The past two years, we devoted the march blog posts to celebrating March Mathness, the math behind the sport of basketball.
Many of you sent in your own math problems for posting. These included scores, records of teams, distance teams have to travel, the basketball court itself, even the numbers on the player’s jerseys. Math plays into this annual event in more ways than you might think.
So check this blog regularly for more fun math problems. Send your ideas for March Mathness math problems to firstname.lastname@example.org
Meanwhile, here is a favorite updated from last year:
A study released by Sports Illustrated magazine last year reveals that colleges with “bird” mascots have done better than those with animals, fantasy figures, or humans for mascots. Here is how it shapes up
|Fantasy figures/inanimate objects/weather
|Canines and felines
According to this study alone which of the following first round teams should win? What is the difference in the winning percentages for their mascot types?
Kansas Jayhawks vs Austin Peay Governors
Duke Blue Devils vs UNCW Seahawks
Seton Hall Pirates vs Gonzaga Bulldogs
Miami Hurricanes vs Buffalo Bulls
Once an intervention program is in place, it can be tempting for schools to leave it in place if students are making at least some progress. But how much progress is enough? If an 8th-grade student began the year at the third-grade level, is it enough to advance that student one grade level by the end of the year? Can you expect a struggling student—one who has slid further behind each previous year—to suddenly begin to grow multiple grade levels in a single year? The answer is an unqualified YES. If a student’s specific skill gaps are accurately identified and addressed in sequence from the bottom up, that student will be armed with both the knowledge they need to make progress in math and a new confidence that they can in fact succeed. If students are instead faced with material that is misaligned, too difficult, or inadequately presented, they may not be as likely to invest in their own growth. If you do not expect students to make impressive gains, chances are they won’t.
Editor’s Note: This is the fourth in a series on Common Mistakes Made in Math Intervention by guest blogger Jeff Hartman.
Mistake 4: Using a Program Not Well Designed for Math Intervention
Precision matters. The math software market is saturated with programs that provide practice problems for students behind grade level, and a select few of these programs offer some kind of instruction or assessment. But what is almost always missing is the ability of a program to automatically identify and address individual student skill gaps without the instructor having to manually make assignments.
A drill-and-kill math software program may offer a quick assessment that helps identify students who are behind grade level, but it usually stops well short of identifying the precise below-level skill gaps that are holding that student back, or even providing an accurate assessment of what level to begin instruction. When using an inferior math program, teachers have to constantly spend time making more accurate assessments themselves. Even then, they still have to devote more time to pairing students with resources over and over again because the program itself can’t automatically do it. An effective math intervention software program should always be able to automatically assess exact skill gaps and guide students through their unique learning paths without constant tinkering by the instructor.
Editor’s Note: This is the third in guest blogger Jeff Hartman’s series on Common Mistakes Made in Math Intervention.
Mistake 3: Using Teachers as Data Clerks
Data is a necessary pillar of intervention, but when the need to document progress consumes the available time of instructors who would otherwise be working with students, the time spent gathering data detracts from any one-on-one teacher time that students really need. If a school is using a large number of separate tools to assess and monitor students, teachers have to master the art of compiling and interpreting data from multiple sources. Using a streamlined program to both assess students and monitor progress liberates classroom teachers from spending too much time managing data, especially when real-time data is consolidated into easy to read dashboards. To quote a happy teacher from one of our Ascend Math partner schools, “There’s more of me for my kids instead of me sitting behind a desk… and my aide teaching my class.”
Editor’s note: This is the second in a series of posts from guest blogger Jeff Hartman on the Common Mistakes made in Math Intervention
Mistake #2: Not Differentiating Enough
In an effort to deal with classes that have many students at varying functional grade levels, some instructors will choose to group students by level to better focus small group instruction. But grouping only by functional level doesn’t necessarily put students with the same needs together. Even if all the students in a group are operating at the same level, they very probably have different skill gaps and need a study plan that is precisely mapped to their individual needs, otherwise some of the students in the group will be spending time on lessons that do not correspond to their needs. For intervention to be most effective, instruction needs to be precisely tied to a student’s demonstrated skill gaps, and material that a student doesn’t need to learn should be removed from their study plan.
