Designing Decimals in Class 4

Entering Room 61, the Class 4 students got right to work tackling the “brain breakfast” warm-up, a daily routine in Lauren Gallagher’s math class. The morning’s colorful lesson focused on decimals.

As the girls learned at the beginning of this unit, a decimal is a number expressed in the scale of tens, such as tenths, hundredths or thousandths. Numbers include a decimal point when they contain part of a whole number (For example: 3.75 equals three wholes and 75/100 of a whole).

To teach the unit on decimals, Ms. Gallagher uses Google spreadsheet grids, which allow the students to create digital designs using the countable rows and columns. For that day’s challenge, she presented her students with a classmate’s design of a house (dark brown and light brown) on a lawn (green) surrounded by an apple tree (red and green), a clear sky (light blue), fluffy clouds (white) and a bright sun (yellow). In total, the design was made up of 300 tiny squares of various hues. It was the students’ job to determine each color’s value and to double-check that the values indeed added up to the design’s total value, three wholes. Ms. Gallagher gave them a hint: One square in the design equaled one hundredth (a visual form with which they were familiar).

Except for the scratching of busy pencils, the rub of an eraser and an occasional whisper, Room 61 was still. While the students concentrated on solving the day’s decimal puzzle, their teacher guided them by suggesting strategies and asking questions. “What if I don’t like to borrow, or regroup, across zeros? What can I do instead?” she asked. “How do you know? Can you show me?” After a few minutes of productive independent work, the class came together to share.

“Who left blue for last?” asked Ms. Gallagher, referring to the sizable sky. Several hands went up. One student explained her reasoning: “There’s a lot of blue to add up.” In this scenario, some students felt it was easier to tabulate the sum of each of the other colors before calculating the value of the expansive blue by finding the remaining difference from the total design. Others chose alternative, equally valid, strategies.

“Now call on someone new for light brown,” Ms. Gallagher instructed another student, who offered her calculation for the house’s front door before calling on a friend to continue the conversation. By the end of the lesson, each student had an opportunity to share her decimal deductions.

As they made their calculations, the girls learned how to write the decimals in four ways: standard, picture, word and fraction forms. For example, if the color blue encompassed 44 out of 100 squares, number representations included: 0.44 (standard); | | | | …. (picture); forty-four hundredths (word); and 44/100 (fraction). They recorded these forms in a table, called the key.

As positive peer feedback is a regular part of the class, the atmosphere was one of camaraderie, not competition. “Mistakes are always learning opportunities,” Ms. Gallagher stated. “Give yourselves a pat on the back for trying.”

During an earlier class, the students designed their own digital pictures based on grids of 100 or 1,000 with an accompanying explanatory decimal key. A creation with Rudolph, complete with a shiny red nose, was clever and timely. Another featured geometric configurations in purple, yellow and orange.

“It’s really cool to represent decimals through pictures,” exclaimed a student, whose enthusiasm for this project was widely shared among her classmates:

“I really like math! Especially in Class 4 [because] you’re making so many connections. Math is all about making connections.”

“You need to find out yourself. We are not sitting for hours and memorizing. We’re not being told the answer. We are discovering it.”

“I love math. It’s my favorite subject. There is always so much more to learn, which is so cool!”

As the morning’s lively lesson wrapped up, the Class 4 students handed in their papers, collected their backpacks and headed to recess, perhaps with an extra boost of confidence from their study of dazzling decimals.

Browse photos from the class below: