Wednesday, June 27, 2012

Summer Solstice: Longest Day of the Year

 Enjoying summer in the San Diego surf.

The summer solstice -- the astronomical beginning of summer in the Northern Hemisphere — took place one week ago today at 7:09 p.m. EDT on June 20. That made it the longest day of the year north of the equator. From now until December, the days will gradually get shorter, though not necessarily cooler.

According to weather reports, the U.S. has had the warmest spring since record-keeping began in the 19th century. June 2011 to May 2012 marked the warmest 12-month period of any 12 months on record for the continental United States.

In Excel Math, students learn how to compute the date within the month, determine elapsed time, create graphs, and calculate expected numbers based on probability. Here's an example of problems using probability from the Excel Math Grade 6 Student Worksheet Lesson 133. Click here for a PDF file you can use with your students:
In this worksheet, students learn how probability can be used to estimate future events. Discuss the first question: "Based on the past 8 years of experience, the probability that an orchid will bloom in June is 1 out of 6. Knowing this, if you have 12 plants, is it probable that you will have a flower in June?"
The problem states there are 12 plants so we would multiply one-sixth by 12, and the problem would be written:
So it would be probable that 2 of the 12 orchids would bloom in June. You can help the students understand that probability does not guarantee an outcome. The answer doesn't mean 2 of the 12 orchids will definitely bloom in June, but it is probable that you will have two flowers in June. Orchids blooming in June is an event that occurs fairly regularly. For this lesson, problems 3-6 are read aloud by the teacher. They do not appear on the Lesson Worksheet. (The answers are given below.)
 The Earth's season's as seen from the north. Far left: summer solstice for the Northern Hemisphere. Front right: summer solstice for the Southern Hemisphere.
Another event that occurs regularly is the earth's orbit around the sun. Earth, turning on its axis as it circles the sun, is tilted at an angle of 23.5 degrees relative to its orbit. Whatever the season, the axis points the same way, with Polaris, the North Star, hovering over the North Pole.

June 20 was the day that the axis, as seen from the north, pointed as much toward the sun as it will all year, and appeared at its highest in northern skies. So Chicago and New York, for instance, got more than 15 hours of sunlight, compared with 9.1 hours on the winter solstice Dec. 21. And everything north of the Arctic Circle got 24 hours of daylight that day -- compared with round-the-clock darkness six months from now. While the summer solstice is happening in the Northern Hemisphere, the winter solstice occurs simultaneously in the Southern Hemisphere. Around December 21 the solstices are reversed and winter begins in the northern hemisphere. Read more at abcnews.go.com.

This year's summer solstice took place a day earlier than it's been for the past three years, due to the fact that 2012 is a leap year. This February got an extra day, to keep our calendar year of 365 days in sync with the astronomical year, which is about 365.24 days. Read more about leap year on our March 14, 2012 blog post.

In general, the exact timing of the summer solstice changes from year to year, "but there's a bigger jump when you have a leap year," explained Mark Hammergren, an astronomer at the Adler Planetarium in Chicago.

The solstices are the results of Earth's north-south axis being tilted 23.4 degrees relative to the ecliptic, the plane of our solar system. This tilt causes different amounts of sunlight to reach different regions of the planet during Earth's year-long orbit around the sun.

On June 20 the North Pole was tipped more toward the sun than on any other day of 2012. (The opposite holds true for the Southern Hemisphere, where June 20 marked the winter solstice, the shortest day of the year.)

As a result of Earth's tilt, the path of the sun across the sky rises in the lead-up to the summer solstice, then begins descending for the rest of the summer. (See pictures of the sun's path across the sky.)

At high noon on the summer solstice, the sun appeared at its highest point in the sky—its most directly overhead position—in the Northern Hemisphere. That doesn't mean the sun was exactly overhead at noon for everyone, said Cornell University astronomer James Bell.

It depended on the viewer's latitude—the sun will shine down directly overhead at noon only along the Tropic of Cancer, an imaginary line that circles the planet at about the latitude of Cuba.

Earth's oceans and atmosphere act like heat sinks, absorbing and reradiating the sun's rays over time. Even though the planet is absorbing lots of sunlight on the summer solstice, it takes several weeks to release it. As a result, the hottest days of summer usually occur in July or August.

"If you think about turning up an oven, it takes it a long time to heat up," explained Robert Howell, an astronomer at the University of Wyoming. "And after you turn it off, it takes awhile for it to cool down. It's the same with the Earth."

