# Tag Archives: Real-world Applications

### Finding Math in Unexpected Places

I was reading Inchworm and a Half with my 6-year-old daughter, Bethany, last night for the 40th time. She loves reading the section, “Squirmy, wormy, hoppity-hoop! We measure everything, loopity loop.” Even before she could read books she memorized this section and would “read” it. The book is about an inchworm that loves to measure fruits and vegetables in the garden, but then one day has a problem. He has measured as much as he could, but there was a fraction of a section left over. He couldn’t do one more hop because he was bigger than the section left. Well another worm comes to help him who is half his size. The half-inchworm explains to his friend that he is half the inchworm’s size because two of the smaller worm’s hops is the same as one of the inchworm’s hops. The book continues to introduce more worms that represent fractions in the same manner.

When I was done reading the book, I thought to myself, how can I help Bethany understand some of the mathematical concepts? She is already engaged, and I can use that to help build her mathematical knowledge.

So, I made her some inchworms and half-inchworms out of pipe cleaners and pony beads. I cut a one and one-half inch strip of pipe cleaner. Then strung the bead and folded the pipe cleaner over, so that the pipe cleaner measured exactly 1 inch. For the half inch worm I started with a one inch pipe cleaner.

She really liked using the “worms” and wanted to keep them. I let her choose the things we measured. She chose a cupcake, a pony and a small dragon.

Initially I was going to have her measure the height of the objects, but she really wanted to trace around each object and measure. I wasn’t concerned about her measurements being exact. I just wanted to help build the concept that when we measure, we can’t have any space between the units. I also wanted to see how she processed the inchworm and the half-inchworm.

The first time she counted the inchworms, she said 12 worms. She wasn’t distinguishing between inchworms and half-inchworms. I explained the two types of worms were different and she needed to count them separately. Then I wrote out a sentence frame: ______ inchworms and ______ half inchworms. After that she didn’t have a problem answering 9 inch-worms and 3 half-inchworms.

I have attached an AIMS activity that explores how many inches are in a foot and a yard called, “What’s In Your Yard.” It is a great way to explore measurement with your students. Click here to download a sheet of just the inchworms so each student could have plenty to manipulate.

Books can be a great way to engage students in a mathematical concept, but I could see even though I have read the book numerous times that Bethany wasn’t grasping the concepts in it. Now when I read the book, Bethany will have an experience that helps her process the mathematics in the book.

How have you built the concept of measurement with your students?

### What Does Twice as Big Mean?

I’m often puzzled by the way we use phrases like twice as big. What does that mean? For example, I understand that if my debt 5 years ago was $10,000 and today it’s $20,000, then my debt is twice as big today as it was 5 years ago. I also understand that if one two-by-four… Continue Reading