# Fractions Day 2: Cover It Up!

Good morning! So I thought I would get this to you prior to Monday in case you have to search for materials to play the game. I love this game! It is easy to play, yet emphasizes so many important fraction ideas that might go missing in a regular math book. We played 3 times and called it quits, because I knew we would continue to play it every day for the entire week and I didn’t want him to tire of it.

## Cover It Up!

Materials: The Fraction Kit (See Fractions Day 1 for how to make the Fraction Kit), one kit per person, sharpie, and ideally a blank wooden cube. (See below for alternatives for a cube.) We also used a whiteboard and dry erase pen, but those are totally optional.

How To Play:

1. Using the sharpie, label the 6 faces (one fraction on each face) of the cube as follows. See below for other options if you do not have a blank cube.
2. Place the 1 whole fraction strip in front of each player. This is your “game board”.
3. Player 1 rolls the die, and puts that fraction piece on his/her 1 whole to the far left.
4. Player 2 rolls the die, and puts that fraction piece on his/her 1 whole to the far left. Who has covered up more of their 1 whole? (In our game, Chris had.) How do you know? (Chris originally said, “Because purple is bigger than pink.” I restated, “Oh, so you mean 1/4 is bigger than 1/16?” This helps them start visualizing the size of pieces and prepare for comparing.)
5. Player 1 rolls the die again and puts that fraction piece right next to the first one so they are touching, but there are no gaps or overlaps (as best as they can). Player 2 does the same on his/her board. Who has covered up more? Who has covered up less? If the two rolls were the same (e.g. I rolled two of the 1/16) How many sixteenths do I have? (2/16).
6. Play continues until a player covers exactly 1 whole. If a player rolls a fraction that is too big to fit, he/she loses that turn.  Some questions to ask (as appropriate):
1. Who has more? How much more? (They can use their pieces to figure it out. No actual arithmetic!!!)
2. Who has less? How much less?
3. Do you need more or less than 1/2 to win the game? How do you know?
4. How much more do you need to win (get to 1 whole)?
7. Once a player has won, have him/her write the number sentence for his/her board. (We totally cheat and I let Chris roll as many times until his board was filled as well.)
8. Repeat the game 2 more times. Best out of 3 is the winner.

Alternatives to a Blank Number Cube: If you don’t have a blank wooden cube, below are some options so that you can still play the game. I have done all of these and they are all great options.

• Make your own die: See below for blank template and write the fractions we used on #1. Note: This is better printed on card stock or heavy paper.
• Make a spinner. See the PDF below and use Spinner #3. Label the sections as we did the cube above in #1. Using a paper clip and a pencil, place the pencil in the paper clip in the center of the spinner and spin the paper clip. Where it lands is your fraction. This can be on plain paper and it works great.
• Roll a regular die. See below for the fraction you get for each number on the die.

For link to die template: https://www.printableboardgames.net/preview/Blank_Die

# Thinking Rationally With Your Tween

Students typically start exploring positive and negative numbers towards the end of elementary or early middle/junior high school. And it can be a bit weird. It is literally the opposite of what they had been taught for the last ten years in a number of ways (Puns intended.). Here are some ways you can support your child in their negative number journey to make it a positive experience (Dang, I am on FIRE!).

1. Bring in finances. “In the Red” and “Black Friday” are references to business. When a company in “in the red”, they are in debt. They owe money. Traditionally “Black Friday” (The Friday after Thanksgiving) was the first day of the fiscal year companies got out of the red and posted a growth. Credit cards are another great place to explore debt and credit. A debt would be what you owe and would be represented as a negative number. A credit would be a positive number. Show them your mortgage and credit card statements and discuss terms such as “deposit, credit, debt, with drawl, etc.”. The stock market is a great place to discuss negative and positive fractions and decimals. Pull up the daily NYSE and discuss which companies have an increase (or positive) and which have a decrease (or negative) change that day.
2. Football Season!!! This is a fantastic place to bring in integers (positive whole numbers and their opposites). If I gain six yards on a drive, how could I represent that change? (+6 or 6). What if the QB gets sacked? How many yards did they lose? (ex: -7). How far do they now have to go to get a TD? If your child is interested in football, use it to your advantage!
3. Playing Cards. Below are a couple of games you can adapt to include negative numbers. I prefer to omit the face cards and only use numbered cards, but you can make Aces = 1 (and -1) and the face cards values after 10 (and -10).

