Why We Use Base 10: The History of Our Number System
Mathnasium tutors trace the history of base 10, from ancient counting systems to the breakthroughs that made it the global standard.
Report cards from Illinois schools typically arrive in late fall, late winter, and again in late spring as the school year wraps up. They give families a snapshot of how their child is doing in class.
While they give a reliable picture of classroom performance, they don't always tell the full story about your child's math readiness. A report card can show that your child is "Meeting Standards" or earning solid grades while still missing important ideas they'll need in the next unit or the next school year.
With that in mind, our education specialists at Mathnasium of Buffalo Grove share what your child's Illinois report card does show, what it doesn't, how you can check their math understanding at home, and what to do next if you spot a gap.
Your child's Illinois report card is designed to give you a clear picture of how they are doing in class over a grading period.
Think of it as a summary of everything their teacher has been watching and tracking since the last time you received one.
Most Illinois report cards include the same core information:
Grades for each subject, including math, based on the work your child completed during that term
Performance labels the school uses, such as "Meeting Standards" or "Approaching Standards," or traditional letter grades like A through F
Teacher comments that briefly describe your child's strengths, areas for growth, and how they are doing in the classroom day to day
Work habit marks like whether your child completes homework, participates, follows directions, and stays on task
Attendance information, including days present, absent, and sometimes late arrivals
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Even a report card with solid grades leaves some important parts of your child's math readiness off the page.
Our education specialists point to several areas that report cards rarely capture fully:
Understanding the "why" in math: Your child may get every fraction multiplication problem right, but their report card won't tell you whether they can explain why those steps work or what the numbers in their answer actually represent.
Using skills in new situations: Math grades mostly come from problems that look like the ones practiced in class. What the report card won't show is whether your child can recognize the same idea inside a word problem, a new type of diagram, or an everyday situation like splitting a recipe or comparing two sale prices.
Strength of core foundations: Grades focus on this year's topics, but often not the prerequisites underneath them. Your child can earn solid marks in 5th-grade math while still feeling uncertain about place value and decimals.
How long ideas actually hold: A grade reflects what happened while the class was on that unit. It won't tell you whether fraction operations, long division, or percent problems will still be there months later when those ideas show up again in harder work.
Math self-checking habit: Report cards don’t show whether your child pauses when they get an area of “600 square feet” for a bedroom that measures 10 feet by 12 feet, or whether they have the habit of checking if their answers make sense before moving on.
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A Mathnasium tutor focuses on how a student worked through a problem, not just whether she got it right.
Your child can carry a solid grade while a specific type of math knowledge gap stays hidden underneath it. These gaps show up in how your young learner works through a problem.
These are the three signs our tutors watch for most in a session:
As you sit with your child during homework or test prep, check their thinking by asking them to explain the reasoning behind their work
Here’s how this may look:
Your 3rd grader solves a problem like, “There are 3 bags with 4 apples in each bag. How many apples are there altogether?” and writes 12. You ask, “How did you figure that out?”
Your 5th grader solves, “A rectangle is 5 units long and 7 units wide. What is its area?” and writes 35. You ask, “What does 35 stand for in this problem, and why did multiplying make sense here?”
Your middle schooler solves, “A shirt that costs 30 dollars is on sale for 20% off. What is the sale price?” and writes 24. You ask, “How did you decide what to do first, and how do you know 24 makes sense?”
If you hear answers like “I just did the steps,” “That’s how we learned it,” or a replay of operations with no mention of why the method fits or what the answer represents, that’s a sign your child’s procedures are ahead of their understanding.
We’ve seen many students who feel comfortable as long as a problem looks just like the examples they saw in class. But if you change the way it’s asked, things can quickly stall.
For example:
Perimeter is no problem when the worksheet says, "Find the perimeter of this rectangle," but the same idea phrased as "You are putting a fence around a rectangular garden. How much fencing do you need?" brings things to a halt.
Adding 3-digit numbers stacked neatly in columns feels manageable, but those same numbers inside a word problem about saving money over several weeks is a different experience entirely.
When a math idea has truly settled in, it shows up reliably across new stories, pictures, and question types, even when the format looks nothing like the original lesson.
