BHS Mathematics Department Overview

Welcome Message:

Welcome to the Mathematics Department at The Boerum Hill School for International Studies! As an International Baccalaureate (IB) World School, we offer the MIddle Years Program (MYP) and the Diploma Program (DP). The MYP comprises Years 1 through 5 (grades 6 through 10) and the DP comprises Years 1 and 2 (grades 11 and 12). Part of the IB mission statement says, “The International Baccalaureate® aims to develop inquiring, knowledgeable and caring young people who help to create a better and more peaceful world through intercultural understanding and respect.” Here at BHS, we believe that every student can excel in mathematics when given the right support, engaging challenges, and opportunities to explore math’s connections to our diverse world. Our dedicated teachers adapt the Illustrative Mathematics (IM) curriculum to fit within the IB framework and philosophy. We focus on developing your child’s problem-solving abilities and mathematical reasoning through collaborative learning experiences that build both confidence and understanding. The team is excited to partner with you in nurturing your child’s mathematical journey. Together, we’ll help them see mathematics not just as a subject to master, but as a powerful tool for understanding and engaging with the world around them.

Mathematics Department Mission Statement

Students at BHS are provided with opportunities to build critical problem solving skills and use their prior knowledge to better analyze situations when math interacts with the real world. Students are empowered to think both creatively and systematically through collaborative mathematical discussions, as they support one another in identifying multiple pathways to both solving and describing solutions. Students are challenged to persevere through obstacles when answers are not clear, learn through discovery, and write justifications of thinking using mathematical vocabulary and evidence. 

Teachers at BHS are tasked with nurturing a growth mindset in students. The growth mindset is communicated and embodied through rich tasks that foster students’ conceptual fluency, creativity, and reasoning rather than speed and formulaic approaches. Teachers encourage students to make connections between different topics in math and cultivate confidence in the face of non-routine problems.

Curriculum Overview

MYP Year 1: Accelerated Grade 6 Illustrative Mathematics (IM)

The Accelerated Grade 6 course introduces students to many of the big ideas that are a cornerstone of middle school mathematics and beyond. Students study ratio and rate, learn to divide fractions by fractions, extend their understanding of the number system to include negative numbers, and understand and use variables.

MYP Year 2: Accelerated Grade 7 Illustrative Mathematics (IM)

The Accelerated Grade 7 course continues on the learning of 6th grade around mathematical relationships and pre algebra. Students investigate geometric transformations, create projects based on real world scenarios and in preparation for the Algebra I course in MYP 3.  

MYP Years 3 and 4: Algebra I Illustrative Mathematics (IM)

This course is structured around seven units that cover one-variable statistics, linear equations and inequalities, two-variable statistics, functions, and introductory concepts of exponential and quadratic functions. IM Algebra 1 emphasizes a problem-solving approach, encouraging students to explore mathematical concepts through real-world contexts and develop their reasoning and communication skills. At the end of the Algebra I course, students are expected to take the Algebra I Regents Exam at the end of the academic year in June.  

MYP Year 4: Algebra II Illustrative Mathematics (IM)

This course is only offered to 9th grade students who have taken and passed the Algebra I course and Regents Exam in middle school, typically as 8th graders. A strong and fluent understanding of core algebraic concepts taught in the Algebra I course serve as a prerequisite for success in Algebra II. Students who take Algebra II are eligible for Higher Level (HL) Applications and Interpretation, the 2-year mathematics course offered in the Diploma Program (DP) to 11th and 12th graders at BHS. At the end of the Algebra II course, students are expected to take the Algebra II Regents Exam at the end of the academic year in June.  

MYP Year 5: Geometry Illustrative Mathematics (IM) 

This course is offered to all 10th grade students and is structured around seven units that deepen students’ understanding of geometric relationships and reasoning. Topics include constructions and rigid transformations, congruence, similarity, right triangle trigonometry, solid geometry, circles, and applications of volume and modeling. Through a problem-based approach, students engage in mathematical exploration, justify their reasoning, and apply geometric concepts to real-world contexts. The course builds on prior knowledge from Algebra I and Algebra II, preparing students for advanced mathematics courses in the IB Diploma Program. At the end of the academic year, students are expected to take the Geometry Regents Exam in June.

DP Years 1 and 2: Applications and Interpretation 

The International Baccalaureate Mathematics: Applications and Interpretation course is a rigorous 2-year course designed to prepare students around the world for college-level mathematics and beyond. During the 11th grade year (DP1), students explore the first three topics – Algebra, Functions, and Geometry & Trigonometry – and extend knowledge learned during their Algebra I, Algebra II, and Geometry courses to real-world situations. During the 12th grade year (DP2), students explore the last two topics – Statistics and Calculus – and undertake a mathematical exploration and sit for the culminating exams. Students who earn qualifying scores may be eligible for college credit.

