# The Herald

## Hoboken Public School District - Mathematics Program

Dear Parents and Guardians,

Recently, the Hoboken Public School District's Office of Curriculum and Instruction shared a Special Edition of The Herald highlighting our English language Arts Program. Today, we are excited to share this Special Edition of The Herald that highlights our focused work in the area of Mathematics. As we explore the experiences of our students from Kindergarten through Grade 12, you will be able to see how our students actively participate in mathematics education. Our goal is to provide our teachers and students with a perfect blend of curriculum and instructional materials for an optimal learning experience. We also recognize the necessity of equipping our students with the fundamental skills required to excel in the 21st-century global economy.

In this Special Edition of The Herald, you will be able to learn more about the District’s participation in upcoming challenges, our comprehensive curriculum, our instructional framework and approach to teaching math, and how we differentiate instruction for our students.

When reading through this resource, you will find:

District Participation in upcoming Challenges

NJIT eSTEM Challenge

NJ Math League

International Olympiads in Math

**Comprehensive Curriculum in Grades K-12**

Introduction

Problem Solving Skills: Mathematical Practices in the Curriculum

Investigations 3 in Grades K-5

enVision Math in Grades 6-8

Desmos Classroom in Grades 6 - Algebra 1

Project Lead the Way in Grades 6 - 8

enVision Math in HS

Pre-AP Curriculum

High School Math: Courses and Electives

**District Math Tools to Challenge & Support Students**

Individualized Learning Pathway Period

Johns Hopkins Center for Talented Youth Spring Math Program

IXL Math Skills Plans

LinkIt!

Passport to Learning Programs

Splash into Math and Literacy Summer Program

**Family Math Resources**

It is our hope that this Special Edition of The Herald proves helpful, serving not only as a resource but also as a tool for communication both at home and with your child's school. We are here to answer any questions that you may have.

Sincerely,

Dr. Christine Johnson, Superintendent of Schools

Ms. Sandra Rodriguez-Gomez, Assistant Superintendent of Schools

Ms. Donna D’Acunto, K-12 Supervisor of Math, Science & STEM

## District Honors and Participation in Upcoming Competitions

The Hoboken Public School District is **outperforming**** **the State of New Jersey in Mathematics on the New Jersey Student Learning Assessments. And, the Hoboken Public School District is the **highest** performing traditional K-12 district in Hudson county in Mathematics.

** NJIT eSTEM Challenge (Grade 5)**:

** **NJIT's Center for Pre-College Programs is proud to announce its 3rd Annual Elementary STEM challenge. The eSTEM Challenge is an annual innovation competition intended to introduce elementary students to the engineering design process and spur interest in Science, Technology, Engineering, and Math (STEM). The focus of the challenge is on engineering and design. This year's challenge will feature an "Emerging Technology" question (involving topics such as Big Data, Artificial Intelligence, Virtual Reality, or Internet of Things) that student teams will solve using the Engineering Design Process (EDP). Students will be using a micro:bit to solve this year’s problem and requires our student competitors to use their computer programming skills to complete the challenge. Student teams will design, build, and demonstrate their working models. Students will be scored in four categories: I.) Engineering Design Device Demonstration, II.) Oral Presentation, III.) Game Show Challenge, IV.) Engineer’s Logbook. The statewide competition is held in March at the NJIT Campus. Good Luck to our 2 teams!

__NJ Math League Competition in Grades 4 - Algebra I:__

The Hoboken Public Schools will enter into the NJ Math League Contest this year. Math contests give students an educationally enriching opportunity to participate in an academically-oriented activity and to gain recognition for mathematical achievement. The main goal is educational and to promote enjoyment and the study of mathematics through these organized contests in grades 4 - Algebra I. These contests help to enrich mathematics programs and each contest covers topics appropriate to the contest grade level. These well-written questions cover a variety of difficulty ranges and involve topics of interest to above-average students. The key is to encourage students to enjoy a challenge, learn from it, and to find problem-solving discussions stimulating. This challenge is what prompts many students to enjoy puzzle books. The enrichment provided is a positive experience for students.

**International School Olympiad in Math (CTY in Grades 2-8): **

The International School Olympiads, a global academic competition, offers a unique opportunity for students in grades 1-8 to showcase their knowledge and skills in various subjects. These subjects include mathematics, English, science, general knowledge, reasoning, and computer studies. The Olympiads are designed to encourage critical thinking, problem-solving, and a passion for learning in a fun and challenging manner. Students will be showcasing their skills in the following areas: I) Logical Reasoning: Patterns, Odd One Out, Measuring Units, Geometrical Shapes, Spatial Understanding, Grouping, Analogy, Ranking, and Problems based on Figures; II) Mathematical Reasoning & Everyday Math: Numerals, Number Names, Number Sense (2-digit numbers), Addition, Subtraction, Lengths, Weights, and Comparisons, Time, Money, Geometrical Shapes and Solids, and Patterns; and III) High-Order Thinking Questions.

## Comprehensive Curriculum in Grades K-12

Here in the Hoboken Public Schools, our Mathematics program is designed to provide a comprehensive and developmentally appropriate approach to mathematics education in each of the grade bands, K-5, 6-8, 9-12, while catering to the diverse needs and abilities of students at each stage of their academic journey. Our Elementary program focuses on building a strong foundation in basic math concepts and skills, and problem-solving strategies while fostering a positive attitude towards learning mathematics. As students enter middle school the programs are designed to build upon the foundational skills acquired in earlier grades while introducing more complex mathematical concepts. The programs focus on developing critical-thinking, problem-solving abilities, and a deeper understanding of mathematical principles. As students begin taking high school courses, our programs are designed to provide a comprehensive and rigorous education in mathematics, preparing students for higher education or entry into the workforce. Our program offers a variety of courses that cater to diverse interests and career goals, while ensuring that students meet or exceed national or state standards.

