Engaging students: Central and inscribed angles

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Theresa (Tress) Kringen. Her topic, from Geometry: central and inscribed angles.

What interesting word problems using this topic can students do now?

After defining the terms central angle and inscribed angle, students can use a central angles to draw a pie graph or pie chart. They can depict the data using a visual. Based in the percentage of any part of a whole, they will crate a fraction of the whole circle by dividing 360 degrees by that percentage to give the piece of the pie in which they needed to find.

Say a student is given the data below and asked to graph the data into a pie chart:

Students’ favorite colors:

Blue 10

Yellow 3

Red 7

Orange 3

Green 10

Purple 6

Pink 9

Other 2

Students would be required to give percentages based on the 50 students with the percentages listed as: Blue 20%, Yellow 6%, Red 14%, Orange 6%, Green 20%, Purple 12%, Pink 18%, other 4%. This would correspond to the percentage of the 360 degree central angle.

To tie in inscribe angles, I would have to students explain why a pie chart would not work with inscribed angles.

How does this topic appear in high culture?

In order to engage students I could help them understand inscribed angles by relating it to the camera angle in their video games. Describing an inscribed angle as a camera angle on their video game would help them understand it better. As they move throughout the game, their camera angle changes. Based on the camera’s location, you are able to see a certain portion of the screen. If there isn’t much of an angle, the range of view is small or zoomed in. This could be explained as the radius of the circle. The smaller the radius, the less view there is. Thus, the opposite is true. If the radius is large, the camera has a larger view of the object. If the camera has a larger angle of view, more is visible in the camera. I would then relate this to the arc length that the angle creates. I would explain that if the angle of the camera is small, the area of the arc length, or view of the camera would also be small. If the angle of the camera is larger, the arc length or view of the camera is much larger.

How can technology be used to effectively engage students with this topic?

Once students are given the application problem listed above, I could then engage them further by asking them to use word or excel to graph the information given into a document. They would be required to make a chart of the data with the listed percentages of each parameter along with the degree of the angle that the parameter requires to make the pie graph. I would require this since the technology would calculate this on its own without the student having to put in the effort. To make it fun, I would give the students a few extra minutes to make their pie graph their own by customizing it to reflect their personality and style.

To further engage them, I could also ask that each student create a questionnaire that asked each student what their favorite choice of any given set of choices were. They would be required to have at least 7 responses as to make a 7 piece pie chart, but they would be able to choose the topic, and find the information for their parameters on their own. Once they did this, they would be required to make an additional pie chart with their results to present to the class.

Engaging students: Finding least common multiples

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Theresa (Tress) Kringen. Her topic, from Pre-Algebra: finding least common multiples.

What interesting word problems using this topic can your students do now?

While having students working on finding the least common multiples I could engage them by having them solve some word problems that would bring up real world problems in a way that they can relate what they learned to problems that deal more than with just numbers. One problem that could be presented ot the students is the following:

If you’re given packages of notebooks that contain 6 each and you are required to repackage them to send them to a school in need in groups of 22, what it the least amount of groups and original packages of notebooks that you can get without any notebooks left over?

In this problem, the students would be required to find the least common multiple of both 6 and 21. Since six doesn’t not go into 22 without a remainder, they would have to find lcm(6,22). Since the least common multiple of both 6 and 22 is 66, the students would have to apply what they know about least common multiples of numbers to figure out the word problem.

To continue with this, the students could then be asked to do the same thing for three numbers.

How does this topic extend what your students should have learned in previous courses?

Students should have covered factors and multiples of numbers around fifth grade. Therefore finding the least common multiple of a number extends the topic from these previous topics. Since students can figure out the factors of a number, they should also know if one number is a factor of the second. If it is, then they will know that the second number is the least common multiple of the two given numbers. Say the students are given 3 and 9. The students should be able to tell right away that 3 goes into 9. Since 3×3=9 and 9×1=9 and since no number smaller than 9 can also be a multiple of nine, the least common multiple of 3 and 9 is 9.