Grade 12: Financial Applications (NGPF)

Financial Applications is a course offered to 12th grade students who elect to be Diploma Program course candidates and not full Diploma Program candidates. Units of study are adapted from the Next Generation Personal Finance (NGPF) curriculum. Topics include but are not limited to paying for college, behavioral economics, budgeting, and the banking system (checking and savings). 

Course Offerings

Mathematics in the Middle Years Program (MYP Years 1 – 5)

MYP Year 1 Mathematics (Accelerated Grade 6 IM):

• The course begins with a study of area and surface area concepts. Then students are introduced to ratios, rates, and percentages using visual representations such as number line diagrams, tape diagrams, and tables. Student understanding of these concepts expands by exploring fraction and decimal representations of rational numbers. They explore sums, differences, products, and quotients using intuitive methods and efficient algorithms.
• Next, students are introduced to algebraic equations and expressions including finding solutions for linear equations in one variable and basic equations involving exponents. They learn about rational numbers less than zero expanding their understanding of arithmetic to negative numbers. 
• Student understanding of ratios and rates combined with a basic understanding of equations leads students to study proportional relationships with special emphasis on circumference and area of a circle as an example and nonexample of proportional relationships. A brief study of data and statistics concludes the new concepts in the course.

MYP Year 2 Mathematics (Accelerated Grade 7 IM):

• Students begin the course with transformational geometry. They study rigid transformations and congruence, then scale drawings, dilations, and similarity (this provides background for understanding the slope of a line in the coordinate plane).
• Next, they expand their ability to work with linear equations in one and two variables and deepen their understanding of equivalent expressions.
• They then build on their understanding of proportional relationships from the previous course to study linear relationships. They express linear relationships using equations, tables, and graphs, and make connections across these representations.
• Building on their understanding of a solution to an equation and inequalities in one or two variables, they understand what is meant by a solution to a system of equations in two variables.
• They apply their understanding of linear relationships to contexts involving data with variability. They learn that linear relationships are an example of a special kind of relationship called a function.
• They extend the definition of exponents to include all integers, and in the process codify the properties of exponents. They learn about orders of magnitude and scientific notation in order to represent and compute with very large and very small quantities.
• They encounter irrational numbers for the first time and informally extend the rational number system to the real number system, motivated by their work with the Pythagorean Theorem.
• The last unit offers students an optional opportunity to synthesize their learning from the year using a number of different applications.

MYP Years 3 and 4 Algebra I (Full Year | 1 Credit | IM): 

• Students begin to expand their understanding of linear equations, inequalities, and systems of linear equations and inequalities. Students write, rearrange, evaluate, and solve equations and inequalities, explaining and validating their reasoning with increased precision. 
• Next, students study functions, continuing the work begun in grade 7. Over the next few units, they deepen their understanding of functions and deepen their ability to represent, interpret, and communicate about them—using function notation, domain and range, average rate of change, and features of graphs. They also see categories of functions, starting with linear functions (including their inverses) and piecewise-defined functions (including absolute value functions), followed by exponential and quadratic functions. For each function type, students begin their investigation with real-world and mathematical contexts, look closely at the structural attributes of the function, and analyze how these attributes are expressed in different representations. 
• Next we take a close look at quadratic equations.  Students extend their ability to use equations to model relationships and solve problems. They develop their capacity to write, transform, graph, and solve equations—by reasoning, rearranging equations into useful forms, and applying the quadratic formula. In solving quadratic equations students encounter rational and irrational solutions, providing an opportunity to deepen their understanding of the real number system.
• We end with one-variable statistics, building on ideas from middle school. Starting with data collection and analysis sets a tone for the course of understanding quantities in context. Gathering and displaying data, measuring data distribution, and interpreting statistical results encourages students to collaborate, communicate, and explore new tools and routines. They then take these insights to a unit on two-variable statistics, where they extend their prior knowledge of scatter plots and lines of best fit. Students use residuals and correlation coefficients to assess linear models, interpret quantitative data, and distinguish correlation and causality. 

MYP 4 Algebra II (Full Year | 1 Credit | IM): 

• Students begin the course with a study of sequences, which is also an opportunity to revisit linear and exponential functions. Students represent functions in a variety of ways while addressing some aspects of mathematical modeling. This work leads students to analyze situations that are well modeled by polynomials before pivoting to study the structure of polynomial graphs and equations. 
• Next, students extend exponent rules to include rational exponents. Students solve equations involving square and cube roots before developing the idea of i, a number whose square is -1. Building on rational exponents, students return to their study of exponential functions and establish that the property of growth by equal factors over equal intervals holds even when the interval has non-integer length. Students use logarithms to solve for unknown exponents, and are introduced to the number e and its use in modeling continuous growth. 
• Students then learn to transform functions graphically and algebraically. In previous courses and units, students adjusted the parameters of particular types of models to fit data. In this course, students consolidate and generalize this understanding.
• Three real world application summative projects are completed during the first, second, and fourth units of study. While students have opportunities to engage in aspects of mathematical modeling during class activities, the summative projects allow students to engage more deeply with the content, making connections to the real world.  