Here are some of the key features of our math program for students in grades K-12:

**Curriculum and Standards**

In K-12, our curriculum follows a logical and sequential progression of mathematical concepts, starting with foundational skills and gradually increasing in complexity; revisiting and reinforcing previously learned concepts while introducing new and more advanced topics. Our curriculum is in alignment with the __New Jersey Student Learning Standards__ to ensure consistency and progression and rigor in content.

**Communication & Reasoning**

In K-5 there is encouragement of verbalizing mathematical thinking through "math talk" to enhance communication skills. In grades 6-12, there is an emphasis on clear and effective communication of mathematical reasoning, both in written and verbal forms.

**Problem-Solving**

In K-5, there’s an emphasis on developing critical-thinking and problem-solving skills through various math problems and scenarios. In grades 6-12, we encourage abstract thinking and the ability to apply mathematical concepts to real-world situations’. There is also the integration of more complex problem-solving scenarios to promote critical-thinking skills such as math in engineering and scientific contexts to enhance practical understanding.

**Representations of the Content**

In K-5, our program is built on learning through the integration of hands-on activities and the use of manipulatives to help students develop a concrete experience, followed by a pictorial understanding, and finally the abstract concept. In 6-12, these three modalities are used as needed to facilitate the teaching and learning of the content.

**Collaboration**

In grades K-12, we provide students with opportunities for collaborative learning and group activities and projects to encourage teamwork and communication skills.

**Project - Based Learning**

Project-based learning opportunities in K-12 incorporate the application of math concepts to real-life situations, making learning more relevant and engaging for students.

**Technology**

In K-12, we incorporate age-appropriate educational technology tools, software, interactive games and simulations to enhance learning experiences that make learning math interactive and fun.

**Differentiation**

In K-12, we recognize the diverse learning styles and abilities of our students and implement strategies for differentiated instruction to accommodate varying student needs. We include challenging and accelerated learning opportunities of advanced content for students seeking these types of activities as well as targeted support and intervention for students who may be struggling with certain concepts.

**Math Fact Fluency**

In K-12, the district works toward the development of our students’ fluency in the appropriate prerequisite math skills at each grade level. This enables students to focus on problem-solving within a given context versus having to focus on the computation as well as the problem-solving components of a problem.

M**onthly Extended Constructed Response Practice Questions**

In K-12, the district further develops students problem-solving and critical-thinking skills through the implementation of Monthly Extended Constructed Response Types of Problems, that are based on multi-step style questions, which align to both the New Jersey Student Learning Standards as well as our math curriculum pacing.

**Monitoring of Learning**

In K-12, we use regular assessment strategies, including both formative assessments to inform instruction and summative assessments to measure overall student understanding and proficiency.

**Home to School Connection**

Establishing a strong home-school connection is an important factor in a child’s learning and developmental journey. We provide regular communication with parents, providing information about the math curriculum and ways to support the child's learning at home.

### The Standards for Mathematical Practice

The Standards for Mathematical Practice describe the habits of mind and behaviors that students should develop to become proficient in mathematics. These practices are designed to be integrated into the teaching and learning of mathematics and provide a framework for developing mathematical proficiency.

**Make sense of problems and persevere in solving them. **

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

**Reason abstractly and quantitatively. **

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

**Construct viable arguments and critique the reasoning of others. **

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

**Model with mathematics. **

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

**Use appropriate tools strategically. **

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

**Attend to precision. **

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

**Look for and make use of structure. **

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7×8 equals the 7×5+7×3 , in preparation for learning about the distributive property. In the expression *x*2+9*x*+14, older students can see the 14 as 2×7 and the 9 as 2+7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5−3(*x−y*)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers *x *and *y*

**Look for and express regularity in repeated reasoning: **

Mathematically proficient students notice if calculations are repeated and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y−2) / (x−1) = 3. Noticing the regularity in the way terms cancel when expanding (x−1)(x+1), (x−1)(x2+x+1), and (x−1)(x3+x2+x+1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

### Investigations 3: Math Grades K-5

Investigations in Number, Data, and Space our K–5 mathematics curriculum, that is designed to engage students in making sense of mathematical ideas. This third edition of the curriculum, Investigations 3, is built on the strong foundation of the first two editions and the six major goals that have guided the development of the curriculum. The curriculum is designed to: support students to make sense of mathematics and learn that they can be mathematical thinkers; focus on computational fluency with whole numbers as a major goal of the elementary grades; provide substantive work in important areas of mathematics — rational numbers, geometry, measurement, data, and early algebra — and the connections among them; emphasize reasoning about mathematical ideas; communicate mathematics content and pedagogy to teachers; and engage the range of learners in understanding mathematics. There are three guiding principles that were touchstones for the Investigations team as they approached both students and teachers as agents of their own learning: I) Students have mathematical ideas. Students come to school with ideas about numbers, shapes, measurements, patterns, and data. If given the opportunity to learn in an environment that stresses making sense of mathematics, students build on the ideas they already have and learn about new mathematics they have never encountered. They learn mathematical content and develop fluency and skill that is well grounded in meaning. Students learn that they are capable of having mathematical ideas, applying what they know to new situations, and thinking and reasoning about unfamiliar problems. II) Teachers are engaged in ongoing learning about mathematics content, pedagogy, and student learning. The curriculum provides materials for professional development — to be used by teachers individually or in groups — that supports teachers’ continued learning as they use the curriculum over several years. The Investigations curriculum materials are designed to be used as much as a dialogue among teachers as a core content for students. III) Teachers collaborate with the students and curriculum materials to create the curriculum as enacted in the classroom. The only way for a good curriculum to be used well is for teachers to be active participants in implementing it. Teachers use the curriculum to maintain a clear, focused, and coherent agenda for mathematics teaching. At the same time, they observe and listen carefully to their students, try to understand how their students are thinking, and make teaching decisions based on these observations.