Another popular misconception, Adler's Hammergren said, is that during the summer—and especially during the summer solstice—Earth is closer to the sun than at other times of the year. In reality, the tilt of the Earth has more influence on the seasons than our planet's distance to the sun.

"During the Northern Hemisphere summer, we're actually farthest from the sun," Hammergren said. Read more at news.nationalgeographic.com.

Here in San Diego, the winter solstice marks a popular time of year to hike Cowles Mountain (pronounced "coles"), part of Mission Trails Regional park. From the eastern horizon, at dawn on the days surrounding the solstice, a peak splits the rising sun so it appears for a short time to be divided in two. This part of the mountain was a Kumeyaay Winter Solstice observatory site. You can see hikers start up the mountain with their flashlights before dawn on the days around December 21. Read more about hiking up Cowles Mountain on our February 2, 2012 blog post.

Here are the answers to the Grade 6 Student Lesson Sheet shown above:

Since Excel Math uses a unique spiraling strategy, students get more out of the lessons when  you teach multiple lessons sequentially within each grade level. This process gets the concepts into your students' long-term memory. Learn more about how Excel Math gives students a strong foundation in elementary math at excelmath.com.

Monday, June 25, 2012

Knot So Fast: Calculating Nautical Miles

On June 26, 1946 the U.S. Army, Air Force, and Navy adopted the "knot" and "nautical mile" as standard aeronautical units for speed and distance. This unit of measurement is used by all nations for air and sea travel. A nautical mile is about 6.080 ft. (1,853 m), and a knot is the equivalent of one nautical mile per hour.

This table shows conversions between knots and other common measurements used for velocity:
convertintomultiply by
knotsft/s1.688
knotsmph1.151
knotsm/s0.5146
knotskm/h1.853

The nautical knot finds its origin in a method sailors once used to measure their speed at sea (invented circa 1500-1600)It is believed the concept originated in the Netherlands. Back in the days of sailing vessels, captains needed a way to measure the speed of their ships through the water. The Dutch had devised a method of tossing a piece of wood into the water and measuring how quickly it drifted away from the ship, called "heaving the log."

A more accurate method, based on this technique, was the chip log. Sailors would tie knots in a long line at regular intervals (about 50 feet apart), then cast out one end (weighted down by a piece of wood) behind their vessel. They would count number of knots let out in a given period of time (measured, usually, by a small sandglass that measured half a minute) to calculate the distance (and consequently, the speed) at which the boat was moving. This was a major advance that made dead-reckoning much more accurate. From this crude speedometer, the sailor could determine the speed the vessel was moving. Read more at boatsafekids.com.

This system remained in use for many centuries. Some simple arithmetic confirms that this system actually does approximate a nautical mile per hour, the definition of a knot:

Interestingly, the chip log has long since been replaced by equipment that is more advanced, but we still refer to miles per hour on the water as knots. Read more at aerospaceweb.org.

 USS Constitution (“Old Ironsides”) Boston, MAU.S. Navy photo by Journalist Seaman Joe Burgess.
USS Constitution (“Old Ironsides”), the oldest commissioned warship afloat, can travel at 13+ knots (approx. 14.95 miles per hour, 24 km. per hour).  Here she is pictured making her annual 4th of July “turnaround cruise” in Boston Harbor where a 21-gun salute was rendered off Castle Island’s Fort Independence in South Boston. In 2002, the Secretary of the Navy, The Honorable Gordon England witnessed a swearing-in ceremony aboard the ship, where more than two-dozen immigrants were sworn in as naturalized citizens.

In Excel Math, we help students learn to calculate distance and speed. Here's one of the 6th Grade Excel Math Create A Problem exercises to help students solve word problems and calculate distance and speed using a map drawn to scale. Click here for a PDF copy you can use with your class. (The answers are included below.)

 (June 21, 2012) Artist rendering of the Virginia-class submarine USS Colorado (SSN 788). (U.S. Navy photo illustration by Stan Bailey/Released)
Secretary of the Navy Ray Mabus will host a ship naming ceremony in honor of USS Colorado, today at 2 p.m. MST at the Colorado State Capitol Building in Denver, Colorado.

Colorado, a Virginia-class submarine designated SSN 788, is the fourth ship to bear the name and the third to be named for the state. The second ship was a battleship that participated in the Tarawa invasion and suffered two kamikaze hits while supporting the landings at Leyte Gulf in November 1944.

