# 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!

# Fractions Day 3: Which is Bigger?

Science and a Birthday gift of slime/putty jars kept us busy and at a very quick math lesson today. ‘Cuz you know…priorities!

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 had more? or Who is winning? How do you know? to front load for today’s lesson.
2. Using a whiteboard (or scratch paper), I drew the equal symbol (=). What does this mean? (Chris said it meant they were the same size, which I was fine with.) Show me which pieces would be equal. He showed the 1 whole and 2/2. I then wrote 1=2/2.
3. Under that work, I drew the greater than symbol (>). What does this symbol mean? (Chris said it was an alligator. More on that another blog. I am not in the mood for that one!) We discussed that it meant the first number you write must be bigger than the second number. The math vocab wasn’t very sophisticated, as I just want him understanding the idea. I had him choose two fraction pieces from the Fraction Kit to compare, with the first being bigger than the second. We then wrote the number sentence that it represented.
4. I had Chris compare pairs of the unit fractions from the Fraction Kit and tell me which one was greater and why.  See the unit fractions to the right for sequence of the pairs we explored.
5. Once he had the idea of comparing we moved on to 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 greater, circling it on the whiteboard. I asked him to convince me why one fraction was larger than the other, and he verbally explained or showed me with his fraction pieces. See below for the sequence of pairs we explored (The circled ones are the greater fractions.).I often asked, How many more of ____ would you need to make them equal?, just to start the seed of equivalent fractions (Day 5). Then I threw a pair of equivalent fractions in our set to see what he would do. (He rolled his eyes and said they were equal. Duh, Mom!)

Overall, Chris did well with circling which fraction was bigger, so long as he could use the pieces to work through the pairs. This is appropriate, as he hasn’t learned any other strategies for comparing. We will move to which fraction is smaller tomorrow to continue comparing sizes of fractions and really understanding what the numerator and denominator mean with respect to the Fraction Kit pieces.

# 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

# Changing Times Call for Changing Posts!

Hi Everyone,

So I started the year wanting to read professionally and discuss within this format. THEN we got put on lock down. So that is stopping NOW (for the time being) and I am altering the nature of my posts.

Two different types of blogs will be coming through this page. The first will be personal vignettes of life as we are all stuck together. I have a Senior in high school who is digging sleeping in and working in his pj’s, but ticked off he is missing his state Art competition and uncertain how AP exams will roll out. I have a second-grader with dyslexia and I am on the fast track to learn how to help him learn to read and write (while being a math-geek). So these types of blogs will be real-time and messy, ugly, funny truths.

The second type will be the math I am doing with my second grader around fractions (for now, but if we stay out FOREVER I will have to move on…sigh…I love fractions…). I will post our daily lessons and try and include pics and videos when applicable. If I used a worksheet or blackline masters, I will attach them at the end of each lesson. These will be lessons you can share with other teachers and parents if you so desire.

Though these blogs are now completely meant for me and my well-being, I hope you find some humor and help as needed in this crazy hot mess of a time.

Take care of yourselves!

Jen