1-on-1 Mastery-Based Algebra I · Taipei

Algebra I, from rules to relationships.

Algebra work for international school students moving into the abstraction, multi-step reasoning, and variable-based problems that Algebra I introduces. Lessons cover linear equations, functions, polynomials, factoring, quadratics, and exponential and rational functions, calibrated to what your child is working on at school.

Audience
Algebra I and equivalent algebra content, international school students
Format
1-on-1, 1 to 1.5 hours per lesson
Duration
Typically 6 to 12 months per program
Begin
Complimentary consultation & assessment class

What Students Learn

Mastery-based Algebra I at the level your child's school actually requires.

Algebra I is for students who could handle the math at K–8 level but are running into difficulty now that algebra introduces variables, abstraction, and multi-step reasoning. The program covers the core algebra content high school mathematics builds on. Solving linear equations and inequalities. Working with systems of equations and graphical solutions. Understanding functions, slope, and rate of change. Manipulating polynomials and factoring expressions. Solving quadratic equations using multiple methods. Working with exponential growth and rational expressions. These are the topics every later high school math course assumes.

Different algebraic content demands different approaches. Linear equations work differently from quadratics, and graphing functions reads differently from manipulating polynomials. Students learn to recognize what kind of algebra problem they're working with and to apply the strategies that fit. By the end of Algebra I, this distinction is what separates students who think algebraically from students who only follow procedures.

Lessons follow Harland's Algebra I curriculum, which is built to bring students to mastery of Algebra I content and matches international school expectations. The program is structured into five units that follow the natural flow of Algebra I content. Each unit closes in a deliverable that measures whether the student has reached mastery of the content before moving on. Lessons calibrate to your child's individual gaps and the topics they're working through at school. If a student is working through systems of equations at school, the teacher works through it with the student, applying the unit's problem-solving structures to the kinds of problems their class is currently doing. Harland's curriculum decides what gets taught. The student's school Algebra I class is where the teaching happens.

Progress shows up in places parents can see. Your child stops dreading algebra homework. They start setting up problems before reaching for a formula. School feedback shifts from "needs work on showing reasoning" toward "engages with the work."

How We Teach It

Algebra taught through what students are working on.

Harland's pedagogy is content-based learning. Algebraic thinking, procedural fluency, and problem-solving develop through the topics, problem sets, and assignments your child is already working on at school. Assessments check whether the thinking holds up when the student moves to new content alone.

That means lessons that work directly with school material. A student working through linear equations and inequalities works on it with their teacher, applying the unit's problem-solving structure to the equations and word problems their school is asking for. A student moving into quadratic equations and factoring works on it with their teacher, applying the unit's analytical structure to the polynomials and graph interpretation their class is doing. A student working through exponential growth, rational expressions, and the introduction to function families works on it with their teacher, building the abstraction skills the next courses in the sequence will assume.

Algebra is also a question of engagement. Some students arrive at Algebra I having lost confidence in math at K–8. The abstraction is harder, the answers don't come as quickly, and what worked in earlier grades stops working. The 1-on-1 format gives teachers room to slow down where the abstraction is unfamiliar, and to keep the work rigorous without losing the student's interest. Skill and patience develop together. Neither moves far in isolation.

The format also lets teachers calibrate within the program's structure. A student arriving with weak K–8 foundations gets work calibrated to fill in those gaps before moving to harder algebra content. They aren't held to a generic remediation script. A student fluent with procedures but missing conceptual depth gets pushed toward the harder questions their school will eventually ask. What does the answer represent. Why does this approach work. What different method would solve the same problem.

Curriculum and Alignment

A structured curriculum that aligns with your child's school.

Algebra I at Harland follows a structured curriculum keyed to the typical Algebra I course content taught in international schools. A student who completes the program has demonstrated mastery of Algebra I content.

Harland's curriculum runs five units. Most school Algebra I courses spread across more. 1-on-1 lessons don't lose time to group pacing or mixed-ability instruction, so the same core content fits in fewer, more substantive units. The time saved goes into the structural reasoning Algebra I rewards.

Lessons coordinate with whatever curriculum your child's school follows. The Algebra I curriculum tracks against the Common Core State Standards for Mathematics. Students from US-curriculum schools work through it as their school's Algebra I course. Students at IB or Cambridge schools, where the algebra content sits within an integrated G9–10 mathematics syllabus, use the program for targeted algebra reinforcement calibrated to whatever their school is currently working on. Where a school uses its own internal curriculum, the Student Coordinator translates school expectations into lesson goals.

Standards
Harland's Algebra I curriculum, with cross-references to Common Core State Standards for Mathematics and school-specific expectations as relevant
Materials
Harland curriculum materials, with school texts, worksheets, and assignments integrated as ongoing input
Assessment
End-of-unit assessments, tracked against Algebra I mastery and school-flagged skills
Reporting
Skill-level tracking against Harland's internal rubrics, matched to international school standards

Prerequisites and What Comes Next

Where Algebra I fits in your child's learning.

