However, through daily reading and writing practice, vocabulary study, and discussion, you can ensure your child overcomes 5th-grade ELA challenges and prepare them for success in middle school.  

Read on to find resources on 5th grade reading and writing support and ELA tips for 5th graders transitioning to middle school.

Reading Skills

The first challenge in 5th grade ELA is more advanced reading requirements. In preparation for middle school, they must 

• start decoding large, multisyllabic words while reading more advanced texts
• learn to extrapolate word meanings from context clues 
• continue to advance comprehension and fluency
• continue to improve vocabulary 

Unfortunately, it’s fairly common for 5th-grade students to read below a 5th-grade level. When that is the case, struggles inevitably arise. Faced with more complex texts and advanced vocabulary, reading fluency and comprehension may suffer, which leads to yet more struggles in writing.

Luckily, there’s plenty you can do to boost your child’s reading and writing skills and help them overcome any challenges in 5th-grade ELA!

How to Help with 5th Grade Reading Comprehension

The first step to overcoming 5th-grade ELA challenges is improving your child’s reading comprehension. Good reading comprehension is the foundation for every other ELA skill they must master. 

Reading comprehension strategies for 5th graders include:

• Previewing the text
• Making Predictions
• Identifying the Main Idea in informational texts
• Identifying main events and summarizing narrative texts
• Discussion and analysis

How to Preview a Text

Previewing is a comprehension strategy that involves collecting information about a text before reading begins. This gives the reader an idea of what the text is about and gives them a framework of understanding that sets them up for better comprehension. 

To preview a text, examine the front and back covers to look for clues about the book’s contents.

• Think about the title and its meaning. The title will always provide some insight into the contents of the text. 
• Read the synopsis. It provides basic information about the story, characters, and plot (for novels) or the focus of the text (for non-fiction). 
• Read the author blurb. This can provide context for the author’s inspiration, interests, and values, which often reveal themes in the text. 
• Read the table of contents. Chapter titles provide a framework for the structure of the content and what topics it will cover. This is especially beneficial when previewing a textbook or other informational text.
• Read section titles and subtitles in informational texts. Headings and subheadings are like a map of an informational text’s main points. They can even be used to structure note-taking.

Making Predictions

After previewing and before the reading begins, have your child make predictions about the text. Ask them what they think will happen and what they expect to learn about based on what they discovered during the previewing exercise.

Making predictions involves using their own knowledge about other texts they’ve read to synthesize what they know about the new text. It also sets your 5th grader up to be an active reader. With the predictions in mind as they read, they will continue to process and analyze the details of the text, revising their predictions based on new information.

For an extra comprehension boost:

• After your child has made their predictions, make some of your own. Be sure to explain why you made the predictions you did. This models the thinking you want them to do and draws their attention to important details from the preview. 
• When they are done reading, ask them to tell you whose predictions were right. This encourages them to analyze the text to make better predictions next time. 
• Ask how and why their predictions changed as they read. What made them change their mind? This trains them to be aware of literary devices, pay attention to details, and recognize structural patterns in writing as they read.

Identifying the Main Idea 

Identifying the main idea is crucial to comprehending informational texts like textbooks, essays, and articles. As mentioned above, one way to do this is to read through the table of contents, chapter titles, and subtitles. These clearly outline of the most important information the text provides and often reveal the main idea. 

However, reviewing titles and subtitles alone is not always enough. To help your child find the main idea of any informational text and maximize their comprehension, follow these steps:

1. Look at the title. This is the topic on which the entire text is focused, and will be central to the main idea. 
2. Examine chapter titles, section titles, and subtitles. These will all move deeper into the main topic, highlighting key issues and details.
3. Study introductions paragraphs. Introductions inform the reader what’s important about the topic by providing a thesis or central claim, which the text will then explore and support with evidence. Central claims are usually located near the end of the introduction.
4. Study conclusion paragraphs. Conclusions paragraphs summarize the most important points of a chapter, section, or article, reiterating the thesis and support/evidence. 
5. Bring it all together: Now that your child understands the topic, main subtopics, and thesis, they should be able to identify the main idea. It’s the thought, issue, or beliefs that the entire text explores.
6. Put it in your own words: Finally, to solidify your child’s comprehension of the main idea, have them put it in their own words. This can be done in discussion, writing, or (ideally) both.

Identifying Main Events and Summarizing 

Summarizing and identifying the main events requires your child to recognize the most important elements of a story. This is equivalent to finding the main idea in narrative texts. It is absolutely key to achieving good comprehension of novels and stories. 

You can help your child practice identifying the main events in three ways.

1. Identifying the beginning, middle, and end 

Most narratives follow the same basic structure. Learning that structure can help your child comprehend every narrative they read more deeply.  Having them identify the beginning, middle, and end of a story is the simplest way to do this. 

• Beginning: Introduces the setting, the characters, and the “problem” that drives the plot.
• Middle: Involves the main character(s) trying to solve the problem, failing, and things getting worse. 
• End: The character(s) engage in a big, climactic conflict and finally solve the problem, followed by a wrap-up when any remaining issues get addressed.

2. Using a graphic organizer to map story elements

Employing a graphic organizer in story mapping is a great way to help your child visualize the plot structure and identify the main events. Story mapping graphic organizers come in many styles including  

• beginning, middle, and end
• chain of events 
• classic story arc 

Find a variety of free story mapping graphic organizers here: Story Maps | Reading Rockets

Note: Using a graphic organizer is also a great way to give your child a little extra writing practice while helping them improve their comprehension!

3. Doing summaries of reading

Finally, doing a summary requires your child to recall, process, and put the story into their own words, which is one of the best ways to deepen reading comprehension. Your child should practice both verbal and written summaries, alternating between the two. 

