*My daughter and I went on a 12 week- journey last year to explore Fractions. We are doing it again this Fall. I am updating the posts from last year, in case you want to join us this year. Click here if you want to know more about the journey.*

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 ! Remember, it is about listening not about teaching 🙂

**Sharing my experience**

- Here are some work samples I gathered last year 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?

No video this week, as the problem is similar to the one explored last week. I will make a video next week, when we start division problems.

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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