**Investigations 3** is fully aligned to the content and practice standards of the __New Jersey Student Learning Standards__ (NJSLS). The culmination of over 25 years of research and development aimed at improving the teaching and learning of elementary mathematics, *Investigations 3* maintains and builds on the philosophy and pedagogy of the first and second editions, and continues to be based on the work of real teachers and students. *Investigations 3* was developed at TERC and is based in part on work supported by the National Science Foundation. TERC is a nonprofit research and development organization whose mission is to improve mathematics, science, and technology teaching and learning. Founded in 1965, TERC is located in Cambridge, MA. TERC staff includes researchers, scientists, and mathematicians, and curriculum and professional development specialists who ground their work on inquiry-based approaches that deepen all learners’ understandings.

When the district was determining the best path forward in terms of a curricular resource that would engage our K-5 students, it was essential for us to find materials that supported inquiry-based learning. This type of learning represents an educational approach that activates curiosity, promotes problem-solving and hands-on learning experiences for students. We know that young children learn best through exploration, play, and hands-on experiences and by integrating these methodologies, we have been able to help foster a strong foundation in math and a positive attitude towards learning.

**Investigations 3** has been our primary curricular resource in K-5 since its implementation in 2018, which has been put into practice with full fidelity since the beginning.

### Mathematical Practices in Investigations 3

When the 3rd edition of Investigations was being drafted, the authors were committed to making the Mathematical Practices an integral part of what students would learn and do. The practices were embedded in the approach to the topics, as part of learning math itself, as targeted, intentional, and planned instruction, and continually reflected upon at each stage of learning. Learning the mathematical practices as a student happens in two ways: I) The curriculum has the eight practices embedded throughout the eight units of study with a focus on two practices in each unit. By doing this, students get a chance to intentionally focus on each of the practices twice per year. II) Teacher’s are the facilitators of how students learn to apply the mathematical practices. They play a critical role in helping students engage in these meaningful experiences by asking guiding questions and assessing students' understanding of these critical-thinking activities.

### Key Features of Investigations 3

Places a strong emphasis on developing students' problem-solving skills through real-world scenarios and engaging mathematical investigations

Utilizes an inquiry-based learning model, encouraging students to explore mathematical concepts through questioning, discussion, and hands-on activities.

Aims to provide a mathematically rigorous curriculum while fostering a deep understanding of mathematical concepts.

Focuses on building a conceptual understanding of mathematical ideas rather than relying solely on memorization of procedures. It aims to develop a solid foundation for future learning.

Involves collaborative learning experiences, where students work together to solve problems, discuss strategies, and share their thinking.

Follows a spiral approach, revisiting and building upon mathematical concepts in multiple grades to reinforce and deepen understanding over time.

### enVision Mathematics: Grades 6-8

**enVision® Mathematics 6–8** was designed to provide students with rich opportunities to build understanding of important new mathematical concepts, develop fluency with key skills necessary for success in algebra, and to gain proficiency with the habits of mind and thinking dispositions of proficient mathematics students. To achieve these goals, the program includes content-focused lessons, 3-Act Mathematical Modeling lessons, STEM projects, and Pick a Project. The major goal in developing **enVision® Mathematics 6–8** was to create a middle grades program that embodies the philosophy and pedagogy of the **enVision** series and was adapted for the middle school teacher and learner. **enVision® Mathematics 6–8** embraces time-proven research principles for teaching mathematics with understanding. One understands an idea in mathematics when one can connect that idea to previously learned ideas (Hiebert et al., 1997). So, understanding is based on making connections, and **enVision® Mathematics** was developed on this principle.

There are many ways to organize a curriculum. However, when the goal is to develop conceptual understanding, followed by procedural fluency and application, the challenge is to organize the curriculum in a way that best promotes mathematical content connections so that students do not view mathematics as small, disconnected pieces of content. **enVision® Mathematics 6–8** was organized to provide a coherent and comprehensive pathway to algebra. This pathway ensures that all students are college- and career-ready when they graduate from high school. The program focuses first and mostly on the key concepts and skills that make up that pathway. In the middle grades, that means an emphasis on proportional reasoning, numbers and computation, and algebra and functions, leading to an understanding of linearity. As part of this pathway to algebra, students revisit key concepts in later topics to highlight the importance of these concepts throughout students’ study of middle grades mathematics.

Another layer in developing **enVision® Mathematics 6–8** relates to the habits of minds and dispositions of proficient math thinkers. Throughout the program, in every lesson, students are provided with opportunities to think about these essential practices and to demonstrate their proficiency with them. There are also math modeling lessons, called 3-Act Mathematical Modeling, that provide regular practice with mathematical modeling, an important math practice.

Take a look at the EdReports.org evaluation in which **enVision® Mathematics 6–8** was highly rated across the three gateways: Focus & Coherence, Rigor & Mathematical Practices, and Usability.

