“Today we are going to finish up our number lines,” Middle School Mathematics teacher Kelsey Konopka announced recently to her Class 4 students as they arrived in Room 601.
Diagrammed on long sheets of paper, the number lines comprised a black horizontal line across the page, intersected by 11 evenly spaced dividers. Jutting out from a section below the line, two green arrows pointed to another divided line, the “magnified” area.
Collecting their work and finding “productive spots” with their partners, these eager mathematicians wasted little time jumping back into this fun and challenging activity, the goal of which was to help them develop a conceptual understanding of numerical relationships. Sharpened pencils, rulers, erasers and orange math notebooks (for practice efforts and computations) covered the tables as these determined scholars got down to business.
For this interactive project, the partners were tasked with determining an increment of numbers of their choosing—whole numbers, decimals or both—to spotlight along the primary line. Then they calculated what the zoomed-in section would look like.
For example, one group selected increments of 10 along the top line beginning with 42, so theirs read “42, 52, 62, 72” and so on. Next, they placed their zoomed-in section between 72 and 82 and decided to count up by 1s (“72, 73, 74,” etc.). Another group added up by 17s on the top line (“0, 17, 34, 51”), and increased by 1.7 in their zoom (“51, 52.7, 54.4, 56.1,” etc.).
After turning on calming “fairy music,” Ms. Konopka gave the math partners 15 minutes to complete their number lines. Once this stage was finalized, they would write about their thought processes on index cards to share with the rest of the class.
Within the designated framework, the students approached this assignment with creativity, a strategic mindset and no shortage of perseverance. Thus, if a particular sequence didn’t add up properly at first go, they re-calibrated and tried again. Moreover, if a group didn’t feel sufficiently engaged, they collaborated to devise a more sophisticated sequence.
“We’re figuring it out,” said one student as she and her partner brainstormed a fresh set of increments. Their paper showed evidence of robust erasing, yet they did not seem deterred. “I get it now!” another declared jubilantly.
Ms. Konopka spent a few minutes with each group, asking questions to make sure they were on track. “Do you want to take anything out?” she asked one pair. “Now what do you have?” For several students, she demonstrated key concepts using light-blue place value blocks.
As time counted down, the students hurried to put the last touches on their number lines and to carefully compose their index cards. A starred reminder, illuminated on the classroom smart board, encouraged them to “pretend you’re a newscaster reporting on your number line.”
“Make your way to a seat where you can see the board,” instructed Ms. Konopka, switching off the fairy music. She then proceeded to call on the students, one group at a time, to present their work to their classmates. After securing their papers with magnets, the young mathematicians took turns describing steps they took and what they learned along the way.
For the final minutes, the students rotated around the room, observing each others’ numbers lines and explanatory cards, which were displayed on the tables. On yellow Post-it Notes, they expressed comments, questions and words of praise. “I like how you showed your work and the numbers you chose,” said one. “I love how you made a number line within a number line,” declared another.
Clearly, these Class 4 students made the most of this exhilarating lesson, tackling their number lines with fortitude and imagination, while kindly supporting their classmates’ efforts. “Nice work today,” said Ms. Konopka. Nice work, indeed.