This is the first in a series of five posts on Common Mistakes Made in Math Intervention by Guest blogger Jeff Hartman
Mistake 1: Starting at the Top
A student who has major skill gaps from previous years is unlikely to fare well in grade level instruction. Unfortunately, too often educators start with just-below-grade-level instruction in hopes of bringing them quickly up to grade level. The temptation is to try to teach objectives that are just under grade level since they seem like the necessary prerequisites for grade-level learning, but often an intervention student is operating significantly behind grade level. It is far more efficient to begin instruction at the level of the student’s lowest skill gap. Not only does this fill in the deepest foundational cracks in their knowledge, it is also where their competency lies. It is where they are most likely to re-discover the sense of accomplishment that can lead to momentum and enthusiasm for learning math.
Too see just how common it is for students to have below grade level skill gaps download this report: Which Math Skills Students Are Missing.
Share these fund math problems with your students
1. Sweethearts candy hearts have been a popular Valentine’s Day treat for more than 100 years. NECCO, the maker of Sweethearts produces about 100,000 pounds of the candy hearts every day in order to meet the Valentine demand, when about 8 billion hearts are sold in six weeks. How many are sold on average each day during those six weeks?
2. Marcus found 32 candies in a box of candy hearts. He divided them up by what was written on them.
8 said Text Me
5 said U R A Star
6 said 4 Ever Fun
8 said Tweet Me
5 said Be Happy
What percent said either Text Me or Tweet Me?
3. The florist sells 150 bouquets of flowers. Each bouquet has a dozen roses. Five bouquets were returned because the flowers were wilted. How many flowers were sold in all?
4. At MathMart, packages of 20 Valentines are on sale for $4.00 each. How much does each card cost?
Share these fun Super Bowl math problems with your students!
1. A Super Bowl ring costs $10,000. There are 53 players on a winning team. How much will it cost to give them all Super Bowl rings?
2. The Panthers and Broncos have played each other four times. The Broncos have won three times and the Panthers once. Add up the scores for each below. Which team scored the most points? By how much?
2012 Carolina Panthers 14 Denver Broncos 36
2008 Carolina Panthers 30 Denver Broncos 10
2004 Carolina Panthers 17 Denver Broncos 20
1997 Carolina Panthers 0 Denver Broncos 34
3. If the final score of this year’s Super Bowl is Carolina 20 Denver 14 name all the different ways they could have earned those points.
Teachers: Some students may need to be told the meaning of a safety and have a brief review of the way football is scored. Here is a basic guide:
- Each touchdown is worth 6 points. After a touchdown, the scoring team can attempt to get an extra point.
- An extra point is worth 1 point. Right after a touchdown, the ball is placed at the opponent’s two-yard line and kicked. If the ball goes through the goal post, the extra point is earned.
- A field goal is 3 points. If the offense can not score a touchdown, they may choose to kick a field goal. A successful kick results in the ball passing through the goal post uprights and over the crossbar.
- A safety is worth two points and is earned when the offensive ball carrier is tackled behind his own goal line.
Check out this great logic puzzle from TedEd. Try to figure it out as a class or just by yourself.
No two students are exactly alike. In a perfect world, we would treat each as an individual, but it’s not a perfect world. Most often, one teacher must guide twenty or more young people to find the path to success and understanding. For many of us that’s okay. Since, with the teacher’s guidance, we often assist in finding our own unique path to learning.
However, the student who falls increasingly behind in math will remain lost and unable to find his way out of a foreboding wilderness. It becomes increasingly confusing and eventually frightening. The only way back into the clearing and back on level will require blazing an individual path out of the confusion. And that cannot be done without individual guidance each step of the way.
Imagine a map of a thick forest. Three students are lost in the forest.
First, we have to locate the student. How far back has this student fallen? At which functional grade level are the student’s math skills? Is he two grade levels back? Three? Four? Once, we know how far back they are, we can begin to plot a unique path to math success for that student. Let’s say our three students have all fallen three grade levels back. They may all have an equal distance to go but each is in their own location in the forest. Each will move in different directions and have different stopping points on their way out. Finding each student’s individual skill gaps is the only way to plot a reliable path out of the forest. If they go in any other direction or make any other stops along the way it will delay their journey back and even possibly put them deeper into the woods.
Teachers need two things to help students out of the forest: 1. An assessment that finds each student’s position and plots their individual paths forward (think of it as a GPS correlated to state standards). 2. The best instructional content providing students with the individual skills to make their way out.