When also looking at the least common multiples of a number, students know what multiples of a number are from previous courses. They will know that 18 is a multiple of nine as well as 27, 36, and 45. Students know that 3 times 9 is 27, but they will also know that since the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30, etc. they will also know that even though 3 times 9 is 27, that there is a number smaller than 27 that is also a common multiple of 3 and 9.

How can technology be used to effectively engage students with this topic?

Students like games and it’s even better for the teacher if they are able to play while they learn or practice a given subject that they have learned. In order to engage each student, there a number of online games students can play to help them practice finding the least common multiples of given numbers. I have found a number of online games that students could go to for an activity. It pushes them, allows the students to go at their own pace, and allows students to be less worried about how fast or slow they are compared to other students.

One game is a timed game that gives the students two numbers to find the least common multiple of. They are given two minutes to see how many they can compute in that amount of time. They are still permitted to go at their own pace, but they are also pushing themselves to do better than the time before.

http://www.basic-mathematics.com/least-common-multiple-game.html

A second game give the students two numbers and asks for the least common multiple. It is basically multiple choice since they are to select a number our of five or six different numbers. If they select the correct answer, they are permitted to “throw a snowball.” Each correct response helps them win the snowball fight.

http://www.fun4thebrain.com/beyondfacts/lcmsnowball.html

Engaging students: Slope-intercept form of a line

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Theresa (Tress) Kringen. Her topic, from Algebra I: the point-slope intercept form of a line.

What interesting word problem using this topic can your students do now?

When learning about slope-intercept from of a line, word problems would help my students engage and help process the information in a real world situation. I would present an equation for the speed of a ball that is thrown in a straight line up into the air. The equation given: $v= 128-32t$ . I would explain that because we’re working with time and speed, height is not a variable in the equation. With $v$ representing the speed or velocity of the ball in feet per second and t representing the time in seconds that has passed. I would include the following questions:

1. What is the slope of the given equation? Since the equation is given in slope intercept form, the students should be able to give the answer quickly if they understood the lesson. The answer is $-32$ .

2. Without graphing the equation, which way would the line be headed, up and to the right or down and to the right? Because the students know that the slope is negative and given that they understood the lesson, they should be able to answer that the line is decreasing and is headed down and to the right.

http://www.purplemath.com/modules/slopyint.htm

How can this topic be used in your students’ future courses in mathematics or science?

Students can use this topic for many math or science courses. When dealing with a linear equation, slope-intercept form of a line can help the student understand what the graph looks like without actually graphing it. This is useful when needing to find the $y$ intercept (when $x$ is equal to zero) and what the slope of the line is. This is also useful to know for understanding what slope is. When students understand that a slope of a particularly large number (a large whole number such as $1,000$ or an improper fraction that equates to a large number such as $30,999/2$ ) is rising quickly as opposed to a slope of a smaller number (a smaller whole number such as two or a fraction that represents a very small portion of one such as $1/30,000$ ) which is not rising quickly. It is helpful for the students to understand that a very large slope will look almost vertical and a small slope will look almost horizontal, with both depending on the degree of largeness or smallness.

How can technology be used to effectively engage students with this topic?

When working with slope-intercept form, a student can actively be engaged through technology by attempting to make connections of how a graph looks on the graphing calculator and what the equation looks like in slope-intercept form. When allowing the students to make connections between them in small groups, they will have discovered the information form themselves. This will allow the students to more effectively program the information into their memories. To set this up, I would give each group a graphing calculator and a list of equations in slope-intercept form. On the paper with the list, I would have the students fill out information pertaining to the graph that they see. This information would include the slope and the y-intercept. I would split up the students into their cooperative learning groups two and ask them to draw a conclusion between where the line ends up compared to what the equation looks like. Once the students have typed their equation into the graphing calculator the students should fill out the paper provided. Once they have finished, I would ask them to see if they see any patterns between the equations and their answers.