When the district was determining the best curricular resource that would engage our 6-8 students, it was essential for us to find materials that supported student-centered learning. This type of learning is an educational approach that places the student at the heart of the learning process. In this model, the focus is on tailoring education to the individual needs, interests, and abilities of each student. Rather than relying solely on traditional teacher-led instruction, student-centered learning empowers students to take an active role in their education. At the middle and high school level, we know that students enjoy learning from their peers. Our resources integrate opportunities for students to engage in collaborative experiences, explore new concepts, discover, think-critically, and be creative to gain a deeper understanding of the subject matter.

**enVision® Mathematics 6–8** has been our primary curricular resource since its implementation in 2020, which has been put into practice with full fidelity since the beginning.

### Desmos Math: Grades 6 - Algebra I

The mission of **Desmos Math 6-A1** is to help every student learn math and love learning math. Based on the innovative problem-based K-12 curriculum from Illustrative Mathematics® and Open Up Resources, students will learn by interacting with dynamic and interactive mathematical representations and illustrations of the world through a digital learning experience. Students will represent their developing ideas with sketches, text responses, card sorts, number responses, multiple choice, and be able to share their ideas with their classmates.

**Desmos Math 6-A1** believes that every student is brilliant, but not every student feels brilliant in math class—particularly students from historically excluded communities. They have designed the program to put students’ ideas at its center. Lessons pose problems that invite a variety of approaches, and the technology helps teachers celebrate and develop all of that interesting thinking in their classrooms. These student-centered lessons empower students to explore new ideas, and our teacher dashboard helps teachers bridge those ideas together. Whether teachers are observing student learning on the lesson summary page or guiding productive discussions with the “conversation toolkit”, the facilitation tools make teaching more effective and more fun.

Take a look at the __EdRepo__r__ts.org__ evaluation in which **Desmos Math 6–8 **was highly rated across the three gateways: Focus & Coherence, Rigor & Mathematical Practices, and Usability.

**Desmos Math 6-A1 **has been a supplementary curricular resource since its implementation in 2023.

### Project Lead the Way: Math Grades 6-8

The philosophy of **Project Lead the Way** is that all students need access to real-world, applied learning experiences that empower them to gain the skills they need to thrive in college career and beyond. They also believe that teachers play an immeasurable role in empowering students so this program provides teachers with professional development, support, and resources to devote more time to inspiring students.** ****PLTW **uses the APB - activity-, project-, and problem-based (APB) instructional design centers on hands-on, real-world activities, projects, and problems that help students understand how the knowledge and skills they develop in the classroom may be applied in everyday life. The APB approach scaffolds student learning through structured activities and projects that empower students to become independent in the classroom and help them build skill sets to apply to an open-ended design problem. This approach provides students with unique opportunities to work collaboratively, identify problems, apply what they know, persevere through challenges, find unique solutions, and lead their own learning. Students complete a designated task(s) that demonstrates outlined knowledge and/or skills of the specific standard or objective. Some of the transportable and technical skills for career readiness that students will acquire are: problem-solving, critical and creative thinking, collaboration, communication, and ethical reasoning and mindset. Research has found them to be some of the most demanded and valued skills by employers. Research also demonstrates that **PLTW** students outperform their peers in school, are better prepared for post-secondary studies, and are more likely to consider careers in STEM compared to their non-**PLTW** peers. Students find **PLTW** programs relevant, inspiring, engaging, and foundational to their future success.

For Math in grades 6-8, we have embedded project-based learning as the last unit of study in grades 6, 7, & 8. We use the following **Project Lead the Way** Modules to accomplish this:

**Grade 6: Green Architecture - **Today’s students have grown up in an age of “green” choices. In this unit, students learn how to apply this concept to the fields of architecture and construction by exploring dimensioning, measuring, and architectural sustainability as they design affordable housing units using Sketch-Up architectural design software. At the end of the unit, students will build a model shed using balsa wood.

**Grade 7: Automation and Robotics** - Students are given the opportunity to combine mechanisms with input and output devices to automate the mechanisms. Construction and programming skills are layered, and projects and the problem provide students the opportunity to connect their learning throughout the lessons in the unit. Students take on the role of interns, and work in teams to identify design requirements and create prototypes to meet the needs of clients. They also explore different aspects of automation and robotics, and experience how solving real-life problems involves the teamwork of mechanical engineers, software developers, and electrical engineers. Students use the metal VEX kits to build and create for this unit.

**Grade 8: App Creator-** This unit will expose students to computer science by computationally analyzing and developing solutions to authentic problems through mobile app development, and will convey the positive impact of the application of computer science to other disciplines and to society. Students will customize their experience by choosing a problem that interests them from the areas of health, environment, emergency preparedness, education, community service, and school culture. Because problems in the real world involve more than one discipline, the unit will introduce students to biomedical science concepts as they work on solutions for the specific problems they choose to tackle. Students use the MIT App Inventor software and simulator to complete these tasks.

**Project Lead the Way** Gateway** **has been a supplementary curricular resource since its implementation in 2018.

### enVisions HS (A|G|A): Math Grades 9-12

**enVision Algebra I, Geometry, and Algebra II** was designed to provide students rich opportunities to build understanding of important new mathematical concepts and develop fluency with key skills as described in the Standards for Mathematical Content, and to gain proficiency with the habits of mind and thinking dispositions described in the Standards for Mathematical Practice. To achieve these goals, the program includes content-focused lessons, Mathematical Modeling in 3 Act tasks, and enVision™STEM projects. All three of these instructional activities are integral to helping students achieve success.