This next-generation attack submarine will have enhanced stealth, sophisticated surveillance capabilities, and special warfare enhancements. Here's a photo of an artist rendering of the USS Colorado.

The future USS Colorado will have the capability to attack targets ashore with highly accurate Tomahawk cruise missiles and conduct covert long-term surveillance of land area, littoral waters or other sea-based forces. Other missions include anti-submarine and anti-ship warfare; mine delivery and minefield mapping. It is also designed for special forces delivery and support.

SSN 788 will be built at Electric Boat in Groton, Conn and will be 7,800 tons and 377 feet in length, and will operate at more than 25 knots submerged. It is designed with a nuclear reactor plant that will not require refueling during the planned life of the ship. Read more at http://www.navy.mil/submit/display.asp?story_id=67975

Here are the answers to the Grade 6 Create A Problem exercise shown above:

Since Excel Math uses a unique spiraling strategy, you will need to teach multiple lessons sequentially within each grade level in order to get the concepts into your students' long-term memory. A student's learning of new concepts takes place during Excel Math Lesson Plans and Activities. The concepts are refreshed through Guided Practice, Homework, Create A Problem and TestsLearn more about how Excel Math gives students a strong foundation in elementary math at excelmath.com.

Wednesday, June 20, 2012

Using Technology in the Math Classroom

This weekend, educators from around the world will begin to gather in San Diego for the 33rd annual conference of the International Society for Technology in Education (ISTE) This conference was formerly called the National Educational Computing Conference(NECC), and is held each year to "discover how educators from around the world are using innovative technologies to help students expand their horizons." You can visit the conference website here: http://www.iste.org/conference.

They've set up a blog roll so you can see what colleagues are writing, a virtual conference for those who can't make it to  San Diego, and even a social Ning to help you make connections with other educators. Even if you don't belong to ISTE, there are lots of ways to connect with educators and find out what's working in classrooms around the country.

The educational networking site, Edmodo, is similar to Facebook, but for educators to provide a way to connect with students and parents as well as with each other. You can find Excel Math (and AnsMar Publishers, Inc.) at http://www.edmodo.com/publisher/excelmath. Be sure to visit our collections and download some free resources for your Edmodo library. You can join communities for math, common core, special ed, technology, and lots more. Plus, you can connect with teachers from your own school, post lessons for your students to access, or avoid your coworkers completely and simply use it as a classroom tool and a resource for new ideas from other educators.

This summer ASCD (formerly the Association for Supervision and Curriculum Development) is offering some free Boot Camp webinarsand the one on July 24 happens to be on technology. Virtual Summer Camp: The Newest Tools on the Web to Explore for Instruction, presented by Mike Fisher.  "Educators looking for new web tools to engage their students should attend this presentation. During his webinar, Fisher will explore some of the exciting web tools of the moment and explain how educators can use them for instruction. In addition, he will discuss specific tasks and appropriate tool choices, as well as share helpful examples that have been implemented in real classrooms."

For videos and tutorials your students can access for the classroom, for tutoring, and at home, the Khan Academy has some easy-to-use videos for addition, subtraction, multiplication, division, algebra, and pre-algebra. If you're considering flipping your math lessons, this would be a good resource. If you teach Grades 5 and 6, you may want to bookmark the video resource page from Excel Math with classroom videos using Projectable Lessons. (Read more about Projectable Lessons here.)

If you're looking for ways to incorporate technology in your math classroom, here are some helpful links:
. . . and some additional online math resources:

Angles
Arithmattack
Build a bug math game
Count us in—variety of math practice
Estimating
Flashcards
Game-oriented math learning
HoodaMath
Links, by math topic—some for speed math
Math Basics
Math Basics Plus
Math Concepts
Math Concepts—games
Math Dictionary
Math edutainment
Math for K
Math Games
Math Glossary
Math Grids II
Math Grids—Car Game
Math Quizzes & Flashcards
Math Playground
Math Practice Test
Math Video Tutorials
Math Video Tutorials Gr. 5 & 6
Math Videos
Math/LA Videos
Math–Grids
Math Playground
Measuring Angles
Mental Math Drills
Minute Math
More Quick Math
Multiflier Math Practice
Multiplication
Multiplication Tables
Multiplication Tables & Flashcards
NumberNut Math Games
Place the Penguin Game (Ones, tens, hundreds)
Quick Math
Quick Quiz
Quizlet
Simulations
Speed Math
That Quiz
Thinkfinity
Timed Math
Timed Tests
Virtual Manipulatives
Wild on Math

