Mathematics Curriculum Samples

Harbor + Sprout's Mathematics curriculum follows goals and strategies to support your child’s understanding and love of mathematics along with respect and affinity for the challenges of mathematics. Key points considered when developing the Harbor and Sprout math curriculum include the following:

Development of Problem-Solving and Critical Thinking Skills

• Our program emphasizes problem-solving and critical thinking. Students are encouraged to use different strategies personally and with peers to apply mathematical thinking and skills to real-world situations. By giving students the opportunity to see the relevance of math in the real world, we hope to prepare them for higher level math and math in everyday life.

Rate of Learning

• It is especially true in mathematics that children learn at different rates. Our curriculum allows for learning to be enjoyable and not stressful, enabling students to work at an enjoyable pace. We recognize that students learn at different rates and accommodate for the differences. We use assessments to understand the child’s current level while providing support or more challenging lessons as needed. Our goal is to provide students with a strong mathematics foundation while allowing them to progress at a pace that is comfortable and appropriate. Some learners will internalize concepts quickly while others will ruminate for longer. Our program is developed such that the timeline can vary by child.

The Support of All Learners

• Our program offers differentiated instruction to meet the needs of all students. We offer additional support as well as the opportunity for the student to move ahead to advanced challenges. By providing these opportunities, we allow each child to engage with math in a way that is meaningful to them.

Spiraling Concepts

• Using spiraling, key concepts are introduced, and then revisited with increasing complexity throughout the year and through the whole curriculum. By seeing the concept first, students make connections using prior knowledge. The prior knowledge allows students to reinforce understanding and make connections between different math topics.

Use of the Concrete, Pictorial, and Abstract (CPA) Approach

• Initially, The Concrete, Pictorial, and Abstract approach allows students to grasp the initial introduction to a topic in math by using physical objects to explore and understand the idea.
• Once the student grasps the concept, the idea can broaden through the use of visual representations with connections to the concrete.
• Finally, students learn to work with the numbers, symbols, and formulas representing the concrete and pictorial representations. 

Growth Mindset in Math

We emphasize that every child can learn and succeed in math. Our focus is on learning rather than perfection and mistakes are seen as opportunities for learning. Through the Growth Mindset, students are encouraged to develop their abilities in math and to foster a positive attitude toward overcoming challenges and solving problems.

• Instructor/Parental Involvement
• We encourage parents to work through the problems and gain a clear understanding of the child’s math education to foster growth, resilience, and a deep understanding of mathematical concepts.
• Teaching tips are included to assist parents/instructors as they introduce math concepts.

All of these techniques work together to provide a well rooted conceptual understanding of mathematics for use in our world.

Curriculum Format:

Structured by Level with Multiple Entry Points

• Each level has a clear scope and sequence allowing students to learn at their own pace and meet them where they are. Students may progress through the curriculum as they complete the scope and sequence.

Hands-On Learning

• With an emphasis on hands-on experiences, students engage in concrete, pictorial and abstract mathematics using real-world scenarios to increase the comprehension of real-world mathematics. 

Interactive Lessons

Because participation is integral to learning, our lessons require active participation by students using methods such as problem solving, math discussions, collaboration, and communication. 

• Active learning component (AVK Connection) included in each lesson
• Assessment for Growth
• The provided assessments allow for the tracking of student progress and point out areas where students may need extra support or enrichment. The assessments are designed to guide learning as well as measure performance.

In preparation for the future, students completing this preK-8 and subsequent upper-level course curriculum will have developed problem-solving abilities, critical thinking skills, and a desire to learn. The Harbor and Sprout curriculum differentiates itself from other curricula by incorporating nature-based projects, personalized learning, and meaningful real-world applications of mathematics while engaging parents in personalized learning for their child. 

Our lessons were designed to be just the right amount- not too little, not too much, with room to expand or simplify as needed. Estimated length of lessons by level are as follows:

• Little Sprouts: 10-20 minutes
• Kindergarten: 10-20 minutes
• Level 1: 15-20 minutes

Each lesson is made up of the following components:

• Objective- "I can" statement
• Materials list
• Warmup: spiral review of a previously learned concept
• Instructional lesson
• AVK Connection: audio/visual/kinesthetic active learning component to engage all styles of learning and reinforce concepts in tangible ways
• 2 pages of learner exercises with multifaceted activities to practice the lesson material

This curriculum includes 36 weeks of material and 180 lessons, thus fulfilling the requirements for states with compulsory schooling standards. You have the option to pace these lessons as needed; for example, you may choose to do two lessons a day as best suits your family's schedule.

At the end of each unit, you will have a skills check to gauge progress and understanding. If more practice is needed, you are encouraged to revisit the AVK Connection portions of the lessons or visit the extensions list at the beginning of the curriculum.

After every 3 units, you will find a mastery assessment to evaluate progress and understanding. In addition, there will be a comprehensive mastery assessment at the end of each curriculum.

For a by-level breakdown of lessons and assessments, please preview the scope and sequence of the level you will be using with your child.

Click here to see a lesson structure overview.

The scope and sequence of our mathematics program was designed thoughtfully with the needs of every family worldwide in mind. Developed by our resident Math Ph.D. and based on consultation with skilled curriculum developers with many collective years of experience refining impactful curricula in innovative ways, every aspect of this curriculum has been carefully researched to ensure it meets the standards of top quality curriculum with the unique, lively, and nature-based Harbor + Sprout twist. Click each level below to see the scope and sequence.

