#### July 5, 2024

# Real World Examples of Number Sense

**What is Number Sense**
Number sense refers to an intuitive understanding of numbers and their relationships. It goes beyond memorizing procedures and formulas, allowing individuals to easily manipulate numbers, estimate quantities, and make sense of numerical information in various contexts.

**Real World Examples**
To understand the usefulness of number sense, let’s start with a simple real-world example. Imagine it’s Saturday evening and you and four of your friends just finished eating at a restaurant. The waiter handed the bill to you and the total on the bill is $108. You think the service was average and the tip should be 15%, but one of your friends thinks that the service was better than average, and the tip should be 20%. Moreover, another friend thinks the service was even better and thinks that you should leave a 25% tip.

You want everyone to understand the difference in the amount for each of these tip percents. Your friends take out their phones to calculate the amount of tip and you tell them that you can do this in your head and give them the answers in under 30 seconds. Your friends are amazed and ask you how you did that. Here is what you tell them:

**10% as a benchmark:** First calculate 10% of the total amount as a benchmark. With number sense you understand that 10% just means 1/10th of the number and can be found by dividing the number by 10 (which is moving the decimal point one position to the left). So, 10% of $108 is $10.80.
**15% tip:** With number sense you understand that 15% is 10% plus 5% (which is half of 10%). To get the half of $10.80, you can separate $10 and 80 cents and get half of each and then add them back. Half of $10 is $5 and half of 80 cents is 40 cents, so half of $10.80 is $5.40. So, 15% of $108 is $10.80 + $5.40 = $16.20.
**20% tip:** With number sense you understand that 20% is double of 10%. To double $10.80, you can separate $10 and 80 cents and get the double of each and then add them back. Double of $10 is $20 and double of 80 cents is $1.60. So, 20% of $108 is $21.60.
**25% tip:** With number sense you understand that 25% is 20% plus 5%. So, 25% of $108 is $21.60 + $5.40 = $27.
**25% tip alternate method:** With number sense you also understand that 25% is 1/4th of the total amount. You can make the division easier by first breaking $108 into two parts: $100 + $8. Now you can divide each part by 4 and then add the results back. So, $100/4 = $25 and $8/4 = $2 and $25 + $2 = $27.

After discussing with your friends, you all decide to give 25% as tip and divide the total amount equally among the five of you. Use your number sense to figure out what each person will pay for the dinner. Answer to this question and all the answers from the next section will be posted in our next blog.

**Other real-world examples of Number Sense**
Here are some more real-world examples for you to test your number sense skills. Answers and the number sense methods to come up with the answers to all these will be provided in our next blog.

**Discounts and Sales:**

o If an item is originally priced at $80 and is on sale for 30% off, what is the sale price?
**Time and Distance:**

o A train travels at an average speed of 50 miles per hour. How long will it take to travel 175 miles?
**Proportions and Scaling:**

o If a recipe calls for 2 cups of flour to make 24 cookies, how much flour is needed to make 42 cookies?
**Interest and Investments:**

o If you take a loan of $50,000 at an annual interest rate of 6%, how much interest will you pay in 3 years?
**Measurement and Conversions:**

o You are 5.5 feet tall. How tall are you in inches?

**Why Developing Number Sense is Important**
**Strong foundation for higher-level math:** Number sense is the building block for more complex mathematical concepts like algebra, geometry, and calculus. A student with strong number sense can more easily grasp abstract ideas and solve problems.
**Real-world problem-solving:** Number sense enables individuals to apply mathematical skills to everyday situations, such as calculating discounts, comparing prices, understanding statistics, and making financial decisions.
**Critical thinking and reasoning:** Number sense encourages students to think critically, analyze information, and develop problem-solving strategies. It fosters a deeper understanding of mathematical relationships and patterns.
**Mental math proficiency:** Number sense enhances mental math abilities, allowing individuals to perform calculations quickly and accurately without relying solely on calculators or written methods.

myQBook offers an industry leading number sense development program (

https://www.myqbook.com/NumberSense.aspx) with more than 350 concepts and thousands of example problems. By incorporating number sense activities into everyday life and classroom instruction, we can empower students to develop a deeper understanding of numbers, enhance their problem-solving skills, and foster a lifelong appreciation for math.

#### June 7, 2024

# Number Sense Competitions: A Fun and Effective Way to Boost Math Skills

Number sense competitions have been gaining popularity in recent years as a fun and effective way to enhance students' math competence and number sense. These competitions challenge students to solve a variety of math problems mentally, without the use of calculators or other tools. While the idea of a math competition might seem intimidating to some, the benefits of participation are numerous and can have a lasting impact on a student's academic journey. The number sense competitions provide a unique platform for students to develop essential math skills, foster a deeper understanding of numbers, and cultivate a love for mathematics.