The level of detail in the summary is also an important point. A highly detailed summary requires greater recall and comprehension but isn’t as helpful with identifying main events. A short summary, on the other hand, requires greater skill at identifying the most important elements and knowing what to leave out. Both types are beneficial for your child to practice. 

A good summary should include:

• Characters that were present
• The setting(s)
• Main Events (anything that moves the story forward)
• Details that are necessary to understand the story 

You can gauge your child’s reading comprehension by the quality of their summary. If the summary seems scattered, out of chronological order or misses important events, their comprehension needs work. Try having them read and summarize smaller portions of the text to build this skill. When they can consistently produce good summaries, move on to summarizing larger portions of text. 

Discussion and analysis

The final way to help improve your child’s reading comprehension is through discussion and analysis. 

Verbal summarizing is an excellent way to begin a discussion with your child about their reading. After you’ve asked them to provide a detailed verbal summary, follow up with questions that require them to:

• Make inferences: use information from the text to draw conclusions or form opinions by “filling in the blanks” through context clues and common sense. 
• Synthesize: generate insight by combining what they learned from a text with things they already know.
• Analyze: look closely at individual parts of the text and think about what each part is doing. Then consider how the parts work together.

Example inference questions:

• Why do you think the main character did that? 
• How do you know? 
• What do you think will happen next? Why?

Example synthesizing questions:

• What does the story remind you of from real life?
• What does this story have in common with the last story you read?
• What would you do differently in the main character’s situation? Why?

Example analyzing questions:

• What is the central theme of the story and what makes you think so?
• What do you think the author’s purpose was for writing this story and why? 
• Find examples of figurative language (metaphor, simile, etc.) and discuss what they mean.

How to Improve 5th Grade Reading Fluency

Comprehension and fluency go hand in hand. A child who reads fluently reads smoothly, at a decent pace, with expression, and with good comprehension. They can tell when they’ve misread something and will independently re-read for understanding. 

The first step to improving fluency is knowing your child’s reading level. It’s very important not to make your child read too far above this level. If a text is too difficult, they will not gain skill from reading it. 

Once you know your child’s reading level, you can easily search for appropriate books using the links below.

Elementary school books by reading level: 

• Find a Book
• Best Children’s Books by Lexile 
• Scholastic Bookfinder

Here are some tips for improving 5th-grader reading fluency:

1. Read to your child: Read from a book you both enjoy, but one that’s above their reading level. Listening to fluent reading models good expression and gets them familiar with the rhythm of complex sentence structures they can’t read alone. 
2. Read with your child/Take turns: Read to your child from a book that’s on their level while they read silently alongside you, or take turns reading a few sentences at a time. This helps them learn new words and models the right pacing and expression. 
3. Call and response reading: Read a few sentences out loud and then have your child read the same paragraph, mimicking your pacing and expression. 

For the best results, do one of these practices for at least fifteen minutes, three times a week. 5th graders reading well below a fifth-grade level should do daily fluency practice to help them catch up. 

How to Improve 5th Grade Vocabulary

Vocabulary can also be a big challenge for 5th graders. At this age, they are expected to decode and extrapolate the meaning of many new multi-syllabic words from context while reading independently. They should also be able to recognize and interpret new phrases and figurative language. If they struggle to do any of these things, their comprehension and fluency will drop. 

Here are some ways to boost 5th-grade vocabulary skills:

1. Track new words: Have your child write down new words as they read, then look up and record the definitions. Then have them write original sentences using the new words. 
2. Study word roots and affixes: Using their list of vocabulary words from #1, help them break each word into roots, prefixes, and affixes. Have them look up the meanings of each word part, then think of other words with the same parts in them. 
3. Use synonyms and antonyms: Once they’ve recorded the meaning of a new word, have your child think of and/or look up synonyms and antonyms. 
4. Context clues: Have your child underline new words as they read, then discuss what the word might mean based on context. Look at the sentences before and after the new word to find clues to its meaning. 

All of these exercises help cement the meanings of new words and expand your child’s functional vocabulary. Learning word roots and affixes also helps them decode and understand new vocabulary. Finally, using context clues to find meaning is a skill they will rely on often in middle school. 

Writing Skills

Writing is another big challenge area in 5th grade ELA. Because writing skills build off reading skills, when your child is struggling with reading comprehension and fluency, they are likely also struggling with writing. As such, doing focused work to improve their reading skills is the first step to improving their writing skills. 

Beyond that, the best way to get better at writing is simply to write—daily! While most 5th graders do a reasonable amount of writing in school and for homework, a supplemental practice of 30 minutes per day at home is highly beneficial. 

Here are some recommended writing activities for 5th graders:

1. Writing summaries: Have your child write a detailed summary of a chapter or story they read. 
2. Discussion questions: Choose some of the inference or synthesizing discussion questions and have them do a written response about their reading. 
3. Creative prompts: Provide an interesting prompt like, “If you were president, what laws would you make?” or “Imagine a world where everything is made of candy. What would that be like?” Make it fun and interesting!
4. Write a story: Making up a story can be fun! Using one of the story maps linked in the “Identifying Main Events and Summarizing” section, have your child plot their own story, then write a little of it every day. 
5. Free-write: Allow your child to write whatever they want. They can write about their day, their interests, or anything that’s on their mind. 

Bonus 5th grade grammar help: If your child’s grammar and mechanics need work, help them edit their writing after they finish. Make a list of the mistakes they often make so they can refer to it when self-editing. Common mistakes among 5th graders include:

• Run-on sentences
• Repetitive language
• Punctuation 
• Spelling 
• Vocabulary use

Encourage your child to look up grammar rules and keep a list of the ones they often misuse. For example, many 5th graders struggle to use commas correctly. Keeping a list of comma rules on hand will help with their self-editing practice.