Before starting

Algebra I assumes proficiency with arithmetic operations, fractions, decimals, ratios, and basic equation-solving. Students whose K–8 mathematics has gaps in these areas typically work in Mathematics K–8 first or alongside Algebra I, depending on how foundational the gaps are.

Some students at Algebra I level still find that mathematical word problems read harder than the math itself, because the English vocabulary is doing more work than the algebra is. Where this is the case, Academic English (Grades 3–12) runs alongside as a parallel program. The Student Coordinator helps families judge whether the gap is in the algebra or in the language carrying the algebra.

The consultation and assessment class establishes whether Algebra I is the right starting point and whether parallel work in another program would help. Some students arrive needing both K–8 review and Algebra I support, and the lesson plan covers what's most urgent first.

What comes after

Most students complete Algebra I in 6 to 12 months, depending on starting position and lesson cadence. At completion, families have a clear decision point.

Many students continue with Geometry and then Algebra II in the standard high school mathematics sequence. Others continue Algebra II directly where their school's curriculum allows. Others step away from Harland once Algebra I content is mastered, returning if later courses become difficult.

Students on AP tracks at higher grades progress to AP Calculus AB or BC and other AP mathematics offerings on our AP Program. Students at IB schools continue through to IB Diploma Mathematics: Analysis and Approaches, or Applications and Interpretation, at Standard or Higher Level on the IB Diploma Programme. Students preparing for SAT, SSAT, or ISEE may use Algebra I work as foundation for Test Preparation.

The longer-term aim of Algebra I is to make itself unnecessary. The program brings students to mastery of Algebra I content. Some continue with Geometry, others don't need Harland until later in the sequence. A parent who's no longer worried about their child's math is the point of all of it.

Common Questions

Common questions about Algebra I at Harland.

Who is Algebra I at Harland for? +
Algebra I at Harland is for students who could handle the math at K–8 level but are running into difficulty with the abstraction algebra introduces. Most of our students fall into one of three patterns. Some are at US-curriculum international schools where Algebra I is the standard G9 course and they're falling behind their teacher's pace. Some are advanced students working through Algebra I at G8 or earlier and want to deepen their mastery. Some are at IB or Cambridge schools where the algebra strand of their integrated mathematics syllabus needs targeted reinforcement.
My child can do basic math but is struggling now that algebra introduces variables and abstraction. Is this the right program? +
Yes, in most cases. The transition from arithmetic to algebra is one of the most common difficulty points in international school mathematics. Arithmetic gave concrete answers. Algebra introduces variables, abstractions, and multi-step reasoning where the answer takes longer to reveal itself. The program focuses on what makes that transition difficult. Reading problems that use variables instead of numbers. Setting up equations that represent relationships. Working through the multiple steps algebra problems require. Building the patience to sit with not-immediately-getting-it that algebra demands.
Can my child begin Harland over the summer? +
Yes. Summer enrollment is available across most Harland programs. The summer block is a 4 to 8 week 1-on-1 program scheduled between late June and early August, typically two to three sessions per week, calibrated to what your child's school will be teaching later in the school year. See Summer Enrollment for full details.
What does Algebra I at Harland cover? +
Algebra I at Harland covers the core algebra content typically taught in a high school Algebra I course. Solving linear equations and inequalities accurately. Working with systems of equations and graphical solutions. Understanding functions, including linear and quadratic forms. Working with slope, rate of change, and graph interpretation. Manipulating polynomials and factoring expressions. Solving quadratic equations using multiple methods including the quadratic formula. Working with exponential and rational functions. Setting up word problems and applied algebra. Lessons calibrate to whichever topics your child's school is emphasizing. If a teacher has flagged a specific skill, the lesson plan can focus on that skill rather than running through the whole program.
How long is each lesson and how often does my child attend? +
Lessons are 1-on-1 sessions of 1 to 1.5 hours, in person at our head office in Da'an or online. Most students attend one to three lessons per week. The Algebra I program is structured around five units of work, each closing in a deliverable. At one or two lessons per week, the program typically takes a school year. At three lessons per week, a semester. The Student Coordinator helps you choose the cadence that fits.
How are lessons scheduled, and what if we need to reschedule? +
Lessons happen on a fixed weekly slot reserved with your child's primary teacher. This protects the teacher's time and keeps a consistent rhythm for your child. If you need to reschedule, give us at least 24 hours of notice and we'll find another time when your teacher is available. Many families add classes during summer or winter vacation, either to accelerate progress or to make up for a slower term. Once a unit has started, it should be completed within a defined window. The Student Coordinator walks through the details when you enroll.
How do you measure progress? +
Progress is measured through the curriculum's assessments. The Algebra I program has five units, each closing in an assessment that measures conceptual understanding, procedural fluency, problem-solving, and mathematical reasoning across the unit's content. Parents receive updates after every lesson and formal progress reports when each unit ends. Skill-level tracking uses Harland's internal rubrics, which match international school standards. Where helpful, the Student Coordinator translates this into the expectations of your child's school.
How do we begin? +
Every Harland relationship begins with a consultation, followed by a 1-on-1 assessment class. The consultation is about your goals and your child's situation. The assessment class is about how your child works in the subject. Together they tell us where to start and what kind of teacher will fit best.

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