SAN PABLO -- When teacher Beth Levine asked her fourth-graders at Montalvin Manor Elementary to figure out how much it would cost to take seven friends to the circus if each ticket cost $4, and treat nine to lemonade at $2 a glass, the methods they used demonstrated how well they understood the problem.
One girl drew seven rows of four dots each to represent the tickets. She added the dots to get $28.
A boy raised his hand and said he disagreed with her answer because she hadn't done the second part of the problem. He showed his drawing, which included nine circles with the number 2 inside to signify nine lemonades, costing a total of $18.
Some other students drew bar charts.
After each step, Levine asked the class if they agreed, disagreed or were confused. One boy said he was confused.
"The ones who are confused right now will learn the most," Levine said. "Mistakes are how learning happens."
Learning to make sense of problems and persevere to solve them is an important skill taught in new Common Core curriculum standards being introduced in classrooms across the country.
Levine, who was recently selected as a Contra Costa County Teacher of the Year, is a working group representative in the West Contra Costa school district to help implement the new standards in math and English language arts.
"I'm educating myself and getting educated," she said. "Students have to be able to talk about doing math in multiple ways and write about it. Those are significant differences from last year."
To illustrate the circus math problem another way, Levine asked seven students to come to the front of the class and act out receiving tickets. The class counted by fours as she pointed to each student: 4, 8, 12, 16, 20, 24, 28.
The class then added $28 and $18 to get the final answer: $46.
Then they moved onto a similar word problem, only this time they were on their own.
"Read the next problem," Levine said. "Draw, write, think on your own and think about what we just did."
After students solved this problem by drawing their answers, Levine praised them for working out the problem and keeping at it until they found the answer.
Earlier in the day, Levine worked with a group of English language learners to identify an author's purpose while reading a biography about Coretta Scott King.
"Are we being entertained by this?" she asked. "Are we being persuaded to do something?"
She asked students to recall what they had read from chapter 1 before moving onto chapter 2, using complete sentences starting with "I remember." When another girl recalled from the book that Scott King saw her house and her father's sawmill burn down, Levine asked students to discuss how that changed her life. One girl said it probably made her sad and pointed out that the family had to rebuild.
Next, Levine asked students to turn to a partner and talk about one fact in Scott King's life, then reread the chapter, before writing about Scott King themselves.
"There is a lot more focus on informative text in the Common Core," she said after the lesson. "We wouldn't have done this text last year."