. . . and some blogs with more links:

Andrew Miller's Blog
Flipped Math Lessons: Pro or Con?
Let's Play Math
Math in the Middle Blog
Middle School Math & Science Blog (also covers Elementary)
MissCalcul8 Blog
The Number Warrior
Teaching Ahead of the Curve Blog

. . . plus some online links to Common Core math standards:

We've just touched the tip of the iceberg when it comes to online resources for math classrooms. If you have additional resources or web links you'd like us to consider adding to this list, just leave a comment and we'll check them out (we do review them for their educational value). Watch for a future post with suggested apps, blogs, and more websites. In the meantime, grab your computer (or e-device) and start your summer with some math web surfing.

Monday, June 18, 2012

Earhart Math Facts

 Earhart by her plane Public domain photo from wpclipart.com
On June 18, 1928 Amelia Earhart became the first woman to fly across the Atlantic Ocean. Her plane took off on June 17 from Trepassy, Newfoundland. She rode as a passenger with co-pilots Wilmer "Bill" Stultz and Louis "Slim" Gordon, landing safely in Burry Port, Wales. The team left Trepassey harbor, Newfoundland, in a Fokker F7 named Friendship and arrived at Burry Port, Wales, 20 hours and 40 minutes later. Their landmark flight made headlines worldwide. In fact, three women had died within the year trying to be that first woman. When the crew returned to the United States, they were welcomed with a ticker-tape parade in New York and a reception held by President Calvin Coolidge at the White House. Less than four years later, Earhart would fly across the Atlantic alone.

Amelia Mary Earhart was born July 24, 1897, in Atchison, Kansas, to Samuel "Edwin" Stanton and Amelia (Otis) Earhart. She was a healthy nine pound baby. She and her younger sister, Grace Muriel, lived in the fine Gothic home of her grandparents, built by her grandfather. As a young child, Amelia enjoyed watching airplane stunt shows. Her mother, before her marriage, had been the first woman to reach the summit of Pikes Peak. Little could she guess that her daughter Amelia would also grow up to be a woman of "firsts." See more photos and images of Amelia Earhart at http://www.wpclipart.com.

• In spite of having to attend six different high schools, she was able to graduate on time.
• Amelia saved enough money to buy her own plane, which she named Canary, because it was bright yellow.
• She was the 16th woman to receive a pilot's license from the FAI (License No. 6017).
• Earhart was called "Lady Lindy" because her slim build and facial features resembled that of Charles Lindbergh.
• Earhart refused to wear typical flying gear. She wore a suit or dress instead of the "aviation togs" and a close-fitting hat instead of a helmet.
• Earhart made such an impression that people often wrote and told her about naming babies, lakes and even homing pigeons "Amelia."
• She became friends with Eleanor Roosevelt, who wanted to learn how to fly.
• Earhart met Orville Wright at the Franklin Institute in Philadelphia in 1937, the same year she disappeared.
• She was the first woman be awarded the Distinguished Flying Cross.
• The United States government spent \$4 million looking for Earhart, which made it the most costly and intensive air and sea search in history at that time.
 Amelia Earhart
On May 20, 1932, five years to the day after Lindbergh, she took off from Harbor Grace, Newfoundland, to Paris. Strong north winds, icy conditions and mechanical problems disrupted the flight and forced her to land in a pasture near Londonderry, Ireland. "After scaring most of the cows in the neighborhood," she said, "I pulled up in a farmer's back yard." As word of her flight spread, the media surrounded her, both overseas and in the United States.

President Herbert Hoover presented Earhart with a gold medal from the National Geographic Society. Congress awarded her the Distinguished Flying Cross—the first ever given to a woman. At the ceremony, Vice President Charles Curtis praised her courage, saying she displayed "heroic courage and skill as a navigator at the risk of her life." She set many other records and wrote best-selling books about her flying experiences before she disappeared in 1937 in the South Pacific during her attempt to become the first pilot to fly around the world at the equator. Read more at AmeliaEarhart.com.

