3 Ways to Help Your Child Spot the Difference Between Rational and Irrational Numbers
Mathnasium tutors explain rational vs. irrational numbers in plain language, with three ways to help your child spot the difference at home.
Lyons Township High School (LTHS) math placement is the process the school uses to decide which math course and which level each incoming freshman starts in.
Most freshmen begin in Algebra or Geometry at a Prep, Accel, or Honors level, and the Math Division Chair evaluates each incoming student using 8th-grade evidence to recommend a course and level.
We are a team of math educators in La Grange, IL, and we have worked with LTHS-bound students for years. Today, we’ll help you understand what LTHS looks at to decide on the students’ math placement and how the level change process works.
LTHS places each incoming freshman in math based on five pieces of 8th-grade evidence, reviewed by the school's Math Division Chair. Together, they determine your child's first high school math course and its level, whether Prep, Accel, or Honors.
The 2026–27 Mathematics Academic Program Guide lists them as the 8th-grade math course, the grade earned in it, math standardized test scores, the first semester exam grade when one is given, and the 8th-grade math teacher's recommendation.
LTHS doesn't publish how much each one counts. Some parents find this reassuring, as one rough week or an off day on a test is less likely to define your child's placement when every piece adds context to the others.
The course your child completes in 8th grade tells LTHS where they already sit in the math sequence. Most freshmen begin in Algebra or Geometry at a Prep, Accel, or Honors level, with Geometry Honors in 9th grade typically reserved for students who already completed high-school-level Geometry in middle school.
This criterion often traces back to decisions made in 6th or 7th grade, when middle schools identify students for accelerated math.
District 102, for example, has notified families about accelerated math placement in late spring and allowed review requests for a limited window. Exact dates shift year to year.
Every district sets its own timeline, and dates change from year to year. If your child is in 6th or 7th grade, ask the school now when those decisions happen.
LTHS considers your child's 8th-grade math performance, taking into account the final grade because it reflects a full year of work across every unit.
What does this mean for parents of 8th graders?
If you notice a dip at any point during your student’s math course, there is no need to worry; they have space to recover.
Where most families make a mistake, however, is overly focusing on the topic the student is struggling with. Seasoned educators look at the unit behind it.
In our experience, 8th graders who struggle to understand a new concept carry gaps in an earlier skill, like fractions or negative numbers, that directly impact how they are approaching the new topic. You can catch those gaps early by checking grades unit by unit instead of waiting for the final mark.
At Mathnasium of La Grange, we do this through a diagnostic assessment, which helps us identify the student’s skill level, including knowledge gaps, and create a learning plan tailored to their needs. The assessment is free and a valuable resource for students of all skill levels.
Standardized scores give LTHS a common measure for students arriving from different middle schools, each with its own courses and grading.
The program guide lists math standardized test scores as a criterion but doesn't name a specific test or say how much the scores count.
Your child's counselor or 8th-grade math teacher is the best person to ask which scores are shared with LTHS.
We always remind parents that a test score captures one morning, and as such, it carries more meaning next to the course grade and the teacher's perspective, which is why LTHS considers it alongside four other measures.
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Some middle schools give a cumulative first-semester exam in 8th-grade math, and LTHS includes that grade in placement when one exists.
Cumulative exams show how well your child retains material from months earlier. Since the exam falls midway through 8th grade, it gives you an early read on readiness while there's still time to talk with the teacher before LTHS winter course selection.
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Your child's 8th-grade teacher holds a key piece of the placement decision, since LTHS names the teacher's recommendation in the prerequisites for Algebra Accel, Geometry Accel, and Geometry Honors.
The teacher sees how your child handles unfamiliar problems and whether they keep going after a tough quiz. In our experience, and we’ll digress slightly, those habits matter as much in an accelerated course as the math itself. This is why we strive to promote the growth mindset in our students, which frames math as a skill they can master and mistakes as an integral part of the learning process.
We encourage you to talk with the teacher in the fall, well before recommendations are due. Ask what they're noticing and what would help your child be ready for the next course. Most teachers welcome that question, and the answer often gives you a clearer picture than any report card.
And if you are unfamiliar with the concept of growth mindset, we highly recommend adding this piece to your reading list:
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If you have questions about math placement, we recommend starting with a conversation with your child's math teacher, then follow a formal request process if a change still makes sense.
LTHS recommends students start in the course they’re placed into and offers support such as a daily math Drop-In Center staffed by peer tutors. Hearing the teacher's reasoning first helps you weigh whether a change would serve your child.
Before freshman year begins, LTHS offers a Placement Concern Form for incoming students on its Future Freshmen Math & Science page. Once your child is enrolled, the formal level change process follows these steps:
Talk with your child's current math teacher about the placement.
Pick up an Academic Course Level Change Form from your child's counselor.
Complete the form with signatures from the teacher, you, and your child.
Submit it to the counselor for review and approval by the Division Chair.
LTHS accepts level change requests during two windows:
Winter course selection
And the first four weeks of each semester
Space is the other factor to consider. Even an approved request depends on an open seat in the new course, and because LTHS builds its master schedule from winter registration requests, seats fill early. We recommend raising a concern during winter course selection to give your child the best chance of a smooth switch.
And remember, the freshman placement is just a starting point. LTHS lets students move up a level based on how they perform.

At Mathnasium, specially trained tutors help students build understanding and confidence in the math skills that high school courses build on.
Mathnasium is a math-only learning center that helps students in grades K-12 catch up, keep up, and get ahead in math.
We help LTHS-bound students truly learn and master math, developing the skills to serve them in the classroom, for math placement, and for the challenging high school courses ahead.
Every student starts with a diagnostic assessment that helps us understand their current skill level, learning goals, and learning style. From there, we build a personalized learning plan that addresses knowledge gaps and builds on what your child already knows.
Our instruction follows the Mathnasium Method™, our proprietary teaching approach. Our specially trained tutors help students understand the math behind each procedure and formula before they use it, so concepts make sense instead of feeling like steps to memorize.
Students learn through face-to-face instruction in a caring and fun group environment, and each session includes time for homework help once they finish their learning plan topics for the day.
Families see the difference:
94% of parents report an improvement in their child's math skills and understanding
93% of parents report improved attitude toward math after attending Mathnasium
90% of students saw an improvement in their school grades
Mathnasium operates over 1,200 learning centers across North America. For families preparing for LTHS, Mathnasium of La Grange has supported local students since 2017 from its center at 1 S Waiola Ave, just down the street from LTHS North Campus.
If your child is heading into high school math, we'd love to help them start with confidence.
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Mathnasium of La Grange is a math-only learning center for K-12 students in La Grange, IL. 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 both in center and online to develop a deep understanding of math, build confidence, and improve academic performance.
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