Marisa Laks’s geometry students might not have realized it when they shuffled into class earlier this month and grabbed “Do Now” worksheets covered with quadrilaterals, but they were on the cutting edge of the Common Core.

While the city’s elementary and middle schools have already started testing students on the new standards, that hasn’t happened yet in high schools. High school students will take their first Common Core tests this year and, after a recent state policy change, they have several extra years before they must meet the higher standards in order to graduate.

But Laks, the math department chair at Global Learning Collaborative on the Upper West Side, isn’t waiting to teach to the tougher standards.

She started connecting her geometry lessons to the new standards last year, and she also applied to join a group of “master teachers” from around the country who are paid to help fill a free online archive of Common Core-aligned lessons operated by a company called BetterLesson. Eventually, Laks will upload a year’s worth of lessons, some with videos and student work attached.

Chalkbeat spent a morning last week in Laks’ class observing a lesson she created where her students — mostly juniors, with a few sophomores and seniors — use a computer program to “sketch” quadrilaterals. As when we chronicled other classes in the past, we spoke to Laks about the lesson afterwards, and have included her commentary in block quotes beneath our observations.

10:25 a.m. The Do Now sheets asked the students to determine which of the pictured quadrilaterals — a parallelogram, square, rectangle, or isosceles trapezoid — did not belong and why. As the 13 students got to work, and chatted a little, Laks began to pass out laptops to partners.

After a timer sounded, the class discussed the question, which led into Laks’ “mini-lesson” — a review of various quadrilaterals and their properties.

At one point, a girl noted that the other quadrilaterals in the Do Now “look more equal” than the trapezoid. Laks quickly corrected her.

“Be specific. Be precise.”

Laks said one of the Common Core “mathematical practice” standards she most often returns to is, “Attend to precision.”

“I don’t allow ‘that thing,’ ‘that one,’” she said, adding that when students are pushed to use correct names and definitions, they are forced to consider the relationships among concepts.

10:42 a.m. After the discussion, Laks directed students’ attention to the classroom’s electronic SmartBoard. She launched a dynamic geometry software program, called The Geometer’s Sketchpad, and asked students to do the same on their laptops. Then she reviewed the basics of the program.

Laks has her students use the program about once a month. Following the standards, students also use more traditional tools, like compasses and rulers, but Laks said the geometry software offers some advantages. For example, it makes sketching quicker and includes features — such as only allowing students to measure the length of segments, not lines — that reinforce geometry concepts.

One student noted that there were enough laptops for everyone to work alone, but Laks said, “I want you to work together.”

“This way they have to talk to each other,” she said. “It’s all about the language and reinforcing the mathematical language. This really helps them get a conceptual understanding.”

10:49 a.m. In pairs, students used the computer program to sketch figures by following directions on worksheets that Laks had made. The worksheets featured slightly different prompts depending on students’ skill levels, but all asked students to sketch a figure, identify it, and describe its properties.

Some students got right to work, but others seemed stumped. “Miss, I don’t even know where to start,” one boy called out.

PHOTO: Patrick Wall
Laks’ class uses dynamic geometry software called, The Geometer’s Sketchpad, to create digital “sketches.”

The small class size allowed Laks to rotate among the groups. She performed the “drag test” on some of their digital sketches, in which she drags a figure’s vertex with the cursor — if the sides’ new slopes are different, then the lines are not parallel.

During this time, some groups asked basic questions about how to operate the computer program. But others wanted to know what figure they were trying to sketch (a parallelogram or rectangle, depending on their worksheet).

Laks refused to tell them. Instead, she asked them questions about the figures (“Are the sides parallel?”). When one student, senior Hiram Dueño, asked if his shape was a rectangle, Laks smiled back, “I don’t know.”

“Yes you do, you’re a teacher, you’re supposed to know this,” Dueño replied. “You got a degree for this!”

“It’s making students accountable for their own learning,” Laks said. “We’re not giving them the information; they are working to discover it.”

“They struggle with this,” she added. “But I feel that it’s a satisfying struggle. They complain, but they complain with smiles.”

During the group work period, a few students became distracted. One boy put his head down and some girls surfed the Internet.

Laks said management issues occasionally bubble up because students grow frustrated with the more challenging Common Core work. Also, the standards assume strong math foundations that many students lack, she said.

Laks added that group work and technology can steer some students off task, but that the risk is worth it.

“In my opinion, the benefits of enhanced comprehension and learning from their math discussions outweigh the negatives of off-topic conversations,” she said.

11:01 a.m. The timer beeped again and the class briefly shared observations about their sketches.

Then Laks passed out “exit tickets,” ungraded assessments that help her see what students took from the lesson. The slips asked students to explain why rectangles are always parallelograms, but the reverse is not always true.

Laks will eventually post the lesson on the Common Core website, called BetterLesson. She said she joined the lesson-sharing project because she believes in the goal of the Common Core — to prepare students for college through more rigorous instruction — but felt teachers had been given too little training and resources.

“We’re not quite ready,” she said. “I just hope we stick with it.”

As students packed up their things, Dueño still hadn’t identified the figure he had been trying to sketch. He asked Laks again to tell him (“It’s going to keep me up at night!”), but she kept pushing him to solve it himself.

Picking up his backpack to leave, Dueño said Laks’ approach could be frustrating, but it works.

“I learn more on my own,” he said. “It’s more independent than counting on the teacher.”