In Excel Math, we help students learn to calculate distance and speed plus teach them higher-order thinking skills. We also combine math with literacy and teach students to read maps drawn to scale. Here's an example from our Grade 4 Excel Math Student Sheet from Lesson 121:
 Excel Math Lesson 121 Student Worksheet
Learn more about Excel Math lessons and its unique Spiraling process. With this strategically constructed process, concepts stay in front of students and repeat throughout the year in a methodical way. No other curriculum achieves the comprehensive, repetitive practice of Excel Math. Perhaps that's why the glowing reports from teachers and principals keep rolling in. Here's what one teacher had to say after using Excel Math:

“I cannot express how impressed I am with your program. Our test results are outstanding, and I am convinced without EXCEL we would be struggling to meet our goals. The spiraling piece that is built in…is what makes this so effective. If I ever move schools and my district does not provide this program, I would purchase it with my own money. Thank you for a wonderful program.”
— Anna Russell, Teacher, San Juan, California

Wednesday, June 13, 2012

Celebrating Flag Day with Math

Since this is National Flag Week, let's take a look at our United States flag and the history of Flag Day.

On June 14, 1893 Philadelphia observed the first Flag Day. In 1916, President Woodrow Wilson issued a presidential proclamation establishing a national Flag Day to be held on June 14.
To commemorate the adoption of our flag, the Congress, by joint resolution approved August 3, 1949 designated June 14 of each year as "Flag Day" and requested that the President issue an annual proclamation calling for its observance and for the display of the U. S. Flag on all Federal Government buildings. Read the proclamation issued this year by President Barack Obama.

Congress also requested, by joint resolution approved on June 9, 1966 that the President annually issue a proclamation designating the week in which June 14 occurs as "National Flag Week" and call upon citizens of the United States to display the flag during that week.

This year the National Flag Day Observance will be held tomorrow, Thursday, June 14. On our street, some of our neighbors have been flying their flags all week long. U.S. flags may come in a variety of sizes, but the look (number and arrangement of stars and stripes) and proportion of each flag remains consistent.

However, a uniform look for the flag was not always the case. Before the Executive Order of June 24, 1912, neither the order of the stars nor the proportions of the flag was prescribed. Instead, the flag maker could decide how what proportions the flag should be and how the stars would be arranged. As a result, flags from this period sometimes have odd proportions and unusual arrangements of the stars. For the most part, flag makers used straight rows or stars and proportions similar to the ones later adopted officially. Read more at usflag.org.

The standard proportions of the flag today are:
Hoist (width) of flag (A) 1.0
Fly (length) of flag (B) 1.9
Hoist (width) of Union (C) 0.5385 (7/13)
Fly (length) of Union (D) 0.76
(E) 0.054
(F) 0.054
(G) 0.063
(H) 0.063
Diameter of star (K) 0.0616
Width of stripe (L) 0.0769 (1/13)
If you have advanced students, you could have them calculate the proportions of a flag that's 6 inches wide (or whichever width you choose), using these standard proportions. Then they could cut out a flag of that size from white paper and a proportional Union from blue paper, glue them together, and add stripes and stars.

Some important acts affecting the flag of the United States include the following:
• On June 14, 1777, in order to establish an official flag for the new nation, the Continental Congress passed the first Flag Act: "Resolved, That the flag of the United States be made of thirteen stripes, alternate red and white; that the union be thirteen stars, white in a blue field, representing a new Constellation."
• The Act of January 13, 1794 provided for 15 stripes and 15 stars after May 1795.
• The Act of April 4, 1818 provided for 13 stripes and one star for each state, to be added to the flag on the 4th of July following the admission of each new state, signed by President Monroe.
• The Executive Order of President Taft dated June 24, 1912 established proportions of the flag and provided for the stars to be arranged in six horizontal rows of eight each, with a single point of each star to point upward.
• The Executive Order of President Eisenhower dated January 3, 1959 provided for stars to be arranged in seven rows of seven stars each, staggered horizontally and vertically.
• The Executive Order of President Eisenhower dated August 21, 1959 provided for the stars to be arranged in nine rows of stars staggered horizontally and eleven rows of stars staggered vertically.
Today each U. S. Flag has 50 stars—one for each state of the Union—and 13 stripes (seven red alternating with six white stripes)—one for each of the original thirteen colonies. The red color symbolizes hardiness and valor; white symbolizes purity and innocence; and blue symbolizes vigilance, perseverance, and justice.