Sources

English Language Arts Standards | Common Core Standards Initiative

Comprehension | Read Naturally

Fifth Grade Reading: Tips to Smooth Out the Transition | Scholastic

Fluency for 4th & 5th Grades | North Carolina Department of Public Instruction

Preparing for Middle School | Scholastic

Strategies that Promote Comprehension | Reading Rockets

Teaching Elementary School Students to Be Effective Writers | Institute of Education Services

Vocabulary for 4th & 5th Grades | North Carolina Department of Public Instruction

Why Do So Many Adolescents Struggle with Content-area Reading? | Iris Peabody Vanderbuild

Writing Help & Resources | Education.com

By encouraging and motivating your child, doing consistent daily practice, engaging in focused discussion, and supporting them with homework, you can help your child succeed in every aspect of elementary school ELA.

1. Motivate your Child

The first step to success in grade school ELA is motivating your child. A self-motivated student is much more focused and engaged. They want to succeed and are willing to put in the effort necessary. Yet many children find reading and writing challenging. So how do you help them find that inner drive?

Express how important reading and writing are to you

Show enthusiasm for ELA in whatever way you can. Read to your child regularly. Share books you read and loved as a kid. Talk about the things you’ve written. Seeing that you value reading and writing will motivate your child to learn.

Note: Reading to your child is an excellent way to create positive associations with reading, but it should be separate from their independent reading practice.

Be patient with your child’s progress

Learning to read and write is challenging, even for the best students. Fear of failure or parental disapproval can kill their motivation.

Remind your child often that it’s okay to mess up. Making mistakes is an essential part of the learning process!

Take breaks if your child gets tired or frustrated. Splitting daily practice into multiple shortsessions is better than doing a marathon.

Offer encouragement and rewards for consistent effort

Positive feedback can give your child the confidence and motivation to keep trying until they get it right. This is especially true if they are struggling.

Verbal praise is often all it takes, but you can also offer physical rewards for milestones set and reached. A chart with stickers for completed assignments can help motivate your child by creating a visual representation of their progress.

Rewards may be small—a new book, a playdate with friends, or even a trip to the park—as long as they are something your child gets excited about.

Make reading and writing fun

Focus on what your child finds interesting. Do they enjoy science? Nature? Fantasy? Choose reading and writing topics that they love. If possible, make learning new skills into a game.

Check out the links below for free elementary reading and writing resources.

• Writing exercises for elementary students: education.com
• Fun reading activities for young students: readingrockets.org
• Best books for elementary readers: k-12readinglist.com

2. Daily Reading Practice

Practice makes perfect, especially concerning complex skill sets like reading and writing! While your child will get practice every day at school, supplemental practice at home is highly beneficial. Daily reading practice helps

• Improve fluency
• Improve comprehension
• Build confidence
• Minimize skill regression over breaks and holidays

Depending on age and reading level, grade school students should read for a minimum of 15 to 30 minutes a day.

Create a routine to establish a daily reading habit. Have your child read at the same time every day, ensuring that they have a quiet and comfortable environment in which to do it.

Keep in mind that students in grades 1-2 require parental assistance to decode new words as they read. 3rd graders should be reading independently but may still need occasional support. Discuss your child’s support needs with their teacher before settling on a daily reading practice.

Finally, if your child struggles to read continuously for the assigned time, try splitting it into two or three shorter sessions throughout the day. Continuing to read when your child is tired or frustrated is counterproductive. Doing so undermines their motivation and confidence, potentially creating a negative association with the practice.

3. Discussion

Another key to boosting your child’s ELA skills is engaging them in discussions about their reading. This improves

• comprehension
• information retention
• speaking skills
• writing skills

The goal is to get your child thinking more deeply about the text. A spirited discussion with a parent also creates bonding and encourages positive associations with reading, which helps increase your child’s enthusiasm and motivation.

Discussion should be done at least three times a week. The more frequently, the better!

Reading Comprehension Questions and Tips

Ask your child questions about what they read (or what you read to them). As a general rule, avoid questions with yes/no answers. Stick to “how,” “why,” and “what” questions.

When your child gets stuck on a question, express your own opinions about the events and characters. Doing so provides an expanded perspective and models the thinking you want them to learn.

Discussion questions that support reading comprehension come in three main types:

• summarizing
• making inferences
• synthesizing

Summarizing

Summarizing requires asking readers to put the story into their own words by “retelling” what they read. A good summary can be short and simple (including only the main events) or extremely detailed. Have your child do it both ways, alternating between the two.

Example summarizing questions:

• What was the story about?
• What are the main events?
• What happened in the beginning/middle/end?
• Tell me everything you can remember about what you read.

Making Inferences

Making inferences means using information from the text to draw conclusions or form opinions. This involves “filling in the blanks” through context clues and common sense.

Example inference questions:

• Why do you think the main character did that?
• How do you know?
• What do you think will happen next? Why?

synthesizing

Synthesizing questions encourage readers to combine what they learned from a text with things they already know to create new thoughts, ideas, and opinions.

Example synthesizing questions:

• What does the story remind you of from real life?
• What does this story have in common with the last story you read?
• What would you do differently in the main character’s situation? Why?

4. Daily Writing Practice

Pairing daily reading practice with daily writing practice is another essential way to help your child excel in ELA. Writing about what they read has similar benefits to discussion including increased comprehension and information retention.

Grade school students should write for about an hour a day, but because they do much of this writing in school or during homework, a supplemental daily practice of 15-30 minutes is usually sufficient.

First, provide your child with a notebook or journal specifically for their daily writing practice. Allowing them to choose a notebook with a colorful cover or to decorate it with stickers can create excitement and positive associations with writing.