Little Sprouts (Pre-K) Scope and Sequence

Kindergarten Scope and Sequence

Level 1 Scope and Sequence

At Harbor + Sprout, we take great pride in offering a curriculum that is deeply intentional, thoughtfully designed, and firmly rooted in proven educational research. Our approach to both mathematics and language arts emphasizes conceptual depth, developmentally appropriate progression, and a commitment to supporting diverse learners.

Mathematics Curriculum

Our mathematics curriculum is built on the highly effective Concrete–Pictorial–Abstract (CPA) approach. This methodology guides students through three stages of understanding: beginning with tangible, hands-on materials; moving to visual representations; and finally progressing to abstract, symbolic notation. This process nurtures deep comprehension and long-term retention of core mathematical concepts.

Each concept in our program is carefully interwoven with others, creating an intuitive and meaningful learning journey. The curriculum emphasizes conceptual connections, encouraging students to see math not as isolated procedures but as a network of ideas that build on one another organically.

The framework for our math program was developed in partnership with a Ph.D. in Mathematics and Curriculum Development, whose expertise has been instrumental throughout the creation process. This expert-led guidance has ensured the program remains grounded in best practices from mathematics education research. Through careful piloting, iterative revision, and rigorous review, we have ensured that every component reflects a deep understanding of how children best learn math.

Language Arts Curriculum

Our Language Arts curriculum is guided by the principles of the Science of Reading, focusing on the foundational elements of literacy development: phonemic awareness, phonics, vocabulary, fluency, and comprehension. These essential components are intentionally sequenced and integrated to support skill development at a pace that matches your child's natural growth.

The framework was designed by a curriculum and instruction specialist with a M.A. in curriculum and teaching, with emphasis on reading education. and a background in research-informed educational design. Drawing from methodologies such as Montessori, Charlotte Mason, and Orton-Gillingham, the curriculum offers a blend of structured literacy and child-centered learning. This multifaceted approach allows us to support a wide range of learning preferences and provide a literacy foundation that is both strong and adaptable.

We understand the importance of inclusivity and accessibility, and have designed both programs to be neurodiversity-friendly, supporting varied cognitive profiles and learning needs with intention and care.

Both our Math and Language Arts programs align with national academic standards while also going beyond to explore concepts more deeply and meaningfully at developmentally appropriate stages. Every lesson, sequence, and activity has been carefully vetted, tested, and refined. We do not take shortcuts. Every decision is the result of collaborative expertise, thorough research, and a commitment to excellence.

We are honored to provide a curriculum that speaks to both the heart and science of teaching and learning.

Q: Is this curriculum mastery based or spiral based?

A: Harbor + Sprout Mathematics is a mastery-spiral hybrid curriculum. Concepts are taught with a mastery-based approach and you will find a spiraled review concept in each lesson. We have combined the best of both worlds to create a full-bodied and impactful comprehensive math curriculum.

Q: How is currency approached to be relevant worldwide?

A: All money lessons are in USD by default. With your purchase- regardless of whether you purchase print or digital- you will receive a printable PDF with coins and bills that you can use for your currency lessons. When the lesson is amount-specific, you may place White-out or a sticker over the numbers to write in numbers relevant to your currency. Currencies of Mexico and Canada are also introduced.

Q: Is measurement approached in Metric or Imperial?

A: Both! You will learn both Metric and Imperial standard measurements in this curriculum.

Q: Is there a separate teacher's manual?

A: All instructional text is combined on-page with the learner exercises. This allows the curriculum to speak to the learner and it eliminates the need for separate pieces and cross referencing.

Q: Should I choose digital or print?

A: If you have a printer at home and plan to print lessons without binding the curriculum, digital is a great fit for you. If you intend to print and bind the book, we highly recommend purchasing the print version. There is a great deal of specific formatting required for the curriculum to print properly double-sided with top binding. Additionally, our prints are the most cost-effective option.

Q: I want to use this curriculum in my school or co-op. What do I need to purchase for each student?

A: Please read our group use guidelines here.

Selecting the right level for your learner is a big decision, and we are here to help! The younger years are inherently full of nonlinear development that occurs at a unique pace for each child. Age bands are given as recommendations, not rules. You may even find that you need a different level of each subject. Every child is different.

Each subsequent level of Harbor and Sprout's core curriculum presents information in a developmentally-appropriate more advanced context than the previous level. The progression is gradual and methodical. Each level will provide the solid foundation your child needs to be prepared for the next. Note that you do not have to begin with Little Sprouts or any other Harbor and Sprout level; you may begin this program at any point in your child's education and fill in gaps from previous learning as needed.

When considering where your child should begin, we recommend that you take the placement assessments (linked below) and read through the scope and sequence (linked above) to determine the best fit. If you begin and find that you need to slow down the pace, you can always start one level earlier and return to the higher level when your child has a firm understanding of the foundational concepts needed to continue through the program.

Little Sprouts Ready-To-Learn Assessment

Kindergarten Math Placement Assessment

Level 1 Math Placement Assessment

Read Cathy Duffy's review here