Every September, high school math teachers open where June left off, without a warm-up week or any kind of catching up. So, the concepts your child was taught last spring are the concepts their teacher will build on from the first lesson.
What our education specialists at Mathnasium see, year after year, is that students arriving in September feeling ready are the ones who spent part of the summer consolidating what they learned.
Our education specialists will walk you through the specific concepts students are expected to carry into each course, so you know exactly where to focus before September.
Geometry tests Algebra 1 fluency from the first week. Angle relationships, coordinate proofs, and geometric constructions all require your child to set up and solve equations quickly, without rebuilding the process from scratch.
The three areas we see come up most are:
Your child needs to set up and solve one- and two-step linear equations, including those with variables on both sides, without hesitation. Geometry introduces angle relationships almost immediately, and those problems are essentially equation problems in geometric clothing.
For instance, your child is told that two angles are supplementary and that one measures 3x + 15 degrees. Setting up and solving an equation has to happen before any geometry can.
Slope-intercept form, line graphing, and an understanding of what slope represents come up throughout the entire Geometry course.
Your student may be able to execute the steps correctly and still not understand what slope means in a given context. That gap surfaces the moment Geometry asks for application rather than computation.
In coordinate geometry, your child will be asked to find the equation of a line passing through two given points, then use it to determine whether a third point lies on that line. Slope-intercept form needs to feel automatic before that kind of problem makes sense.
Geometry proofs follow the same logical structure as algebraic justification:
Here is what I know
Here is the rule I am applying
Here is the conclusion
Your child will find proof-writing disorienting from the first day if they have never been asked to explain their algebraic reasoning step by step. The format feels new even when the underlying logic is not.
We find the clearest check is to ask your student to solve 3x + 7 = 2x + 15 and walk you through each step and why they did it. Your child may be able to solve it and still not be able to name the property used at each step, such as the subtraction property of equality or combining like terms.
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Mathnasium's small-group sessions give students the space to work through problems together, building both understanding and confidence along the way.
Algebra 2 moves faster than Geometry and assumes students arrive with working fluency in several concepts from the year before.
The three areas we see trip students up most at this transition are:
Your child will meet quadratic functions, complex numbers, and polynomial operations in the first few weeks of Algebra 2. Their teacher will assume they can factor fluently, recognize standard form, and connect the factored form of a quadratic to its roots. If your learner coasted through that unit in Algebra 1, they may find themselves in difficulty before October.
Ask your child to factor x² + 5x + 6 and explain why those factors are correct. Getting the answer is one thing; being able to explain the reasoning is what Algebra 2 will rely on.
Your student needs to understand f(x) notation, evaluate a function for a given input, and recognize how transformations such as shifts, stretches, and reflections change a graph. These concepts appear in the first few weeks of Algebra 2 as assumed knowledge.
We find that treating function notation as a mechanical formality in Geometry tends to catch up with students earlier than families expect.
For instance, your child may be asked to describe how the graph of f(x) = (x + 3)² differs from f(x) = x². Their teacher will build on that understanding from the first lesson, so your child needs to see that as a horizontal shift and know why the notation produces it.
Proportional reasoning runs through much of the equation-building that Algebra 2 requires. Your young learner will encounter rate problems, mixture problems, and compound equations that all depend on comfort with ratios and proportional relationships.
Ask your student to set up a mixture problem, such as how much of a 20% solution to combine with a 50% solution to get 300ml of a 30% solution. What you are looking for is whether they can translate the scenario into an equation at all.
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Where your student lands at the end of Precalculus determines whether they enter college having completed calculus or still working toward it, and that window opens in the fall.
The three areas we see matter most at this transition are:
Precalculus builds an entire course around functions: polynomial, rational, exponential, logarithmic, and trigonometric. Your student needs to arrive knowing what a function is conceptually, how to read, write, and evaluate one, and what it means for a function to have an inverse.
Ask your learner to evaluate f(g(x)) for two simple functions. If your young learner can do this fluently, they have nothing to worry about, but if they are still staring at the notation, they might be carrying a gap that Precalculus will expose quickly.
