## Proportions and Action Figures

My fifth graders are in the middle of a unit on ratios and proportions.  Two weeks ago the fifth grade kids worked through a detective mystery.  It was a good start and a decent opportunity for students to explore proportions.  This week my students came back from spring break.  It took a while to get back to our regular schedule after a week off. We had to complete some review on Monday and started a new project today.  I was meaning to start it before break but we ran out of time.  I researched a few different sites (1,2,3) and decided to modified my original project.

The class began by talking about proportions and scale models.  The discussion lasted around five minutes and then we reviewed the concept and vocabulary with a Kahoot  The majority of kids were able to answer the questions using estimation, but many were challenging, which was good because we were able to stop and use different strategies.  Most students wanted to cross-multiply for everything, but by the end of the activity students were starting to see the value in diversifying their strategies.  I felt like spending time on this was worthwhile.  This experience reminded me of a Tweet from #msmathchat from last night.

Afterwards, I introduced the action figure project to the students.  Students measured the dimensions of the action figures.  They measured the figure in millimeters, converted it to centimeters and eventually to inches.

They then measured their own dimensions with a partner and compared them to the action figure.

Many of the students were able to use proportions as a tool to find a solution.  Some students had a bit of trouble tackling the issue of converting the units.  Overall though, students are becoming better and using different strategies to solve proportion problems – an #eduwin in my book.  You can access the files that I used for this project here.

## Experiencing Proportions

My fifth grade class just started a unit on ratios and proportions.  This is fairly new vocabulary to them, although students have used proportions before.  They’ve used them before to convert measurements and fractions, as well as other items.  They weren’t called proportions at that time.  Instead, I remember discussing them as conversions or creating equivalent fractions.

So, on Tuesday the class was formally introduced to proportions.  I started off by using a Brainpop video that helped introduce the concept.  We watched the video twice and answered the quiz as a class.  Through this process it seemed as though students were starting to become more familiar with proportions.

The class then picked up their math reflection journals.  The class completed a few proportion examples.  They were able to use a few different strategies to complete the proportions and seemed most comfortable by using a cross-multiply and solve for x strategy.  Maybe so, because that’s what’s fresh in their minds from a past pre-algebra unit.  We continued to work on a few different math journal pages.  The majority of students were starting to pick a strategy to solve the proportions.  Although most were feeling confident about proportions, I had a group of students that were having trouble.  I decided to reach out to a few different people about proportions and found the Tweet below.

After reviewing the documents, I decided to try out the Illuminations activity with my kids.  I brought all the kids to the front of the classroom and explained that they will be solving a mystery.  The kids were stoked.  I had to go over the directions multiple times, but after around 1o minutes I believe they were all on board.  I put the students in teams.  I then told them that not all students would be catching the same culprit.  Students were confused about this, but I thought it added a wrinkle to the activity.  I passed out the sheets to the students and they were off to working on their own.

Almost all of the teams had questions about how to proceed.  I had the teams tackle the problems on their own for the first ten minutes.  Fortunately, teams started to show some perseverance and solved the first problem based on the clue that they were provided.  The teams used the strategies discussed earlier in their journal pages.  After around 20 minutes I had teams starting to come up to me with their final answer.  I gave them a thumbs up or thumbs down.  If they didn’t have the right culprit I asked them to redo a specific question that would move them in the right direction.

I feel like this was an activity that helped students become more aware of proportions and how to solve them.  The overall goal was successful, although I need to reflect on some of the team dynamics that played out.  Not all the teams worked well together.  Some students were more confident than others, and some students wanted to let others do the majority of the work.  I think this tends to happen in varying degrees during group work.  Although this happened, I still feel that the student conversations added to activity.  The ideas and strategies that were being discussed seemed to benefit all involved.

Next week I’ll be using the questions to have the students reflect on this activity.

## Proportional reasoning

This summer I’ve had opportunities to review math units that I’ll be teaching in September.  I’ve been beefing up the units with formative assessments and intentional questions that focus on math reasoning.  One skill that seems to need bolstering every year falls in the category of proportional reasoning.  This becomes quite evident when students encounter fractions and rates. Some students may use proportional reasoning,but it’s not necessarily identified as a strategy or communicated using that specific vocabulary.

I also picked up this book over the summer.  I read it about a year ago, but I’m finding so many gems in there a second time around. The authors reveal research that indicates teaching proportional reasoning has benefits.  The authors also showcase that proportional reasoning is difficult to define, but they can categorize what people can do with this type of reasoning. People that use proportional reasoning understand the relationships that numbers have put together and how they relate individually.  They can analyze numbers and look the difference (additive) between them and observe the ratio (multiplicative).

My takeaway from this section of the book comes from the authors’ five reminders.  These reminders come in handy when thinking of how to create learning experiences involving proportional reasoning.

1.) Use unit and multiplicative models.  Double-down on using the idea of a rates, which can be applied to the idea of a proportion.  Specifically, I can think of rate tables to be helpful with this.

2.) Identify proportional and non-proportional comparisons.

3.) Include measurement, prices, graphs, and geometry to show proportions. Proportional reasoning can be found in a variety of contexts.

4.) Solve proportions using different strategies.  Focus on reasoning.  This may be ignited by planting questions that elicit different ways to solve the problem. Students should be able to compare and discuss what comparisons exist.  This can also be addressed through the use of “what’s my rule” tables.

5.) Have students recognize that short-cut methods such as cross-multiplication aren’t helpful in developing reasoning.

Being able to identify proportional reasoning can help teachers emphasize its usefulness. Having in-depth conversations about this type of reasoning has benefits.  I realize that this post is heavy on tables and that’s not the only form that proportions take.  I do feel as though the tables help students observe the relationships a bit easier since it’s organized. While exploring this topic I came across a MARS activity that I’m planning on using in September.