Next, provide a writing topic that interests your child. Many grade school students have difficulty thinking of something to write without a prompt. Topics can be anything from “Tell me about your day” to “If you could have any superpower, what would you choose and why?”

Other good writing topics include

• favorite movies
• favorite games
• favorite activities
• recent events

You can also use the discussion questions above to form a good writing topic based on their daily reading.

What your child can accomplish in a 15-30 minute writing practice will vary by age and skill level. Below is a loose guideline by grade. However, discuss your child’s writing level with their teacher before settling on a routine.

1st and 2nd grade

First and Second-graders are just learning to write. Most can write 3-6 sentences in fifteen minutes with parental support. They will need help with

• spelling
• grammar
• penmanship
• composing single sentences

At this age, they cannot write independently. They may be unable to think up a sentence, and they will struggle to spell most words. For this reason, it’s beneficial to

• provide them with a grade-appropriate writing workbook
• have them copy words and sentences
• have them compose sentences together with you

3rd Grade

Third graders are still beginning writers. Most can write 6-10 sentences in fifteen minutes. They should be able to compose simple sentences and spell many words correctly but need support with

• grammar
• vocabulary
• sentence structure variety

At this age, they may or may not be able to write independently for fifteen minutes. Spelling and penmanship may still be a challenge, but they are old enough to sound words out phonetically and correct their work with moderate support.

4th and 5th Grade

Fourth and fifth graders are intermediate writers. Most can write 10-20 sentences in fifteen minutes. They can spell most words correctly and use a variety of sentence structures on their own.

At this age, they should be able to write for 15-30 minutes independently, but will still need assistance correcting grammar and spelling errors.

Note: If your child is resistant to writing or finds it especially difficult at any stage, try allowing them to do their daily writing without correcting their work. As long as they’re practicing daily, rest assured, they are improving their writing skills! Once they’ve gained some confidence, you can reintroduce correcting as a separate practice with a break in between.

5. Help with ELA Homework

Helping your child complete their homework is the final step in setting them up for success. If ELA curriculum for elementary students isn’t your strong suit, don’t worry! Here are some tips and tricks to get your child’s homework done right.

Find the Right Place

Make sure your child has an appropriate place to work. It should be quiet, well-lit, and free of distractions like

• screens
• toys
• pets
• siblings

For 1st-3rd graders, you will need to sit with them and be an active participant. For 4th and 5th graders, choose a spot nearby where you can observe and jump in when support is needed.

Follow a Schedule

Do homework at the same time and in the same place every day. This will help get your child into the correct mental space and impress upon them how important homework is.

Helping your child with organization and time management is also a crucial part of this process. At the beginning of each week, go over their upcoming assignments with them. Help them figure out when to do each one so they have time to complete everything without rushing.

Use a calendar or planner to help them keep track of everything. Before each homework session, bring out the calendar to review what needs to be done. Have them write their assignments in, and mark the time they need to complete them.

Note: While some 4th and 5th graders are capable, most grade school students require support to use a calendar/planner and manage their time effectively. Even older students will often miss assignments without a parent to remind them.

However, modeling this behavior consistently is the best way to teach your child organization and time management so they can do it independently later.

Help with Instructions

Once homework is underway, ensuring that your child understands and follows the instructions is half the battle! Here are some ways to help them with instructions.

• Read the instructions aloud AND have your child read them aloud. Reading and listening use different parts of the brain. Doing both helps your child process the instructions more deeply.
• Check for understanding. Ask, “What do you do first?” Many grade school children have difficulty remembering instructions for more than a few minutes, so guide them through completing their homework one step at a time.
• Rephrase to clarify. If your child is still struggling to understand, try rephrasing the instructions. Ask if any words in the instructions are confusing. Sometimes using different words will help the meaning click.
• Return to the instructions often. When they finish one step or start to flounder, point them back to the instructions. Ask, “Did you do the first part? What’s next?”
• Always double-check that all instructions have been followed. When the assignment is complete, have your child review the instructions again. Ask, “Did you do everything?”
• Let your child check their work first. Only point out mistakes if your child misses them. With repetition, they will start to remember the steps independently, spot mistakes easily, and eventually follow instructions independently.

Rely on Teachers

Sometimes you just won’t know how to help, or you won’t have the time. It’s ideal to communicate regularly with your child’s teacher throughout the school year.

Check in on your child’s progress often. The teacher should have helpful advice and resources to support your child with homework.

Finally, encourage your child to seek help from their teacher whenever they need it. Ask if your child’s teacher has time before or after school to review assignments and clarify homework.

When All Else Fails

If you’ve done all of the above and your child is still consistently struggling with ELA, it may be time to seek outside help. Consider having your child assessed for learning disabilities and/or hiring an experienced ELA tutor – contact us today to learn more about how our tutoring services can make a difference in your child’s academic journey.

Sources

9 Tips from Teachers to Help Your Child Catch Up on Reading Level | Scholastic

50 Books All Kids Should Read Before They’re 12 | Common Sense Media

Helping Your Grade Schooler With Homework | Kids Health

How Children Learn to Read: Typical Reading Development | Reading Rockets

Reading Lists for Elementary School Children | K-12 Reading List

Reading Motivation: What the Research Says | Reading Rockets

Strategies that Promote Comprehension | Reading Rockets

Teaching Elementary School Students to Be Effective Writers | Institute of Education Services

The Role of Motivation in Learning | The Education Hub

Writing Help & Resources | Education.com

What is Integrated Math?

Integrated Math is an alternative to the traditional high school math pathway, which typically separates Algebra, Geometry, Algebra 2/Trigonometry, and Precalculus into distinct courses. Instead, Integrated Math weaves together concepts from these areas so that students can see the connections between different math topics. This approach reflects the way math is used in real-world applications and makes it more relevant and engaging.

