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Spiders Are Your Friends!

Spiders! We see pretend ones in the store as Halloween decorations (some are pretty terrifying) or real ones outside in a web they have created.  For some reason, these creatures are always something that students want to learn about. How are spiders different than insects? What is an orb web? Are all spiders poisonous? How does the spider not get stuck in her own web? These are questions that students will ask because they are curious and inquisitive.

Did you know spiders are really useful animals and serve mankind well? They eat mosquitoes, grasshoppers, locusts and other insects that are harmful to man. A single spider may kill about two thousand insects in its lifetime. Even though you may be afraid of spiders, very few are dangerous. The black widow and the brown house (recluse) spider do have poisonous bites, but there are no other common house spiders known to be dangerous.

Spiders are not insects, and insects are not spiders. Spiders are arthropods because they have spinning glands used to create silken threads. Sometimes spiders are called arachnids because of their eight legs. Spiders and insects have different attributes. All insects have six legs, but all spiders have eight legs. An insect has a three-part body, but a spider has only two parts to its body. Insects have antennae or feelers, and spiders do not. Spiders can usually be found in basements, barns, garages, or attics. In warm weather, you can find them under rocks or logs, sitting on fences, or in the grass and flowers. There are about forty thousand different species of spiders.

Interested in learning more?  Check out a ten page short mini reading/science unit  about spiders. First, the students read a short passage about spiders. Then they answer several questions about the reading based on Bloom's Taxonomy, or they do an activity related to the reading passage. Activities include dictionary work, spider math problems, labeling the parts of a spider, and completing a spider web. This mini unit is appropriate for grades 3-5 and will take about five days to complete.

A Go Figure Debut for a Texan Who Is New

Her Store - Math Imagination
Today my Go Figure Debut is for a Texas girl, Linda Bernal, who is in her 27th year of helping children’s minds to grow and to learn to love math. (Like me, she cures mathphobics!) She currently teaches seventh grade math although she has also taught 5th, 6th and 8th graders as well. (She must love that middle school aged student!)

Ever since she was a little girl, Linda has wanted to be a teacher. Her house was the “hangout” spot in the neighborhood, and she can still remember playing “school” with all of the kids on the block. Of course, Linda was the teacher! Her dad even bought her one of those play chalkboards that would flip vertically, and she swears it was her most favorite thing ever!

Believe it or not, Linda actually struggled with math in elementary and middle school. Her forte was reading. Not only was she in a book club, but she had shelves full of books at home; so, you would assume she would want to be a reading teacher, right? WRONG! The turning point was when she attended high school. She claims she had the most patient and amazing math teachers who made it so easy to understand the “numbers with the letters” (a.k.a., algebra) and “all the stuff around the shapes” (a.k.a., geometry). These two teachers inspired her to become a math teacher which still boggles her parents’ minds.

In her math classroom you will see students walking around during a loop game, having discussions on how to solve a problem or sometimes even debates. During practice time, students may be writing on their desks with dry erase markers or creating entries in their interactive journals using foldables. Linda thinks students retain more when they are actively involved and when they have to explain math to another person. (I agree!) She firmly believes students get more out of working on a game with a partner than completing a 30 problem worksheet alone. She still does the worksheet thing; she just doesn’t do it on a daily basis with as many problems.

Only $3.00
One of the games in her store is a 12 problem loop game, and best of all, it is free. In the game, students practice in determining the surface area of nets that create three-dimensional figures. Students find the surface area of each figure by using the formulas for finding the area of rectangles and triangles.

Free Item
Linda currently has sixty-nine items in her TPT store, six of which are free. Most are math activities, but she does have some posters that can be used in any classroom. One of her free resources is called the  Simplifying Fractions Spinner Game. This game has students simplifying fractions by spinning two spinners to create their own fraction so that every student will have a different fraction.

Other resources in her store include Loop Games, Matching Cards, Smack Down, and Fact or Fib. Some of the activities are interactive power points that create great discussions between students! She also has a blog called My Math Imagination. You should take time to go there and read her article called "Nail It."  Not only does she have a mathematical sense of humor but what she does with fingernails is amazing.  Check it out for yourself!

Mathematical Patterns

Since all math is based on patterns, this week, I want to target some mathematical problems in which we investigate developing patterns.

In the first example below, you will notice we begin by multiplying one by one; then 11 by 11, and so forth. Each time we multiply, the number of digits in the multiplier and the multiplicand increases. Do you see the pattern that progresses in the answer (product)? Notice how this multiplication pattern forms a triangle? Can you figure out what kind of triangle it is?

Here is another interesting pattern. In this one, instead of multiplying by 1, then 11, then 111, the answer (product) looks like the multiplier in the pattern above. Do you notice anything else significant?

Yes, we are multiplying by 9 each time. Now look at the number being added, and count the number of ones you see in each answer. Surprised? Isn’t it amazing how math is ordered, methodical and precise? Maybe that is one reason I love to teach it!

"Sum" Trick

In the book Ten Black Dots book, there are a total of 55 black dots. Normally, to find that answer, you would add the numbers together.

But did you know there is an easier way? Take 10 and divide it by 2. That equals 5. Multiply 10 x 5 and you get 50 then add in the 5 which equals 55. Too confusing? Well let's look at it in groups that equal 10.

As illustrated above, 10 is by itself so it is 10. Then if we group the numbers so that each group equals ten, we have four additional sets. All together, we have five groups of ten with five left over which equals 55.   5 x 10 = 50 + 5 = 55

This will work for every sequence of consecutive numbers which begins with one and contains an even set. In other words, sets that contain 2, 4, 6, 8, 10, 12... numbers. Merely divide the largest number by 2; multiply the largest number by the quotient, and then add the quotient.

Example:  14, 13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2, 1

This will also work for an odd numbered sequence like 11 but the formula or quick trick for finding the sum is a little different. As seen below, we again divide 11 by 2, which 5.5 or rounded up equals 6. Again we group sets of two that equal 11. There are five groups plus 11 by itself so that makes a total of six groups.
Since there are no numbers left by themselves, simply multiply 11 by 6 (the rounded up quotient) to get the sum which is 66.

I love to write a series of consecutive numbers which begin with one on the board, and have the students find the answer using their calculators while I do the math in my head. Of course, they are amazed and swear that I have memorized the answer. I then ask me to give me a series (not off the wall or so large that it would take forever to use the calculator) and again I quickly give them the answer. I then teach them that math trick.

Students love "tricks" like this, but I always burst their bubble by telling them mathematicians are astute people. That's why they are always looking for faster, quicker, and smarter ways to do math!