patterns of misunderstandings.

  1. Counting different representations is tough! The students were used to having to ‘add’ (i.e. count one-by-one) two dot dice, but hadn’t yet used a number cube WITH a dot die. When we started to play, at least one in each group said their sum was 2, no matter what was on the dice. This is because there were 2 dice. It only took a few rolls for all of them to get the hang of it.
  2. For this time of year, the 0-5 number cube was too easy (with the exception of 1 pair of students). I would use the 6-10, as most of our misconceptions surfaced once they passed the number 10. Here are the misconceptions after 10.

Example: 9 + 5 dots

  • Misconception 1 (counted backwards from their number):  “9…8, 7, 6, 5, 4.”
  • Misconception 2 (started counting by 10’s):  “9…10, 20, 30, 40.”
  • Misconception 3 (counted them separately and got stuck): “9 and 5…pause…”
  • Misconception 4 (wanted to put 14 squares on the game board, not see it as one-14)

After about 2 minutes of playing with me direct instructing, the students were successfully independent, taking turns and excited to see what their value was. In 15 minutes, I was able to watch, assess, and intervene every child in my group several times. They were engaged and excited to be playing. We averaged 18 sums per player in the 15 min, which is a LOT of addition!

Favorite Quotes of the Day

  • You cheated! You can’t keep rolling until you get your number! (This would have been me as a child!)
  • Wait. We can’t play anymore? Awe.
  • I only need two more 12’s to win! You need two more 7’s! It’s a tie! (I get giddy when students do more math than asked!)
  • Thanks for playing games with us, Chris’ Mom!

Game Board for 0-10 (Change as needed depending on the number choices for your dice)

Race to the Top Game Board


Race to the Top: Kinder Observations

5 Easy Daily Math Ideas

I was walking Chris (5 yo) to school yesterday (as we do most days) and was stopped by his Principal. He commented, “You always are counting when you come to school. I wish more parents would do that with their kids.” So it got me thinking; what are some easy-peasy ways parents can support their kiddos with math in the early years? Here are 5 ideas that you could start TODAY! Choose 1 or 2, and use them every day for a few weeks to really see their number sense and mad math skills bloom! Please comment with other ideas as well so we can have a huge vat of fantastic learning opportunities to use with our babes!!!

  1. Counting, Counting, Counting! We do count on the way to school. EVERY. SINGLE. DAY. At first, it was to 20, then to 50, and now we are up to 150! We count by 1’s most days, but sometimes we go rogue and count by 10’s (gasp!). Just like singing the alphabet, rote counting is a must to learn numbers. Start with 1’s, then 10’s for Kinders and younger. Move to 2’s, 5’s, 3’s, etc… and you have provided a solid foundation for initial multiplication! Move to counting by 1/2’s, 1/4’s, 1/3’s (you get the idea) and you are rocking initial fractions! Start with a different value that 1 and you are moving mountains!
  2. Counting Forwards AND Backwards: Stairs are great for this. Count up when you go up stairs, down when you go down. Don’t know how many stairs? Start at 20 and count down. If you don’t hit 0, oh well!
  3. I have...: In the produce section of the grocery store, you need 6 potatoes. Ask you tiny human, “I have 2. How many more do I need to have 6?” This is AMAZINGNESS! I cannot tell you how many teachers have students who struggle with missing addend problems. This will help so much!!! Do it at home with the silverware. “We need 4 plates. I have 1. How many more do I need?” The opportunities are endless for this!
  4. Sort! Sort! Sort! Kids can sort the silverware that comes out of the dishwasher (Take out sharp objects first, please!), socks, toys, coins (when you are at a restaurant or doctor’s office), mail, school work, books, buttons, etc. Sorting is super important, as it builds the idea of structure and patterns as well as organizing and classifying information.
  5. Guess my Number: A car-time fav in our family. “I am thinking of a number. It is bigger than 5 and smaller than 10. What is my number?” And you can amp this up for older students as well. Use multiples, even/odd, negative values, fractions, square roots, etc. And once they get the hang of it, each person in the car gets a turn to be the number-chooser. Super easy, and builds magnitude of numbers, place value, and relational thinking.
5 Easy Daily Math Ideas

Race To The Top! Counting On

So my tiny human, Chris, loves to add, but always has to start from one (no matter what the values are). I finally figured out a game to play to push into Level 2: Counting On (see previous blog for more info on the levels of single digit addition/subtraction).

