*This is the third post related to our Time 4 Fractions journey. Please click here to start from the beginning.*

Hope you had fun with your child exploring Problem 1. Here is Problem #2, a second multiplication problem, before introducing division problems next week. Please remember that the goal of our journey is to provide children with plenty of opportunities to explore fractions through Equal Sharing problems (Empson & Levi, 2011), and solving multiplication and division problems will prepare them to do so (Empson & Levi, 2011, p 9).

**Time 4 Fractions – Problem #2 – Gardening**

Level Yellow: Mr. Purple loves gardening. He planted3rows of pumpkin seeds. In each row, there were2seeds. How many pumpkin seeds did Mr. Purple plant?

Level Orange: Mr. Purple loves gardening. He planted5rows of pumpkin seeds. In each row, there were4seeds. How many pumpkin seeds did Mr. Purple plant?

Level Red: Mr. Purple loves gardening. He planted ____ rows of pumpkin seeds. In each row, there were ____ pumpkin seeds. How many pumpkin seeds did Mr. Purple plant ?

As with Problem #1, invite your child to solve one of the problems (you can pick one, or let him/her pick one) by

- modeling the problem with manipulatives (such as buttons, marbles, etc, and small containers),
- representing the problem on a piece of paper, and/or
- writing an equation.

With Level Red, invite the child pick numbers he/she feels like comfortable using. For instance, if your child picks 5 pumpkin seeds, he/she may end up counting the seeds by 5, or he/she may use from memory the 5s times table (i.e 5 x 12 if he/she picks 12 rows of seeds).

When your child is done, invite him/her to share his/her reasoning with you. If he/she writes only an equation, encourage him/her to share his/her strategy with a visual representation, or with manipulative.

Enjoy following his/her way of thinking !

**Sharing my experience**

- I experienced this week what it is to pick the
*wrong*time for a child to explore a problem. If it happens to you, just stop and try later ! We had fun the*second*time we tried. - Starting with Level Orange, and then going to Level Red worked well for us. I think my child truly enjoyed the freedom of exploring different sets of numbers with different manipulatives, and visual representations. And starting with Level Orange or Yellow first helped her pick the right numbers for her. You may want to give it a try !
- Here are some work samples I gathered this week from working with my child and the children of a friend. Please remember that I am sharing these samples to help you see what a child
*may*come up with, not as examples of what a child*should*come up with :-)- Level Orange – “Mr. Purple loves gardening. He planted
**5**rows of pumpkin seeds. In each row, there were**4**seeds. How many pumpkin seeds did Mr. Purple plant?” The child decided to model with marbles and paper. She counted the marbles by 1. Your child may count by 4? - Level Orange –
*“*Mr. Purple loves gardening. He planted**5**rows of pumpkin seeds. In each row, there were**4**seeds. How many pumpkin seeds did Mr. Purple plant?” The child drew a picture representing the rows of pumpkin seeds. She wrote, as an equation, a repeated addition. Your child may write a multiplication (4 x 5 = 20) instead? - Level Red – “Mr. Purple loves gardening. He planted 8 rows of pumpkin seeds. In each row, there were 5 pumpkin seeds”. The child modeled the problem with Duplos®. She counted the blocks by 1 up to 15, and noticed that she was counting by 5. She started over, counting by 5, and answered 40 pumpkin seeds. This sure was fun to watch, a child, noticing a pattern of counting, and changing her strategy to a more efficient one.
- Level Red – “Mr. Purple loves gardening. He planted 8 rows of pumpkin seeds. In each row, there were 5 pumpkin seeds”. The child did a picture, drawing the seeds in the first row, and writing the number of seeds instead on the next rows. I enjoyed watching this kid move naturally from a concrete representation to a more abstract representation. Gradually but surely !
- Level Red – “Mr. Purple loves gardening. He planted 7 rows of pumpkin seeds. In each row, there were 5 pumpkin seeds”. The child modeled the problem with buttons, and wrote as an equation, a multiplication 7 x 5 = 35.
- Level Red – “Mr. Purple loves gardening. He planted 2 rows of pumpkin seeds. In each row, there were 4 pumpkin seeds”. The child drew a picture representing the rows of seeds, and wrote, as an equation, an addition.

- Level Orange – “Mr. Purple loves gardening. He planted

- Examples of questions I asked to follow the child’s reasoning:
- Tell me about what you did.
- Could you tell me about the marbles you used ?
- I see you wrote the equation 4 + 4 + 4 + 4 + 4 = 20. Could you show me on your drawing where the 4 comes from? The 20 ? Why did you add 4 five times? What does the symbol “+” mean? And the symbol “=”?
- You said “20”. 20 what? Could you tell me the unit?

Have fun, and see you next week for Problem #3 !

Reference:

Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.

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