One major goal in developing **enVision A|G|A** was to create a high school mathematics program that reflects the latest research in mathematics education and learning theory and supports all learners on their pathway to college- and career-readiness. To achieve this goal, **enVision** developed a brand new program built from the ground up around three foundational principles: I) A balanced pedagogy- Research has shown that teaching for understanding requires equal attention to helping students develop deep understanding of concepts, fluency with important processes and skills, and the ability to apply these concepts and skills to solve real-world and mathematical problems. The organizing structure and the lesson features of **enVision A|G|A** provides students with appropriate and frequent opportunities to develop understanding and proficiency, and apply these new concepts and skills to solve problems. II) A focus on visual learning. Recent research has found that powerful learning occurs when students use different areas of the brain, specifically the area that governs symbolic thinking and the area that focuses on visual thinking. **enVision A|G|A** makes extensive use of visuals to encourage students to use these different parts of the brain, resulting in powerful learning. III) A focus on effective teaching and learning. Recent research has also shown that students make significant academic gains when they explore “worthwhile tasks” and engage in meaningful mathematical discourse using mathematical language. Research also suggests that teachers need to create learning environments that facilitate and encourage this meaningful discourse. Every lesson in **enVision A|G|A** opens with a worthwhile task, a student-centered activity that requires students to think critically and construct sound mathematical arguments to defend their reasoning and their solutions. b was designed with a particular focus on mathematical modeling and the mathematical modeling process. This focus can be seen in two key features, the Mathematical Modeling in 3 Acts activities found in each topic of the program and the Model & Discuss tasks that are found at the start of many lessons.

The EdReports.org evaluation in which **enVision A|G|A** was highly rated across the three gateways: Focus & Coherence, Rigor & Mathematical Practices, and Usability.

When the district was determining the best curricular resource that would engage our high school students, it was essential for us to find materials that supported student-centered learning. This type of learning is an educational approach that places the student at the heart of the learning process. In this model, the focus is on tailoring education to the individual needs, interests, and abilities of each student. Rather than relying solely on traditional teacher-led instruction, student-centered learning empowers students to take an active role in their education. At the middle and high school level, we know that students enjoy learning from their peers. Our resources integrate opportunities for students to engage in collaborative experiences, explore new concepts, discover, think-critically, and be creative to gain a deeper understanding of the subject matter.

**enVision A|G|A** has been our primary curricular resource since its implementation in 2018, which has been put into practice with full fidelity since the beginning.

### Pre-AP Curriculum HS (A|G|A): Math Grades 8-10

With the College Board **Pre-AP** Curriculum, the program’s objective is to offer every student access to a high-quality education that prepares them for success in high school and beyond. The program also provides educators with engaging resources and targeted assessments to support student success with grade-level expectations. **Pre-AP** challenges students to build critical-thinking skills through these shared principles: Close Observation and Analysis- Students carefully observe a data set, text, image, or problem, capturing relevant details before attempting to explain, analyze, or evaluate. Evidence-Based Writing: Students learn to craft precise sentences before progressing to longer forms of writing, applying these skills as they craft claims, develop arguments, and provide explanations. Higher-Order Questioning: Students engage with questions that are elevated beyond simple recall as they make predictions, synthesize, evaluate, and compare, learning that deep questions lead to deeper understanding. Academic Conversation: Students become active participants in their own learning through frequent opportunities to compare, critique, debate, and build upon others' ideas, recognizing that all voices, including their own, deserve to be heard. With **Pre-AP**, students own their learning. They learn to think for themselves, defend arguments, and solve real-world problems. **Pre-AP** courses are mapped back from AP courses giving students a head start on the skills and content needed to succeed in AP. All **Pre-AP** Courses share common language and strategies so interdisciplinary skills are continually reinforced.

Within the past few years, the College Board has created a **Pre-AP** program as a way to introduce all high school students to the skills and resources they'll be using in college classes. It will also broaden access to AP testing. **Pre-AP** classes were created to ensure that students come into AP classes well-prepared for both the content and the expectations of the AP program. If you take one of these courses, you’ll have the opportunity to develop the necessary skills in a lower-stakes environment, compared with AP courses. The Hoboken Public Schools has offered these courses since 2021.

### Computer Science: Embedded within Math and Science Grades K-8

Computer Science education equips students for success in today’s knowledge-based economy by providing equitable and expanded access to a high-quality standards-based education. The New Jersey Student Learning Standards vision for students is to:

Develop and apply computational and design thinking to address real-world problems and design creative solutions

Engage as collaborators, innovators, and entrepreneurs on a clear pathway to success through postsecondary education and careers

Navigate the dynamic digital landscape to become healthy, productive, 21st century global-minded individuals

Participate in an inclusive and diverse computing culture that appreciates and incorporates perspectives from people of different genders, ethnicities, and abilities

In K-5, our students study one unit of Computer Science during the school year. This is embedded within our Project Lead the Way Science Program.

Grade K: Animals and Algorithms

Grade 1: Animated Storytelling

Grade 2: Grids and Games

Grade 3: Programming Patterns

Grade 4: Input/Output Computer Systems

Grade 5: Robotics and Automation

In 6-8, our students study one unit of Computer Science during the school year. This is embedded within our Project Lead the Way Math Program.

Grade 7: Automation & Robotics

Grade 8: App Creator

### High School Math and Computer Science Course Offerings

**Algebra I**

Algebra I is a fundamental course in mathematics that introduces students to basic algebraic concepts and techniques. Algebra 1 serves as a foundational course for more advanced mathematics and is essential for understanding topics in higher-level courses such as Algebra II, Precalculus, Calculus, and beyond. It covers topics such as solving equations and inequalities involving one variable, graphing linear equations and inequalities on the coordinate plane, working with polynomials, including operations like addition, subtraction, multiplication, and division, factoring polynomials, solving systems of linear equations and inequalities, understanding and applying exponents and radicals, analyzing and interpreting linear functions and their graphs. This course is fully aligned to the New Jersey Student Learning Standards.

