Math at CDS: Skills, Application and Reasoning

2/26/2025

Susie Friendlander-Holm, CDS Math Specialist

Math at CDS follows a learning equation: skills + application + mathematical reasoning = confident, curious mathematicians!

At Children’s Day School, we believe math is more than just numbers—it’s a powerful way to make sense of the world, predict possibilities, and shape the future. Our approach to math nurtures confidence, curiosity, and problem-solving skills, ensuring students see themselves as capable mathematicians.

How do we do this? We focus on three key areas: math skills, real-world application, and mathematical reasoning. Through hands-on experiences, engaging discussions, and meaningful projects, students develop a deep understanding of math that goes beyond memorization—they learn how to use data strategically, solve problems creatively, and lead their learning!

Let's take a deeper look at each of these three key areas to better understand CDS's approach to math:

1. Building Math Skills

What do I need to know? What models support my understanding?

At CDS, students learn and practice skills in a variety of ways. Concepts are often introduced through concrete models before transitioning to abstract strategies, ensuring deep comprehension.

In our second grade classrooms, for example, students have been learning about how to efficiently add and subtract multi-digit numbers (up to 1000.) Instead of jumping straight to traditional algorithms, they start with visual models like number racks, moving to more efficient strategies like open number lines and adding with expanded notation.

Why don’t teachers just start with the algorithm first? By focusing on modeling and structure through visual or hands-on methods first rather than simply memorizing an algorithm, students truly understand what it means to “carry” or “borrow” between sets. This helps reduce mistakes carrying across place value by building a strong foundational understanding of the math concept.

In seventh grade, students are learning how to analyze proportional relationships to solve problems. They started by comparing distance, rate, and time with ratio tables, and then practiced showing proportionality on graphs. This all came together during their Cost of Entertainment math project where students analyzed proportional relationships of favorite hobbies based on time spent and overall cost and represented this information via graphs and infographics. A bonus challenge was for students to compare how these rates were impacted by “enjoyment multipliers.”

2. Applying Math to the Real World

How can I use words, numbers, logic, and reasoning to help me solve problems? What patterns or structures of a problem will help me solve it efficiently?

At Children's Day School, we emphasize inquiry- and project-based learning that authentically connects what students learn to real-world experiences. Math is experiential and applied to real-world problems, too!

For example, in fourth grade’s Big Snack Project, students applied multiplication and division skills to plan, shop for, and prepare apple crisps for 160 students in our Extended Program. They interviewed staff, considered dietary needs, scaled recipes, built a budget, went to the store in small groups to purchase ingredients, and even harvested apples from our garden to reduce costs! Finally, students cut and prepped 16 pans of apple crisp, baked them, and distributed the treat into smaller serving cups for everyone to eat.

Through this experience, they not only practiced multiplication and division but also practiced many other valuable life skills, such as time management, budgeting, measurement conversion skills, and teamwork. They also learned about the behind-the-scenes preparation that our extended program team does every day, developing an appreciation for our school community and giving back!

3. Mathematical Reasoning

How can I justify my strategies so that it makes sense to others? Can I critique and evaluate the ideas and strategies of others?

Math at CDS is social and hones students' communication skills, too. Justification and critique are incredibly important skills for life and are explicitly taught and practiced in CDS math classrooms. Students regularly engage in math talks—short classroom conversations around purposefully crafted problems that are solved mentally where students have the opportunity to explain their thinking to each other. Here is a short video from Jo Boaler (Stanford) explaining more about why number talks are effective.

For example, in kindergarten, students are learning about flexible combinations up to 20, analyzing visuals to help describe how they “made” (added towards) the total. Here's the conversation students had about how they analyzed a visual of 13:

“I saw 5 fingers on two hands, 5+5=10, and then added 3 more fingers from the third hand.”
“I saw 4 fingers from two hands (excluding thumbs), 4+4 = 8, then I added the 2 thumbs to the 3 fingers on the last hand, 2+3 = 5. Last, I added 5 more to the 8, 8+5 = 13.”

As they move through the grades, these conversations grow in complexity. Sixth graders, for example, recently debated how many candy corns could fit in a quarter-cup measuring spoon, using area and net models and logical reasoning to support their arguments. By building the language of mathematical reasoning and argumentation, students are able to better evaluate their own strategies, and learn or critique ideas from others—skills that extend far beyond the math classroom.

Support Math Learning at Home

Parents and caregivers can support math learning in these three areas by:

Skills: Practicing basic facts out loud or visually.
Application: Including young learners in activities that use math, such as cooking (measuring and scaling recipes), shopping (budgeting, change, discounts), and budgeting for things like family trips (transportation, accommodations, meals).
Reasoning: Asking questions about homework or schoolwork to practice math talk skills. Use questions such as, "How did you solve this problem? Why did you solve it this way?" Make sure conversations are open-ended to encourage evaluation of strategies and sharing of different ways of solving problems. Math games are a great way to start math conversations, too!

At CDS, we don’t just teach math; we nurture mathematical thinkers who approach challenges with curiosity, confidence, and resilience. Whether they’re exploring ratios, solving real-world problems, or debating mathematical strategies, our students develop skills that prepare them not only for advanced math but for life.

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