The Integrated Math Sequence

IM1: Building a Strong Foundation

IM1, or Integrated Math 1, is the starting point of this sequence. Generally, students start the sequence in 9th grade, but advanced learners can begin in 8th grade. IM1 introduces students to fundamental concepts across algebra, geometry, and statistics.

• Algebra: IM1 covers the basics of algebra, including linear equations, inequalities, and functions. Students learn to solve and graph equations, laying the groundwork for more complex problem-solving.
• Geometry: The geometry component of the course introduces students to basic shapes, congruence, and transformations. Students begin to understand how algebra and geometry are interconnected.
• Statistics: Basic data analysis and probability are also introduced in IM1. Students learn to interpret and present data and are taught skills that are increasingly important in a data-driven world.

IM1 is crucial for building a solid foundation. Success in this course sets a student up for more advanced mathematical thinking in the following years.

IM2: Expanding and Deepening Understanding

IM2, or Integrated Math 2, builds on the concepts learned in IM1 and introduces more complex topics.

• Algebra: Students delve deeper into quadratic functions, polynomials, and systems of equations. Other types of functions such as exponential functions with growth and decay models are introduced. The algebraic skills gained in IM1 are expanded to include more sophisticated methods of solving equations.
• Geometry: The geometry component covers more topics like similarity, basic triangle trigonometry, circles, and analytic/3D geometry (finding area and volume). Students begin to apply their algebraic skills to geometric problems, fostering a more integrated understanding.
• Statistics: IM2 expands on the statistics from IM1, focusing on probability and the interpretation of more complex data sets. This helps students develop a better understanding of randomness and variation.

IM2 is designed to solidify a student’s understanding of how mathematical concepts connect.

IM3: Preparing for Advanced Math

IM3, or Integrated Math 3, is the culmination of the Integrated Math sequence. It prepares students for higher-level math courses such as Pre-Calculus, AP Calculus, or AP Statistics.

• Algebra: IM3 covers more advanced algebraic concepts, including rational, exponential, and logarithmic functions, sequences and series, and advanced polynomial functions with transformations. These topics are essential for the math used in higher education.
• Geometry: In IM3, the focus shifts to the application of trigonometric identities and the exploration of more complex geometric properties. This course ties together all the geometric concepts learned in the previous courses.
• Statistics: IM3 often includes an introduction to inferential statistics. Students learn to make predictions or inferences based on data, a critical skill in many fields, from science to economics.

By the end of IM3, students should have a well-rounded mathematical education and be well-prepared for comes next.

How We Can Help

At MathTowne, we understand that the Integrated Math sequence can be challenging. Our experienced tutors are here to guide students through the integrated math sequence, ensuring they build the skills and confidence needed to succeed. Whether your student is just starting IM1 or needs support in IM3, we provide personalized tutoring that meets their unique needs.

Get in Touch! If you or your student needs help with any of the Integrated Math courses, don’t hesitate to reach out. We’re here to help make math less intimidating and more manageable, one concept at a time.

AP Precalculus

Pros:

1. College Credit: One of the most significant advantages of taking AP Precalculus is the potential to earn college credit. Scoring well on the AP exam can allow you to skip introductory college courses (depending on the college), saving time and tuition costs.
2. Standardized Curriculum: AP courses follow a standardized curriculum set by the College Board, ensuring a consistent level of rigor and quality. This can be beneficial for students who plan to apply to competitive colleges, as it demonstrates the ability to succeed in a nationally recognized program.
3. Advanced Content: According to College Board, AP Precalculus is designed to prepare students for subsequent AP Calculus courses or college-level calculus by ensuring students have a depth of understanding to be ready for calculus.
4. College Application Boost: Having AP courses on your transcript can strengthen your college applications. Admissions officers often view AP courses as a sign that a student is willing to take on challenging coursework.

Cons:

1. High Pressure: As with any AP course, the pressure to perform well on the AP exam can be intense.
2. Pacing: The pace of AP courses is often faster than that of honors courses because the last month before the AP exam is usually spent on exam preparation. This can be challenging for students who need more time to grasp complex concepts.
3. Exam Focus: The curriculum is tailored to prepare students for the AP exam, which means there might be less flexibility in exploring topics outside of the exam’s scope.
4. Potential for Burnout: The workload can be significant, potentially leading to burnout, especially if a student is juggling multiple AP courses.

Precalculus Honors

Pros:

1. Rigorous Curriculum: Precalculus Honors courses still offer a challenging curriculum (compared to regular Precalculus) that prepares students well for calculus, but again, this depends on the school. The depth and complexity are sufficient for students who aim to excel in math without the added pressures of an AP exam.
2. Flexibility: Honors courses often allow teachers more flexibility in their teaching methods and the topics they cover. This can provide a more enriched and diverse learning experience.
3. Balanced Workload: Without the need to prepare for a standardized exam, the workload in an honors course can be more balanced, reducing the risk of burnout and allowing students to focus on understanding the material deeply.
4. Strong Foundation: Honors courses can provide a strong foundation in precalculus concepts, helping students succeed in future math courses, whether in high school or college.

Cons:

1. No College Credit: Unlike AP courses, honors courses do not offer the opportunity to earn college credit. This can be a drawback for students looking to get ahead in their college coursework.
2. Varied Curriculum: Since honors courses do not follow a standardized curriculum, the quality can vary significantly between schools and teachers.
3. Perception by Colleges: While honors courses are respected, they may not carry the same weight as AP courses to college admissions officers, particularly at highly competitive institutions.
4. Less Focus on Exam Skills: Honors courses may not place as much emphasis on developing the test-taking skills that are often cultivated in AP courses. For students who plan to take standardized tests such as the SAT or the ACT, developing these test-taking skills would be useful.