Engaging students: Order of operations

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Theresa (Tress) Kringen. Her topic, from Pre-Algebra: order of operations.

How can this topic be used in your students’ future courses in mathematics or science?

Order of operations is commonly used in most mathematics problem that involve more than one operation or when parenthesis are involved. It would be easy to show the students what the answer to a given problem, say 5+20/5, would be when using the proper order of operations, then solve the problem by solving left to right as you would read a book. It is clear, to a math major, that the answer is 9. For someone who does not know the order of operations, they most likely would come up with the answer of 5. The difference in the correct answer and the incorrect answer is only 4, but the problem is only working with numbers less than or equal to twenty. It would then be beneficial to point out that when dealing with more complex problems, that this answer may become even larger. If the class was working on given problems, I would give them a few word problems to solve. Once they solved them on their own, I would show them that the difference between the correct way to answer the given problem and the incorrect way to answer the problem to help them connect the concept to why it is important to compute answers in the way.

How does this topic extend what your students should have learned in previous courses?

This topic extends what students should have previously learned by allowing them to use their skills of multiplication, division, exponents, addition, and subtraction to solve more complex problems. When learning how to solve problems more complicated than what they have been given in the past, they use this topic to guide them through to the next step. They must already be familiar with all of the operations by themselves prior to using the order of operations to solve a problem. Once they are accustomed to using the order of operations, the will be given more challenging problems and their math skills will build upon itself. It is clear that if a student is unable to solve a simple problem, such as an exponent problem or a more complicated division problem, they will not be able to use the order of operations for problems that contain what they have not learned.

How did people’s conception of this topic change over time?

It is believed that the idea of using multiplication before addition became a concept adopted around the 1600s and was not disagreed about. The other operations took their place in the order over time, beginning in the 1600s. It seems that although it was not documented well, most mathematicians agreed upon the same order. It wasn’t until books stated being published that it was important to document the order of operations. The notation may have been different depending on who was writing on the subject, but the concept was the same. It seems that although it was not documented well, most mathematicians agreed upon the same order. Once books were being published, the order, PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction), was put into print. Now, teachers use the phrase Please Excuse My Dear Aunt Sally as a way for students to remember the acronym and are able to put it to use.

http://jeff560.tripod.com/operation.html

http://mathforum.org/library/drmath/view/52582.html

Art of pi

The picture below is just one of many creative artistic representations of $\pi$ and $e$ found at http://mkweb.bcgsc.ca/pi/

In the words of the author, “Numerology is bogus, but art based on numbers have a beautiful random quality.”

Engaging students: Powers and exponents

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Kayla (Koenig) Lambert. Her topic, from Pre-Algebra: powers and exponents.

A) Applications: What interesting word problems using this topic can your students do now?

I chose the problem below from http://www.purplemath.com because I think that solving a problem that deals with disease would be interesting to my students. People have to deal with sickness and disease everyday and I think that solving a real world problem would entice the students into wanting to learn more.

A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant “k” for the bacteria? (Round k to two decimal places.)

For this exercise, the units on time t will be hours, because the growth is being measured in terms of hours. The beginning amount P is the amount at time t = 0, so, for this problem, P = 100. The ending amount is A = 450 at t = 6. The only variable I don’t have a value for is the growth constant k, which also happens to be what I’m looking for. So I’ll plug in all the known values, and then solve for the growth constant:

$A = Pe^{kt}$

$450 = 100 e^{6k}$

$4.5 = e^{6k}$

$\ln(4.5) = 6k$

$k = \displaystyle \frac{\ln(4.5)}{6} = 0.250679566129\dots$

The growth constant is 0.25/hour.

I think this kind of problem would be beneficial to students because it would help them understand how bacteria grows and how easily they can get catch something and get sick.