**Developing Number Sense**
At its core, number sense is the ability to understand numbers and their relationships. It involves skills such as mental math, estimation, and the ability to recognize patterns and relationships between numbers. Number sense competitions directly cultivate these skills, as participants must quickly analyze and manipulate numbers in their heads. Through regular practice and exposure to different types of problems, students develop a stronger intuition for numbers, allowing them to approach math problems with greater confidence and efficiency.

**Enhancing Math Competence**
Number sense competitions are not just about speed; they also test students' understanding of mathematical concepts. The problems often require participants to apply their knowledge of arithmetic, algebra, geometry, and other areas of math in creative ways. As students prepare for these competitions, they deepen their understanding of mathematical principles and learn to approach problems from different angles. This broader perspective translates into improved performance in math classes and standardized tests.

**Building Confidence and Problem-Solving Skills**
One of the most significant benefits of participating in number sense competitions is the boost in confidence it gives students. As they succeed in solving challenging problems, they develop a sense of accomplishment and a belief in their abilities. This newfound confidence can have a ripple effect, leading to increased engagement in math classes and a willingness to take on more difficult challenges. Furthermore, the problem-solving skills honed in these competitions are transferable to other areas of life, from science and engineering to business and finance.

**Fostering a Love for Math**
Number sense competitions can also spark a genuine interest in math. The competitive aspect can make learning math fun and engaging, while the sense of community and camaraderie among participants can create a positive and supportive environment. For some students, these competitions may even ignite a passion for math that leads them to pursue careers in STEM fields.

**Tips for Getting Involved**
If you're a student, parent, or teacher interested in number sense competitions, there are many ways to get involved. Many schools and organizations offer number sense programs and competitions, and there are also online resources and practice materials available. For instance,

myQBook offers an industry leading

number sense preparation program online and they also sponsor community and individual school competitions. With regular practice and dedication, students can reap the many benefits of number sense competitions and unlock their full mathematical potential.

**In conclusion,** number sense competitions are a valuable tool for improving students' math skills, confidence, and overall academic performance. They provide a platform for students to challenge themselves, learn new concepts, and develop a lifelong love for math. By participating in these competitions, students not only enhance their math competence but also gain essential problem-solving skills that will serve them well in all aspects.

#### May 24, 2024

# Number Sense: The Key to Unlocking American Students' Math Potential

The most recent results from the

Program for International Student Assessment (PISA), released on December 5th, 2023, have brought an unsettling reality into sharp focus: American students are lagging significantly behind their international peers in mathematics. Even more concerning is that American students scored 13 points lower in this assessment than they did in 2018, equivalent to losing two-thirds of a year of math education. The issue isn't solely about complex equations or advanced calculus; it's a fundamental lack of number sense that's holding them back.

**What is Number Sense?**
Number sense refers to an intuitive understanding of numbers, their relationships, and how they can be manipulated to solve problems. It involves skills like:

**Understanding magnitude:** Recognizing the relative size of numbers.
**Estimating:** Learning to make reasonable approximations.
**Grasping the relationships between numbers:** Making math easier by understanding how numbers relate to each other.
**Mental math:** Performing calculations quickly and accurately in one's head.
**Number flexibility:** Understanding different representations of the same quantity (e.g., fractions, decimals, percentages).
**Reasoning with numbers:** Applying numerical concepts to real-world situations.

**Real-Life Examples of Number Sense:**
**Estimating grocery costs:** A shopper with strong number sense can quickly estimate the total cost of their groceries ensuring they stay within their budget.
**Understanding discounts:** Number sense helps you determine if a 25% discount on a $50 item is a better deal than a $10 off coupon.
**Calculating tips:** Someone with good number sense can easily calculate a 15% or 20% tip in their head.
**Comparing quantities:** When cooking, number sense helps you determine if doubling or tripling a recipe will yield enough food for your guests.
**Understanding data:** News articles often present data using percentages and statistics. Number sense enables you to interpret this information and draw informed conclusions.

**Why is Number Sense Crucial?**
Research has consistently shown a strong correlation between number sense and overall math achievement. Students with well-developed number sense tend to:

**Understand math concepts more deeply:** They see the underlying logic behind mathematical procedures, rather than just memorizing steps.
**Solve problems more flexibly:** They can approach problems from multiple angles and choose the most efficient strategies.
**Be more confident in their math abilities:** This can lead to greater engagement and motivation in math class.

Without a strong sense of numbers, students struggle to grasp more complex mathematical concepts. They may be able to memorize formulas and procedures, but they lack the understanding necessary to apply them effectively.

**The PISA Results: A Wake-Up Call**
The PISA results should serve as a wake-up call for parents, educators and policymakers in the United States. American students' lackluster performance in math is not merely a statistic; it's a reflection of a systemic issue that needs immediate attention.

While there are many factors contributing to this issue, a significant one is the neglect of number sense in early math education. Too often, the focus is on rote memorization and procedural fluency at the expense of developing a deep understanding of numbers.

