## Posts filed under ‘Math’

### Review/Extension Activity: Sometimes, Always, or Never

When you get your kids to think and then they ask you to do it again, you know you have a winner.

This is a versatile activity that can be adapted for any setting, time frame, and group dynamic. It engages students in processing vocabulary and ideas, helping them get comfortable and familiar with new words without any memorization pressure. Preparation and setup can be as easy as you need it to be. Here is the basic idea with one simple variation:

Create a list of statements about the topic you wish to explore or review. The statements should be sometimes, always, or never true. For example, here are some of my statements from a lesson about quadrilaterals:

A rhombus is a square

A rectangle is a parallelogram

A parallelogram has a right angle

A quadrilateral has 4 acute angles

A quadrilateral has exactly 2 right angles

I played the game with intensive students individually or in pairs, so I did it as a board game: Take any follow-the-path game board and randomly label the spaces *sometimes, always, *and* never*. In turns, each player picks up a statement card, reads the statement, and decides whether it is sometimes, always, or never true. The player must PROVE or at least reasonably demonstrate their answer through logic or examples. Often, the student develops their answer through the process of proving it. They can sketch examples, look up a definition in a reference book, and discuss with others. Some of the students surprised me – and themselves! – with the insights this process brought out. Once the players are collectively satisfied with the answer, the player moves to the next unoccupied matching spot. The game can be adapted to different game boards or simply collecting cards. Adapt for levels of knowledge/memory by making different reference resources available (or not). When students are already familiar with the way this works, you can make it an independent center activity for groups or individuals. You can have students make up the statements and then pool them together. Making up statements for a S/A/N game center can be an “early finisher” activity.

Another way to play that limits it to more of a categorization exercise is to write just the words on the card instead of full statements. Make several copies of each. Then, students draw the cards and place them on a template that looks like this:

A ______________ is a _________________

This will result in many of the same permutations you might have created in the first place, but it’s easier to prepare and adds a fun randomness.

This activity works especially well with topics involving a lot of categorization or attributes. Try it in science:

An elephant is a mammal.

A bird can fly.

A reptile lives in the desert.

Or in social studies. Or even in grammar. I love metacognition!

### Friday Finds: PurpleMath.com

It started one embarrassing day when my resource student began to learn about factoring quadratic equations. Now, I teach elementary/middle school. In my day, you didn’t meet one of these until at least the middle of high school, and I don’t think I understood them until college – and even that was, ahem, *x* years ago. The textbook was no help. I excused the student from homework that night and went home with a headache.

Then I found PurpleMath.com. Their “factoring hard quadratics” page here did more than just clarify the lesson – it introduced a graphic method that I’d never seen before but made the entire process simpler and more organized. The lesson included clear, step-by-step examples, and a quiz that went through the steps one at a time instead of just leaving you to figure out how to independently apply the new skill, as most web quizzes I’ve seen do.

I was so excited to bring the strategy to my student the next day, and we both shared the heady feeling of being able to easily and accurately do something that had been beyond us just yesterday.

The content is very thorough and covers topics relevant to middle school through college. It is geared to students but, as in my case, can be helpful to teachers too, especially in elementary grades where you need not be a math specialist to have math on your curriculum. Even if you are naturally good at math, it can help to see the steps clearly explained in a way that your students will understand. A clearer understanding of the math will help you teach it more clearly.

The site also includes a forum for users to submit questions. There’s a lot of homework help going on there, and it seems to be up-to-date and reasonably active, if not really buzzing (I guess math homework isn’t that viral).

All the content is free and organized decently. You can download the lessons on CD for a reasonable price. There are ads but all I have seen so far are appropriate and unobtrusive. I would feel very comfortable directing students to this site for extra help.