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

Here is Problem #4, a second measurement division problem.

**Time 4 Fractions – Problem #4 – Making Toys
**

*Level Yellow *: Ms. Butternut makes wooden toys. She has 5 wheels. She needs 2 wheels to make a motorcycle. How many motorcycles can she make?

*Level Orange *: Ms. Butternut makes wooden toys. She has 14 wheels. She needs 4 wheels to make a car. How many cars can she make?

*Level Red *: Ms. Butternut makes wooden toys. She has 31 wheels. She needs ____ wheels to make a heavy truck. How many heavy trucks can she make?

**What to do as a parent ?**

As always, invite your child to solve one of the problems, and *listen* to his/her way of solving it. He/she can make sense of the problem while using small objects (such as buttons, marbles, etc, and small containers) or drawing a picture. He/she may write an equation. Each child should pick the problem that he/she feels like exploring.

With all Levels, Ms Butternut has a left over of wheels. (Level Yellow: 2 motorcycles can be made, with 1 wheel left, Level Orange: 3 cars can be made, with 2 wheels left).

If your child calls out the answer right away,* r*emind him/her that the answer is fine, but *how* it was obtained is even more important in this journey. How would he/she explain it to a younger child? Could he/she represent the problem with a drawing? a diagram? Using small objects ?

When your child is done, invite him/her to share his/her reasoning with you. By now, you know the routine, right ? :-)

**Sharing my experience**

It is quite interesting to me, so curious about children’s mathematical thinking, to follow my child’s reasoning over the years.

A couple of years ago, she explored Level Orange with drawing 14 wheels, taking away groups of 4. With such strategy, she quickly saw the equation that could be associated to her reasoning: a repeated subtraction (which is how division can be seen). She used the left over to make a bicycle, but your child may state that Ms Butternut has 2 wheels left. With Level Red (31wheels, 6 wheels / truck), she drew tallies (by groups of 5) to represent 31 wheels. Then, as previously, she took away groups of 6, to end up with 5 trucks (and a tricycle i.e 3 wheels left). Now, I do not know how she did not get confused with taking groups of 6 out of her tiny groups of 5 tallies, but she did say along the process that “maybe using tallies was not such a good idea”. It is good for kids to have opportunities to discover on their own that some representations may work better in some situations, and less in others. Indeed, it is going to be up to them to select the most useful one depending on the problem.

Last year, she explored Level Red as well, by but she added the groups of wheels needed for one vehicle (e.g. 6 wheels to make a truck) until she reached the total number of wheels available.

Now this year, she went back to an approach similar to what she did 2 years ago, drawing 31 wheels, and grouping them by 6, to make 5 trucks, with one wheel left.

I just found it fascinating to see the various ways a child may solve a problem, leading him/her to exploring the relationship between all operations. Who knows what next year will bring in Rosie’s world.

I am also sharing below the work of a friend’s child, a 5th grader solving Level Red. In parallel with writing the equation, and labeling each part of it, the child also explained the model she could use to solve the problem.

Enjoy !

Reference:

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