C) Culture: How has this topic appeared in pop culture?

Exponents and powers are everywhere around us without the students knowledge. Many movies and video games have ideas related to powers and exponents. Take, for example, the movie Contagion that was released in September 2011. This movie is about “the threat posed by a deadly disease and an international team of doctors contracted by the CDC to deal with the outbreak” (http://www.imdb.com/title/tt1598778). In this movie, there is a scene where the doctors are using mathematical equations with exponents to find out how fast the disease spreads and how much time they have left to save the majority of the population. There are many movies like this that involve powers and exponents, Contagion is just one example. There are also popular video games that deal with the spread of disease. For example, in the video game Call Of Duty: World At War the player is a soldier in WWII and his mission is to kill zombies, and zombie populations grow exponentially. Now, my brother plays this game and I know for a fact that he doesn’t think about the mathematics behind it, but I think talking about pop culture while teaching would really bring some excitement to the classroom and get the students thinking.

D) History: Who were some of the people who contributed to the discovery of this topic?

Exponents and powers have been among humans since the time of the Babylonians in Egypt. “Babylonians already knew the solution to quadratic equations and equations of the second degree with two unknowns and could also handle equations to the third and fourth degree” (Mathematics History). The Egyptians also had a good idea about powers and exponents around 3400 BC. They used their “hieroglyphic numeral system” which was based on the scale of 10. When using their system, the Egyptians expressed any number using their symbols, with each symbol being “repeated the required number of times” (Mathematics History). However, the first actual recorded use of powers and exponents was in a book called “Artihmetica Integra” written by English author and Mathematician Michael Stifel in 1544 (History of Exponents). In the 14^th century Nicole Oresme used “numbers to indicate powering”(Jeff Miller Pages). Also, James Hume used Roman Numerals as exponents in the book L’Algebre de Viete d’vne Methode Novelle in 1636. Exponents were used in modern notation be Rene Descartes in 1637. Also, negative integers as exponents were “first used in modern notation” by Issac Newton in 1676 (Jeff Miller Pages).

Works Cited

Ayers, Chuck. “The History of Exponents | eHow.com.” eHow | How to Videos, Articles & More – Discover the expert in you. | eHow.com. N.p., n.d. Web. 25 Jan. 2012. http://www.ehow.com/about_5134780_history-exponents.html.

“Contagion (2011) – IMDb.” The Internet Movie Database (IMDb). N.p., n.d. Web. 25 Jan. 2012. http://www.imdb.com/title/tt1598778/.

“Exponential Word Problems.” Purplemath. N.p., n.d. Web. 25 Jan. 2012. http://www.purplemath.com/modules/expoprob2.htm.

“Mathematics History.” ThinkQuest : Library. N.p., n.d. Web. 25 Jan. 2012. http://library.thinkquest.org/22584/.

juxtaposition.. “Earliest Uses of Symbols of Operation.” Jeff Miller Pages. N.p., n.d. Web. 25 Jan. 2012. http://jeff560.tripod.com/operation.html.

World’s Most Accurate Pie Chart

Source: Houghton College Facebook page, https://www.facebook.com/photo.php?fbid=10151682563311916&set=a.127025151915.116224.22485036915&type=1&theater

Engaging students: Finding the area of a square or rectangle

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Kayla (Koenig) Lambert. Her topic, from Geometry: finding the area of a square or rectangle.

B) Curriculum: How can this topic be used in student’s future courses in math or science?

Finding the area of a square or rectangle can be applied in many other subjects throughout a student’s school career. This topic is learned around 4^th or 5^th grade, and around this time students will just be using the formulas to find the areas. In middle school, they might be finding the areas by way of more difficult problems, like word problems. The real fun for this subject, in my opinion, doesn’t start until high school. In high school you can use the area of squares and rectangles to find the solutions to many problems. In high school geometry, the Pythagorean Theorem is taught. The area of squares is related to this depending on how the teacher presents this to the student. The Pythagorean Theorem states that “in any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs of the right triangle” (Square-geometry).

