Reflex Math

One mathematics goal for 4th grade students is to be able to demonstrate fluency with related multiplication and division facts (0-12). Now that we have started studying multiplication and division during Math Workshop, this fluency is becoming more important than ever.

The Reflex online fluency building program that we use during Math Centers scaffolds to each individual child's needs, offering re-teaching and additional practice with facts often missed by students until mastery is achieved. This program also offers reward incentives such as coins and points which can be redeemed in the "store" for Avatar "flair"- new hats, sunglasses, jackets, and other cool items to keep them motivated. Best of all, teachers and parents can gain access to track student progress.  It takes only about five minutes for a parent to create an account so that updates on your child's progress can be emailed to you bi-weekly. It's so convenient.  Information on how to set up a parent account was sent home in mid-September, but if you missed it and would like more information on how you can track your child's progress, write a quick note in your child's planner and information can be sent home again. :-)

It is recommended that students participate in Reflex Math fluency building 3-4 times each week. Each session lasts approximately 20 minutes. Each student logs in and participates in Reflex learning activities while at school at least once each week, but it is also helpful if they can spend time learning from this valuable resource at home too.

Happy Fluency Building!!

Categories of Numbers

During our first investigation in our unit Factors, Multiples, and Arrays, our classes have created posters of the arrays for various numbers. Using these posters, we have put numbers into different categories based on the kind and number of arrays they could make.

We have identified numbers that can make "only one array", numbers that make "square arrays", and numbers that make "many different arrays". These initial ideas have now developed into classifying numbers in five ways: odd, even, prime, composite, and square. Numbers may fall into as many as three different categories.

Here is a list of the mathematical ideas that are being developed during Math Workshop as a result of these student-made posters:

Odd Numbers: * have a 1, 3, 5, 7, or 9 in the ones place * have only odd factors * odd x odd = odd

Even Numbers: * have a 2, 4, 6, 8, or 0 in the ones place * always have a factor of 2 * each factor pair must have at least one even factor * odd x even = even, even x odd = even, and even x even = even

Prime Numbers: * only have 2 factors (one and itself) * only produce one array * 2 is the only even prime number

Composite Numbers: * have more than two factors * make at least 2 different arrays * can be even or odd

Square Numbers: * make a square array * have an odd number of factors * follow a pattern of odd, even, odd, even, ... * can be made by multiplying a number by itself (ex: 1 x 1 = 1, 2 x 2 =4, 3 x 3 = 9, therefore, 1, 4, and 9 are square numbers)

Students, can you identify a number between 100-200 that is composite and square? Leave a comment and share your answer (and your reasoning) and you will earn  Behavior Bucks!!

Addition and Subtraction Strategies

The first part of our mathematics journey this year has been to deepen our understanding of place value and number sense through exploring addition and subtraction. We have built upon many mathematical ideas learned in 3rd grade in order to find more efficient ways to solve problems involving larger numbers as 4th graders.

Decomposing

This helpful strategy helps us "see" the value of each digit so that we can make sense of combining and separating numbers because each part of the problem is broken down into its place value "parts". An addition (combining) example is shown below.

Compensation

This awesome strategy is useful when one of the numbers we are computing with is near a landmark number.
When adding, we might take one from the second addend and combine it with the first addend to make an "easier" problem.

When subtracting, we might adjust both the subtrahend and minuend by the same amount (keeping their distance/difference the same) so that we can subtract easily (without regrouping).

There are also other ways to compensate when adding and subtracting- these are just two examples.

Straight Subtraction

This strategy reminds us that we can NOT just switch digits around among our minuend (whole) and subtrahend (part) when subtracting (even though we might want to in order to make subtraction easier). We CAN subtract larger numbers from smaller numbers...we just end up with negative numbers that need to be dealt with.

 

Traditional Algorithm & the Expanded Algorithm

Decomposing each number to be computed into its place value parts helps to show HOW the traditional algorithm works. This works well with both addition and subtraction. A subtraction example is shown below.

We will continue to explore a variety of strategies when adding and subtracting numbers to the millions throughout the course of the school year.

 

Students, what is your favorite strategy?
Leave a comment and let us know.