War! Black Cards are positive values; Red Cards are negative values

1. Shuffle and divide the cards evenly among players. Keep your cards in a pile face down. Everyone flips over their first card. Player with the greatest value wins all the cards for that round. Tie? Flip another card and whoever has the greatest value that round wins all the cards from both rounds. Whoever has all of the cards at the end (or the most cards when you get bored) is the winner.

Example: I flip over a red 9 (-9) and you flip over a black 2 (2 or +2). A gain of 2 is greater than a loss of 9 so you win the cards.

You can also play that the winner is the one with the smallest value.

1. For students who are learning to add integers. Shuffle and divide the cards evenly among players. Keep your cards in a pile face down.

Everyone flips over TWO cards and finds the sum (add them). Whoever has the greatest (or least) sum wins the cards for that round.

Example: I have a black 2 and a red 4. 2 + (-4) = -2.

You have a red 4 and a red 2. -4 + (-2)=-6.

Since -2  is greater than -6 (a loss of 2 is better than a loss of 6), I would win.

1. Go Fish! Black Cards are positive values; Red Cards are negative values

Shuffle and hand each player 7 cards. The rest are in a pile in the middle face down.  The objective is to be the first one out of cards.

How do you get rid of cards? By making matches of cards that have a value of 0.

Example: Jen has a 5 black (5 or +5). She says to Chris, “Do you have a negative 5 (5 red)?” Chris does, and hands the 5 red (or -5) to Jen. Jen takes the positive 5 and the negative 5 and lays the pair in front of her.

This is not an exhaustive list so I will be adding other fun ways to integrate math into your home conversations. Let’s make math a positive experience for our kiddos!

# Road Trippin’: Math Games for the Car

Special thanks for requesting this, Jen Duley!

Many of us are taking summer road trips with our tiny humans. Here are some ideas for keeping math in their brains and ditching the ‘summer slump’.

### Counting Circle (sort-of)

This is something I have blogged about before. Kids must practice rote counting. Count up and down. Each person in the car takes a turn, counting by what the designated amount is. Below are a few ideas that I hope your kids will enjoy (And save your sanity!).

1. Count by 1’s, first starting at 1, then building to start at a different value. Count up and down!
2. Count by 2’s, 3’s or 5’s. Again, start with the value and practice skip counting, then start with different values. (Don’t forget to go backwards too!) One of the best things I ever did was make my clock in the car off by 5 min (too fast). My oldest had to figure out the time every time he got in the car. He had to regroup in his head almost every time!
3. Count by 10’s, first starting at 10 to 100, then back down. Also start with different multiples of 10’s, different values other than tens, etc. Example: Start at 12 and count up by 10’s. Or start with 87 and count down by 10’s. (Super important for regrouping and subtraction!)
4. Older kiddos: count by fractions. Start at 0 and add 1/2 each time. Start at 3 and count back by 1/3 each time (Gearing up for mixed number subtraction). Start at 1 2/3 and count up by 1/6.
5. Older kiddos: count by integers. Start at 0 and add -2. You get the idea.

### Guess My Number

Again, one that I have previously discussed, but super important.

• I am thinking of a number between 11 and 13. What is my number?
• I am thinking of a number that is less than 40 but greater than 35. It is odd. What is my number?
• I am thinking of a number that is less than 100 and a multiple of 5. Now let them start asking yes/no questions to narrow it down.
• I am thinking of a number between 11 and 12. Start them on fractions!!!!

### Count the Cars

Choose a color, type, make, or model. Kiddos count all of that category of vehicles. Each child can count a different type (EX: Ev counts all the blue vehicles and Chris counts all the red ones) and whoever gets the most when you park wins!

### Find the Number

Print out a 100 chart. Put it in a sheet protector and clip with a clipboard. With a dry erase pen (I attach the pen with yarn to the clipboard.) he/she crosses out every number he/she sees. Look at license plates, signs, billboards, etc. See who can cross out the most in a trip! You can also print out a partially filled in chart and they have to fill in the missing numbers before playing. For PDF 100 Charts: https://www.homeschoolmath.net/worksheets/number-charts.php

### Three in a Row

Two options: print out a Three in a Row page for each child, put in sheet protector, and clip to clip board. Or print the blank, and allow them to fill in values 1-10 (they will have 1 missing since there are only 9 spots for 10 numbers).