**Geometry**

Geometry is a branch of mathematics that deals with the study of shapes, sizes, properties, and the relationships between points, lines, angles, surfaces, and solids. It encompasses concepts such as points, lines, planes, angles, triangles, circles, polygons, and three-dimensional figures. Geometry plays a crucial role in various fields such as architecture, engineering, physics, art, and computer graphics. Properties and relationships of geometric figures are studied through inductive reasoning and concepts are applied to real-world applications. While proof is not emphasized, students are introduced to both inductive and deductive reasoning to demonstrate theorems. This course is fully aligned to the New Jersey Student Learning Standards.

**Algebra II**

Algebra II is a continuation of Algebra I, building upon the concepts and skills introduced in the earlier course. It covers more advanced algebraic topics and techniques, including: quadratic equations and functions, rational expressions and equations, exponential and logarithmic functions, systems of equations and inequalities, polynomial functions, conic sections, and matrices and determinants. Algebra II provides students with a deeper understanding of algebraic concepts and prepares them for more advanced mathematics courses like Precalculus, Calculus, and beyond. Included is a review of the content of the state mandated NJGPA. This course is fully aligned to the New Jersey Student Learning Standards.

**Pre-AP Algebra I**

In Pre-AP Algebra 1, students develop a deep understanding of linear relationships emphasizing patterns of change, multiple representations of functions and equations, modeling real world scenarios with functions, and methods for finding and representing solutions of equations and inequalities. Taken together, these ideas provide powerful conceptual tools that students can use to make sense of their world through mathematics. This course is fully aligned to the New Jersey Student Learning Standards.

**Pre-AP Geometry with Statistics**

Pre-AP Geometry with Statistics provides students with a conceptual bridge between algebra and geometry that deepens their understanding of mathematics. The course includes a unit of statistics and probability to support students’ understanding of concepts essential to quantitative literacy. Throughout the course, students solve problems across the domains of Algebra, Geometry, and Statistics. This course is fully aligned to the New Jersey Student Learning Standards.

**Pre-AP Algebra II**

In Pre-AP Algebra II, students solidify and extend the understanding of functions and data analysis developed in prior courses. Students build upon linear, quadratic, and exponential functions as they work to define logarithmic, polynomial, rational, square root, cube root, and trigonometric functions. Quantitative literacy is developed by weaving data sets, contextual scenarios, and mathematical modeling throughout the course. This course is fully aligned to the New Jersey Student Learning Standards.

**Precalculus**

Precalculus begins with the enhancement and further development of several topics introduced in intermediate algebra and trigonometry. Topics include trigonometry, and exponential, logarithmic, and polynomial functions. Students explore more advanced topics of conic sections, sequences, series, and limits. This course provides foundation work for calculus and beyond.

**Statistics**

This course is designed to prepare students for real-world applications and explorations of the many aspects and uses of data analysis. Topics include understanding categorical and quantitative data, exploring relationships between variables, graphical displays, summary statistics, curve fitting, data collection, randomness, probability, and distributions. Students will use a variety of tools and strategies throughout the course including, but not limited to, graphing calculators and spreadsheets. In this course, students will investigate how statistics and probability can be used to make inferences, predictions and decisions in the real-world.

**AP Precalculus**

AP Precalculus centers on functions modeling dynamic phenomena. This research-based exploration of functions is designed to better prepare students for college-level Calculus and provide grounding for other mathematics and science courses. In this course, students study a broad spectrum of function types that are foundational for careers in mathematics, physics, biology, health science, social science, and data science. Furthermore, as AP Precalculus may be the last mathematics course of a student's secondary education, the course is structured to provide a coherent capstone experience and is not exclusively focused on preparation for future courses. The AP Precalculus course is strongly recommended for students planning to take AP Calculus.

**AP Calculus AB**

Advanced Placement Calculus AB is roughly equivalent to a college Calculus course devoted to topics in differential and integral calculus. The AP course covers topics in these areas, including concepts and skills of limits, derivatives, definite integrals, and the fundamental theorem of calculus. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections among these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

**AP Calculus BC (24-25)**

AP Calculus BC is roughly equivalent to both first and second semester college calculus courses. It extends the content learned in AB to different types of equations (polar, parametric, vector-valued) and new topics (such as Euler's method, integration by parts, partial fraction decomposition, and improper integrals), and introduces the topic of sequences and series. The AP course covers topics in differential and integral calculus, including concepts and skills of limits, derivatives, definite integrals, the fundamental theorem of calculus, and series. The course teaches students to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections among these representations. Students learn how to use technology to help solve problems, experiment, interpret results, and support conclusions.

**AP Statistics (24-25)**

Advanced Placement Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.

**Computer Science Essentials**

Computer Science Essentials (CSE) is a full-year course implemented in the 9th grade. This course is an excellent entry point for new high school computer science (CS) learners. Students who have prior CS experiences will find ample opportunity to expand upon those experiences in this course. All students who take CSE will have many opportunities for creative expression and exploration in topics of personal interest, whether it be through app development or connecting computing with the physical world. Though CSE is not an instance of the AP Computer Science Principles course (CSP), it will boost student success for those who continue in the PLTW CSP course. These intentional connections to widely accepted standards will help students gain confidence and reinforce essential concepts and skills that build toward life-long success in the computer science pathways beyond just PLTW courses. PLTW CSE introduces students to coding fundamentals through an approachable, block-based programming language where they will have early success in creating usable apps. As students sharpen their computational thinking skills, they will transition to programming environments that reinforce coding fundamentals by displaying block programming and text-based programming side-by-side. Finally, students will learn the power of text-based programming as they are introduced to the Python® programming language.