MYP Year 5 Geometry (Full Year | 1 Credit | IM): 

• Students begin the year with a study of constructions and rigid transformations. They explore the properties and definitions of rotations, reflections, and translations, and learn to make and justify precise geometric constructions.
• Students examine the relationships between shapes through the lenses of congruence and similarity. They analyze corresponding parts of figures, justify congruent relationships, and investigate dilations and proportional reasoning leading to triangle similarity theorems and applications.
  Trigonometry and coordinate geometry are used together to explore and prove properties of geometric figures. Students apply trigonometric ratios to right triangles and use algebraic tools—such as distance, midpoint, and slope formulas—to investigate and justify properties of triangles and quadrilaterals in the coordinate plane.
• In the solid geometry unit, students revisit three-dimensional shapes learned in middle school and deepen their understanding of cross-sections, surface area, and volumes of additional 3D figures. As part of the unit, students also design and create a 3D model, applying their knowledge in a hands-on project.
• We end the year with the circles unit, where students investigate properties of circles including central and inscribed angles, chords, arcs, and sectors. They develop a strong understanding of circle theorems and formulas, and apply these concepts to solve a variety of complex problems, connecting geometry to real-world contexts.

Mathematics in the Diploma Program (DP Years 1 and 2)

Applications and Interpretation (2 Full Years | 2 Credits):  

• The beginning of 11th grade starts with Geometry & Trigonometry where students build on concepts learned the previous year in their 10th grade geometry class. The unit culminates in a real-world application project where students are able to see how math informs decision-making in urban planning. 
• Students then review linear and quadratic functions and explore their applications. Next, students review sequences/series and compound interest, and they learn about annuities/amortization in the form of loans and investments. Students engage in a life finances project where they explore some of the big ideas such as budgeting, investing, and taking out a loan. 
• Next students explore exponential, logarithmic, and sinusoidal functions as well as their applications in modeling real-world phenomena. 11th grade culminates in an introduction to univariate and bivariate statistics, with students engaging in a mini statistical analysis that serves as the foundation for their senior year mathematical exploration.
• The beginning of 12th grade DP2 math starts with a review of the statistical topics covered in DP1 and then delves further into more complex analyses. Students learn about probability as well as random variable distributions including binomial and normal distributions. The unit finishes with students learning about hypothesis testing including t-tests and chi-squared tests. Students then complete a statistical analysis as their mathematical exploration for the IB requirement.
• The spring semester of senior year begins with an introduction to Calculus where students learn basic differentiation and integration techniques. In April, students review the content learned over the two-year course in preparation for the IB exams held in the beginning of May.

Mathematics Elective (Grade 12)

Financial Applications (Full Year | 1 Credit | NGPF):

The Financial Applications course covers all of the essential personal finance topics necessary to become financially capable adults. Topics include racial discrimination in finance, preparing for college and career, behavioral economics, budgeting, and the banking system. By the end of this course, students will have a thorough understanding of personal finance topics and be prepared to handle the financial responsibilities that exist after graduation. 

Instructional Approach

Our teaching emphasizes student-centered learning through the IM curriculum’s “Notice and Wonder” approach, where students explore mathematical concepts through rich, open-ended problems before formal instruction.

Key Strategies:

• Collaborative Learning: Students work in diverse groups to solve complex problems and share multiple solution strategies
• Mathematical Discourse: Daily opportunities for students to explain their reasoning and critique others’ mathematical thinking
• Culturally Responsive Teaching: Problems and contexts that reflect our diverse school community and global perspectives
• Differentiated Support: Multiple entry points for problems, with scaffolding and extension opportunities for all learners
• Technology Integration: Strategic use of graphing calculators, Desmos, and other digital tools to enhance understanding

Assessment Philosophy: 

As an IB school, our Mathematics Department embraces a comprehensive assessment philosophy that honors both the journey and destination of mathematical learning. We utilize a balanced approach that includes formative assessments to guide instruction and support student growth, alongside summative evaluations that measure mastery of key concepts and skills. Our assessments align with IB principles by emphasizing conceptual understanding, mathematical communication, and real-world application rather than rote memorization or procedural fluency alone. Students are assessed through diverse methods including problem-solving tasks, mathematical investigations, collaborative projects, and reflective portfolios that demonstrate their thinking processes and mathematical reasoning. This multifaceted approach ensures that every student can showcase their mathematical understanding in ways that align with their strengths while meeting the rigorous standards of the IB program, ultimately preparing them to become confident, globally-minded mathematical thinkers.

Student Work & Achievements

Recent Projects:

• Road Trip project: MYP Year 2 students are given a random budget and asked to design their own road trip, calculating costs such as gas, hotel and food and creating an inequality to mathematically represent their situation. 
• Poster Project: MYP Year 2 students choose a design that means something to them and apply geometric transformations on graph paper to reflect their learning.