**The Long-Term Implications of Neglecting Number Sense**
The consequences of neglecting number sense extend far beyond the classroom. Students who struggle with math often develop math anxiety and a negative attitude towards the subject. This can have long-term implications for their academic and career choices, as well as their everyday lives.

Furthermore, a lack of mathematical competence can limit economic opportunities for both individuals and the nation as a whole. In an increasingly complex and data-driven world, mathematical skills are more important than ever.

**Building a Foundation for Success**
To improve American students' math performance, we need to prioritize the development of number sense in early math education. This means shifting the focus from rote memorization to hands-on, engaging activities that promote a deep understanding of numbers. It means encouraging students to think flexibly about numbers, estimate, and use mental math. Math should be seen as a subject of exploration and discovery, not a source of fear and frustration.

To get a head start on learning number sense, students can utilize myQBook’s industry leading

number sense preparation program. myQBook provides a positive environment where students feel safe to take risks and make mistakes.

**Conclusion**
The PISA results highlight the urgent need to improve American students' math competence. By prioritizing number sense development in the early years and throughout students' math education, we can lay the groundwork for a future generation of mathematically literate citizens who are prepared to succeed in the 21st century. It's an investment in our students, our economy, and our future.

#### May 10, 2024

# Empowering Future Business Leaders: The Crucial Role of Math and Number Sense in Business Success

In the fast-paced world of business, creativity, passion, and leadership are often hailed as the keys to success. But what many underestimate is the fundamental importance of a strong math foundation. From budgeting and forecasting to data analysis and investment decisions, math plays a critical role in every aspect of running a successful business.

Here's why a solid grasp of

math and

number sense is a secret weapon for aspiring entrepreneurs and business leaders alike, along with examples of how some of the world's most famous business minds leveraged their mathematical prowess:

**1. Quantitative Analysis**
At the heart of business lies the need to make informed decisions, often under conditions of uncertainty. Here,

mathematics, particularly in the form of quantitative analysis, plays a pivotal role. Whether it's assessing the financial viability of an investment, optimizing production processes, or analyzing market trends, the ability to wield mathematical tools empowers entrepreneurs and business leaders to make sound judgments.

Consider the case of Warren Buffett, widely regarded as one of the most successful investors of all time. Buffett's investment philosophy is deeply rooted in mathematics and probability theory. His legendary prowess in valuing companies and identifying undervalued stocks stems from a rigorous application of mathematical principles to financial analysis. By crunching numbers and assessing risk with precision, Buffett has amassed a fortune and built an investment empire that continues to thrive.

**2. Strategic Planning**
In the dynamic landscape of business, strategy reigns supreme. From charting growth trajectories to outmaneuvering competitors, strategic planning forms the backbone of organizational success. Here again, math provides invaluable tools for modeling scenarios, predicting outcomes, and formulating winning strategies.

Elon Musk, the visionary entrepreneur behind Tesla and SpaceX, exemplifies the marriage of math and strategic acumen. Musk's ambitious ventures into electric vehicles and space exploration are underpinned by sophisticated mathematical models. Whether it's optimizing rocket trajectories or engineering energy-efficient batteries, Musk relies on mathematical principles to drive innovation and disrupt traditional industries.

**3. Data-driven Decision Making**
In today's digital age, data has emerged as the new currency of business. Every click, swipe, and transaction generates a deluge of data, ripe with insights waiting to be unearthed. However, extracting meaningful intelligence from this data requires more than just intuition—it demands a deep understanding of mathematical concepts such as statistics, probability, and machine learning.

The story of Jeff Bezos and the rise of Amazon epitomizes the power of data-driven decision-making. From personalized recommendations to dynamic pricing algorithms, Amazon leverages data analytics to anticipate customer needs and stay ahead of the competition. Behind the scenes, mathematicians and data scientists crunch petabytes of data to extract actionable insights, driving innovation and fueling Amazon's relentless growth.

**4. Risk Management**
Business is inherently risky and math is crucial for assessing and managing risk. From calculating return on investment for different scenarios to managing cash flow and assessing risk, proficiency in mathematical finance empowers business leaders to navigate the treacherous waters of business with confidence and precision.

Bill Gates, co-founder of Microsoft, is known for his strategic thinking and ability to identify profitable ventures. His strong understanding of market trends and financial calculations has been instrumental in Microsoft's continued success.

**5. Building Confidence**
Math isn't just about calculations; it's about confidence. Students who master math concepts learn to trust their analytical skills and approach challenges with a logical perspective. This translates to the business world, where business leaders need to be confident in their decision-making abilities, especially when faced with uncertainty.

**The Takeaway: Math Skills are an Investment in the Future**
Encouraging a strong math foundation in students isn't just about test scores. It's about equipping them with the tools they need to be successful in business. While creativity and passion are important for business success, a solid foundation in math provides the critical thinking skills and analytical power to run a successful business.