On June 14, 1923, the first National Flag Conference was held in Washington, D.C. to establish a set of rules for civilian flag use. The U.S. Flag Code, first published in 1923 and adopted by Congress in 1942, is based on the belief that the American flag “represents a living country and is itself considered a living thing.” In 1989 the U.S. Supreme Court struck down flag-protection laws as violations of free speech. However, the Flag Code is still maintained as a code of etiquette, enforced by tradition rather than by law. Read more at the National Museum of American History.

Monday, June 11, 2012

Flipped Lessons Using Excel Math

One of the buzz-word phrases in the education community today is "flipped lessons" or "flipped classroom." Read more on our blog post from June 6. Many teachers are flipping their lessons to change the concept of homework from "figuring it out on your own" to include "student-led learning." However, the "flipped lesson" has become a controversial subject.

"With a flipped lesson, instead of introducing a topic in class, the students are first exposed to it at home. That is their homework. They are to watch videos or take notes on designated pages in order to prepare them for the practice that they will do in class. It's basically a way to 'front-load' the instruction so when students come to class, they're prepared and the concept will not seem so new." Read more on Teaching Ahead of the Curve Blog.

Each teacher must decide whether to "flip" the entire classroom, flip individual math lessons, use a more traditional teaching method, or use a combination of methods. When students take a homework assignment home, there can be a void with no teacher to help them. For many students, there is no one at home to help them at all.

Some math texbooks assume that if a teacher gives help in class, the student is therefore 'ready' for independent practice. The problem, however, is that in many mathematics curriculums, students are asked to complete homework on concepts that have just been introduced a few hours before. As a result, kids come back to school the next day with unfinished homework, confusion, and more questions than answers.

Here's where Excel Math's true spiraling process with spaced repetition and a built-in feedback loop help close the achievement gap and make homework more of an independent study and review process:
 Excel Math Spiraling Process with built in assessment and review
New concepts are first practiced (guided by the teacher) for at least one week before they are sent home for independent study. So by the time the concept goes home for independent instruction (homework), the student is able to complete the homework successfully most of the time. The CheckAnswer system provides immediate feedback, letting the student know if the answers are correct or if they need to be reworked. (Read more about the CheckAnswer system.)

After the lesson of the day is taught, students can begin working on the Guided Practice section of the worksheet. This is where mastery and long-term memory of a concept is achieved. Students are able to see at a glance which problems they miss. If the CheckAnswer doesn't add up, the student goes back and checks his work to find out where he made the mistake. As the teacher assists students who need more help, others can work independently. When a student has a question, he simply raises his hand so the teacher knows to give the student individualized attention. If several students have similar questions, the teacher can address the entire class with a review of the concept.
So a typical Excel Math lesson format would include:
• 3-5 Minutes: Warm up with Basic Fact Practice (provided on Excel Math Student Worksheets).
• 10-15 Minutes: Lesson of the Day direct instruction.
• 20-35 Minutes: Guided Practice (during this time the teacher can help students individually)
• Extension: Homework outside of class.

A flipped lesson may give students more time in class to practice and ask questions because the teacher is spending less time teaching. According to one group of teachers, "for a classroom to truly be 'flipped,' prepared instruction must continue at home, not just in the classroom."

If you decide to flip your classroom (or some of your lessons) and use Excel Math, here's what your flipped lesson format could include:
• 5-10 Minutes: Warm up with Basic Fact Practice (provided on Excel Math Student Worksheets).
• 5-10 Minutes: Clarification of the video or DVD lesson and questions from note taking. (Modified Lesson of the Day direct instruction.)
• 20-35 Minutes: Guided Practice (during this time the teacher can help students individually)
• Closure: Students self-assess the number or percentage of questions they got correct.
• Extension: Homework plus video or DVD assignment of the next day's lesson outside of class.

Since Excel Math homework is designed to last just 10-15 minutes, students can complete the homework page plus watch a 5-10-minute YouTube video or DVD of the next day's lesson at home.

Here's a video one teacher, Mr. Bedley, created to explain Excel Math concepts from Lesson #2 to his 5th Grade students:

Grade 5 Excel Math Lesson 2 [5:34 min]

This video shows how the Excel Math Projectable Lessons can be used to explain the Lesson of the Day to the entire class. You can create your own videos by simply recording each lesson as you teach it. To accommodate students without internet access at home, some teachers are creating DVDs for students to view on their computers. Others create YouTube presentations of the lessons and post them on secure sites where students can access them from home.