Objective: To get to the top of one of the columns (doesn’t matter which one) first!

Materials: 2- Race to the Top Game Boards (click on link) Race to the Top Game Board 2-dice:  Since Chris is working on making sums to 10, I created my dice. You do not have to, but it is super easy and cheap! Go to a hobby store or home improvement store and buy wooden cubes. On the first one, label with the numbers 0-5. On the second one, draw dots on it (like a normal die), but use 0-5. Notice my mad dot-drawing skills! img_8144.jpg

How to Play: First player rolls the dice. He ‘traps’ the number (in the case above, the 3) and counts on one-by-one if need-be the dots. He puts an object above the sum’s number on the game board. Please view the example. Note the time it takes for Chris to figure it out, but he still gets it. This is tough when children are used to adding with objects and we replace one set of objects with a number!

Notice how he is also doing some mental work with figuring out “how many more” he needs to win the game.

IMG_8148Player 2: Roll dice, count on, and place the object on her game board. Continue until someone reaches the top of a column.

Look at how many addition problems he had to complete to finish the game! He never even noticed all the fantastic work he did! (Insert evil laugh.)

For Differentiation

Level 1 (Counting All): Use dot dice for both instead of one dot and one number cube. That way he is working on his one-to-one counting and adding all together! You can also make a 0-6 page and use 0, 1, 1, 2, 2, 3 dots for each cube.

Level 3: Use both number cubes instead of dots. You could also use number cubes 1-6 and create a game board from 2-12.




Race To The Top! Counting On

Levels For Single-Digit Addition: Where Is Your Child?

‘Tis the season in Kindergarten for learning addition and subtraction. You may wonder where your child is with respect to these foundational operations. Most educators will think about their students’ learning of single digit addition/subtraction as a 3-level progression. I will focus on addition for sake of space.

Level 1: Counting All

This is where most kinders should be. They can even end the year in this level and be awesome! At Counting All, students typically use concrete objects to count one-by-one in order to find the sum. Below is an example, using 2 + 3.

Level 2: Counting On

This is the “trap and keep” idea. The first addend is “trapped” in your mind, and you count on from that value. This is a more sophisticated idea, because you have to understand that the first addend is a quantity of its own, and you are moving forwards from that value (versus starting at 1 every time). Often your child will “trap and keep” the first addend by taking their hand to their head to “trap” it in their mind, then use their fingers to count on. So for 5 + 3, they would “trap the 5” and count on, “siiix….sevennnnn…eighhhht”. This is a level many children live in for quite some time.

Level 3: “Messing with Math!”

That is actually NOT what it’s called, but I like this title much more! This is when children start realizing that there are certain “cheats” that they can use to do more of the math in their head. (Mathematically, they are called properties, but that is for another blog!) I will actually devote an entire set of blogs for this Level, as it is that important. But for now, here is an example using ten-frames with the expression, 9 + 5.9+5

9+5cStudents can see that, if they take one of the five (reds) and move it up with the nine (blues), they can make a 10. 9+5 can be renamed as 10+4=14. This is HUGE for students in terms of flexibility with numbers and algebraic thinking!

Children will ebb and flow between these three levels. The important thing is to play, explore, and play some more! The next few blogs will encourage this through games that I am trying out with my son’s Kinder class!!!

For more information, please visit: https://www.cde.ca.gov/ci/ma/cf/documents/mathfw-appendixc.pdf (This is one of the best versions…Go CA Framework Committee!)

For the ten-frames (I love these because they are soft and quiet!): https://www.schoolspecialty.com/magnetic-board-set-1400695



Levels For Single-Digit Addition: Where Is Your Child?

Rolling to 100

I had the pleasure of volunteering in my son’s Kinder class for 100 day. She had a great ‘filler’ game that I wanted to adapt and share. This is a great one to take to a restaurant where they hand out crayons!

