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.

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

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.

Use the readiness assessments to determine which level best suits your learner's needs.

Little Sprouts Ready-To-Learn Assessment

Kindergarten Math Placement Assessment

Level 1 Math Placement Assessment