Four Methods for Solving Proportions (and When to Use Each)
Mathnasium tutors walk through four methods for solving proportions, when to use each one, and how to choose the most efficient approach.
Algebra 1 is where your child's steady math progress can suddenly stall. It is the first course in the Broward County Public Schools (BCPS) sequence to shift from arithmetic computation to algebraic reasoning, and that shift is where prior gaps surface for the first time.
Mathnasium tutors put together this guide so you can identify what is driving your child's Algebra 1 struggles and which home strategies address each one directly.
In our experience, the most common reason BCPS students struggle in Algebra 1 is unresolved gaps from middle school. Algebra 1 assumes your child already owns four skills from grades 6 and 7:
Integer and signed number arithmetic
Middle school tests these skills one at a time, in familiar formats. Algebra 1 uses all four inside the same problem simultaneously. A skill that was shaky but passable in 7th grade stops your child mid-problem the moment it has to carry weight alongside three others.
A landmark study by Siegler et al., published in Psychological Science, analyzed nationally representative data from the US and UK and found that 5th graders' knowledge of fractions and division uniquely predicted their algebra achievement in high school five to six years later.
Here are a few checks you can run at home to locate where the gap is.
Test the skills in isolation first. Ask your child to solve \(-\Large\frac{3}{4} +\Large\frac{1}{2}\), then find x in \(\Large\frac{4}{6} = \Large\frac{x}{9}\), then -3x - 4. Hesitation or errors on any of these tells you exactly where the foundation needs work.
Then test them in combination. Give your child a problem like \(-\Large\frac{3}{4}x = 9\). It pulls signed numbers, fraction operations, and a variable into one equation simultaneously. Your child may handle each skill separately and stall the moment all three appear together.
Have them explain the steps out loud. Ask your child to talk through what the equation is telling them to do at each step. Hesitation or relying blindly on memorized tricks without understanding why reveals a conceptual gap rather than a simple calculation slip.
Write down where the hesitation happens. Note which step it is. That skill needs attention now, and addressing it directly is the most efficient path forward.
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The second reason BCPS students struggle in Algebra 1 is that arithmetic thinking and algebraic thinking are two distinct skills.
Computing an answer and describing a relationship between quantities are also two different cognitive tasks. Your child has spent six years becoming fluent in the first. Algebra 1 requires the second from day one.
Our tutors at Mathnasium of Plantation see this transition produce three specific and predictable errors:
The variable misconception. Your child treats x as a single hidden number waiting to be uncovered rather than a quantity that can take different values depending on the problem. This produces consistent errors the moment functions and multi-variable expressions appear.
The equal sign misconception. Your child reads the equal sign in 2x + 5 = 13 as an instruction to perform an operation and write an answer, rather than a statement that both sides hold the same value.
Transfer errors. Your child applies familiar arithmetic rules to algebraic expressions where those rules produce wrong answers. Take 3x + 5. Simplifying it to 8x feels completely logical because arithmetic taught them that two numbers next to an operation always combine.
These obstacles are well-documented in research.
For example, a 2025 study by Obot & Delavari, published in Curriculum and Teaching Dialogue, found that misconceptions about variables and the equal sign are the two most persistent barriers students carry into Algebra 1. Both are rooted in arithmetic habits that stop working the moment algebraic reasoning is required.
Here are a few checks you can run at home to identify which of these is affecting your child.
Test the variable concept. Write x + 3 = 7 and ask your child what x is. Then write x + 3 = y . Now ask what x stands for. A stall on the second equation tells you that x is being read as a hidden number rather than a quantity that can vary. Ask your child to name a few values x could take if y were 10, then 15, then 20. The point is that x changes every time y changes. Seeing that pattern is what builds the flexible understanding Algebra 1 requires.
Test the equal sign. Write 3x + 4 = 19 and ask your child what the equal sign tells them before doing any math. An answer like "It means you do 19 - 4 divided by 3" tells you the symbol is being read as a set of action steps, not a statement that both sides hold the exact same value.
Watch for the same wrong answer across different problems. Take note if 3x + 5 becomes 8x. That is a transfer error. Ask your child to explain why those two terms combine. A clear explanation signals a momentary slip. Confusion signals the concept needs attention at the root level.
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Mathnasium tutors teach students what each symbol in an equation means before teaching them how to solve it.
The third reason our tutors see BCPS students struggle is that word problems demand a skill that algebra class leaves unaddressed. In other words, students may spend most of the algebra practice solving equations that are already set up.
A word problem asks them to build that equation from a written description of a situation. That is a different cognitive task entirely. The Florida B.E.S.T. standards and the Algebra 1 EOC test evaluate both skills, but classroom practice focuses primarily on equation-solving.
A 2025 study published in Scientific Reports found that reading comprehension and arithmetic operate as two separate and distinct skills in word problem performance.
