# “I never want to see a puppy that big.”

Since Winter Break, friends friend have been learning to measure length. We moved from using nonstandard units like popsicle sticks and shoes to standard units like inches, feet, and yards. Friends measured the lengths of their jumps, the width of the classroom, and the length of the Lower School hallways.

This week, friends began to compare lengths to find the difference between two lengths. Today, they compared the height of a puppy and a dog. We’re still on the hunt for a dog this big–“More like a horse,” Georgia suggested–and some are fearful of how big a puppy that size will grow to be. But in the meantime, we compared.

We continue to push friends to model the story problem instead of jumping to ask, “Is it adding or subtracting?”

“We’re not adding the height of the dogs together! They’re not growing!” Georgia reminded. Redirecting the focus from the operation toward the model helps students understand the problem and to, as Justin reminded us, “Make a plan for the best strategy before starting.” Drawing on their experiences solving addition and subtraction story problems, friends generated different strategies for solving the problem.

Today, we dug into two strategies:

Strategy One: Kamari’s Unifix Cube Line Strategy

First, Kamari built 42 and 63 with unifix cubes to represent the height of the dog and the puppy. She used place value to model the numbers using tens and ones. This is often the first move friends make when they see a story problem with two-digit numbers.

Kamari quickly realized that it would be difficult to compare the two numbers in this format. She suggested, “How about I put them together to see?” So she stuck the cubes together into two long lines.

To compare the height of the puppy and the dog, she lined the two sticks up side-by-side, clearly showing where the additional height was on the dog.

Kamari then broke off the “more” from the “dog” stick of unifix cubes.

She labeled the three parts: the puppy, the dog, and the more, to keep herself organized as she worked.

Finally, Kamari counted the “more” to see how much taller the dog was than the puppy.

In the end, this concrete modeling allowed Kamari and others to compare the two. The visual supported them in really understanding the problem, seeing that in fact, nothing was changing–nothing was going away, being eaten, or going home like in many subtraction problems.

Strategy Two: Justin and Sandra’s Number Line Strategy

Justin and Sandra were both trying to draw multiple yardsticks to represent the height of the dog and puppy. “The dog is even taller than a yardstick!” When they found a meter stick, they decided that they could use the centimeter side to represent inches, allowing them to count without needing multiple yardsticks.

First, they marked the height of the puppy and the dog on the meter stick.

Next, they decided to count the number of inches (centimeters in the case of the meter stick) between the height of the dog and the height of the puppy. Some friends were having difficulty visualizing the dog on the meter stick so we grabbed some construction paper from the art center and built a model. Side note from Marjorie: “Tell them to ignore the drawings–this is math, not art. It’s just a quick sketch.” Thanks, Marjorie.

With the addition of the pictures, it became easier to see where the difference in height began. We cut off the “more” (yikes!) to make it especially clear.“See? That is the more!” Carroll pointed to the group.Finally, Justin counted up from 42 to 63. “1, 2, 3, 4 . . .” to find that that the dog was 21 inches taller than the puppy.