Fractions Day 8: Thirds, Sixths and Twelfths! (Oh My!)

Now that Chris is comfy with the denominators 2, 4, 8, and 16 (and halving/doubling to make equivalent pieces) we tried denominators of 3, 6 and 12. Why 12? I just figured it was easier to work with 2, 4, 3, and 6 once we move to equivalent fractions. Also, it was easier to fold (no joke).

Note: I would suggest you fold for your kiddo. Or have a set already folded for them in case they need it. I did not, and then had to spend time cutting more pieces to make new folds (He laughed…I did not.)

  1. Show the 1 whole again. Explain we are making new fraction pieces for our kit (YAY!).
  2. Let your child choose a color (Chris chose green). Fold into thirds. I cheated and measured it out, then divided by 3 and made marks with a ruler. He then folded on the marks. How many equal sized pieces do we have? (3) What do we call each piece? (1-third). Write 1/3 on each piece and cut them out. Count them out as you cover 1-whole strip: 1-third, 2-thirds, 3-thirds or 1 whole. You can write 3/3 on the whole strip if you would like.
  3. Have your child choose a different color (Chris chose orange.) For the sixths, fold again into thirds, then in half. How many equal-sized pieces do you think we have? (5???) Open it up and see. (Oh-6! Well yeah, because 3 doubled is 6.) What do we name each of these pieces? (1/6) Write 1/6 on each piece and cut them out. Again, name the amount as you cover up the 1 whole strip with 1/6 pieces. 1-sixth, 2-sixths, 3-sixths, …, 6-sixths or 1 whole.
  4. Take one final color and fold into thirds, fold in half once, then fold in half a second time. How many equal-sized pieces do you think we have? (I don’t know…ummmm…10?) He opened it up and saw 12 pieces. What is the name of each piece? 1/12. Write 1/12 on each, cut them out, and count them as you cover the 1 whole.
  5. I asked Chris to show me different values.
    1. Show me 3/12.
    2. Show me 5/6.
    3. Show me 2/3. (I soo wanted to start comparing, but that is not the focus for today. Keep it focused so they get what you want out of the lesson.)
    4. Show me 7/6. (HA!) He just grabbed one of my pieces to make 7/6.
    5. Show me 5/3. Same. Grabbed my pieces to figure it out.
    6. If you can’t grab my pieces, how could you show 5/3 with your pieces? I wish I had taped it. I thought he would show 1 whole and 2/3. But no. He used the 3/3 then 4/6! I love when we let them do their own thing. They always seem to surprise us!
Fractions Day 8: Thirds, Sixths and Twelfths! (Oh My!)

Fractions Day 7: Cooking with 1/4

Today was our first day of Distance Learning from our school. Though I am grateful for all of the lessons now being planned out and having some awesome challenges to engage in (Shout Out to Coach SMITH and Mrs. NEAL!!!!), it messed up the routine we had been rolling with. I spent so much time navigating the different sites and trouble shooting that I didn’t have time to prep the new colored strips I needed to start thirds, sixths and ninths for the Fraction Kit.

I honestly thought Chris wouldn’t ask about the math, as he had so much to do for his other classes. (I was ready to ditch out on the fractions today.) But he asked at lunch, When are we having our fraction time, Mom? How can you say no to that?!!! (Well, okay lots of us can, but anyone who knows me knows I can’t. Ask my good friend who had to wait for me to write on receipt paper math tutorial links for the cashier at Total Wine the other day!)

Fortunately, a good friend had posted on Facebook a recipe for making salt-dough ornaments. See below for the recipe, but what I loved about it was there are only 3 ingredients (And I had them all!!!!) and the amounts were cups and halves. Perfect!

Naming the Measuring Cups
  1. I pulled out all of my measuring cups and asked Chris how he would name them. He called the full circle 1 whole. He took the others and rotated them within the cup to figure out how many fit inside. Pretty similar to the Fraction Kit, but with circles. We named them verbally and I asked him to find the fourth. We put the rest away.
  2. I asked him to measure 1 cup of flour with the 1/4. How many fourths would you need to make a whole cup? 4 How do you know? Because it takes four of them to make a fourth. (He rotated the 1/4 in the air to show the whole circle.) 1-fourth, 2-fourths, 3-fourths, one-whole.
  3. We needed to measure 1/2 cup of salt. How can you use the 1-fourth to find 1-half? Well, since 4 of them made a whole, I need only 2.
  4. We needed to measure 1/2 cup of water. I didn’t bother asking; I knew he got the gist of it.
Measuring Out 4-Fourths (1 Cup)

The recipe is super easy to make and fun to create different ornaments to paint and share with friends during this isolation time. I am having Chris write a letter with each to send out next week so we can get some Pen-Pal action going!

May the Force Be With Us ALL!!!!

Note: We did not put parchment paper down the first time we rolled out the dough and it was a huge mistake! Place parchment or wax paper down and sprinkle some flour before rolling out the dough.