As educators and mentors, it is incumbent upon us to nurture these skills among students, equipping them with the numerical fluency they need to thrive in the competitive world of business. For in the equation of success, mathematics is the catalyst that propels dreams to fruition.

#### April 26, 2024

# Widening Gender Gap: Girls Fall Behind Boys in Math Scores Post-Pandemic

America's students experienced a significant setback in math achievement according to the latest National Assessment of Educational Progress (NAEP) scores, often referred to as the "

Nation's Report Card". The 2022 results, the first major assessment since the pandemic began, paint a concerning picture: math scores for fourth and eighth graders have dropped to their lowest levels in a decade.

The decline is substantial. Compared to 2020, average scores for 13-year-olds fell by a disheartening 9 points. The recent decline in math scores (see chart below) seems to have begun even before the pandemic, leaving the latest scores just 5 points above the level observed in 1973, but 14 points lower than the level observed in 2012.

While the downward trend affected all students, the decline appears to be more severe in girls’ scores compared to boys’ scores. While girls on average scored 1 point higher than boys in 1973, they scored 7 points lower than boys in 2023.

While data on the exact reasons for this disparity is still emerging, research suggests several potential factors. One study suggests that girls may be more adversely affected by the isolation of remote learning, as they often rely on social interactions and peer support to thrive academically. The lack of in-person interaction during the pandemic may have hindered their ability to engage fully in their studies and collaborate with peers, leading to decreased motivation and academic performance.

Another factor to consider is the potential for a wider impact of pandemic-related stress and anxiety on girls. Studies have shown girls are more likely to experience these issues, which could negatively affect their academic engagement and performance.

The consequences of this widening gender gap are concerning. Strong math skills are crucial for success in many fields, and falling behind could limit girls' career opportunities in STEM (Science, Technology, Engineering, and Math) related fields.

Addressing this issue requires a multifaceted approach. Educators may need to implement targeted strategies to support girls in math classrooms, fostering a more engaging and inclusive learning environment. Additionally, providing targeted resources such as

myQBook and mentorship programs specifically geared towards girls in STEM fields could be instrumental in reigniting their interest and confidence in math.

Furthermore, efforts to promote gender equity in education must extend beyond the immediate crisis response and address the systemic barriers that contribute to disparities in academic outcomes. This includes challenging gender stereotypes, promoting inclusive curricula and teaching practices, and creating supportive learning environments that empower girls to excel academically and pursue their passions without constraints.

The pandemic undeniably disrupted education for everyone. However, the data from the Nation's Report Card underscores the need to be particularly vigilant about the achievement gap between girls and boys in math. By recognizing this disparity and taking steps to address it, we can ensure all students, regardless of gender, have the opportunity to excel in this critical subject.

#### April 12, 2024

# Sharpen Your Mind: How Mental Math Boosts Brainpower

We all know math is important, but did you know that ditching the calculator and cranking out calculations in your head can be a surprising brain booster? It's true! Regularly engaging in mental math offers a range of cognitive benefits that can keep your mind sharp and enhance your overall well-being.

## Flexing the Cognitive Muscle

One of the most remarkable aspects of the human brain is its capacity for neuroplasticity—the ability to reorganize and form new neural connections in response to experience and learning. Engaging in mental math exercises stimulates this neuroplasticity, promoting ongoing brain development and lifelong learning.

Just as physical exercise is vital for maintaining physical health and mobility, mental math serves as a form of cognitive exercise that keeps the brain agile and adaptable.

Whether you're a student looking to improve academic performance, a professional seeking to sharpen cognitive skills, or an individual interested in preserving cognitive function as you age, incorporating mental math into your routine can yield significant long-term benefits.

## Boosting Memory and Concentration

Engaging in mental math exercises can also enhance memory and concentration. As you mentally manipulate numbers, you challenge your working memory—the cognitive system responsible for temporarily storing and manipulating information. Over time, this can lead to improvements in memory retention and recall. Recalling multiplication tables, for instance, is a key component of mental math. This regular retrieval of information strengthens memory pathways and improves overall recall abilities.

Furthermore, mental math provides a great mental workout, demanding concentration and filtering out distractions, particularly when performing complex calculations. By honing your ability to maintain focus during mathematical tasks, you develop a valuable skill that can be applied to other areas requiring sustained attention, such as studying, problem-solving, and decision-making.

## Emotional Well-being

There's even growing evidence that suggests a link between mental math and emotional health. According to a

brain-scanning study published by Duke researchers in the journal Clinical Psychological Science, engaging a specific part of the brain during mental math exercises is connected with better emotional health.

Other studies have shown that engaging in mental math activities can be associated with reduced symptoms of anxiety and depression. This is likely due to the activation of the dorsolateral prefrontal cortex, which also plays a role in regulating emotions. Participants with higher dorsolateral prefrontal activity were also less likely to have a mental illness diagnosis.

