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

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

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

Playing with Math: The Function Machine

I love this game, because you can tailor it to the level of your child. Any child, preK through adult, can play and find it challenging and fun!

The Function Machine

Grade Levels: Any, depending on how complex you make the function.

Materials: paper and pencil (whiteboards or Magna Doodles are great, too!  We just used the Magna Doodle in the car on a 3-hour drive and it worked great!!)

  1. Draw a function machine. It need not be fancy, but if you google image function machines you will get tons of ideas. function machie twoMine (as I am on the lazy side) typically look like a rectangle with an opening at the top (for the input) and an opening at the bottom (for the output). They are just very boring and sad. The one to the right is super cute and soooo not me.
  2. Choose a rule (function) to use. So my rule for my PreK could be “one more” or “+1”.
  3. Your child gives an input number. You give the output number. Example: My son loves the number 5 (after all, he IS 5).  So he would put in the number 5 and I would tell him the output is 6. [It is better if you make cool sounds as if the function machine is DOING something. This is supposed to be FUN, remember???]
  4. Your child keeps guessing numbers, as you fill in the outputs each time, until they realize the pattern and can express it either in words or as a ‘math rule’ (expression). If they guess the rule wrong, keep playing until they get the correct rule.
  5. This is really fun when you have more than one kiddo playing. However, they may only guess when it is their turn. That way, everyone has a chance to play and learn.

Let’s Try One! 

  1. You enter 5 into the function machine. beep boop beep boop! Out comes 7.
  2. You enter 2 into the function maching. beep boop beep boop! Out comes 4. (Got a guess for what the function rule is????)
  3. You enter 10 into the function machine. beep boop beep boop! Out come 12.
  4. You say the rule is “plus two each time”. Yup! The rule is the machine adds two to each input (or y=x+2 for your middle schoolers).

Suggestions for Different Grade Levels:

Grades K-2: add 1, add 2, add 5, add 10, add 100, subtract 1, subtract 2, subtract 10, subtract 20, etc

Grades 3-5: same as above (Fluency in arithmetic is important!) and multiply by 2, multiply by 5, multiply by 10, take half, divide by 10

Grades 6-up: combine operations multiply by 2 and add 1 (2x+1), triple a number minus 1 (3x-1),  a number times itself (square it), take half of a number and add 1 (1/2x+ 1), etc. You can also include negative rules as well (like multiply by -3).

You can also create a function table and just fill in as input/outputs as well, if they are above having a cute function machine. I have inserted one below as an example. function table

These are so great for trips and such, because all it takes is a napkin and a pen (and your rule). Finding relationships is imperative for algebra. This is a great way for kids to play with the ideas they need for later mathematics!


Playing with Math: The Function Machine

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!)

How Many Are Hiding?

This is a great game for tiny humans in need of some entertainment while waiting at a restaurant. Just make sure to ask for an extra children’s cup to play.

Age Level: 3-6 year olds

Materials: children’s plastic cup (any cup will do, just not transparent), a set of objects (I used goldfish for the example, as that was what was in my purse! Other options are pennies, beans, tiny annoying toys, etc.)

How to Play: Place out a certain number of ‘stuff’. Normally for me, it is however many I have in my purse! I would recommend starting with 5 or less, see how they do, and adjust as needed. The first time I played with my 5 year old, we started with 10 and it was quite frustrating for him. They catch on and you can up the number as they grow!

  1. Have your child count how many there are. IMG_5269
  2. Have your child close his/her eyes. Hide some of the objects under the cup.IMG_5276      IMG_5275
  3. Ask your child to open his/her eyes. Ask the following:
    1. How many do you see?
    2. If there were _________ to start with, how many are hiding?
  4. Allow your child to check their answer by lifting the cup.
  5. Ask the following:IMG_5274
    1. How many were hiding?
    2. How many were out?
    3. How many in all? (Woah! It is the same as what we started with! Weird!)
  6. Switch who hides and who plays.

Why play? Aside from counting one-by-one and ‘holding’ that number in their heads, students need lots of practice understanding that a number can represent an amount. That amount can be broken into parts (decomposed), but when we put them together (add them) they make the original number we had. This is part of the idea of conservation, which is critical for young mathematicians to understand (not the word but the idea) in order to add and subtract numbers.

Special thanks to my tiny human for playing this morning! Love ya, bud!



How Many Are Hiding?

Playing With Math: Circles and Stars

Ahhh…summer. For many of us, that means more time with the kids…waiting. Waiting at a restaurant, doctor’s office, airport, etc. For many kids, it may also mean waiting to use their brain. Research suggests that students can lose as much as 2 months of learning skills during the summer months (Oxford, 2017).  So how can we use the waiting times (or times at home when they are claiming boredom) to retain and advance their learning in mathematics? Play games/activities.

While there are many great apps for kids, I would request less screen time and more interaction with your children.  For the next three months, I will suggest a game/activity that you can use with your child. I will suggest different levels, so that you can play it often and in different ways. I use these same games with my own children, and find the time waiting goes much quicker, with less outbursts and meltdowns. Further, I am modelling playing with math, which is truly the way I feel our children learn and understand math best.

Circles and Stars (Marilyn Burns)

Grade Levels: Though used in grade 3, if all you are doing is counting the number of stars I would recommend grades 1-5. My preK has played it and just counts one by one. He cannot make the stars, so he draws x’s.

Materials: die (number cube or dots; doesn’t matter), paper or napkin, pen or pencil (I prefer a travel size Magna Doodle or whiteboard with dry erase marker)


  1. Roll the die. Draw that many circles.circles
  2. Roll a second time. Draw that many stars in EACH circle. stars
  3. Total the stars. Whoever has the most stars wins the round. (Play as many rounds as you want. The winner could be the one with the most stars total. Woo hoo! More math!)
  4. Alternative: The winner is the player with the least amount of stars.


  1. Roll 2 dice (or the die twice in a row). Player chooses which die represents the number of circles and the number of stars in each circle.
  2. Total the stars. Whoever has the most (or least) stars wins the round.

Questions to ask:

  • If I was to switch which die represented the number of circles and stars, what would happen? (The picture would look different, but the total stars would stay the same. This is the beginning of understanding the commutative property for multiplication.)
  • How could we represent what we did in words? (Example: 4 groups of 3 stars is 12 total stars.)
  • How could we represent what we did as an expression?                                   (Example: 4 x 3 = 12)

Link for Summer Learning: https://www.oxfordlearning.com/summer-learning-loss-statistics/



Playing With Math: Circles and Stars