The videos can be used as homework the night before the lesson to give the students a preview of the concepts that will be practiced in class the next day. Even if you don't flip your classroom, you can use the videos (your own or those on our website) as a review of the concepts taught during class. Videos can be especially helpful for students who need remediation or review of certain lessons or concepts.

Even without videos, Excel Math provides an efficient way to prepare students for homework. Here's how Excel Math with its unique spiraling process works: a concept is introduced and then reviewed and reinforced through spaced repetition over a period of one week before it is included in homework. That concept is then assessed with a test two to three weeks later.

With the Excel Math spiraling process, students are not sent home to figure things out for themselves. And they are not asked to remember concepts they have just been taught that day. Here's a more detailed look at how the process works on a weekly basis:

If you're ready to make the flip, read Andrew Miller's blog post, "Five Best Practices for Flipping Your Classroom" at Edutopia.com. Join Excel Math on Edmodo to find out what other teachers are doing. Then take a look at the Excel Math lesson videos on our website for some well-presented
math lessons you can use with your own classes.

Wednesday, June 6, 2012

Flipped Math Lessons: Pro or Con?

One of the buzz-word phrases in the education community today is "flipped lessons" or "flipped classroom." Many teachers are flipping their lessons to change the concept of homework from "figuring it out on your own" to include "student-led learning." However, the "flipped classroom" has become a controversial subject. Today we'll take a look at some conversation around "flipped lessons."

Excel Math works well even if you don't flip your math classroom. It is a proven method (established over 35 years) for teaching math to students in ways they learn best. So whether you flip your class or not, Excel Math will work to increase long-term retention of math concepts, build confident students, introduce them to regular testing (and help them develop test-taking skills), provide them with a natural feedback loop so they can check their own answers, help them combine math with literacy, increase their understanding of math as well as their test scores, and much more.

Here's an example of how one math teacher flipped his classroom:
"With a flipped lesson, instead of introducing a topic in class, the students are first exposed to it at home. That is their homework. They are to watch videos or take notes on designated pages in order to prepare them for the practice that they will do in class. It's basically a way to 'front-load' the instruction so when students come to class, they're prepared and the concept will not seem so new. What this means is that there is less time for demonstrations at the beginning of class, as the students have already been introduced to the material." Read more on Teaching Ahead of the Curve Blog. Here's a breakdown of what a typical flipped lesson format might look like:
• 5-10 Minutes: Warm up, problem checking, notes for today's lesson.
• 5 Minutes: Clarification of the lesson and questions from note taking.
• 30-40 Minutes: Individual practice with teacher checking for understanding and posting answers in class.
• Closure: Students self-assess the number or percentage of questions they got correct.
• Extension: Notes on the lesson plus video assignment outside of class. Read more on Elevated Math Blog.
And here's what a traditional math lesson might include:
• 5-10 Minutes: Warm up, problem checking, debrief of previous night's homework.
• 20-25 Minutes: Explanation of the lesson, learning objectives.
• 15-20 Minutes: Guided practice with teacher checking for understanding.
• Extension: Homework outside of class.
This same teacher feels a flipped lesson gives students more time in class to practice because the teacher is spending less time teaching. According to another group of teachers, "for a classroom to truly be 'flipped,' prepared instruction must continue at home, not just in the classroom." To accommodate students without internet access at home, some teachers are creating DVDs for students to view on their computers. Others create YouTube presentations of the lessons and post them on secure sites where students can access them from home.

However, Excel Math provides a much more efficient way to prepare students for homework. Here's how Excel Math with its unique spiraling process works: a concept is introduced and then reviewed and reinforced through spaced repetition over a period of one week before it is included in homework. That concept is then assessed with a test two to three weeks later. As a result, students are not sent home to figure things out for themselves. And they are not asked to remember concepts they have just been taught that day.

In addition, Excel Math gives students a natural feedback loop with its CheckAnswer system. Students are able to see at a glance which problems they missed. If the CheckAnswer doesn't add up, the students go back and check their work to find out where they made the mistakes. Guided Practice in class and Homework after class all include this special CheckAnswer system so students don't keep making the same mistakes over and over. This is an example of  how the CheckAnswer system works. Add together the answers for problems A, B, and C. The sum, CheckAnswer (D), should equal the number in the box (5,927). If not, students go back and check each of the four problems:

When students take an assignment home, there obviously is no teacher to help them. It is assumed that if a teacher gives help in class, the student is therefore 'ready' for independent practice. The problem however, is that in many mathematics curriculums, students are asked to complete homework on concepts to which they have just that morning been introduced. It should be no surprise that kids come back to school the next day and say, "I didn't understand this, so I couldn't do it." Here's where Excel Math's true spiraling process with spaced repetition and a built-in feedback loop help close the achievement gap and make homework more of an independent study and review process.

