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!)

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

Beyond Counting: Ideas and Activites For Your Little Ones

While waiting for his big brother at the orthodontist, my little boy, C,  had the following conversation…

Dr. T: How old are you, cutie?

C: I’m three!

Dr. T: How old is your brother (pointing towards my thirteen year old)

C: Four!

This was such a proud mama moment for me!

Now you may ask yourself, “Why is she getting all excited over this? Clearly, he is not four. Why is she so proud of her little boy?”

There are a number of reasons why this is a critical step towards numeracy. I truly believe that if you start children purposefully thinking about numbers early on, their chance for success in mathematics increases dramatically. So let’s highlight a few of the big ideas C is working towards.

bears

1. Cardinality– This is the idea that the number being used is measuring some amount. It answers the question, “How many?” For example, I can ask my son, “How many bears do you see?” He would count them one by one until he got to the number six. That last number, 6, tells you the number of bears in the set. This is a big deal! The child is no longer counting from memorization; he is recognizing that the number relates to a certain amount of “things”. The more things you have, the further you have to count. C recognized that his brother was older (or “bigger”). Therefore, his brother was tagged to a number after the one he identified with, three. He did not know how many more to go, just that he had to choose a number beyond his own. Cool.

2. Inclusion– This is the idea that the number labeling “how many objects” in a group includes all of the preceding numbers. So even though we have six bears, we can also think of it as “one and some more”, “two and some more”, “three and some more”, and so on. This is critical for addition and subtraction. If I have the number 14, I can think about it as “ten and four more”, which helps me when I want to add or subtract and regroup to make the problem easier. C knew that his brother was older, and therefore had to include his age (three) and some more. Again, he isn’t at the point of knowing how much more, but is on his way. Awesome.

3. Magnitude– The size of the object. In this case, a number (or value) given to a quantity (age) for the purpose of comparing with another quantity. This idea is instrumental for estimation, particularly with very large and very small numbers. In fact, one of the posts requested of me to write is helping students compare fractions. If a child does not know the relative size of the number they are considering then it is very difficult to compare, operate or manipulate it with any real fluency or number sense. How do I know my answer is reasonable if I haven’t a clue what the numbers I am working with represent??? For C, he was able to recognize that his brother had to be a larger quantity than three, because he is older. Super rad!

These three ideas are certainly related, but each has a different feel. You can work with them simultaneously, so long as there is purpose to the questions and tasks you present to your kids. Below are some simple, but powerful, activities you can play with your little ones to build these concepts. I choose the games that you can take on the road, to the doctor’s office, to a restaurant, etc. Instead of sitting around being squirrelly, play a game while you wait. Even five minutes will have a significant impact!

1. Count and Check: Grab a handful of ANYTHING (balls, pennies, beans, cheerios, etc) and ask your child to count how many. Make sure the amount of objects is appropriate. (For example, C is working on objects through 5.) When he finishes counting the last object, ask, “How many _____ are there?” If he cannot answer, that is okay! He is working towards cardinality. He is able to say the objects one by one (which is called one to one correspondence), but hasn’t figured out that the last number he says represents the entire amount. Have him count again, and ask again. If he cannot answer again, say, “There are (say the amount) ______ here.”  You can play this at the grocery store (count the apples, bananas, etc), setting the table (How many forks?), etc.

2. Match Me! Grab a die (one dice) and a handful of ANYTHING in a baggie. (I typically do this with pennies at restaurant.) Have your child roll the die. Let’s say she rolls a five. She takes out that many pennies and lays them out for you to see. Ask her to count them one-by-one to make sure she has five. At the end ask, “How many pennies do you have?” If she doesn’t know, that is okay! Have her recount, then ask again. If she still isn’t able to tell you, say, “I see you have five pennies.” Make sure you roll next and model for your child. Take turns until you get bored or dinner comes!

To bring the difficulty up, after playing each of these, ask, “If I gave you one more item, how many would you have?” This brings in the concepts of magnitude and inclusion! If your child has to recount with one more added in, that is fine! You know he’s got it when he can answer quickly without physically adding in another item and recounting.

Need another level of difficulty? Ask, “If I took away one of the items, how many will be left?” Same idea, but working backwards, and just as important!

Beyond Counting: Ideas and Activites For Your Little Ones