Spanning the Curriculum

Silvia Santos struggles to align her second-grade math textbooks and other resources with the new state math standards. While she implements active, hands-on learning activities, she has difficulty maintaining order. Meanwhile, one of her students discovers that learning math can make sense and be a lot of fun.

A second-grade teacher struggles to align her math textbook with new state standards. [dial-up OR broadband]

Silvia works late to finish planning a math unit.

Scene Photo

Silvia has high hopes for her third year of teaching.

Silvia Santos looked up at the clock and groaned. How could it be 5:00 already? Her second-grade class had been dismissed almost three hours ago, yet she was still at school trying to prepare for the rest of her unit on data and algebra. There was so much to think about! Maybe that was the problem?

Silvia had expected her third year of teaching to be a little…easier. She knew the first year of teaching, after switching from a brief but unsatisfying career in accounting, would be tough. She even expected the second year to have its challenges. However, her third year in the classroom was half-way over and she was still just as busy as ever—thanks in part to a huge revamping of the state standards.

The difficulty of the content was one of the things that still surprised her about teaching. Not the content itself—this was the second grade, after all!—but figuring out what content to teach and how to teach it.

Take math, for example. Silvia still had all of her math education textbooks that recommended strategies for creating a student-centered, problem-based math classroom where students could play an active role in developing mathematical understanding. She was also a member of the National Council of the Teachers of Mathematics (NCTM) and tried to keep up-to-date on journal readings. Then there were the standards and other curriculum guidelines to consider: NCTM’s Principles and Standards, NCTM’s Curriculum Focal Points, and the recently revised state standards. Incorporating all of these into her instructional plans wasn’t an easy task!

Investigate NCTM’s Principles and Standards for School Mathematics and Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics

None of the textbooks and other math resources she used perfectly aligned with the standards, and she spent hours figuring out the best way to use the textbook. Even the experienced teachers on the second-grade team seemed overwhelmed by all of the changes to the state standards, and math was just one of the many subjects they were responsible for teaching!

Learn about the new math standards

Silvia stretched and resolved to leave no later than 5:30. The math lessons for the next two days, focusing on data, measurement and algebraic thinking skills, were ready. She wanted time to be able to take a walk tonight after eating dinner. The exercise might be just what she needed to clear her head.

Read Silvia’s lesson plan

Silvia’s lesson helps students build data analysis, measurement and algebraic reasoning skills.

Silvia started the day with a fresh resolve to discuss her concerns about the math curriculum at the next team meeting. Surely they could find a way to work together to align their resources with the new standards?

Scene Photo

Students strengthen their measurement skills while finding the length of their partner’s arm span.

Right now though, she was excited to begin today’s math lesson. Students would be measuring each other’s arm spans and then sorting and organizing the data. She tried to find ways to relate math to other subjects whenever she could, and the arm span lesson made an interdisciplinary connection to an upcoming science lesson on bird wing spans. Plus there would be many opportunities for students to strengthen their algebraic thinking skills as they made predictions and observations and then analyzed the data.

As the students returned to the room from lunch, she made sure a copy of the lesson flow map was ready on the visualizer so she could display it for the class. She began with a brief review of yesterday’s lesson and then gave the students an explanation of today’s activity.

See a copy of the lesson flow map


Silvia explains today’s arm span lesson to the class and introduces new vocabulary. [dial-up OR broadband]


Scene Photo

Martha is excited to begin her teacher certification program.

As students began measuring and gathering data, Silvia was glad that she had an extra pair of hands to help. Martha, a university student in a teacher education program, was doing her first field observation in Silvia’s class and she could work with students in small groups. Silvia preferred to plan very active, hands-on learning activities whenever possible. She sometimes found that the children tended to get more off-task during these kinds of lessons, and she was still trying to figure out how to strike the perfect balance between action and chaos. She liked the noise and energy though, and she figured the kids would learn more if they were having fun too.


Students work together to measure their arm spans and record their data. [dial-up OR broadband]


Scene Photo

A pair of students models how to find the median of a set of data.

Noticing that some of the students were having trouble following directions, Silvia tried to get them back on track. Great, she thought to herself. She remembered writing up reactions during her own field observations and she wondered what Martha might have to say about this lesson. She got the students settled into their seats, and they began to make observations and predictions about the data. She hoped the post-it activity would help students really “see” how to find the median of the set of data.


Silvia introduces the class to the concept of median. [dial-up OR broadband]


Silvia glanced at the clock and once again was surprised by how quickly a 50-minute math lesson could fly by. Sometimes she wondered if less than an hour a day on math was enough to cover all of the content. She was glad this was a two-day lesson—they would need the extra time tomorrow. For now, she wanted them to complete their frequency tables and bar graphs before they had to move on to science.


The class organizes their data and creates bar graphs. [dial-up OR broadband]


Silvia was particularly thrilled when Taylor’s group noticed that her arm span was the longest and wondered if her arm span had anything to do with her height—Taylor was the tallest student in the class. This observation was exactly the type of algebraic thinking that Silvia was hoping the students would expand on tomorrow when they explored the functional relationship between height and arm span.

Silvia chuckled to herself—functions in the second grade! She hadn’t learned functions until the ninth grade. She had never even thought of algebra as an elementary school topic before she started teaching, but she soon found that algebra seemed to connect to all of the other elementary math content strands. By teaching her students how to think and reason, to observe and generalize patterns, and to begin to think about functional relationships, she knew she was helping them develop the ability to think mathematically. These algebraic thinking skills would be essential throughout all of their studies in math.

Silvia stopped herself from thinking too much about tomorrow’s lesson. She didn’t have a lot of time for discussion at the end of the class because they ran out of time. She quickly collected the students’ math journals so she could check their tally sheets and bar graphs before tomorrow’s lesson. During the brief sticker review activity—a favorite with her students—it seemed that they were starting to gain a better understanding of the use of frequency tables and bar graphs.

See an example of a student’s frequency table and bar graph

Flannery reflects on her favorite subject on her way home from school.

Scene Photo

Flannery has a growing sense of confidence in her ability to understand mathematics.

Another cool day at school! I’ll have to remember to tell Mom and Dad about my arm span when we share our “news of the day” at dinner. That’s something my mom started because I can never remember anything when she asks me how things went.

IBut I really do love the second grade. Ms. Santos is such a nice teacher, and she makes things so interesting. My favorite subject is math. We always get to move around and do fun things, like when we surveyed teachers yesterday to see what kind of ice cream was the most popular. Most of them liked mint chocolate chip the best. Yuck! We never did cool stuff like that in the first grade though! I never really got math before, but now I’m really good at it.

One of the neatest things I’ve learned this year is that math is all around me. Well, I already knew that you have to know how to count and add so you can pay for stuff at the store, but there is so much more math in the world too. Even sorting groceries to put them away is math. Ms. Santos helped me see that there is math everywhere: in science, music, nature, and even art! When I told Ms. Santos that I love math, I really meant it.