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On the Road to Algebra

Grasping the concepts of algebra is a big step in a student's career, and Bennet Middle School Royal 7 math teacher Taryn Kutniewski is helping students understand the reasons behind the rules before moving on. Included: Lessons to help students with linear equations.

Seventh grade math classes at Bennet Middle School have two goals: ensuring students are prepared for the state tests in eighth grade and they are ready to tackle first-year algebra either in eighth or ninth grade.

"The second half of the year, particularly, is focused on priority strands for the Connecticut Mastery Tests," says Royal 7 math teacher Taryn Kutniewski. "This includes algebraic thinking, data analysis, and geometry.

Bennet eighth graders have three math options; they can take pre-algebra, the first half of first-year algebra, or first-year algebra. An agreement with Manchester High School allows students who take the first half of algebra in eighth grade to complete it in ninth grade.

"A lot of what we do is based on the framework of the Connecticut standards," Mrs. Kutniewski continues. "We're trying to include all the priority standards. We also want them to think critically and be able to express things."


Classes usually begin with a problem of the day, which students copy from the board into their math journals. Today students are asked to identify the pattern in the sequence 1,1, 2, 3, 5, 8 and then write four sentences describing the pattern in their journals. Several students say they understand the sequence, but don't know how to explain it, but Mrs. Kutniewski is firm; a written explanation if part of solving the problem. (To view the solution, see the end of the article.)

In some classes, to help students review ordered pairs and understand linear equations, students draw grids, labeling the X axis and the Y axis. Then after putting numbers on the axes, they divide into groups and play Tic Tac Toe, using coordinates from the grid. Some played consistently to a tie, while others produced winners in almost all the games.

Other classes are working on different skills. Eighth period worked on determining quantities, solving the problem of how many gallons of water per minute the Prometheus Fountain in Rockefeller Center in New York City pumps. Mrs. Kutniewski shows students a picture of the fountain, and explains its history. According to information they students are given, the fountain pumps 1 million gallons every 250 minutes. (The answer also is at the end of the article.)


Seventh period students already are identifying equations based on coordinates on the grid, according to Mrs. Kutniewski.

She has the seventh period students draw, and write positive and negative numbers on either side of zero. Then using small cars, they "drive" back and forth on the line to illustrate the addition and subtraction of negative and positive numbers. Students are able to see why the outcome of a problem is a negative or positive number.

"I try to have something visual," says Mrs. Kutniewski. By starting with an illustration first, she hopes students will have a deeper understand of the concepts. The week after these lessons, she plans to teach them the "rules" for what they are learning to do.

"When I was a student, I learned all the rules, but didn't understand the reasons for them," she says. "Now they do."

(Problem of the day solution: adding the first two numbers in the sequence gives you the next number, and the pattern continues. The two preceding numbers add up to the next number.

Prometheus Fountain: 1 million divided by 240 equals 4,000 gallons per minute.)

Education World Goes Back to School

Education World news editor Ellen R. Delisio is spending several days a month this school year with the Royal 7's, a seventh grade team at Bennet Middle School, a grade 6 to 8 school in Manchester, Connecticut. She is observing and participating in students' learning, and talking with staff about their strategies and perspectives on improving student performance. She is a graduate of W. Tresper Clarke Junior-Senior High School in Westbury, N.Y.

(Editor's Note: All students' names have been changed) 

Article by Ellen R. Delisio
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