In college, possibly high school calculus, students will learn to approximate the total area under a curve (or integral) using the Riemann Sum. To approximate the integral, you find the area of each rectangle, and all of the rectangles areas added together give you the approximated integral. The area of rectangles is also used in Statistics. When creating a histogram, you multiply the height (density) and width of the bars (rectangles). Then adding the areas (relative frequencies) of all of the bars should be equal to one. Students will also need to use the area of squares and rectangles on college placement exams and standardized testing.

C) Culture: How has this topic appeared in high culture (art, classical music, theatre, etc.)?

In my opinion, anything and everything is a form of art, so the area of squares and rectangles can appear in an infinite amount of high culture. M.C. Escher has used squares and rectangles to create tessellations and “portrayed mathematical relationships among shapes, figures and space” (MC Escher). The area of a rectangle was used to Polykeitos the Elder who was a Greek sculptor. He used the area of a rectangle to create the perfect ratio for the human body. Painters also needed to figure out how to depict 3D scenes onto 2D canvas during the Renaissance (Mathematics and Art).

However, one of the more well-known applications of mathematics in art is the Golden Rectangle, which just so happens to involve the area of squares and rectangles. The Golden Rectangle is the area of the original rectangle to the area of the square, which is also the Golden Ratio. In other words, the Golden Rectangle is a rectangle wherein the ratio of its length to its width is the Golden Ratio (Golden Rectangle). Many ancient art and architecture have incorporated the Golden Rectangle into designs. The Golden Rectangle was used in the floor plans and design of the exterior of The Parthenon, which was a Greek temple dedicated to goddess Athena in 5^th century BC (Mathematics and Art). Leonardo DaVinci also used the Golden Rectangle in his work. When painting the Mona Lisa, he used this to “draw attention to the face of the woman in the portrait” (Mathematics and Art). DaVinci also used the Golden Rectangle in the Last Supper using it to create a “perfect harmonic balance between placement of characters in the background” and also used it to arrange the characters around the table (Mathematics and Art).

D) History: Who were some of the people who contributed to the development of this topic?

Finding the area of squares and rectangles didn’t just come out of the blue; we can thank geometry and ancient mathematics for the development of this topic. One person in particular who contributed to the development of this topic was Euclid, or Euclid of Alexandria, who was a Greek mathematician and known as the “Father of Geometry” (Euclid). He was said to revolutionize geometry and his book The Elements is considered the most influential textbook of all time (History of Mathematics). The collection of his books, all thirteen of them, contain all traditional school geometry (Solomon).

However, Euler wasn’t the only one to contribute to this topic. Pythagoras and his students discovered most of what high school students learn in geometry today (History of Mathematics). In the classical period, Aryabhata wrote a treatise including the computation of areas. From the kingdom of Cao Wei, Liu Hui edited and commented on The Nine Chapters of Mathematics Art in 179 AD (History of Mathematics). There are so many people who contributed to this topic, and people are still contributing and developing to the area of squares and rectangles today!

Works Cited

“Euclid – Wikipedia, the free encyclopedia.” Wikipedia, the free encyclopedia. 20 Feb. 2012. http://en.wikipedia.org/wiki/Euclid.

“Golden Rectangle.” Logicville : Puzzles and Brainteasers. 20 Feb. 2012. http://www.logicville.com/sel26.htm.

“M. C. Escher – Wikipedia, the free encyclopedia.” Wikipedia, the free encyclopedia. 20 Feb. 2012. http://en.wikipedia.org/wiki/M._C._Escher.

“Mathematics and art – Wikipedia, the free encyclopedia.” Wikipedia, the free encyclopedia. 20 Feb. 2012. http://www.en.wikipedia.org/wiki/Mathematics_and_art.