## Practical Applications and Real-World Benefits

Beyond its cognitive advantages, mastering mental math has numerous practical applications in everyday life. From calculating tips and splitting bills at restaurants to estimating quantities while shopping or managing finances, mental math skills streamline everyday tasks and empower individuals to make quick, informed decisions without relying on external tools.

Moreover, in professions such as finance, engineering, and science, where numerical analysis is integral, proficiency in mental math can confer a competitive edge and facilitate faster, more accurate decision-making.

## Conclusion

In a digital age where calculators and devices abound, the ability to perform mental calculations might seem like a lost art. However, far from being obsolete, mental math remains a valuable skill with profound cognitive benefits. By regularly engaging in mental math exercises, individuals can strengthen neural connections, enhance problem-solving skills, boost memory and focus, improve emotional well-being, and enjoy a host of real-world advantages.

Whether you're aiming to sharpen your mind, improve academic or professional performance, or simply cultivate a lifelong love for learning, embracing the challenge of mental math is a worthwhile endeavor—one that promises to unlock the full potential of your brain and enrich your life in countless ways.

#### March 29, 2024

# Building Strong Foundations: Fostering Number Sense in Young Learners

Number sense is the cornerstone of math proficiency. It's more than just memorizing facts; it's a deep understanding of numbers and their relationships. This understanding allows students to solve problems flexibly, estimate effectively, and approach math with confidence.

Number sense is a gateway to higher-level mathematics. Without a strong foundation, students struggle to grasp more complex concepts like fractions, decimals, and algebra. Number sense allows them to make connections between different areas of mathematics, fostering a deeper understanding of the subject as a whole.

So, how can we develop strong number sense in young students? For some students, number sense comes naturally. For others, number sense can be developed with practice. myQBook offers a comprehensive

number sense development curriculum.

Utilizing myQBook’s number sense curriculum, students can learn more than 350 number sense concepts and practice their skills with sample problems. Developing this type of number sense will not only make their current schoolwork a child’s play but also enable them to advance to higher level math classes.

Take for instance how a deeper understanding of one of the simplest mathematical properties, associative property of addition and multiplication, can make mental calculations easier. The associative property states that the value of mathematical expressions does not change when the order or grouping of the numbers used in the expression are moved around.

This is true only when all the operations in the expression are either all additions or all multiplication. In other words, to add or multiply three or more numbers it is not necessary to add or multiply them in the same order they are given.

Students can use this property and their understanding of numbers to make calculations easy by following the 3 simple steps below:

- Group the numbers in such a way that the sum or the product of the numbers in the group is an easy number to add or multiply such as a ten or a multiple of ten.
- Now find the sum or product of each group.
- Finally add or multiply the results to get the answer.

For example, let’s say we need to find the sum of 9 + 78 + 91 + 22. Following the above 3 steps gives us:

- Group the numbers for easy addition: (9 + 91) + (78 + 22).
- Find the sum of each group: 100 + 100.
- Then find the final sum: 100 + 100 = 200.

Let’s use another example to see how this will work for multiplying numbers. Let’s say we need to find the product of 4 x 358 x 25. Following the above 3 steps gives us:

- Group the numbers for easy multiplication: (4 x 25) x 358.
- Find the product of each group: 100 x 358.
- Then find the final product: 358 x 100 = 35,800.

Although the above is a very simple concept, it clearly demonstrates how a deep understanding of simple mathematical properties and numbers can enable students to do quite complex calculations in their head. Developing strong number sense fosters a sense of confidence in students. They can approach mathematical problems with a sense of curiosity and exploration, knowing they have the tools to make sense of the numbers involved. This confidence spills over into other areas, encouraging critical thinking and problem-solving skills that are valuable in all walks of life.

#### March 15, 2024

# How to Prepare for the UIL Mathematics Competition

As we discussed in our previous insight, fostering strong math skills in students is not just an academic pursuit; it's an investment in their future. To motivate students in developing strong math skills, the

University Interscholastic League (UIL) created by the University of Texas at Austin conducts yearly Mathematics competitions for all Texas schools.

Unlike the UIL Number Sense contest however, the UIL Mathematics contest is offered only at the middle school and high school levels. The middle school (grades 6 to 8) UIL mathematics contest is a 30-minute test, and it consists of 50 multiple choice problems. The high school (grades 9 to 12) UIL mathematics contest is a 40-minute test, and it consists of 60 multiple choice problems. While calculators are prohibited in the middle school UIL mathematics contests, students are allowed to use calculators in the high school contests.