Word problems demand additional skills that the Algebra 1 class requires:
Understanding the situation. The problem describes a real scenario first. What is happening, who is involved, and what is changing all require comprehension before math begins.
Filtering the information. EOC word problems include details designed to distract. Knowing which numbers matter and which are irrelevant is a skill in itself.
Building the equation. The mathematical relationship exists inside the language of the problem. That relationship needs to become an equation before any solving can begin, and algebra class assumes your child can make that conversion without being taught how.
We see this produce a consistent pattern. A student reads the problem, goes quiet, and puts nothing on the page.
The obstacle is identifying what the problem is asking and recognizing the mathematical relationship hidden inside the language. Your child has algebra skills. The translation layer is what stops them.
You can try a few simple strategies at home that focus entirely on the translation layer rather than the algebra:
Read the question first. Ask them to read the problem and say out loud what it is asking before touching any numbers. A clear restatement of the question in plain language tells you the situation was understood. Going straight to the numbers without that restatement tells you the translation step was skipped.
Separate the relevant from the irrelevant. Ask your child to underline the information the problem needs and cross out the rest. Identifying what matters is a skill that can be practiced independently of the algebra itself.
Build the equation in words first. Ask your child to describe what is happening in the problem before writing any symbols. Once that plain language description exists, replacing each phrase with a variable is the only step left.
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Home practice with word problems allows your child to focus entirely on the translation step before calculating.
The fourth reason BCPS students struggle in Algebra 1 is that the course moves through a demanding sequence of topics in a single academic year.
The Florida B.E.S.T. Algebra 1 covers four topics in a fixed order:
Linear equations
Systems of equations
Exponential functions
Statistics
Each unit assumes the previous one is solid. The course is designed that way by necessity. A full year of algebra content has to fit inside a full year of school.
The course moves at a pace that requires your child to consolidate each topic before the next one begins. Your child attends class, follows the lesson, completes the homework, and moves forward.
A concept that landed fully supports the next unit. Your child builds the next unit on shaky ground when the previous one landed partially, and the course keeps moving.
Here is how you can support your child in keeping up with the material week by week:
Test the concept a week later. Pull out one problem from that unit and ask them to solve it from memory. Fluency under delay is the true measure of consolidation. A correct answer tells you the concept landed. Hesitation tells you it needs more time while the foundation is still fresh.
Prioritize prerequisite connections over test scores. When time is short, focus on old topics that directly feed the upcoming unit. Resolving linear equations right before starting systems of equations prevents a known gap from instantly doubling.
Address both the homework and the gap. Complete the current homework first so your child stays current with the class. Then spend fifteen minutes on the concept from the previous unit that did not fully land. Even one focused problem per day on that earlier concept, explained out loud, closes the gap faster than a full review session on the weekend.
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Mathnasium's specially trained tutors trace Algebra 1 struggles back to their source and build the foundations students need to move forward with confidence.
Mathnasium is a math-only learning center dedicated to helping K-12 students learn and master math at every level.
Behind our work is the Mathnasium Method™, a proprietary teaching approach designed to meet your child exactly where they are. In the Algebra 1 context, that means tracing a current struggle back to its source and addressing it directly rather than working around it.
Every student begins with a diagnostic assessment that tells us which foundational skills are solid, which need attention, and what needs to happen first.
From those insights, we build a personalized learning plan tailored to your child's current skills, goals, and pace.
Our specially trained tutors deliver face-to-face instruction, in-center and online, using verbal, visual, mental, tactile, and written approaches so every concept makes sense rather than just feels executable.
We teach the how and the why behind math, building the problem-solving skills and critical thinking your child needs to move through Algebra 1 with confidence.
Fun is built into how we work. Sessions include game-based activities, consistent encouragement, and celebration of progress at every step. Your child leaves each session more capable than they arrived, and that is how lasting confidence builds.
The results speak for themselves:
94% of parents report an improvement in their child's math skills and understanding
93% of parents report their child's improved attitude toward math after attending Mathnasium
90% of students saw an improvement in their school grades
With more than 1,100 learning centers across North America, Mathnasium brings top-rated math instruction close to home.
For families in and around Plantation, Mathnasium of Plantation serves students from Plantation High School, South Plantation High School, Plantation Middle School, West Broward High School, and schools throughout Broward County.
Whether your child is looking to catch up, keep up, or get ahead in math, our team is ready to help.
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Mathnasium of Plantation is a math-only learning center for K-12 students in Plantation, FL. Trusted by over a million parents, Mathnasium uses personalized learning plans and the proprietary Mathnasium Method™ to help students catch up, keep up, and get ahead on their math journey.
Our specially trained tutors deliver face-to-face instruction in a supportive and fun small-group environment, working with students to develop a deep understanding of math, build confidence, and improve academic performance.
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