Working Backward to Improve Standardized Test Scores

One of the projects I started this year was to again look at my state’s math standards and then focus on how they are tested in the standardized test that students take every year. In my state, we refer to these standards as G.L.E.’s (Grade Level Equivalents) and the standardized test our students take is the N.E.C.A.P. (New England Common Assessment Program)

I set up a big binder with a divider and clear plastic sheet protector for each of the math GLE’s at my grade level, and also for the previous grade level which I try to review in the fall in preparation for the test. I went to the school’s library and made copies of all the math released items from the NECAP tests. There were about five years of them. I cut apart each question and identified which GLE it tested and put it in the plastic sleeve for the corresponding GLE. Doing all the items was time-consuming, but the results were worth it.

Over the years I could see which standards were tested more heavily, and this was helpful. But more than that, I now have a question bank for each skill. When teaching a specific math skill, I can look at how questions are asked to assess that skill. I can see how different vocabulary is used, and in many cases, the question is worded differently from how I would ask it , or how our math book asks it. I can give students sample questions throughout the year, and not just at practice test time. And I can save the questions I create and add them to my collection in the binder.

This approach has certainly been working backward; I started with the test and worked to match a skill to it rather than the other way around. But I have gained some good information from it.

Better Than Luck

There is an activity I like to do with my classes when they are in the probability unit. I start by holding up my brown paper bag and telling them that there are colored tiles in the bag. I pull out one tile of each color to show them as I say there are red tiles, blue tiles, and green tiles. And there are twenty tiles total in the bag. Can they now predict how many of each color are in the bag? At this point, some try, but I point out they are just making random guesses. I do encourage them to write down their guess to see how lucky they will be.

Next, I go around the room letting each student pull out one tile from the bag without looking. They must put it back in the bag once we have seen what color it is. Another student keeps a tally on the board. We do this several times to get some data. Then we proceed to turn the data into a fraction of how many picks were of each color. The fraction is then turned into a decimal, and then a percent. Next, we use the percent to make our (educated) guess about how many of the tiles are red, blue and green. For example, if 25% of our picks were blue, we would guess that there are 5 blue tiles in the bag because 5 is 25% of 20.

After figuring out all of our guesses, known as experimental probability, and discussing our final hypothesis and the process used to make it, we are ready for the “big reveal”. We examine how close we came and most always discover that statistical data based upon probability is better that just plain old luck!

Exploring Careers

I wrote about this website last year, but didn't get my students using it as much as I have been doing with them lately. The website is:
www.xpmath.com
There is a variety of information on there including a "math arcade" where students can play games that help them with specific skills.

But this week I asked my students to do a little research into careers using this website. I typed up a worksheet that has two parts. The first part asks them to list a career or occupation and then tell how many math skills are used by someone in that field. They then have to list some of the math skills listed for that job. This is accomplished by clicking on "math jobs". The second half of the worksheet has the students list a math skill and how many careers in the database require that math skill. They then list a few of the careers. A simple click on one of the math skills gives this information.

The worksheets make an impressive display on my wall and students can see not only that math is important in everyday life, but that being proficient at math skills will give them more careeer options.

One Hundred Eighty Degrees

There is an activity I like to do to help kids remember that the number of degrees in a straight line and the sum of the angles in a triangle are the same number. It is a good visual demonstration to drive the point home.

On a piece of paper draw a straight line using a ruler. This can also be done on an overehead transparency if you are demonstrating it for a whole class. Have several triangles cut out of construction paper. I ususally have one that is scalene, one that is isosceles, and one that is equilateral. Tear off the three angles of the triangle and arrange them with their points together on the straight line. I do this with each of the three different triangles.

Some years, I have told the class that I would give ten dollars to anyone that could come up with a triangle that had angles that didn't fit together on a straight line. But I am sure that I will never have to pay up, because it works for every triangle every time!

ETA Cuisenaire Daily Math Reinforcers

I've been using this resource for nearly ten years, and it has been a tremendous way to improve student math skills as well as review and pre-teach concepts that need to be met. These work well as a warmup for math classes as well as a tool for remedial groups. There are three sheets to each reproducible page. Each daily sheet has a mental math section, a word problem, and a skill review section. The newest edition of the manual also includes concept sheets and section quizzes. The series has a book for each of grades 1-8.

The mental math section has three questions which I just read to the class. I usually read them twice and ask the students to answer the questions by thinking about it, but not by writing anything down except the answer. I've seen a number of students improve tremendously in the area of mental math as the year progresses. When we go over the questions, we share how we thought about the problem to get the answer. Then we realize that there is often more than one way to solve the problem. Sometimes we have the opportunity to correct faulty reasoning or misconceptions.

The word problem section requires students to list the steps to solving the problem in a format that fits the acronymn, TIPS. (Thought, Information, Plan, Solution)Occasionally, problems are given that do not have enough information to solve. Students know this and if there is not enough information, they write NEI and then tell what information they would need to solve the problem.

When I was teaching regular ed middle school math, I started many of my classes with this activity as a warm-up. I handed the slips out as students came in the door, and then just went to the front of the room and started by saying "Number 1" which was the mental math section. When I did this, students settled right down. I allowed about eight minutes for the work. Now as a remedial teacher, I often use these daily warm-ups with my students. In both situations, I go over the slips inviting students to give answers and model solutions.

The ADD acronymn is on every sheet for Arithmetic Daily Developed. This series has truly helped my students become more proficient in math.

A New Math Word

My husband's seventh grade class has come up with a new math term! In science they have learned that the prefix "eu" means true. So eubacteria, as opposed to archeabacteria, means true bacteria.  And eukariotic means true nucleus. 

In math, they are learning about variables. Now the definition of variable is "a value that can change". In the the equation y=2x + 5, the variables are x and y. And their values can change.

But sometimes variables or letters are used just to hold a place and the value is pre-determined. An example of this is in the equation 2x +3 = 7. In this case x=2 and the variable is holding the place of the 2.

So the new math word? Here it is: EUVARIABLE!!! It means a true variable and not just a place holder.

Congratulations to my husband and his seventh graders! Good thinking!

Integer Hi-Lo

I came up with a new game and my last period eighth grade group named it! I needed to review multiplying integers with them.

I started by dividing the students into groups of two, three, or four and giving them a deck of cards. I wrote on the board that black cards were positive and red cards were negative. I told them it was that way with the phrases "in the black" and "in the red."

The dealer hands out all the cards to the players. The cards are placed face-down and the players don't look at them. Whoever has been designated to go first puts out one card. If it is black, they are looking for the highest product; if it is red, they are looking for the lowest product. Then the first player lays out another card and announces the product of his two cards. The next player puts out two cards and announces their product until all players have done this. They then decide who has the high or low depending on what they are looking for based on the first card out. The winner takes all the cards and puts them under their deck face-down.

Players are trying to end up with all the cards. If there are more than two people playing, I cut the game off when one person has no cards and the person with the most is declared the winner. If the class ends, the person with the most cards wins.

This is a good game not only for multiplying integers, but also comparing integers. Sometimes students struggle with the concept that -50 is less than -1, and this game helps them review magnitude.