Fractions Day 7: Cooking with 1/4

Fractions Day 6: The Return of Equivalent Fractions

Good morning! We needed more time with equivalent fractions and doubling/halving ideas before moving on to the family of thirds. Note: In two lessons, we will be making 3 more sets of colored fraction sets for our Fraction Kit. You will need 3 strips of equal size to the others in different colors.

There is no shame is repeating lessons. We do not master something in 15-20 min, and certainly not a new idea/concept. So this is going to sound a lot like Lesson 5. Trust me, it is helpful for later on!!! (And you really don’t have to prep anything new! BONUS!!!)

Trying to “Trick” his Mother!!! Commutative Property in Action!
  1. Play “Cover it Up!” twice. Please see Fractions Day 2 for how to play the game. We again focused on equivalence. How much more would I need to have the same amount as you? How much more would you need to be the same as me? How much more would we need to win? As always, I have Chris write his addition sentence once he covers the whole.
  2. We revisited the half and made equivalent fractions using only same-size pieces. See Fractions Day 4 for the lesson (the picture is above).
  3. Keeping with the half strip, I asked him to show 2 different ways to make a half without using ALLLLL of the same size pieces. I had to adapt and ask for 3 ways (As you will see why in the video above!). This was important to do, as it allowed him to really think about which pieces were equivalent and how to fill in the space to make half.
  4. My ink was out (and waiting for my Office Depot shipment!!!) so I hand wrote the fractions I wanted him to explore. See the picture below for the fractions and sequence we explored. This went much faster than I anticipated! I was especially excited to hear him stating things like, Well 2-eights is the same as 1-fourth or, If 2-sixteenths is an eighth then count by 2’s to get to 3-eighths. 2, 4, 6. So 6-sixtenths is the same as 3-eighths. I love making him tell me his thinking. It helps him learn how to explain and it helps me know what to do the next day!
Equivalent Fractions Work with Fraction Kit

Coming Next: Fractions and Cooking! We used the Visual Measuring Cups (I got mine on Amazon), but you can use whatever you have! We only used the 1-fourth measuring cup.

Fractions Day 6: The Return of Equivalent Fractions

Fractions Day 5: Which are Equivalent?

Equivalence is everything when it comes to fractions. Kids who understand which fractions are the same size and how to create fractions that are the same size are the ones in math class that say, “It’s easy!”. It’s not easy; it makes sense to them. Since I am at home with my tiny human for A-WHILE, I decided we would spend a good grip of time on equivalence. The next 3 lessons (and many more after introducing the family of thirds in Lesson 8) will focus on understanding equivalence with fractions.

Finding Equivalent Fractions to 1/2.
  1. Play “Cover it Up!” twice. Please see Fractions Day 2 for how to play the game. My questions to Chris focused on when our amounts were the same, or how to make them the same. How much more would I need to tie you? Which fraction would you need to have the same amount as me? I still had him write the addition sentence once he covered up the whole.
  2. I asked him to pull out one of his half pieces. How many eights would I need to cover up the half? (2). I then directed him to do the same with each fraction size. He had to cover up with only that size piece. We counted them out (One-eighth, two-eighths, three-eighths, 4-eighths…4/8 is the same as 1/2.) and wrote down each fraction amount that was equivalent to half. See image above for our work.
  3. On the whiteboard, I wrote 3/4. How many eighths would it take to cover 3/4? How many eighths are the same as 3/4?
  4. We continued looking at different fractions and finding the equivalent amount. The fraction sequence is below (See Equivalent Fractions Practice doc.), but looking at it now I would suggest less sixteenths and more fourths and eighths. Will need to do that tomorrow.
  5. I let him create two of his own. This was not easy. He just kind of stared at me. (Soooo tough not to just tell him, but the struggle is good for him!) I rephrased: Choose a fraction and find another that is the same size. Though this limited him at first, it helped get the ball rolling. He chose 1=2/2 for his first one. Though not what I was looking for, it is true! He second was more interesting (Wish I had asked for 3!) He chose 2/1=4/2. I was shocked, because we haven’t even talked about anything over a whole. However, when concepts make sense to kids, they can naturally apply them to unique situations.
Finding an Equivalent Fraction to 3/8.

Hope you have a great day exploring new ideas and making fractions fun!

Fractions Day 5: Which are Equivalent?

Shut up! Dance it Out.

Today was tough. I don’t need to tell any of you all the feels, as I am sure you have them as well. But I just couldn’t get my teacher mojo going. I felt lost; I felt out of control; I just didn’t feel like myself.

I feel like these days are going to come more often than I would like. I am going to need to take my Type A-ness and shove it down, because I need to give myself grace and space. And my advice today is this: Give yourself grace and space. Hug your littles, play a game, act silly, laugh, and above all, Dance it Out! (Or do Star Wars moves…whatever works!)

Shut up! Dance it Out.

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 frunit fraction compareactions 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.)lessI 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 4: Which is Smaller?

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 frunit fraction compareactions 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.).comparing fractionsI 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 3: Which is Bigger?