When a concept has been practiced by the student and guided by the teacher for at least a week, by the time it goes home for independent instruction (homework), the student is able to complete the homework successfully most of the time. The CheckAnswer system provides immediate feedback, letting the student know if the answers are correct or if they need to be reworked.

After the lesson of the day is taught, students can begin working on the Guided Practice section of the worksheet. This is where mastery is achieved. Students are able to see at a glance which problems they miss. If the CheckAnswer doesn't add up, the student goes back and checks his work to find out where he made the mistake. As the teacher assists students who need more help, others can work independently. When a student has a question, he simply raises his hand so the teacher knows to give him individual attention. If several students have similar questions, the teacher can address the entire class with a review of the concept.

So a typical Excel Math lesson format would include:

• 3-5 Minutes: Warm up with Basic Fact Practice (provided on Excel Math Student Worksheets).
• 10-15 Minutes: Lesson of the Day direct instruction.
• 20-35 Minutes: Guided Practice (during this time the teacher can help students individually)
• Extension: Homework outside of class.

Excel Math lessons ensure that a higher percentage of students attain mastery of all concepts. With Excel Math, students are taught in ways they learn best, according to the latest studies in brain research.  Read more on our May 9 blog post. Attitudes changed completely when this teacher made the switch to Excel Math:
“I LOVE IT! What’s most important - THE STUDENTS LOVE IT! Some of the students’ comments include: ‘I like how I don’t need to wait to see if I got the right answer’, ‘I really love Math now’, ‘Can we do this every day?’, ‘This is fun!’ Thanks for helping me out.” — Mrs. Tanya Streicher, Teacher, Good Shepherd Catholic School

You can still have a flipped classroom and use Excel Math (more about that next week). Read more about flipping your classroom at TheDailyRiff.com. But it's not necessary to flip your math class in order to use Excel Math curriculum with your students. In fact, once you see your students begin to get math concepts into their long-term memory and watch their test scores rise, you may just do a few flips in celebration!

Read more teacher success stories with Excel Math. Take a look at samples of Excel Math curriculum on our website. Leave a comment to let us know if you're flipping your math class and what you've done to make it work or why you've not yet made the flip.

Monday, June 4, 2012

Time for Analog Clocks

In Excel Math, students learn to tell time using analog and digital clocks.
A clock with a minute and an hour hand is called analog. An analog clock has hands to point out the time:

Here's a cool analog chalkboard watch our friend Mike brought back from a recent trip to England. He can even customize the face with his own piece of chalk:

digital clock has only digits to the indicate the time (no hands):

Bring an analog clock with movable hands to your class, or make one using this analog clock from Excel Math First Grade Manipulative M14. Cut out the hands and attach them to the clock face with a paper fastener:
Show the students your clock. Explain that the shorter (usually fatter) hand indicates the hour and the longer hand indicates the number of minutes after the hour. If the minute hand is pointing straight up, the time is on the hour with zero minutes.

Display 3:00 on your clock. Show it to the students and ask them what time it is. Point out the face and the hands of the clock. Explain that as the minute hand moves around the clock face, the hour hand will gradually move to the next hour mark. Show how this happens by moving the hands around the clock to show 4:00.

Explain that the hour hand points directly at a numeral only when it is exactly on that hour. The rest of the time the hour hand will be pointing in between two numerals.

Point out the minute marks on your clock. Have a student count the marks. Ask the class if there is a pattern in the number of minute marks between each of the hour marks. (There are five minute marks between every two hour marks.)

Set your clock to 4:25. Show the students the clock face and ask them what time it is. Ask them how they might calculate the minutes after the hour. (They can count each minute mark or count by five.)

Repeat this process several times where the minute hand points to a multiple of five.

Next, set your clock to 4:27. Ask the students what time it is.  Ask them how they might calculate the minutes after the hour. (The can count each minute mark or count by five until they get close to the minute hand and then they can count each minute mark.) Repeat this process several times where the minute hand points to a number that is not a multiple of five.

Print the following Excel Math worksheet for your students. Let them complete numbers 1-6 on their own. Offer help as needed: