Growing and Shrinking Patterns: What They Are and How to Help Your Child at Home
Mathnasium tutors break down what growing and shrinking patterns are, how they connect to later math skills, and how to practice them at home in just minutes.
Working with students across Cincinnati, we often find that 6th-grade math struggles trace back to earlier gaps, such as difficulties with multiplication, division, and early fractions in 3rd grade or multi-digit operations and fraction and decimal work in 4th grade.
At Mathnasium of Blue Ash, we help students identify and fill these gaps, rebuilding confidence in the foundational skills behind them.
Today, we’re sharing a look at our approach. Read on to discover the common reasons behind math struggles in 6th grade, along with practical tips and local Ohio insights to help students move forward.
Drawing on our experience supporting students with middle school math, together with relevant educational research, we've identified five distinct reasons students struggle with middle school math.
Longitudinal research by Nicole Hansen, Nancy C. Jordan, and Jessica Rodrigues followed students from 3rd through 6th grade and found that children with early difficulties in fraction understanding were much more likely to continue struggling and to miss later math benchmarks.
Under the Ohio Learning Standards for Mathematics, skills build in a clear progression.
Students develop multiplication and division in grade 3, strengthen fraction and decimal fluency in grades 4 and 5, and then use those number skills as they move into grade 6 ratio reasoning and other algebraic work.
If one of these pieces is missing, it destabilizes every skill that follows. Math doesn't let students skip a step and catch up later, as each new skill builds on the one before it.
So if your 6th grader is having a hard time grasping ratio concepts, it might stem from lingering gaps in foundational skills like multiplication and early fractions.
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As students move through the elementary grades and into middle school math, they may build number ideas that seem logical at first but later cause confusion. Our tutors often see examples like:
A student thinks 0.65 is bigger than 0.7 because 65 is bigger than 7.
A student tries to add \(\Large\frac{1}{4} + \Large\frac{1}{3}\) by adding the numerators and denominators separately instead of finding a common denominator.
In a 2019 study, researcher Yasemin Deringöl found that primary teachers often see students having difficulties with numerators and denominators, ordering fractions, working with number lines, and doing fraction operations. Those are exactly the kinds of “wrong rules” many kids carry into middle school.
None of this fades with more worksheets. Students need to drop the old idea before the correct one lands.
If students used to get by with memorized procedures in earlier grades, those procedures may not be enough now that sixth-grade math is more abstract.
In grade 6, Ohio’s math standards require students to:
Read and interpret expressions
Work with variables
Reason through ratios
Solve multi-step word problems
In other words, sixth grade asks students to do more than follow steps. They have to connect symbols, operations, and real-world situations in order to make sense of the math.
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Math anxiety is a feeling of worry or tension that can interfere with math performance.
Research shows that math anxiety can rise in sixth grade. In one 2-year study, 413 sixth graders reported a significant increase in math-related anxiety toward the end of the year.
Whether it comes from repeated negative experiences, frustration from earlier gaps, or both, math anxiety can make it harder for students to learn new middle school math.
Parents may notice symptoms such as:
Rushing through homework
Freezing on multi-step problems
Saying “I’m bad at math”
Avoiding math altogether
Left unchecked, these signs can make math feel even more overwhelming and widen the gap over time.
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As much as Ohio’s math standards emphasize coherent progression, reasoning, and the mathematical practices, the curriculum still moves at a steady pace that can make it hard for students with gaps to catch up.
In sixth grade, the first major focus is typically ratios and proportional reasoning, then the work builds into the number system, expressions and equations, geometry, and statistics.
For a student heading into 6th grade with shaky fraction skills, that can mean spending the year trying to catch up, as each new concept depends on the last. Before long, it can turn into a race to keep up.

When the classroom curriculum moves steadily from one topic to the next, students with lingering gaps can quickly feel left behind.
Parents can make an actual difference at home, with no math background required. These practical habits give Ohio families a starting point with their 6th grader today.
Students often make more progress when practice focuses on one clearly defined weakness, like fraction operations or word problems, rather than an hour of mixed, scattered review, according to a U.S. Department of Education practice guide on math intervention.
Ask your child's teacher which skill to prioritize, then spend 10 to 20 minutes a few times a week working on just that one area.
For many 6th graders, that might mean focusing on fraction operations, multiplication and division facts, or setting up multi-step word problems, instead of assigning random extra worksheets.