Solomon, Robert. The Little Book Of Mathematical Principals, Theories and Things. New York: Metro Books, 2008.

“Square (geometry) – Wikipedia, the free encyclopedia.” Wikipedia, the free encyclopedia. 20 Feb. 2012. http://en.wikipedia.org/wiki/Square_(geometry).

“History of mathematics – Wikipedia, the free encyclopedia.” Wikipedia, the free encyclopedia. 20 Feb. 2012. http://en.wikipedia.org/wiki/History_of_mathematics.

Engaging students: Solving proportions

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Kayla (Koenig) Lambert. Her topic, from Pre-Algebra: solving proportions.

C. Culture: How has this topic appeared in the news?

Solving proportions, or the idea of a proportion being solved, appears in the news more often than not. One specific example that can be used is the effect of the economy on real estate companies. Say we are given 25% of 16 real estate companies that have closed their businesses due to poor economy. We can use proportions to determine the number of real estate companies that closed. We know that the percent is 25 and that the whole is 16. Therefore $25/100 = x/16$ which gives us 4 real estate companies that closed (Review of Proportions). Proportions can also be used to determine how many miles we can drive on a certain amount of gas, and gas prices are constantly on the news. Also, this will be relevant to high school students who drive and need to find how much money they need to buy gas for the week, etc.

We can also use proportions to find the unit price of an item at a grocery store, or if an item costs a certain amount, you can find out how many of those items you can buy with a fixed amount of money you have. Buying items and saving money are also all over the news. If you find the unit price you can compare items therefore saving money by buying the item that you get the most out of your money. Another way solving proportions can appear on the news is by the stock market. You can use proportions to find out how much the stock market will rise in a given amount of days given the current amount of points it has raised in a certain amount of days. Making a proportion problem for students to solve is relatively easy and can be related to anything that is on the news. We can use this to our advantage to get the students to be a little more interested in proportions (and mathematics) so they can see different ways it is related to real life.

D. History: How was this topic adopted by the mathematical community?

The idea of proportions was adopted and used by many in the mathematical community. Proportions were used by Greek writers, including one named Nicomachus, who include proportions and ratios in arithmetic (Math Forum). Proportions were also adopted by Exodus who used them in geometry and by Theon of Smyrna who used proportions in music (Math Forum). In 2000 B.C., the Babylonians adopted proportions to represent place value notation (Pythagoras – Geometrical Algebra). Using proportions was accepted by mathematicians and was used to solve so many different equations used for so many different ideas, and is still used today. Early proportions were adopted by the Egyptians and were used to calculate fractions and measurement of farmland (Mathematics History). Later, proportions were adopted by so many more in the mathematical community like in Greece, China, India, and Babylonia in order to learn geometry. Greeks, like Plato, adopted proportions in order to study them with the Egyptians. I think that proportions were well liked by mathematicians and were adopted by many because you can use proportions to solve so many things.

D. History: How did people’s conception of proportions change over time?

From the beginning, people have used proportions. Early humans used proportions to see if one tribe was twice as large as another or if one leather strap is only half as long as another (Math Forum). It is obvious that the idea solving proportions hasn’t really changed that much, but what we can use proportions to solve has changed. In 2000 B.C. Babylonians used proportions to evolve place value notation by allowing arbitrarily large numbers and fractions to be represented (An Overview of Egyptian Mathematics). Around 1600 B.C. in Egypt, proportions were used to calculate the fraction and superficial measure of farmland (Mathematics History). Egyptians then used proportions to find volumes of cylinders and areas of triangles.

Vitruvius thought of proportions in terms of unit fractions for their architecture calculations (Proportion (architecture)). Also, scribes used “unit fractions” for their calculations in Egypt and Mesopotamia. Egyptians based proportions on parts of their body and their symmetrical relation to each other; like fingers, palms, hands, etc. Multiples of body proportions would be found in the arrangement of fields and buildings people lived in (Proportion (architecture)) and from here, proportions evolved. In 600 B.C., the idea of using proportions evolved and was then used for geometry (Mathematics History). Proportions are still used in geometry, like in architecture and land, like it was 3000 years ago. When you think about it, proportions have evolved, but the use of proportions has evolved even greater. There are so many topics we can now solve using proportions!