Since the UIL Mathematics contest covers a multitude of math concepts, students should devote an adequate amount of time to prepare for the contest. The amount of time each student should devote on preparing for the contest will depend on the student’s existing skill level. Students in lower grades will need to spend more time learning the concepts as some of the concepts would be entirely new for them. Students in higher grades would need to spend relatively less time to prepare. We recommend the following preparation times based on about 2 to 3 hours of preparation time per week:

Student Grade |
Preparation Time |

Grade 6 - 8 |
6 to 12 months |

Grade 9 & 12 |
3 to 9 months |

Students seriously preparing for the UIL Mathematics competition should follow these steps:

- Devote the first 4 to 12 weeks (depending on existing skill level) entirely to review and internalize the concepts and tricks by working through the myQBook UIL mathematics concepts and practice problems. At this stage, don’t worry about taking the sample tests at all.
- Make sure to do all the sample problems after learning each concept. If needed, repeat doing the practice problems after few days to fully internalize the concept and the problems that appear in the contest.
- About 16 to 20 weeks before the contest date, start taking one test every week. Schedule the practice test approximately at the same time and day of the week that the actual context will take place. Make sure you will not be disturbed during the time of your practice test.
- After taking the test, go back and review your completed test and understand what problems you got wrong and why. Also understand how you solved each problem and whether that was the fastest way to solve the problem. Compare your approach to the myQBook recommended method and understand the difference.
- Throughout the following week review the concepts you didn’t score well on the test and practice sample problems.
- On the week of the contest, try to relax and not study too much. Just review some of the concepts as you were doing in the previous weeks. Don’t take any more tests during the last week.

As you prepare for the contest, here are some other important points to keep in mind:

- Learn your multiplication tables – Middle school level at least till 25, and high school level till 30.
- Memorize the most commonly used squares, square roots, cubes, and cube roots listed in the myQBook UIL mathematics concepts.
- Understand and learn the Equivalent numbers (relationship between fractions, percents and decimal numbers) listed in the myQBook UIL mathematics concepts.
- Memorize the “Measures to Remember” in the myQBook concepts.
- While learning a concept think about why does the concept work and other applications of the same concept.
- Learn how to recognize various number patterns.
- Learn to break complex problems into smaller parts and then solve each part separately.

#### March 1, 2024

# Math Competence is Essential for Success in the Rapidly Growing Field of AI

The world around us is becoming increasingly intertwined with technology, and at the forefront of this revolution stands

**artificial intelligence (AI)**. AI is rapidly transforming various sectors, from healthcare and finance to manufacturing and entertainment. This growth translates to

**abundant job opportunities** for individuals with the right skillset. Whether it's designing intelligent robots, building self-driving cars, or developing AI-powered healthcare solutions, students entering the field of AI can contribute to solving some of the world's most pressing challenges.

While AI might seem like a field driven by futuristic technology and complex algorithms, the foundation upon which it thrives is surprisingly familiar -

**mathematics**. Developing strong math competence is not just an advantage for students interested in AI, it's

**essential** for success in this rapidly growing field.

Here's why:

**The Language of AI**: At its core, AI relies on complex algorithms that learn and adapt. These algorithms are essentially mathematical models, and understanding the underlying mathematical concepts is crucial for designing, implementing, and interpreting their results. Concepts from **linear algebra, calculus, probability theory, and statistics** form the building blocks of these algorithms, enabling them to process data, identify patterns, and make predictions.
**Data Manipulation and Analysis**: Data lies at the core of AI applications, driving insights and powering decision-making processes. To effectively work with data, students need a solid grasp of mathematical concepts like **linear regression, matrix operations, and probability distributions**. Proficiency in these areas allows students to preprocess, analyze, and extract meaningful **patterns from large datasets**—a fundamental aspect of AI development.
**Machine Learning and Neural Networks**: Machine learning techniques, particularly neural networks, have revolutionized AI by enabling systems to learn from data and improve performance over time. Neural networks rely heavily on **calculus for optimization algorithms** such as gradient descent and backpropagation. Additionally, **linear algebra** plays a crucial role in understanding the **structure and operations of neural networks**. Without a strong mathematical foundation, students may struggle to comprehend and effectively utilize these powerful techniques.
**Beyond the Code**: Strong math skills go beyond simply understanding equations. They equip students with **critical thinking, problem-solving, and analytical reasoning** abilities, all of which are vital for success in AI. These skills allow individuals to effectively analyze complex problems, break them down into smaller, more manageable components, and develop innovative solutions using AI techniques.
**Adapting to the Evolving Landscape**: The field of AI is constantly evolving, with new applications and advancements emerging at a rapid pace. A strong foundation in math equips individuals with the **flexibility and adaptability** needed to navigate this dynamic landscape. They can not only understand and implement existing technologies but also contribute to the development of new and more sophisticated AI models in the future.