Call out either addition or subtraction problems. You can just do number problems or put them as word problems. Example: Chris has 3 Stormtroopers. If he loses one in his car seat, how many does he have left? 3-1=2, so they cross off the 2 on their game board (if they have a 2). Once they get 3 in a row, they win! Link below for PDFs created for you.

3 in a Row

### Target Value

Print out the Target Value sheet and put in the sheet protector. Clip to clipboard.

Give your child a target value (EX: 10). They write 10 in their Target Value box. They create as many addition problems that add up to 10. I honestly would rather just have the target box and let them make all kinds of equations (such as 1 + 4 + 5 or 20-10), but below is an example you are free to use.

Target Value

### Shape Spotting

Great idea from my amazing friend and colleague, Kelli Wasserman! I found geometry cheat sheets if they need it. https://www.math-salamanders.com/geometry-cheat-sheet.html   Just put it in the handy-dandy sheet protector! Have your kids see who can spot each shape (square, rectangle, circle, etc) and they can cross it out on the sheet with a dry erase pen. Or, give them a shape to spot, and see who can spot the most. Love it!

# Relational Thinking to 10, More or Less

Our lives in kindergarten land are immersed in the idea of making 5’s and 10’s. Here is an activity you can do (After playing Make a 10…See previous blog!) to build relational thinking to 10.

Materials: Deck of Card, 3 post-its

Objective: To determine whether two addends (cards) make a sum (total) that is less than, more than, or the same as 10.

1. Have your student write less than 10 on the first post-it, the same as 10, or just 10 on the second post-it, and more than 10 on the third post-it. (Note: You can also include the symbols <, =, >, but I prefer to work on the concept FIRST then introduce the symbolic notation later.) Place the post-its on a workspace that has lots of room.
2. Shuffle the cards. Place deck face-down. I typically hold the deck and place two cards face-up for the child, but if students are playing in small groups they take turns taking the top two cards and placing them face-up. The child decides whether the sum is less than 10, the same as 10, or more than 10. If in small group, the others confirm or debate. Once the value is established, the student puts the cars face up as a pair under the correct post-it.
3. Continue until all cards are used (That is A LOT of addition they are doing!).

Note: I totally stack my deck. I want to make sure some of the first pairs have a variety of sums so that the child (or children) see cards under each post-it. Here are a few of my favorite sets of cards to ‘stack’…

• 1+2 (I like to start with a known fact and something a lot smaller than 10.)
• 1+9 (Again, building on the “one more” facts, but this time it is 10.)
• 3+9 (Relational to 1+9. If 1+9 is 10, then adding more makes more than 10. HUGE!!!!)
• 10+4 (Any 10+ is great, as students really need to build to 10+ for first and second grade. It is amazing how many children do not see this as immediately more than 10, so it is a great one to have a conversation about!)
• 2+3 (We have done so many that are greater than 10, nice to go back to a set less than 10.)
• 5+5 (One of the first known facts for making 10.)
• 5+8 (Similar to 1+9 above. If 5+5 makes 10, then adding more makes more than 10.)
• 5+2 (Conversely, if 5+5 makes 10, then adding less makes less than 10.)

## Alternative Games for Older Students

• Use larger value cards and work less than, equal to, or greater than 20, 50, 100, etc.
• Use cards with decimal values and play less than, equal to, or greater than 1.00.
• Use cards with fraction values and play less than, equal to, or greater than 1.
• Use black and red cards (reds are negative, blacks are positive) and play less than, equal to, or greater than 0.

# Game: Making Ten

Kindergarten kiddos are immersed in addition and subtraction right now! They are exploring addition as adding more ‘stuff’ and subtraction as taking away (or removing) ‘stuff’. Many of the kids are in their Level 1 Counting All stage in which they rely on counting one-by-one to get the sum or difference.

For example: 3 + 4. A child at this level would count 1, 2, 3 then 1, 2, 3, 4; putting them together, 1, 2, 3, 4, 5, 6, 7.

This is acceptable for Kinder kiddos! This is awesome! This is the first step! But it isn’t where we want them to stay, particularly at the end of first grade. I tutor some students in grade 1 who haven’t moved past this level. So I took a game that has been around and edited to push kids into Level 2 Counting On.

## Make a Ten!

Object: To find as many pairs of cards that add to 10 in your round.

Materials: Cards 0-10 (4 of each). Note: This is the most crucial component. I will talk more about the cards below.