Materials: 100 chart, one per player (see below for link), die (dot for one-to-one correspondence, numbered for numeral recognition with counting), crayons (at least 2)

Objective: To be the first person to color in all 100 numbers!

How to Play

  • Player 1 rolls the die and colors in that many spaces, starting at 1. Player 2 does the same on his/her gameboard. (Example: rolling a 5)rolling 5
  • Player 1 rolls again and, in a different color, colors in that amount. So if I rolled a 2, I would color in the next two squares in a different color. Continue playing until someone reaches 100.

How I would change it

  1. Give your child a blank 100 grid and have him/her fill it in for writing practice. Then use their board to play.
  2. Change out the dice as your child grows in his/her number sense. Using larger numbers will create patterns and encourage counting by larger groups instead of by ones.
  3.  We are going to play to 20 and write the addition sentences on a whiteboard.         So 5 + 2=7 for the last play.  Also you could relate to counting on. Start at ______ move forward ______. I am now at _______. Starting at numbers other than 1 or 0 to chris 100count is a BIG DEAL!
  4. We are going to start at 100 (or 20) and go backwards to roll to 0! Counting backwards is just as important as counting forwards!
  5. Find the values. After Chris finishes up his very crumply 100 chart, he is going to guess my number. Example: My number is blue and is bigger than 23 but less than 26. Guess my number!
Rolling to 100

War!(HUH!) What is it good for? (Absolutely lots in Math!)

With my family on the go so much during the non-lazy days of summer, we need easy games to entertain the tiny humans that don’t require mass amounts of attention from the adults (who are often in conversation). Enter the game of War. This versatile game can be used for all age groups and can really keep your child’s skills in arithmetic in check during the “summer slump”.

How to Play (Basic Version)

  1. Grab a deck of cards (I keep one in my purse and in the car at all times). You don’t have to, but I prefer to take out the face cards and jokers. Shuffle the rest and divvy out to all who are playing.
  2. All players shove all of their cards into a “deck” and keeps the deck face down.
  3. All players (at the same time to avoid cheating) flip the first card. The player with the largest value is the winner and takes all of the cards in the round.IMG_5434
  4. If there is a tie (that is the largest value), those players place 3 cards on their original face down and flip the fourth card. Whichever player NOW has the largest value gets all of the cards from the round. IMG_5435
  5. Continue playing until either a) one player has all of the cards; or b) you get sick of playing. The player with the most cards is the winner.

Additional Versions

  • For younger players: Use only 2-5 from the decks and play with those. The game dot cardsgoes faster and they are working only with 2, 3, 4, and 5. You can use the aces as 1. Even better, use number cards or dot cards (see below for links). Print on cardstock (4 cards per number) or go online and buy a set.
  • For any age: You can also play and whoever gets the smallest value wins. This is great for preK-1st graders!
  • For students who need review with addition: Play two cards at a time and add them. The player with the largest sum is the winner of the round.
  • For students who need review with multiplication: Play two cards at a time and multiply them. The player with the largest product is the winner of the round.
  • For grades 5-7: red cards are negative values; black cards are positive values. Flip over one card. If I have a red 6 and you have a black 2, you are the winner since positive values are always greater than negatives. IMG_5434
  • For grades 6-8 (or 7-8 if using Common Core): Play two cards and add them, using reds as negatives and blacks as positives. The player with the largest sum is the winner of the round.
  • For grades 6-8 (or 7-8 if using Common Core): Play two cards and multiply them, using reds as negatives and blacks as positives. The player with the largest product is the winner of the round.
  • For grades 6-8, use only values ace (for 1) through 5. Flip the first card; that is your base. Flip the second card; that is your exponent. The player with the highest value wins  the round.

Different Sets of Cards:

  • You could probably look on Amazon for different card types, but I love the sets at 52 Pickup. They are of high quality and there are many different types ranging from dot cards to ten frames to cards that go through the thousands (so you can work on place value!)



War!(HUH!) What is it good for? (Absolutely lots in Math!)