Algebra 2 introduces exponential and logarithmic functions, but takes them only partway. Precalculus picks them up at a higher level of abstraction and moves through them faster.
We see students struggle here when they remember the procedures from Algebra 2, but never fully consolidate the core relationship between the two function types.
Ask your student to sketch y = 2^x and y = log₂(x) on the same axes and describe what they notice. They can do this when they understand that the two functions are inverses of each other, and that understanding underpins half of what Precalculus covers.
Many Algebra 2 courses introduce right-triangle trigonometry and the unit circle toward the end of the year, when attention is often elsewhere. Your child's Precalculus teacher will expect familiarity with sine, cosine, and tangent in right triangle contexts and some working knowledge of radian measure.
We find this is one of the most common gaps in students arriving at Precalculus, precisely because it tends to be taught last and reviewed least.
Ask your learner to find the sine, cosine, and tangent of a 30-degree angle without a calculator. A little focused review before September will go a long way for any student pausing on this question.
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Some skills affect performance across every course, regardless of where a student is in the sequence. We come back to these with learners at every level, because they tend to separate students following a worked example from those solving an unseen problem on their own.
When your student reads a written scenario and needs to identify the correct operation or equation, they are exercising a math interpretation skill. That is where we consistently see students get stuck.
According to the National Council of Teachers of Mathematics, true procedural fluency means being able to transfer a skill to a new context and problem type, not just execute a familiar procedure correctly.
Your learner may handle a practised problem type well and still struggle the moment the same concept appears inside a word problem. That gap tends to widen as courses get harder, because the problems get less familiar, not more.
Ask your student to write the equation for a word problem before solving anything. If they can do that step cleanly, that means they are in a better position heading into any of the courses above.
Unit conversion and dimensional analysis come up in every science class alongside math. We see it catch students out in applied problems where the numbers look manageable, but the units require careful handling.
Ask your student to convert 90 kilometers per hour into meters per second and show their work. If they can set that up correctly, they likely have a solid grasp of how units behave in calculations.
The habit of substituting an answer back into the original equation to verify it is one of the simplest things to build over the summer and one of the most consistently overlooked.
We find that self-checking their work and therefore catching errors before they become patterns is a habit that pays off across every course they take.
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Mathnasium's specially trained instructors meet each student where they are, stepping in with guidance at exactly the right moment.
Mathnasium is a math-only learning center dedicated to helping K–12 students build confidence and strengthen math skills at every level.
We have worked with many students who arrived in August carrying exactly the gaps this article describes, unsure whether they were ready for the course ahead, and left with the foundational skills and the confidence to handle it.
At the heart of what we do is the Mathnasium Method™, our proprietary teaching approach designed around each student's needs and learning style. Rather than moving every child through the same material at the same pace, we build instruction around how your young learner thinks and learns.
Every student begins with a diagnostic assessment that maps which skills are solid and which need attention. From there, we create a personalized learning plan and work through it with specially trained instructors, face-to-face, in-center, and online.
We teach for understanding, not just for procedure. Our instructors explain math in plain, familiar language and use a combination of verbal, visual, mental, tactile, and written techniques to show each concept from multiple angles. When your child can see the same idea several different ways, the concept stops feeling abstract.
Our instructors are trained in both the technical and emotional sides of teaching. They know when a student needs encouragement, when more practice is the answer, and how to rebuild confidence in a learner who has started to feel like the course is already beyond them.
And we keep it fun. Games, hands-on activities, and consistent encouragement are part of every session. For a student heading into a course they're nervous about, walking into a room where math is treated as something fun and manageable can shift everything.
Parents report 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 learning centers across North America, there is likely a Mathnasium close to you.
Families in Altadena, Pasadena, and the surrounding San Gabriel Valley trust Mathnasium of Altadena, a center with experience helping high schoolers arrive at each new course with the skills their teacher will expect from day one.
If your child is heading into a new math course this fall and you want to know exactly where they stand, our team is ready to help.
📅 Schedule a Free Diagnostic Assessment at Mathnasium of Altadena
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Mathnasium of Altadena is a math-only learning center for K-12 students in Altadena, CA. 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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