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# 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
1. 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.
2. 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.
3. 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.
4. 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.