**AP Computer Science**

AP Computer Science A is equivalent to a first-semester, college-level course in computer science. The course introduces students to computer science with fundamental topics that include problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data (algorithms), analysis of potential solutions, and the ethical and social implications of computing. The course emphasizes both object oriented and imperative problem solving and design using Java language. These techniques represent proven approaches for developing solutions that can scale up from small, simple problems to large, complex problems. The AP Computer Science A course curriculum is compatible with many CS1 courses in colleges and universities.

**Innovation Science and Technology**

This course equips students with essential tools for innovation, entrepreneurship, and problem-solving in STEM, design, and business. Through a dynamic curriculum, students explore design thinking, entrepreneurship, marketing, patent law, and business management with real-world applications. Throughout the year, students engage in activities developing critical-thinking, creativity, sales skills, and leadership. Emphasis is on fostering an entrepreneurial mindset, risk-taking, and resilience. Students collaborate, interact with professionals, and participate in experiential simulations, design challenges, and competitions. They gain knowledge in entrepreneurship, marketing, and business development, fostering confidence to pursue entrepreneurial aspirations and become effective communicators, problem solvers, and leaders. The program prepares students for college and careers in today's ever changing business world.

**Intro to Engineering Design**

Introduction to Engineering Design (IED) is a high school engineering course in the PLTW Engineering Program. In IED, students explore engineering tools and apply a common approach to the solution of engineering problems, an engineering design process. Utilizing the activity-project-problem-based (APB) teaching and learning pedagogy, students progress from completing structured activities to solving open-ended projects and problems that require them to plan, document, communicate, and develop other professional skills. Through both individual and collaborative team activities, projects, and problems, students apply systems thinking and consider various aspects of engineering design including material selection, human-centered design, manufacturability, assemblability and sustainability. Students develop skills in technical representation and documentation especially through 3-D computer modeling using a Computer Aided Design (CAD) application. As part of the design process, students produce precise 3D-printed engineering prototypes using an additive manufacturing process. Student-developed testing protocols drive decision-making and iterative design improvements. To inform design and problem solutions addressed in IED, students apply computational methods to inform design by developing algorithms, performing statistical analyses, and developing mathematical models. Students build competency in professional engineering practices including project management, peer review, and environmental impact analysis as part of a collaborative design team.

**Launching into Aviation**

This course will provide the foundation for advanced exploration in the areas of flying, aerospace engineering, and unmanned aircraft systems. Students will learn about engineering practices, problem-solving, and the innovations and technological developments that have made today’s aviation and aerospace industries possible. Students will look at the problem-solving practices and innovative leaps that transformed space exploration from the unimaginable to the common in a single generation. Students will also gain historical perspective, starting from the earliest flying machines and leading to the wide variety of modern aircraft and the integral role they play in making today’s world work.

**Exploring Aviation and Aerospace**

This core aerospace and aviation course provides the foundation for students. It is designed to give students a clear understanding of career opportunities in aviation and aerospace and the critical issues affecting the aviation system. Students will also begin to drill down into the various sectors of aviation and the elements that make up the aviation and aerospace ecosystem. They will discover how advances in aviation created a need for regulation and will learn about the promulgation of civil aviation oversight. Students will explore modern innovations and develop their own innovative ideas to address real-world challenges facing the aviation industry. They will be exposed to a variety of career options in aviation and aerospace and take an in-depth look at the opportunities available.

**Introduction to Flight (24-25)**

In the Introduction to Flight Course, students pursuing the pilot and UAS tracks will take a closer look at the aircraft they may one day operate. Students will begin with an exploration of the types of aircraft in use today before going on to learn how aircraft are made and how they fly. Students will understand how aircraft are categorized, be able to identify their parts and learn about aircraft construction techniques and materials. They will gain an in-depth understanding of the forces of flight—lift, weight, thrust, and drag—including how to make key calculations. They will then touch on aircraft design, looking at stability, aircraft controls, and maneuvering flight. The course will conclude with a focus on career skills related to these topics.

**Aircraft Systems and Performance (24-25)**

In the Aircraft Systems and Performance course, students in the UAS and Pilot tracks will take an in-depth look at the systems that make manned and unmanned aircraft work as well as the instrumentation powered by those systems. Beginning with aircraft powerplants and fuel systems, students will learn about the different options available and how they affect aircraft design and performance. They will go on to explore other key aircraft systems, including electrical, pitot-static, and vacuum systems. Throughout, they will learn about the flight instruments associated with each system and how to identify and troubleshoot common problems. This unit also covers airplane flight manuals, the pilot's operating handbook, and required aircraft documents. Finally, students will learn about the factors that affect aircraft performance and how to determine critical operating data for aircraft.

## District Math Tools to Challenge & Support Students

### Individualized Learning Pathways: Grades K-8

Individualized Learning Pathways (ILP) are defined by progressive and rigorous standards-based programming and take place during the ILP Period. The purpose of the ILP Period is to provide all children with an opportunity to engage in independent and customized learning that best support their unique learning journey. Each marking period, based on district assessments in the areas of Math and ELA, students will be flex-grouped in alignment to identified priority standards. While in this academic school year (in K-5) the instructional focus has been placed on literacy during the ILP period, next year we look forward to our traditional schedule of differentiating for both Math and ELA during this period. This means students will receive an additional 45-minutes of math or literacy instruction in addition to their 90-minute Math or ELA block on their designated ILP period days. In 6-8, we currently provide two ILP periods a week, which are built into students' individual schedules and this is where instruction is personalized to what students need in the area of math, which could be extension activities or reteaching activities.

