Monday, October 31, 2011

Our Animal Adventures!

Our world abounds with countless and intriguing animals.  They need oxygen to breathe, food to eat, water to drink, a shelter to live in, and they need to be able to produce offspring. Some of the animals have backbones (vertebrates) and some do not (invertebrates). 
Some animals breathe oxygen with lungs, some with gills, and others, like sea jellies, through their skin. Birds and mammals are warm blooded while other animals are cold blooded. Some animals have live birth, yet others lay eggs for their young to hatch.They can be carnivores, herbivores, or omnivores, and habitats of all kinds are their homes.  
Fascinated with animals, our young scientists have been exploring this diverse world of captivating animals. Throughout the unit, they have been asking, pondering, and answering questions. 
In what ways can animals be grouped?
How can we sort animals?
How can we classify vertebrates?
How can we classify invertebrates?
How do animals adapt to survive?
How does an animal's body coloring help it survive?
How do animals in Florida's Everglades National Park respond to changing seasons? 
To explore, they have created lists of animals and sorted them into groups based on common characteristics. They have sorted vertebrate animal cards into groups of mammals, birds, reptiles, amphibians, and fish.  They have sorted invertebrate animal cards into groups of sea jellies, worms, mollusks, and arthropods. Furthermore, they've discussed, in great depth, the animal adaptations that help them to survive in the places where they live.
Some animals, for example, have protective adaptations like camouflage, armor, mimicry, and poison, while others have behavioral adaptations like the instinct to migrate and hibernate to survive the winter. In addition, animals have physical adaptations that help them survive. Birds, for example, depending on the food they eat, have different kinds of beaks. Cardinals have short, strong bills to pick up and crush seeds. The pelican, on the other hand, has a long, pouched bill that helps it swoop down and pick up fish.
From the very first introduction of this unit, our students took a special interest. To promote this enthusiasm, we designed an independent study for students so they could explore an animal and a project of their choice. We created a menu of options, stocked the classroom with reference materials and texts for research, and gave them a rubric to guide their exploration. Each day, the students come to the classroom excited to get to work and they have been self-directed in their learning.  Stay tuned. We can't wait to share some of their polished products with you when they are finished.    

Arrays Make Math Easy to Visualize

As young mathematicians, we are exploring the use of arrays to help us with multiplication. It is imperative that we develop strong visual images of multiplication to develop conceptual strategies for solving multiplication problems. When we can clearly visualize how the numbers being multiplied are related, we can develop flexible, efficient, and accurate strategies for solving any multiplication problems.

One way we are learning to visualize these relationships is through the use of arrays. An array is a rectangular arrangement of an equal number of items in rows and columns. Arrays can be helpful when solving more “difficult” multiplication situations. Being able to visualize how to break multiplication problems into parts becomes even more important when we begin to solve multi-digit problems.

The following is an example of how we can split an array into smaller arrays making it easier to find the product.

Another way we can lay a strong foundation for multiplication is to practice skip counting by multiples of numbers 2-12. The goal is to skip count fluently (within 3 seconds) from one multiple to the next.This task can be practiced at home, between commercial breaks, or even in the car. Being able to skip count fluently will undoubtedly help us in our work with multiplication and division. Check out this website that helps with skip counting.

Sunday, October 30, 2011

Comparing Arrays

Last week in Math Workshop, our young mathematicians spent time arranging different amounts of chairs into rows and columns (arrays). We looked first at ways to arrange 12 chairs. Then, during Work Session students paired up to explore with two other arrangements. Exploring with the numbers 9, 15-21, 23-25, 27, and 30 helped us to see how differently numbers can be arranged, and gave us the opportunity to discuss the similarities and differences among the varying arrays.  

For example, look at the arrangement of 16 and 17 chairs below:

What do you notice about these arrays? Do any of the arrays have a special or unique shape? What do you notice about the number of arrays that can be made with 16 chairs compared to 17 chairs?

Hopefully, you notice that 16 chairs can be arranged in several different arrays. That is because it has many factors: 1, 2, 4, 8, 16. A number that has more than two factors is called a composite number. You probably noticed that 17 only has two arrays. This is because 17 is a prime number. Any number that has only two factors, one and itself, is a prime number. The factors of 17 are 17 and 1.Also, you may have noticed that 16 can be arranged into a perfect square with 4 rows and 4 columns. Any number that has an array that is a square is a square number.  Our young mathematicians talked about square numbers when we analyzed the arrays for 9 (3x3) and 25 (5x5).