Works Cited

“Math Forum – Ask Dr. Math.” The Math Forum @ Drexel University. 7 Mar. 2012. <http://www.mathforum.org/library/drmath/view/64539.html>.

“Mathematics History.” ThinkQuest : Library. 7 Mar. 2012. <http://library.thinkquest.org/22584/>.

“Proportion (architecture).” Wikipedia, the free encyclopedia. 7 Mar. 2012. <http://en.wikipedia.org/wiki/Proportion_%28architecture%29>.

“Review of Proportions.” Self Instructional Mathematics Tutorials. 7 Mar. 2012. <http://www.cstl.syr.edu/fipse/decunit/ratios/revprop.htm>.

“An Overview of Egyptian Mathematics.” 7 Mar. 2012. < http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Egyptian_mathematics.html >

Engaging students: Adding and subtracting decimals

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Elizabeth (Markham) Atkins. Her topic, from Pre-Algebra: adding and subtracting decimals.

Applications

Adding and subtracting decimals is a fun subject to learn about. Decimals are everywhere in the world! Sports use decimals when timing people. Let’s try this problem: “Billy Joe ran a lap in 61.7 seconds the first time and 59.3 seconds the second time. How long did both laps take Billy Joe?” We use decimals to measure rainfall. “On Monday it rained a total of 1.27 inches, measured in a rain gauge. By Tuesday .23 inches had evaporated. Tuesday night’s big storm gave us another 3.58 inches. How much rain was in the rain gauge after Tuesday’s big storm?” We also use decimals with money! “Let’s say you found a lost cat. You return it to its owner for a reward of $50.00.Then you receive your allowance of $50.00. You then get your pay check from work which states you earned $108.75 for a week after taxes were taken out. It’s been a good week! You decide to spend a little money. You put $10.03 of gas in your car. You then by three items: Shoes ($51.99), jeans ($71.27) and gun ($0.97). How much do you have left?”

Technology

Technology is an awesome tool that we have to use to engage your students. On YouTube there is a song called the decimal song about how to add, subtract, multiply, and divide decimals. There is also a website where you can buy mathematical songs like his YouTube hit the Rappin’ Mathematician Decimals. He has a catchy way to grab student’s attention and they still learn. Technology can be used to enhance a lesson, an anchor video for example. Many website provide games. Mathgamesfun.net is a good example. Calculators are not a good enhancement tool because students can simply have the calculator do all the work for them. Calculators are a good technology to use to check a student’s work! Math.harvard.edu provides examples of math in movies. This way a student can see how math is used in the world. Learnalberta.ca/content/mesg.html/math6web/index.html?page=lessons&lesson=m6lessonshell01.swf is a website devoted to fractions. Another good technology for the teacher’s advantage is kaganonline.com. It is a website of different tools to use when teaching mathematics!

Curriculum

Decimals, along with fractions, numbers, and other basics, are a key foundational mathematical stepping stone to schooling and in life. Students will use math every day of their lives. In their science classes students will use decimals in measurement, weights, and time. Also when the student learns about scientific notation, they will use decimals. Students will use decimals to answer half-life questions. Decimals are used in economy. All of economy deals with money. Money deals with decimals. When learning about the stock market they use decimals. When looking at the mileage on their car, they use decimals. Students will have to learn decimals to help with percentages, sales, interest, sales tax, loans, and any sort of measurements in everyday life. Percentages are just decimals with a fancy symbol. If the students want to save money they need to know how to add and subtract decimals. Decimals are all around us we just have to teach the students how to see and use them!