Nurturing Number Sense In Middle School And High School.

Number sense, the intuitive understanding of numbers and their relationships, is a fundamental skill that underpins mathematical proficiency. Although students work on developing number sense in elementary school, most students need more practice in middle school and high school. By developing a strong number sense, students can approach math problems with confidence and solve them more efficiently. Here are some strategies to help middle and high school students cultivate this essential skill:

First, find real world applications to help students learn to use their number sense.  Encourage students to apply math to real-world situations. For example, have them calculate discounts, tips, or unit prices. Involve students in cooking or baking activities, where they can measure ingredients, follow recipes, and understand fractions and ratios. Ask them to change the recipe to feed 100 people or only 2.  Teach students about budgeting, saving, and investing. This can help them develop a sense of number value and financial literacy.

Second, incorporate hands-on activities into daily instruction.  Use manipulatives like blocks, counters, and base-ten blocks to help students visualize and understand number concepts. Incorporate math games and puzzles into lessons to make learning fun and engaging.  Combine math and art to create visually appealing projects that reinforce number sense.

Third look at using games and puzzles designed for developing number sense. Use Sudoku, KenKen, and other number puzzles since they can help students develop logical reasoning and problem-solving skills.  In addition, card games like blackjack and poker can be used to teach probability and statistics. Use board games like Monopoly and Settlers of Catan involve strategic thinking and number sense.

Fourth, focus on developing estimation and mental math.  Play games that require students to estimate quantities, such as guessing the number of jelly beans in a jar. Practice mental math exercises regularly to improve calculation speed and accuracy. Teach students how to round numbers to the nearest ten, hundred, or thousand to make calculations easier.

Fifth, start using number talks. Pose open-ended questions that encourage students to think critically about numbers. Encourage students to share different strategies for solving problems. Facilitate discussions among students to help them learn from each other.

Finally, utilize technologically based tools.  Use educational apps and online games to practice number sense skills.  Explore interactive simulations to visualize mathematical concepts. Teach students how to use data analysis tools to collect, organize, and analyze data.

By incorporating these strategies into their learning, middle and high school students can develop a strong foundation in number sense. This will not only benefit them in their math classes but also in other academic subjects and everyday life. Let me know what you think, I'd love to hear. 

The Importance of Number Sense

  I've noticed that each year, the incoming freshman class has little or no number sense.  They do the math and whatever the answer is, it is right in their minds.  I am not bemoaning the job their previous teachers did because of the books they had.  They've gotten a whole new program which will work on that but it will be a few years before results start showing but in the mean time I need to work on that now.

Number sense is defined as being fluid and flexible with numbers.  It is a skill needed by all students to do well in math because with a strong foundation in number sense, students do better.  The ones who struggle with it, have never really developed it.

With an undeveloped number sense, students are unable to develop a strong foundation even in mathematics let alone higher maths.   These are the students who struggle when they get to high school, potentially choosing to drop out.

Why be concerned with it?  It is something needed in real life to ensure success at what ever job is chosen.  With out it, it leaves adults unqualified for many of today's jobs.  So what are ways that we can use in our classrooms to help develop number sense.

1.  Model different ways to do the computation - This exposes students to ways to solve problems they may not have thought of.  One of the methods just might be right one which allows the student to "get it".

2. Encourage mental math because it helps students develop the understanding of numbers and their relationships. At the same time, have the students discuss how they found the answer in their head.  Take time to talk about the numerical relationships used.

3.  Lead classroom discussions on strategies for solving equations because it helps crystallize their own thinking and consider classmate's approaches.  Be sure to write ideas on the board so students see the connection between mathematical thinking and symbolic representation.

4. Encourage more estimation in school because it is used all the time in real life.  Note that estimation is not always about rounding. Encourage them to estimate an answer for calculations before completing the math.  My students love doing the math before rounding to create their estimate.  I'm working on turning that around.

5.  Ask students to share their reasoning both for mistakes and for correct results because math needs to make sense to them.

6.  Pose questions that have more than one right answer so they can see that not every problem has a single correct answer.

It is important to encourage the development of number sense.  Although it should happen in elementary, it does not always work out that way.  Integrate it in your classroom to encourage those whose number sense is not as advanced to improve and to fine tune those with a decently developed number sense.

What do you think?

Number Sense

Number sense is the other free math game with 6th Grade Learning Games.  Number Sense is a racing game where you have to move your car to avoid oil spills, trucks and other race cars.  Ever so often, you are given a question to answer

 It might involve Roman numerals or absolute values.  It may use any of the 4 major operations.  Every time you run a race, the questions are different and/or mixed up so they are not in the same order. 

To move your car, you tap the left or right side of the screen to move your car to the left or right.  In order to speed up, you have to answer the questions correctly or hit a speed boost.  If you answer a question wrong, hit the oil slick, or hit a truck, you automatically slow down. 

I have played the game several times and I have never managed higher than a 3rd place finish but I am getting much better at steering my car and avoiding obstructions.

I am going to try this app with my pre-algebra because I already know their number sense is weak.

speeds and number sense

Today, one of my students told me I was getting really weird because I wanted to know which was faster, a sloth or a snail, and by how much.  This required them to do  bit of an internet search.  Another class got to compare the speed of a cheetah vs man and this lead to a discussion on average speed via a math equation vs reality.  The other question I asked required them to convert units so they could actually compare 22 in/sec or 1 mph.  Turns out its the 22 in/sec by about 5 in/sec.  I need them to be fluent in conversions for their science class. The science teacher and I work together.  So last week, we looked at information given in parts such as 18 miles in 15 min to obtain a speed of miles per hour rather than miles per min.  This gave me a chance to initiate the idea that if you get information in one unit, it does not automatically mean that you must present it in that unit.  You need to step back and check to see what the common usage is.  In the 18 miles in 15 min, students were giving me the answer in miles per min even though they normally give speeds in miles per hour. 
The next step in this is to find information such as a guy ran the 100 yard dash in 28 sec so how fast was he going in mph and could he really maintain that speed. 
This falls under the student considering if the answer is reasonable.  Too often my students say yeah its reasonable without stopping to really think about the information and I am hoping things like this will improve their internet research skills and help them develop the number sense they really need in everyday life.