# Fractions Day 4: Which is Smaller?

I am a fan of repurposing (NEW WoRd!!!) problems. I figure, if you can read a book for different purposes, why not math problems? Plus, it makes planning that much easier for you! And right now we have enough on our plates!

1. Played “Cover it Up!” twice. Please see Fractions Day 2 post for how to play the game. The questions I used were focused on were:  Who has less? or Who is losing? How do you know? to front load for today’s lesson. NOTE: I still make him write the addition sentence at the end of each game to work on notation and such.
2. Using a whiteboard (or scratch paper), I drew the equal symbol (=). What does this mean? Today Chris said they were equal, or the same. We moved on.
3. Under that work, I drew the greater than symbol (>). What does this symbol mean? (The first number is bigger or greater than the second number.) Again, I had him choose two fraction pieces from the Fraction Kit to compare, with the first being bigger than the second. He actually did not choose the same ones as yesterday. We then wrote the number sentence that it represented.
4. I drew the greater than symbol (<). What does this symbol mean? (The first number is smaller or less than the second number.) I had him choose two fraction pieces from the Fraction Kit to compare, with the first being smaller than the second. He actually did not choose the same ones as yesterday. My little Sassy Sam just reversed the ones he had. We wrote the inequality and moved on.
5. I had Chris compare pairs of the unit fractions from the Fraction Kit and tell me which one was smaller and why.  They were the same ones I used yesterday. He didn’t notice!
6. We moved on to the fractions with different numerators (still only using the denominators from the Fraction Kit). I gave him (one at a time) pairs of fractions to compare. He could use the Fraction Kit pieces to determine which was smaller, circling it on the whiteboard. I asked him to convince me why one fraction was smaller than the other, and he verbally explained or showed me with his fraction pieces. See below for the sequence of pairs we explored (The red fractions are the smaller fractions.)I often asked, How many ________ would you need to make them equal?, just to start the seed of equivalent fractions (Day 5). I threw at him two unit fractions (1/2 and 1/7) to see if he could apply his understanding without always using the Fraction Kit pieces.

Happy Comparing!

# 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!

# 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!!!

# It’s The Little Things…Writing Notes

When I took Chris to register for Kinder, he was terrified. He looked right at the Vice Principal and told her he would NEVER come to this school. I was mortified and heart broken. How could my child (coming from MEEEEEEE!!!!) be so fearful of school??? Was I in for days of tears and refusals to get up to go?

Fortunately, we were blessed with the most AMAZING Kindergarten teacher.  The first week of school she sent home a note to Chris.  It was the first thing he handed me (all crumpled and loved on) that afternoon. He was so proud that his teacher wrote HIM a note. He asked me to read it again and again, and taped it to his wall near his bed.  This note takes him through the good and the bad; the ‘easy’ and the challenging. I have heard him read this note over and over (when he was busted and in time-out!). This note has carried him through the year.

We have since received numerous notes from his teacher, all as important to him as the first. This one hangs on our fridge as a celebration for his daily counting to learn up to 100! When he struggles with sight words, counting by 5’s, or any rote memorization, we look at that note as a reminder that all things take time to learn.

Is it just Chris that loves a little note? Nope. Fast forward to his recent eval for speech. I will be honest. It was a lot of pages expressing a lot of jargon that I forgot the minute I was done reading, except for the part on the back of the eval… I am still teary-eyed when I reread it.  At the end of the day, at the end of the struggles he has, my boy is a good person, and someone noticed.

In this electronic age, let us not forget the little things, like hand-written notes. Why are notes so important? It is unique; someone took time out of their day to physically express something to another person. It expresses that you matter so much that, instead of texting or emailing (which could be a cut/paste), someone took the time to individualize and express thoughts just for you. Wow.

### So let’s each commit to writing one note this week:

• Put a post-it note in your child’s (or students’) lunch or binder letting him/her know how much you care for them
• Put a note in your significant other’s car specifically telling him/her one kind thought
• With this being Teacher Appreciation Week for so many districts, send a note letting your child’s teacher know how much they mean to you and your child
• Mother’s Day (wink…wink…nudge…nudge…) doesn’t have to be just the kids making handmade cards. Let a mama know how much they mean to YOU
• Put a kind thought on a random door, car, locker, etc.

# 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.

# 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?

### 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!

# 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.

# 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.

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

# 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!