Directions: (Below is a video clip. Sorry about the sniffling; it is allergy season here in TX!)

1. Shuffle the cards. Lay out 4 rows of 4, face up.
2.  Player 1 finds as many pairs of cards that add up to 10. He takes the cards and (I made them do this!) says, “________ and __________ make 10!” He continues until there are no more cards that pair up to make ten.
3. Take the remaining cards (if any) and put them back in the pile. Reshuffle and lay out 4 more rows of 4 cards.
4. Player 2 finds as many pairs of cards that add up to 10. She takes the cards and (I made them do this!) says, “________ and __________ make 10!” She continues until there are no more cards that pair up to make ten.

Continue alternating until there are not enough cards left to play. Player with the most cards wins.

Chris did struggle with 4 + 6 (or 6 + 4). I pulled out a ten frame to help with, “How many more do you need to make 10?”.

Chris refused to have any extra cards. In fact he got quite cheeky about it. This was his modification (he called it a ‘cheat’). I was perfectly fine with it, as I am sure you would be as well! I did not give him the word ‘altogether’ to use; that was a natural piece of the conversation. Woot! Woot!

## Card Choices

• If you are just starting out, only use 0-5 and make sets of 5. This is foundational and kids do not spend enough time on fact fluency to 5 before jumping in to 10.
• The cards I used were from Eureka Math. I love them, as they are friendly shapes and are in sets of 5’s. So 10 is represented as two-fives. This link will get you to the cards I used as well as others they have (like ten-frames) http://eurekamath.didax.com/exclusive-items.html/
• If students do not need the symbols (or you are pushing to counting on or fact fluency) I would suggest just write the numbers 0-10 in four colors on index cards. That would be cheap and easy.  You could also make your own cards with dots (if they need the dots to count) or ten frame cards this way as well.
• You can mix/match as well. Use 2 of each number card 0-10 and 2 sets of each dot or ten-frame card. That way, students have to use counting on for some of the sums.
• Another site for cards would be Sumboxes. They have number cards larger than 10 so you can play to other sums (like 20, 50, 100, etc.). They also have fantastic dot cards/ten frame cards together for some great exploration! https://sumboxes.com/collections/types?q=52+Pickup+Card+Decks&page=2

Whatever cards you choose to use, make sure they are appropriate for the level of the learner!!!

# Cross-Out: Sums to 12

Chris asked for a new game yesterday, and I didn’t have one ready (Gasp!) So we made one up together called “cross-out”. This was quick, easy to organize, and he had fun playing it and ‘cheating’.

Materials: white board, dry-erase marker, two dice (we used dot dice, but you can use number cubes to up the level of thinking)

Objective: We played as a team. The goal is to cross-out every sum when rolling two dice (2-12).

How to Play

1. Have your child write the numbers 2-12 on the white board. This is great fine-motor practice!
2. Player 1 rolls the dice and adds up the values. Player 2 crosses out the sum on the board. I rolled a 9, so Chris had to find the 9 and cross it out (see below).
3. Player 2 rolls the dice and adds up the values. Player 1 crosses out the sum on the board. If a sum is already crossed out, continue rolling (and therefore practicing addition and counting on) until you get a sum that you can cross out. No losing turns here!
4. Once your team has crossed-out every sum, you won! Do a silly dance to celebrate your success!

Fun Note:
When we only had the 3 to cross-out, Chris asked if we could change dice to be 0-5 instead of 1-6. “Why?” I asked. “So that I have a better chance of rolling a 3! The only way I can get it is with a 1 and a 2 and that’s tough!” If I had the 0-5 dice at my fingertips, I would have totally given in. This is a great statistics insight for such a tiny human!

He rolled a few more times, got sick of rolling and decided to just roll one die. BAM! First roll he got a 3. He was very proud of his ‘cheating’ scheme!

Differentiation Ideas:

• Use a number cube and a dot die to work on counting on (Level 2).
• Use two number cubes to work on addition rather than one-to-one counting with dots.
• Use cubes that have larger values and work on the teens/twenties. I buy square wooden cubes at a hobby/craft shop and use a Sharpie to make whatever dice I want to use. Easy and cheap!
• Play against each other. Each person could write 2-12 and see who can cross-out their board first.

# 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! 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!

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.

Player 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.

# 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)
• 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 count 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!

# 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. Mine (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).