As you keep an eye on your child working through problems, notice how they react to the answers they write down.
Pushing past an obvious error without pausing is a signal.
For example:
A word problem about how many students are in a class comes out as 27.5, and the pencil keeps moving without a second thought about half a student.
A question about the length of a pencil produces 30 meters, with no pause to consider what 30 meters actually looks like compared to something that fits in a pencil case.
If you do not catch these moments in the flow of homework, try giving a problem where an unreasonable answer should stand out and watch whether your child pauses before accepting it.
When answers like these go unquestioned regularly, it usually means your child is leaning more on remembered steps than on number sense, even when the report card reads well.
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Once you have noticed signs that your child may be relying on steps more than understanding, the natural next question is what to do with what you have seen.
Instead of asking "How are they doing in math?" share a short example and ask something specific. You might say:
"At home, I have noticed my child can solve problems but struggles to explain their thinking. Do you see anything similar in class?"
"They seem unsure when a problem is written as a story instead of a straight calculation. How are they doing with word problems?"
This gives the teacher something concrete to respond to and opens the door to specific suggestions.
Every child has off days, tricky topics, or problems they rush through. A single stuck moment does not mean there is a gap. What matters more is what shows up consistently, such as repeated trouble explaining why a method works, frequent hesitation when a problem looks slightly different, or a habit of accepting answers that do not fit the situation.
When you and the teacher are both noticing the same things, that is a signal that extra support would help.
Catching a pattern of unreasonable answers or unexplained steps is a useful starting point. What it does not tell you is where the breakdown actually begins. That is what a diagnostic assessment is for. It is a structured skill check that traces the gap back to its source rather than just identifying that one exists.
If you want to try this at home first, Illinois Learning Standards for Mathematics are published publicly by grade level. Pick two or three skills from your child's current grade and ask them to solve a problem, then explain their reasoning out loud.
Their explanation will tell you more than the answer.
If that feels outside your comfort zone, Mathnasium of Buffalo Grove offers a diagnostic assessment as the first step of every tutoring journey. It looks at how your child understands facts, concepts, and problem types across grade levels and maps out exactly where understanding is secure and where it breaks down.
From those findings, we build a personalized learning plan that targets the specific ideas that need attention before they create bigger problems in the next grade.

A Mathnasium tutor works through a problem with a student in a fun, small-group environment.
Mathnasium is a math-only learning center helping students of all skill levels excel in math.
We work with many students in and around Buffalo Grove to help them find and bridge knowledge gaps grades or report cards don’t always reveal. To help students build true math mastery, we use the Mathnasium Method™, our proprietary teaching approach built around each student's specific needs.
It starts with a diagnostic assessment that gives us a clear picture of your child's current skills and knowledge gaps. From those insights, we build a personalized learning plan tailored to your young learner's goals, whether that means solidifying the reasoning behind a topic already covered in class or building the conceptual foundation a new unit will require.
Once the plan is in place, our specially trained tutors deliver face-to-face instruction in a caring, fun small-group setting. We teach for understanding using a mix of verbal, visual, mental, tactile, and written techniques, so your student encounters math from several angles and builds real comfort with the ideas behind each method.
When your child gets stuck, we break the problem down and walk through both the how and the why together. Over time, students learn to reason through unfamiliar problems the same way, developing the confidence to explain their thinking on any report card, standardized test, or homework page in front of them.
Fun is built into how we work. Game-based activities, earned rewards, and consistent recognition of progress keep your young learner engaged, motivated, and aware of how far they have come.
Our approach brings measurable results.
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 over 1,100 centers across the US, we bring the Mathnasium Method™ close to your neighborhood.
For families in and near Buffalo Grove, IL, Mathnasium of Buffalo Grove is a trusted local center with years of experience building confident math thinkers.
Whether your student is looking to catch up, keep up, or get ahead in math, our team is happy to help.
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📅 Schedule a Free Assessment at Mathnasium of Buffalo Grove
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Mathnasium of Buffalo Grove is a math-only learning center for K-12 students in Buffalo Grove, 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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