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!)

https://sumboxes.com/collections/types?q=52%20Pickup%20Card%20Decks

 

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

That Moment You Realize Your Child Is Suffering

All who have multiple children know that each one is wonderfully different. You can raise ’em the same, yet they have their own amazing quirks and personalities, strengths and passions. This could not be more true of my two boys.

My youngest is now 5. He has always been the rough and tumble type. Everything is a competition to him. (Even last night he was standing on his tippy toes trying to be ‘taller’ when raising his hand at church!) He is funny, outgoing, and a firecracker. He is a joy.

Yet school stuff has not yet become his thing. He seemed disinterested in learning his letters, yet loved to be read to. He never wanted to sit with me and learn the components all say are so important for kinder. His preschool teachers said it would come; that he just was a busy bee and had other, more important things to care about. And honestly, I believed that too. He loves to create, tell stories, sing, build, and live outdoors. Who was I to take that away from him?

So when his amazing preK teacher suggested a hearing test, I was on board. No big deal; just go do it and cross it off as another thing we did. It came back inconclusive. Went for an ENT hearing test. The results were staggering; at least 30% hearing loss in each ear. The doctor said, “Think of being submerged underwater for 5 years of your life, trying desperately to hear what people are saying. That is what your son has lived through.” I am still teary thinking about this. I am a fricking educator! How did I not catch this?  I was in denial as well, until that very day driving home I asked my boy if he saw the cool tree. “Tree?” “Yes, the tree over there (I pointed out the car window.).” “Like, dessert?” And that is when it hit me. My child wasn’t hearing.

We started to notice. He said, “What?” almost every time you told him something.  He couldn’t hear the TV clearly; he was reading lips (which we now know why he would never answer us when watching TV; he was too focused on the screen to hear us). In preK, during circle time, he struggled to hear all the conversations and his body would just be exhausted from trying to listen that he gave up.  When listening to a story, he focused on the pictures for meaning versus our words. He was trying his best, his very best, and it was exhausting. My heart broke. My baby boy, sweet thing he is, was struggling under my teacher nose, and I hadn’t caught it.

Long story short, he is now hearing much more, with just a tweak of medication. He still has a hearing loss, and we will test every year to make sure it isn’t degenerative. He is learning how to deal with sounds he hadn’t heard before. (At church last night he couldn’t believe they played bells!) He begins speech therapy (I had no idea he would need that either) next week and they are excited to see his progress, as am I. And funny enough, he is now interested in learning his letters, sounds, words, etc. It all makes sense; for how can you be interested in something you never knew existed?

I bring this story up for one reason. We are not perfect. Even if we have our children’s best interests at heart, we may miss something. It takes a true village to raise our children. If you do not have a village to help, find one. If your children go to daycare or summer camp, get to know their counselors. Ask them questions. Find out what your children are doing, and how they are doing. Talk to your children’s teachers next year. Get to know them, because they see your children more often than you do! And listen, even when you don’t want to. In a world that is so negative right now, I feel strongly that we need to support, build, and nurture each other and our tiny humans in order to make them the best they can be.

 

That Moment You Realize Your Child Is Suffering

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)

LEVEL 1

  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.

LEVEL 2

  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

Developing Perseverance

giving upI don’t get it. Can you help me? My teacher didn’t explain it. I forgot. This is stupid.

We have all been there. We have all heard each of these when our child is working on math homework. The question is, how do we get him/her to stop being helpless? Here are a few ideas to start with.

Listen to their frustrations. Then move on. Look. Being frustrated is okay. We don’t want to say it isn’t. But being helpless is not okay. This is a life lesson. Not everything is easy, but we don’t get to give up.

Don’t do the math for them. That only lets your child know you will let them off the hook every time.

Help them find resources and look at them together. Some questions to help you out:

  • Where are your notes from today? Let’s review them and see if there is anything there we can use.
  • What are you learning? Let’s look up some videos (mathtv.com is a great site for video lessons, but if you just go to utube or teachertube you will find others) and see if we can relearn it together.
  • Let’s look at your book and see if there are any examples that might help us.
  • Call/Facetime/text a friend and see if they can assist you. (Research shows that study groups truly help all students in mathematics!!!
  • Email the teacher and see if s/he has tutorials to help. (Many teachers put up videos, the solutions, etc on-line. Find out if yours does!)

Above all, let them know that it is okay to not know everything, but NOT OKAY to give up. This is a biggie. Most math worth doing  takes time. Students assume that if they don’t get the answer right away, they must have done it wrong (or don’t know what they are doing and are not good in math). So not true! Help your child use resources available to be successful, but they need to do the work and put in the effort.

 

Developing Perseverance