In conclusion, math competence is not just a desirable trait for students pursuing a career in Artificial Intelligence—it's a prerequisite for success. A strong foundation in mathematics provides the tools, insights, and problem-solving skills necessary to navigate the complexities of AI development and drive innovation in this rapidly evolving field. As AI continues to reshape the world, students equipped with mathematical proficiency will be poised to make meaningful contributions and shape the future of intelligent technology. Fostering strong math skills in students is not just an academic pursuit; it's an investment in their future, opening doors to exciting possibilities in the ever-evolving field of AI and beyond.

#### February 16, 2024

# How to Prepare for the UIL Number Sense Competition

As we discussed in our previous insight, developing Number Sense is foundational to math competence and deeper problem-solving abilities. To motivate students in developing strong number sense, the

University Interscholastic League (UIL) created by the University of Texas at Austin conducts yearly Number Sense competitions for all Texas schools.

Since the UIL Number Sense contest covers a large variety of Math concepts, students should devote an adequate amount of time to prepare for the contest. The amount of time each student should devote to prepare for the contest will depend on the student’s existing skill level. Students in lower grades will need to spend more time learning the concepts as some of the concepts would be entirely new for them. Students in higher grades would need to spend relatively less time to prepare. We recommend the following preparation times based on about 2 to 3 hours of preparation time per week:

Student Grade |
Preparation Time |

Grade 3 & 4 |
9 to 12 months |

Grade 5 & 6 |
7 to 10 months |

Grade 7 & 8 |
5 to 8 months |

Grade 9 & 12 |
3 to 6 months |

We strongly recommend students follow the steps below to prepare for the contest:

- Devote the first 4 to 12 weeks (depending on existing skill level) entirely to review and internalize concepts and tricks by working through myQBook Number Sense concepts. At this stage, don’t worry about taking any sample tests.
- Make sure to do all the sample problems after each concept. If needed repeat doing the practice problems after few days to get used to the concept and the problems that appear in the contest.
- About 16 to 20 weeks before the contest date, start taking one test every week. Schedule the practice test approximately at the same time and day of the week that the actual context will take place. Make sure you will not be disturbed during the time of your practice test.
- After taking the test, go back and review your completed test and understand what problems you got wrong and why. Also understand how you solved each problem and whether that was the fastest way to solve the problem. The first two tests in the myQBook Number Sense library provide explanations and the fastest way to solve each problem. Compare your approach to the myQBook recommended method and understand the difference.
- Throughout the following week review the concepts on which you didn’t score well on the test and practice sample problems.
- On the week of the contest, try to relax and not study too much. Just review some of the difficult concepts as you were doing in the previous weeks. Don’t take any more tests during the last week.

As you prepare for the contest, here are some other important points to keep in mind:

- Learn your multiplication tables – Elementary level at least till 20, Middle school level at least till 25, and high school level till 30.
- Learn the most commonly used squares, square roots, cubes and cube roots listed in the myQBook Number Sense concepts.
- Understand and learn the Equivalent numbers (relationship between fractions, percents and decimal numbers) listed in the myQBook Number Sense concepts.
- Memorize the “Measures to Remember” in the myQBook Number Sense concepts.
- While learning a concept think about why does the concept work and other applications of the same concept.
- Learn how to recognize various number patterns.
- Learn to break complex problems into smaller parts and then solve each part separately.

#### February 2, 2024

# Demystifying Math: Why Number Sense is the Key to Unlocking Student Competence

Numbers are everywhere. From calculating tips to balancing budgets, mathematical fluency weaves its way through our lives. But for many students, math remains a mysterious land, filled with confusing symbols and frustrating equations. The key to mathematical fluency lies not in rote memorization or endless drills, but in developing a foundational skill:

**number sense**.

Number sense is more than just knowing your 123s. It's an intuitive understanding of

**what numbers represent, how they relate to each other, and how they can be manipulated to solve problems**. It's the ability to estimate quickly, compare quantities with ease, and visualize numbers in different forms (fractions, decimals, etc.). Imagine the difference between memorizing the formula for area and effortlessly understanding that a 3x4 rectangle has the same area as a 6x2 rectangle – you're not just crunching numbers, you're

**utilizing your number sense**.

Or imagine you want to buy 25 pieces of an item worth $48 each. With your number sense you intuitively understand that 25x48 is the same as 100x12 (100 = 25 x 4) and that your total cost would be $1200. This intuitive grasp of numbers forms the bedrock upon which all higher-level math is built. Without a strong number sense, students struggle to grasp complex concepts in algebra, geometry, and statistics. They become reliant on algorithms and formulas, unable to understand the underlying logic. This not only hinders their mathematical progress but also limits their problem-solving abilities in other areas of life.

Developing number sense takes time and dedicated practice. But the rewards are far-reaching:

**Enhanced problem-solving:** With a firm grasp of numbers, students can approach problems creatively and strategically, breaking them down into manageable steps and choosing the most efficient solution.
**Increased confidence:** Success in math fosters a sense of accomplishment and boosts confidence in other academic areas, too.
**Real-world application:** Number sense equips students to deal with everyday situations involving money, measurement, budgeting, and more.
**Higher academic achievement:** Studies have consistently shown a strong correlation between well-developed number sense and higher academic achievement in math and other subjects.

