# Math personified: a teaching story

### Prologue

My friend Mark R., his identical twin Expo, and I are sitting on the chalk rail. It’s not really a chalk rail but I think that’s what you call it even though we’re mounted to a white board. The three of us love exercise and we get a great workout in math support but sometimes we get abused. Sam will put me in choke hold and press my face against the white board. Ellie will forget to put the cap back on Mark R. so he’s all stuffed up. And poor Expo has lost his head completely. We now call him the Headless Horseman.

By this account you would think the students don’t like us. They actually do. Students can’t wait to get their hands on us because for the better part of the day they learn using an iPad.

### Story I

This past week our caretaker, Mrs. Dooms, used us for a form of visual storytelling. Ellie, a seventh grader, struggles with mixed numbers to improper fractions. Her class is working on rational numbers, specifically adding and subtracting negative fractions. Mrs. D. picked me up to visually explain.

“Remember last week when I served you guys pizza and cut it up?”

“Yeah! That was good. Where was it from?” Ellie asked.

“It was a frozen pizza and I heated it up during my plan period. Let’s get back to fractions.”

Mrs. D. uncapped me and began to draw circles to represent 2 1/4.

“This is where the short-cut comes from,” she said. “Two wholes cut into fourths plus the remaining one fourth equals 9/4. Ellie needs more examples. Mrs. D. writes two mixed numbers for Ellie to model. She hands me over to Ellie for more practice.

### Story II

In sixth grade support, Sam picks me up with his usual choke hold. We’re multiplying decimals, 4.31 x. 2.2 and I brace for the decimal point. His math is fluent; the ink flows freely onto the whiteboard. Sam generally follows the algorithm but I hear Mrs. D. ask, “How do you know your answer is reasonable?”

“Because there are a total of 3 place values to the right of the decimal,” he said.

“There are a total of 3 place values to the right of the decimal so I move the decimal three times.”

“If we were to estimate, to what whole numbers would we round 4.31 and 2.2?”

Sam’s eyebrows furrow, his hand grips me tightly. “We round 4.31 to 4.3 and we’d leave 2.2 alone?”

Mrs. D. picked up Expo from the chalk rail, saw his head was missing so she grabbed Mark R. instead. She lightly wrote next to Sam’s work ‘Estimate: 4 x 2’.

Sam reveals to Mrs. D. that he relies on memorizing a procedure and needs more support with the meaning of decimals and place value. My buddies and I are gearing up for next week’s lessons.

### Epilogue

If Mrs. D. was writing this she would want you to know that most students enjoy math support. In fact some seventh graders drop in on their non-scheduled days.

As far as I’m concerned, students appreciate learning with us Expo Markers, even though I wish they would treat us with a bit more affection.