So while AP Precalculus aims to standardize the curriculum and offers the potential for college credit, its novelty means some teachers may still be getting accustomed to teaching it. Precalculus Honors, on the other hand, still provides a rigorous but potentially more varied and flexible curriculum, but without an AP exam to demonstrate sufficient knowledge. Ultimately, the choice between the two should be based on individual academic goals and learning preferences.

For more info, check out our blog post for a detailed breakdown of the AP Precalculus curriculum and exam.

1. Review the Digital Format

Familiarize yourself with the digital format of the SAT – understand how the test is structured, including the number of sections, types of questions, and overall layout, as outlined in our blog post.

2. Practice with Official Tools

Use the College Board’s official SAT practice platform – the Bluebook app – which provides digital practice tests and sample questions. So far, four official digital SAT practice tests are available. These allow you to become comfortable with the digital interface and tools, such as highlighting, flagging questions, and using the on-screen calculator.

3. Simulate Test Conditions

Practice taking digital SAT practice tests under timed conditions to simulate the experience of the actual test. Use a quiet, distraction-free environment and follow the timing guidelines for each section.

4. Use Classic Techniques

Although the format is different, the classic techniques for answering the SAT’s multiple-choice questions still work. For example, using the process of elimination to eliminate obviously incorrect answer choices will narrow down your options and increase your chances of selecting the correct answer. Or for math questions, consider plugging in answer choices to see which one fits the given conditions or equations. This can help you quickly identify the correct solution.

5. Practice Time Management

Time management is crucial on the digital SAT, so practice pacing yourself to ensure you can complete each section within the allotted time. Use strategies such as skipping difficult questions and coming back to them later if necessary.

6. Utilize Tools Effectively

Familiarize yourself with the digital tools provided, such as the highlighting features and the Desmos calculator that is available for use on the entire math section. This is the version for the digital SAT, PSAT, and NMSQT. Practice using these tools efficiently to solve problems and annotate passages effectively.

7. Review Technical Requirements

Make sure your device meets the technical requirements for taking the digital SAT. Check compatibility with the official testing platform, ensure a stable internet connection, and familiarize yourself with any additional requirements or guidelines.

8. Stay Updated

Keep abreast of any updates or changes to the digital SAT format or testing procedures. Visit the College Board website regularly for the latest information and announcements.

9. Stay Calm and Confident

On test day, stay calm and confident in your abilities. Trust in your preparation and strategies, and approach each question methodically and thoughtfully.

How to Study for the Digital SAT

Need more targeted practice problems to prepare for the test effectively? Our digital SAT tutors can work with you to pinpoint which areas to work on and offer plenty of practice problems for specific topics!

Precalculus typically includes a comprehensive review and extension of the topics that students have already learned in Algebra 2, such as polynomial and rational functions, exponential and logarithmic functions, and systems of equations. There are a few topics of trigonometry it goes deeper into, such as trigonometric functions, identities, and equations. It also introduces other topics such as conic sections, polar coordinates, and parametric equations, which is typically covered in AP Calculus as more advanced material. Assessing your understanding of these foundational concepts is key – if you thrived in Algebra 2, you may have no issue skipping precalculus. Ask yourself:

• Can you confidently solve algebraic equations, manipulate functions, and work with trigonometric identities and inverse trigonometric functions?
• Do you understand the properties of logarithms and exponential functions?
• Are you comfortable graphing various functions and interpreting their behavior?

What Does Precalculus Cover?

Many schools have not yet implemented the new AP Precalculus course from College Board and regular precalculus is not a standardized course, so topics that your school’s class covers may vary slightly. Some precalculus classes may choose to omit certain ones. However, if you crack open a precalculus textbook and take a look at the table of contents, here are some common topics typically included in the curriculum:

1. Functions and Graphs

• Understanding various types of functions (linear, quadratic, polynomial, rational, radical, and inverses) and their graphical representations.

2. Exponential and Logarithmic Functions

• Understanding the properties of exponential and logarithmic functions, solving exponential and logarithmic equations, and applications such as exponential growth and decay.

3. Complex Numbers

• Exploring the properties and operations involving complex numbers, including complex roots of polynomials and applications in engineering and physics.

4. Sequences and Series

• Investigating arithmetic and geometric sequences, series, and sums, including convergence and divergence.

5. Trigonometry

• Exploring trigonometric functions (sine, cosine, tangent), trigonometric identities, equations, and their applications in solving triangles and analyzing periodic phenomena.

6. Trigonometric Identities and Equations

• Deriving and manipulating trigonometric identities, solving trigonometric equations, and applying trigonometric techniques to solve real-world problems.

7. Analytical Geometry

• Studying the properties and characteristics of conic sections – circles, ellipses, hyperbolas, and parabolas.

8. Polar Coordinates and Parametric Equations

• Understanding the representation of points using polar coordinates and parametric equations, as well as converting between different coordinate systems.

9. Matrices and Vectors

• Introducing matrix operations, determinants, inverses, and applications of matrices, as well as vectors and their properties in two and three dimensions.

10. Limits and Continuity

• Introducing the concept of limits and their properties, evaluating limits algebraically and graphically, and understanding continuity of functions. This one in particular will be taught in more depth at the beginning of AP Calculus.

These topics provide students with the necessary skills to tackle calculus and other advanced mathematical subjects. Mastering these concepts is essential for success in higher-level mathematics and various STEM fields.

Can You Skip Precalculus?

If you’re uncertain about the material you’ll need to know before taking AP Calculus after Algebra 2 and/or Trigonometry, consider working with a tutor to bring you up to speed with the topics necessary to skip Precalculus. Our Precalculus, Integrated Math, and Algebra 2 tutors provide tailored support to match and expand on your current level of understanding. Schedule a free consultation with us today!