### Johns Hopkins Center for Talented Youth Spring Math Courses: Grades 2-8

During the Individualized Learning Pathway (ILP) period, students in Grades 2 - 8 who have qualified to participate in the Johns Hopkins Center for Talented Youth (CTY) Math programming engage in a variety of math course offerings that address their specific strengths and interests. Johns Hopkins CTY believes in researching and advancing ways to identify and nurture academically talented learners. CTY furthers research, guides educators and families and inspires students from diverse communities and backgrounds to pursue their intellectual passions and create the world of tomorrow.

### LinkIt! in Grades K-12

Students in Grades K-12 participate in the **LinkIt! **New Jersey Student Learning Standards Benchmark. Students will engage with this assessment in the Fall, Winter, and in the Spring. Unlike traditional tests that measure mastery of concepts and skills after students have received instruction, the **LinkIt! **Benchmarks provide immediate feedback and serve as an assessment FOR** **learning, not OF learning. After each of the three administrations, parents/guardians will receive an Individual Student Report detailing your child's current progress on reaching the end-of-year expectations for select New Jersey Student Learning Standards. We ask that families/guardians not be alarmed by low scores on the initial baseline assessment. The family, the student, the teacher, and the school administration, will continue to receive additional feedback from the winter and spring benchmark administrations. Benchmark results, combined with other information about a child's academic performance, inform individual student goals and help teachers strategically differentiate instruction and measure growth on specific standards and the overall curriculum. When reviewing the **LinkIt!** Benchmark scores you will see that there are 5 achievement levels including Exceeding, Meeting, Approaching, Partially Meeting, and Not Meeting as found on the state assessment. Each level is correlated to be predictive of students’ actual performance on the NJSLA. **LinkIt! **Benchmarks also include a sixth achievement level called Bubble. A student who scores in the Bubble range has a score that is mathematically correlated with a Meeting level of achievement, but is at the bottom 10% of that meeting cohort. Therefore, this additional achievement level helps ensure that students who may be at risk of not maintaining a Meeting score are supported appropriately and can be provided the additional support they may need to ensure that they are in the meeting category for the following administration.

### IXL Math Skill Plans: Grades K-HS

IXL is a supplemental tool being utilized in our Math classrooms. Our students use this learning platform to engage in personalized instruction. IXL is aligned to the New Jersey State Learning Standards as well as our curricular resources.

Please see the links below:

### Math-Focused After School Programs

__Passport to Learning Math Academy (K - 5)__

Students who are interested in fostering a more stable mathematics foundation, or who are interested in further honing their math skills will enjoy this personalized course that meets each student where they are currently in their skill set mastery. All students will use technology, manipulatives and work in small group Academy components to further their math skills and build confidence to approach mathematical tasks.

__Splash Into Math and Literacy Summer Program (K - 5)__

Over the summer months, Splash into Math is a program where students can extend their learning in fun and engaging ways. Students will participate in technology components, small group manipulative instruction, leveled reader groups, and more instructional strategies to further math and literacy skills to build confidence to approach world and classroom tasks. Splash students also have daily use of the Hoboken High School pool, equipped with lifeguards to assist in fun and play.

__Steven’s Math Circle (K - 8)__

The Stevens Math Circle Initiative is an enrichment program for elementary and middle school students intended to inspire and nurture a love for mathematics, and to teach critical reasoning skills. Math Circles expose students to mathematics that is interesting, challenging, and fun, and that goes well beyond the material covered in a typical math class. They aim to show students a different side of mathematics—one where ingenuity, creativity, collaboration, and deep learning take priority over rote memorization, routine problem-solving, and standardized assessment. At meetings, students are taught to actively explore problems and to articulate their reasoning— without being pressured, and without being handed the answer. They are encouraged to collaborate, engage in mathematical discussion, and participate in mathematical games and activities.

__Middle School Math Lab (6-8)__

Students eager to enhance their mathematical foundation, or refine their skills will find this customized tutoring session beneficial. Tailored to individual skill levels, the program incorporates small group instruction, and confidence-building in approaching mathematical tasks. Our Hoboken High School National Honor Society students are some of the tutors that participate in this program and this has enabled our students to learn from their peers.

### Problem-Solving, Critical-Thinking and Computational-Thinking After School Programs

__Chess (2-5)__

Classes are taught in small groups, divided by skill level. Children are placed in a particular group based on his/her level, which allows them to benefit the most from the chess curriculum provided by AlphaMinds. During meetings, children master the basic rules and principles of chess; learn the full range of tactical skills (pins, forks, skewers, etc); are introduced to opening, middle, and endgame theory; become capable of in-depth analysis of their own and others’ games; and get familiar with chess notation. Most importantly, they acquire the love and appreciation for the Game of Chess for life!

__Scratch Coding: Game Design (2-5)__

In this computer science club, children are taught how to solve problems and engineer solutions through coding. As children develop their coding skills, they are presented with the problems and challenges of increasing levels of difficulty. Students are motivated to experiment with code to come up with the right solution, rather than just copy the code from the instructor’s screen. Thus, children start honing their problem- solving skills as soon as they take on their first coding challenge. This program is run by AphaMinds.

**Lego Legends (K-3)**

Scholars will create LEGO worlds utilizing STEAM principals. Students will learn coding techniques and explore the fundamentals of the engineering process. Builders will learn about constructing LEGO projects while implementing the learned coding and engineering techniques. Students will then create an original LEGO project inspired by the course's instruction.