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Numbers land more naturally when your child sees them doing real work outside a workbook. Here are a few activities that tap into curiosity, strategy, and practical thinking:
Custom Mix Ratios: Your child creates a recipe for a custom drink using strict ratio rules. For example, "The ratio of water to mix must be 3 : 1, and [math[\Large\frac{1}{4}\) of the final batch must be juice." From there, they calculate the exact fractional amounts needed for a single glass and scale those measurements up for a full pitcher.
Budgeting with Ratio Constraints: Working with a hypothetical budget (like $100), your 6th grader plans an event based on specific financial rules. They balance fractional allocations and ratio guidelines, such as spending at least \(\Large\frac{2}{5}\) of the budget on supplies while keeping the ratio of food to entertainment at 1 : 3.
Fraction Scaling: Give your child a simple list of fractional measurements, like \(\Large\frac{3}{4}\) inch, \(\Large\frac{1}{2}\) cup, or \(\Large\frac{2}{3}\) yard and challenge them to scale the entire list up by 5or down by 12. This gives them direct, hands-on practice multiplying and dividing fractions to solve for new totals.
In a 2019 study, Annie Sussman and colleagues found that when teachers used questions to draw out students’ ideas and explanations, students were more engaged in meaningful mathematical thinking than when the focus was just on right answers.
That means, if your child gets stuck, resist the urge to walk them through the steps. Ask questions instead, like:
What do you already know about this problem?
Does that answer make sense to you?
This kind of questioning encourages your child to make their thinking visible and choose a strategy on their own, which builds deeper understanding and problem-solving skills that last longer than an answer they were simply told.
A 2025 meta-analysis by Ewan Murray and colleagues reported that students remember mathematics better when practice is spaced over multiple shorter sessions instead of packed into one long session.
A short, predictable routine beats a long, stressful cram session every time. Set aside 15 to 20 minutes a few days a week, break the work into small pieces, and point out progress when it happens, even something as small as sticking with a tough problem.
This kind of low-pressure consistency helps your child build a steadier relationship with math over the weeks that follow.
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Some gaps need more than a home routine can fix. If more than one gap shows up for your child, or frustration keeps building despite your best efforts, outside support can help.
Look for a program that pinpoints your child's specific gaps, teaches the concepts behind the shortcuts, and tracks progress along the way. That kind of structure closes gaps faster than trying to manage everything alone at home.
Mathnasium is one option Ohio families turn to for this kind of support. Each student starts with a diagnostic assessment, which helps us understand their current skill level, learning goals, and learning style. From there, we build a personalized learning plan around exactly what your child needs.

Mathnasium is a math-only learning center that helps K-12 students unlock their math potential.
Mathnasium is a math-only learning center dedicated to empowering students of all skill levels to learn and master math.
We've worked with many middle schoolers, helping them rebuild foundational skills and keep up with the demands of middle school math.
To support them, we use the Mathnasium Method™, our proprietary teaching approach designed around individual student needs and learning styles.
Each student starts their Mathnasium journey with a diagnostic assessment, which helps us identify which concepts are truly solid, which skills are familiar but still fragile, and which gaps may be affecting the math that comes next.
With these insights, we create a personalized learning plan tailored to what your student needs, whether that means revisiting a 3rd-grade concept or working toward 6th-grade material.
Once the plan is ready, our specially trained tutors follow it closely, delivering face-to-face instruction in a supportive environment, both in-center and online. We teach through a mix of verbal, visual, written, tactile, and mental techniques so each concept lands clearly.
During sessions, the focus goes beyond finding the correct answer to also understanding the why and how behind it. This builds critical thinking and problem-solving skills that benefit students far beyond math class.
Fun is a core part of how we teach. Our activities are often game-based and hands-on, keeping students engaged and motivated. We celebrate every bit of progress, big or small, so confidence grows with each session.
And the results speak for themselves:
94% of parents report an improvement in their child's math skills and understanding
93% of parents report a more positive attitude toward math after attending Mathnasium
90% of students saw an improvement in their school grades
With more than 1,100 learning centers, Mathnasium brings top-rated math instruction close to home.
For families in and around Blue Ash, OH, Mathnasium of Blue Ash is a trusted local center with experience helping students transform how they think and feel about math. Our center has been recognized for the quality of instruction we bring to the community:
Winner of Cincy Magazine's 2025 Family's Choice Awards "Tutoring/Learning Center" category
Winner of City Beat's Best of Cincinnati 2025 "Best Tutoring Center" category
Whether a student is catching up, keeping up, or getting ahead, our team is committed to helping them experience what it feels like to find the rule, trust their reasoning, and enjoy the math that follows.
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