Integrated Math III, or IM3 for short, is the last course in the integrated pathway organized by the Common Core State Standards as an alternative to the traditional math pathway. Integrated Math is a comprehensive series of courses aimed at blending key concepts from algebra, geometry, statistics, and other mathematical fields into a unified curriculum. Rather than treating these subjects as separate fields as the traditional math curriculum does, the IM pathway “integrates” these classes by highlighting their connections to each other and real-world applications.

What Does IM3 Teach?

The mathematics framework for California public schools contains an overview of what students are expected to be able to do in the class. There are five main topics that students will learn about.

1. Number and Quantity

• Learn about complex numbers vs. real and irrational numbers, and continue to use basic operations such as addition, subtraction, multiplication, and division.

2. Algebra

• Manipulate algebraic and rational expressions
• Create and solve equations and inequalities by apply algebraic techniques
• Use polynomial identities and the Binomial Theorem to solve problems
• Understand factors and zeros of polynomials

3. Functions

• Understand the behavior and characteristics of various types of functions and their graphical representations.
• Emphasis is placed on analyzing functions, identifying key features such as domain, range, intercepts, and transformations, and solving problems involving function notation.

4. Geometry

• Topics may include properties of geometric shapes and figures, congruence and similarity, trigonometry, geometric transformations, and coordinate geometry.
• Students also explore applications of geometry in real-world contexts, such as area and volume calculations and geometric proofs.

5. Statistics and Probability

• This topic introduces students to basic principles of statistics and probability and their applications in data analysis and decision-making.
• Students learn to collect, organize, and interpret data using statistical measures such as mean, median, mode, and standard deviation.
• Probability concepts cover topics such as theoretical and experimental probability, probability distributions, and basic statistical inference techniques.

What is Integrated Math 3 Equivalent To?

Generally, the topics found in IM3 are what a regular Precalculus course would cover.

Can I still Take AP calculus After Finishing Integrated Math?

Absolutely, many students typically take AP Calculus during their senior year of high school after completing Integrated Math 3 in their junior year. Integrated Math 3 provides a solid foundation in algebra, geometry, trigonometry, and other essential mathematical concepts that are prerequisites for success in calculus.

Students who are interested in pursuing more advanced mathematics and potentially earning college credit while still in high school naturally progress from IM3 to AP Calculus. AP Calculus covers topics such as limits, derivatives, integrals, and differential equations, building upon the knowledge and problem-solving skills developed in Integrated Math 3.

Can I skip IM2 or 3?

Skipping earlier Integrated Math courses in the pathway is possible in some cases, but it largely depends on several factors, including your individual academic readiness, school policies, and curriculum structure.

For example, if you’d like to skip Integrated Math 2 in order to take AP Calculus earlier, keep some considerations in mind:

1. Prerequisite Knowledge:

Integrated Math 2 typically covers essential concepts that are foundational knowledge for Integrated Math 3 and AP Calculus. Skipping IM2 means potentially missing out on crucial topics such as linear equations, quadratics, geometric proofs, and basic trigonometry. Make sure you have a strong understanding of these concepts before considering skipping the course.

2. Academic Readiness:

AP Calculus is a rigorous course that requires a solid understanding of algebra, geometry, trigonometry, and precalculus. Skipping IM2 or 3 and jumping to AP Calculus might be feasible if you have demonstrated exceptional proficiency in mathematics and are confident in your ability to handle advanced coursework. However, it’s essential to assess your readiness and ensure that you won’t be overwhelmed by the jump in difficulty.

3. School Policies:

Some schools may have specific prerequisites or policies regarding course sequencing and eligibility for AP courses. Check with your school’s guidance counselor or mathematics department to see if skipping IM2 is allowed and advisable based on your profile.

4. Alternative Pathways:

If skipping IM2 isn’t feasible, consider alternative pathways to accelerate your math education. For example, you could take IM2 concurrently with IM3 to catch up on missed content. Additionally, you may explore summer enrichment programs, online courses, or dual enrollment options as supplements to advance more quickly, if your school allows for it.

Are you considering skipping any of the Integrated Math 1, 2, or 3 classes to fast-track your math education? At MathTowne, we offer personalized guidance and support to help you navigate this decision with confidence. Our experienced tutors for the Integrated Math courses provide tailored instruction, filling any knowledge gaps and preparing you for the challenges ahead, including AP Calculus and beyond. For Schedule a free consultation to explore this with us today!

1. Factoring

If the coefficient a in front of x is 1, usually factoring is the most efficient method to go with. The purpose is to turn the quadratic in standard form into x-intercept form so that the roots can be easily identified. For example, take the problem

$$x^2-6x+8=0$$

What we are looking for is two factors that multiply to 8 and add to -6. These will be -2 and -4. So the quadratic in factored form is

$$(x-2)(x-4)=0$$

$$x=2, 4$$

If the coefficient a is not 1, you can use the Diamond Method to factor it. For example, take $2x^2+7x-15=0$. In this problem, $a=2$, $b= 7$, and $c = -15$. Take a and c and multiply them together to get -30. The coefficient b is 7. Now we’re looking for two numbers that multiply to ac (-30) and add or subtract to b (7).

The simplest way to search for those two numbers is to write out the factors of -30 in pairs, starting with 1, as follows:

$$\pm 1, \pm 30$$

$$\pm 2, \pm 15$$

$$\pm 3, \pm 10$$

Here we can see that 10 and -3 will add up to 7, so these are the factors.

Next, split up the x term in $2x^2+7x-15=0$ into those factors:

$$2x^2+10x-3x-15=0$$

Then factor by grouping.

$$2x(x+5) – 3(x+5)=0$$

$$(2x-3)(x+5)=0$$

$x=3/2$ and $-5$.