**So, how can we cultivate number sense in students?**
**Start early:** Early childhood is a crucial time for building number sense through play, exploration, and concrete manipulatives.
**Make it engaging:** Use games, puzzles, and real-world contexts to make math fun and relatable.
**Focus on understanding, not just memorization:** Encourage students to explain their thinking and explore different ways to solve problems.
**Integrate technology:** Use educational sites, apps and games to create engaging practice opportunities.
**collaboration:** Collaborative learning allows students to share strategies and learn from each other.
**Encourage participation in friendly competitions:** Participating in competitions, such as UIL Number Sense, motivates students to practice and develop strong number sense capabilities.
**Celebrate effort and progress:** Recognizing and praising students' efforts, not just perfect answers, fosters a positive attitude towards math.

Developing number sense is not a race, but a journey. By nurturing this crucial skill through engaging and meaningful experiences, we empower students to become confident and competent math thinkers, ready to tackle challenges and thrive in a world increasingly shaped by numbers. Remember, math is not just about equations; it's about understanding the world around us, and number sense is the key that unlocks that understanding. Let's open the door and invite students to explore the wonders of mathematics!

#### January 19, 2024

# The Case for Daily Math Practice: Building America's Future, One Student at a Time

The alarm bells are ringing. International assessments consistently paint a

concerning picture of American students' math performance. In the most recent Program for International Student Assessment (PISA)

results released on December 5th, 2023, American students ranked 28th out of 38 member countries of the Organization for Economic Cooperation and Development (OECD), an international organization that oversees the PISA exam. More concerning is that American students scored 13 points lower than they did in 2018, equivalent to losing two-thirds of a year of math education.

These were the lowest U.S. math scores recorded in the history of the PISA math test, which began in 2003. This educational gap has profound implications, not just for individual students' futures, but for America's global competitiveness and economic well-being. In this critical context, the question arises: what concrete steps can we take to improve math proficiency? The answer lies in a deceptively simple solution –

**prioritizing daily math practice for K-12 students**.

But why is daily practice so crucial? To begin,

**it's the key to building strong foundational skills**. Math, like any language, relies on mastery of building blocks. Consistent practice allows students to internalize basic concepts, develop fluency in calculations, and solidify their understanding. Imagine trying to write a novel without knowing the alphabet; that's the struggle many students face without solid math fundamentals.

Beyond rote memorization, daily practice unlocks

**enhanced problem-solving and critical thinking abilities**. Math isn't just about numbers; it's about navigating challenges, analyzing patterns, and devising creative solutions. Regular practice trains students to approach problems strategically, break them down into manageable steps, and persevere until they find the answer. These skills are not confined to math classrooms; they're essential for success in all aspects of life, from science and engineering to navigating personal finances and making informed decisions.

Furthermore, daily practice fosters

**confidence and motivation** in students. Witnessing their own progress through consistent effort empowers them to tackle more complex problems. This intrinsic motivation is invaluable, propelling them further on their mathematical journey. Conversely, infrequent practice often leads to frustration and fear, creating a negative cycle that discourages further engagement.

The benefits extend beyond individual students. Daily practice lays the

**groundwork for success in higher-level math**, which opens doors to numerous career paths in STEM fields. Strong math skills are increasingly a prerequisite for well-paying jobs and neglecting them limits opportunities for future generations. In a globalized world, the workforce of tomorrow needs to be fluent in the language of math to ensure America's economic competitiveness.

However, achieving this vision requires addressing challenges.

**Math anxiety** is a real hurdle, often stemming from negative experiences or ineffective teaching methods. Creating engaging and supportive learning environments is crucial to combating anxiety and fostering a positive perception of math. Additionally,

**inequitable access to resources** and

**teacher competency** can exacerbate existing disparities. We must ensure all students have access to qualified teachers, technology, and engaging materials, while promoting active learning approaches that personalize instruction and cater to diverse learning styles.

Of course, concerns about

**adding to student workload** are valid. However, daily practice doesn't have to translate into hours of tedious drills. Short,

**engaging activitie**s integrated into different parts of the day can make a significant difference. Gamification, real-world applications, and collaborative learning can transform practice into a stimulating and enjoyable experience. Finally, encouraging

** parental involvement** can play a significant role. When parents support and celebrate their children's math efforts, it reinforces the value of the subject and fosters a positive learning environment at home.

The time for action is now. American students deserve the opportunity to reach their full potential in math, and daily practice is the key to unlocking that potential. By implementing effective strategies, addressing challenges, and fostering a culture of math appreciation, we can build a generation equipped with the critical thinking, problem-solving, and analytical skills required to thrive in the 21st century. Let's turn those alarm bells into the chimes of progress,

**one student at a time**.