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!