However, sometimes you may not be able to find integer factors for ac that add up to b, in which case use the quadratic formula or complete the square.

2. Square Roots Method

Whenever a quadratic equation has only $x^2$ terms (and no $x$ terms), the square roots method is most efficient. For example, to solve

$$2x^2 + 4 = x^2 + 20$$

Start by combining the like terms of $x^2$ together on one side, and the constants on the other (by subtracting $x^2$ and then 4 from both sides).

$$2x^2-x^2 + 4 = 20$$

$$x^2 + 4 = 20$$

$$x^2 = 16$$

$$x = \pm4$$

Don’t forget the $\pm$ since both are solutions that will give the positive square number!

Caution – if the last step with $x^2$ equals a negative number (for example $x^2 = -16$, then the equation has no real solutions, although your math class may ask you to include imaginary solutions (which will be $\pm4i$).

3. Completing the Square

Generally, the purpose of completing the square is to turn a quadratic in standard form into vertex form $y=a(x-h)^2+k$, where $(h,k)$ is the vertex of the parabola, since it is the least efficient way of solving an equation. But it can still be used for when the solutions may not be rational numbers. Let’s say we want to solve, by completing the square,

$$3x^2-12x+7=0$$

First, factor out the coefficient in front of $x^2$ and include the $x$ term in parentheses as well:

$$3(x^2-4x) + 7 = 0$$

Next, we want to find a number to add to $(x^2-4x)$ so that it will turn into the binomial squared form $(x-h)^2$. To find it, take the b coefficient in front of the $x$ term, divide by 2, and square it – in this case, the coefficient is -4.

$$(\frac{-4}{2})^2 = 4$$.

Add the 4 inside the parentheses

$$3(x^2-4x+4) + 7 = 0$$

Because we’ve effectively added 3$\times$4 = 12 to the left side of the equation, we have to subtract 12 in order to keep the original equation!

$$3(x^2-4x+4)+7-12 = 0$$

$$3(x^2-4x+4)-5 = 0$$

Now the $(x^2-4x+4)$ can be factored into $(x-2)^2$.

$$3(x-2)^2-5 = 0$$

From here, use the square roots method to solve.

$$3(x-2)^2=5$$

$$(x-2)^2=\frac{5}{3}$$

$$x-2=\pm\sqrt{\frac{5}{3}}$$

$$x=2\pm\sqrt{\frac{5}{3}}$$

The two solutions are irrational, but roughly 3.29 and 0.71.

If you find yourself struggling with quadratic equations or any other aspect of algebra, don’t hesitate to reach out for help. Our Algebra 1 and Algebra 2 tutors are here to guide you through your math class, providing personalized support tailored to your learning style and pace. Ready to take your algebra skills to the next level? Schedule a free consultation with us today!

Traditional math typically involves separate courses – generally, students progress through Algebra 1, Geometry, Algebra 2 and/or trigonometry, Precalculus, and then Calculus, with each course focusing on specific topics related to that area of math. This approach has been the standard in many educational systems for decades.

On the other hand, integrated math combines topics from algebra, geometry, and other areas of math into a single course. For example, students in Integrated Math I learn foundational algebra topics such as linear equations, inequalities, and how to graph these functions, but topics from geometry such as quadrilaterals and congruent triangles are also included, or “integrated.” The goal of integrated math is to show the connections between different math concepts and to present math as a coherent, unified subject rather than a series of isolated topics.

Students may be presented with more real-life application problems to develop their overall understanding of the purpose of math. Sometimes, these problems are more challenging as they require more critical thinking about the concepts that the students have learned. By tackling problems that require the integration of multiple concepts, students can develop a deeper understanding of how mathematics is used in practical situations.

However, whether one approach is more advanced than the other depends on the curriculum, how in-depth a teacher might go into each topic, and the goals of the course. Some integrated math courses may cover advanced topics earlier than traditional courses, while others may cover the same material but in a different order or with different emphases.

Integrated math is not necessarily more advanced than traditional math; it’s just a different approach to teaching mathematics that emphasizes the connections between different topics.

Looking to excel in an Integrated Math 1, 2, or 3 class? Our Integrated Math tutors provide personalized support and guidance tailored to the curriculum – schedule a free consultation today!

The quadratic formula is a powerful tool used to solve quadratic equations – these are equations involving a variable squared, such as x² (“quad” meaning square), and no higher power. Generally, the problems you encounter will be in standard form $ax^2 + bx + c = 0.$

The solution(s) you get will be the roots, or x-intercepts of the graphed function which will be a parabola. The quadratic formula is as follows:

$$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$

When To Use the Quadratic Formula?

Whenever you see the words “solve for x” in a problem or “find the roots,” the quadratic formula is an option that you can use. For example, take the function $$y=2x^2-5x-3$$ with the problem asking you to find the roots. From the equation, $a=2, b=-5,$ and $c=-3.$

Plugging these into the quadratic formula,

$$x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-3)}}{2(2)}$$

$$x=\frac{5\pm\sqrt{25+24}}{4}$$

$$x=\frac{5\pm\sqrt{49}}{4}$$

$$x=\frac{5\pm 7}{4}$$

$$x=3,-\frac{1}{2}$$

These are the two solutions. As an aside, these roots will the cross the x-axis at the points $(3,0)$ and $(-\frac{1}{2},0).$

And there you have it! The quadratic formula is not the only way to solve a quadratic equation – the other methods are factoring and completing the square leading into the square roots method, alternative ways to be discussed in a later blog post.

Extra Practice

For extra practice on using the quadratic formula, try out these worksheets with the answer key included.

Worksheet 1

Worksheet 2

Worksheet 3