Students also realized that you could skip count by either the column or the row to get the product. Sixteen, for example, has an array that is a 2x8. You can count by 2's eight times... 2, 4, 6, 8, 10, 12, 14, 16 or you can count by 8's two times... 8, 16.

Stay tuned this week as our young mathematicians learn how to decompose an array to make a more difficult multiplication equation simpler.

Monday, October 17, 2011

The UN people!

This week, we are studying the prefixes re, un, non, and pre. Check out the video's below to see how adding a prefix to the beginning of a word can change the meaning of the word completely!

Thursday, October 13, 2011

All About Patricia Polocco

Who is Patricia Polacco? She is an author and illustrator that has written over 50 books. That’s a lot! She was born on July 11, 1944 in Lansing ,Michiagan and lived on her grandparents farm. Then when she was 41 years old she began writing books. Here are some cool facts about her:

- She struggled reading when she was a child.
-She loves eating apples and popcorn.
-She has 2 goats 1 lamb 2 cats.
-She has two kids one is Traci.
-At the age of 41 her 1st book was published.
-She lived in Caliaforina for almost 37 yeas.

She is a great author you should read her books!

Written by guest bloggers, Samantha and Ashley

Monday, October 10, 2011

Flexible Thinking Young Mathematicians

Thinking flexibly about numbers is one of our goals for students in third grade. Throughout our MI Unit 3, Addition, Subtraction, and the Number System, we’ve been highlighting multiple strategies in Closing Session. We do this because subtraction is the distance between two numbers, and based on the problem, the most efficient strategy isn't always the same strategy. 
In addition, we want students to be able to check their work using a different strategy than the one they used to originally solve the problem. Many times, if a student checks their work with the same strategy, it’s common for them to make the same computational error they did the first time. However, if they make an error in the first solution and then check their work with a second strategy, they are more likely to catch their error.
We are working toward students' ability to recognize, based on the situation, the most efficient strategy with the least likelihood of error, and with the idea that mental math can be one of the most effective ways to solve. For example, we don’t want students to use the traditional algorithm to solve 1000-989, because it would be easy for them to make a computational error when regrouping multiple times. Rather, we want students to recognize that the distance between these two numbers can easily be done by counting up, 989+1=990 and 990+10=1000, therefore the difference is 11.  Of course, in other situations, it’s simply easier to solve using the traditional algorithm like 876-563.  Flexible thinking based on the situation is key.
In order to develop number flexibility, we’ve been working on several strategies in class.
Sample Problem:  245 - 178 = m
Adding up
Turn the equation into a missing addend 178 + m = 67. Put the number 178 on a number line and count up to the next landmark number. (Landmark numbers have a O or 5 in the ones place.) 178 count up 2 to 180, count up 20 to 200, and then jump 45 from 200 to 245. Adding the jumps gives you the answer, m = 67.

Decompose the number by place value. This is also known as expanded notation. Then, subtract each place value. In this problem, 200-100 = 100, 40-70 = -30, 5-8 = -3, therefore 100-30-3= 67.  Sometimes, this strategy has you in negative numbers, but students know that 0 is the middle of the number system and can flexibly use negative numbers. Some students use this strategy and regroup from the larger place value. If they did that in this problem, they would take a group of 100 from 200 and put 140 in the tens place.

            245  :     200    40    5
          -178  :    -100  +   70  +   8
                            100   - 30  - 3 = 67

Counting backward
245 - 178 = m                                                                    

Put 245 on the open number line and count backward by 178. You can make the jump of 178 any way you want. Most kids jump backward to landmark numbers. 245 jump back 45 is 100, and then jump back 30 is 70, then jump back 3 is 67.  Left to Right
Students think 200 – 100 = 100 and 40 – 70 = -30 and 5 – 8 = -3.
            245  :    
          -178  :   
            100 – 30 – 3
                70 – 3 = 67

Furthermore, in some situations, we also encourage students to compensate. For example,
  56   + 3        59
-47     -3       -44

Remember, the purpose of exposing students to multiple strategies is two-fold. First, students need to be able to solve using two different strategies to check their work, and secondly students will be able to identify the strategy that is most efficient based on the problem. Students who successfully accomplish this have number sense and are able to work with numbers mentally and flexibly. Our students are busy every day becoming young mathematicians.

Friday, October 7, 2011

Math Unit 3 Assessment

In math class, we have been diligently working on our number sense unit. We will have our Unit 3 End of Unit Assessment on Wednesday (10/12/11). The following are some examples of questions that students should be able to answer:

1.) What is the value of the 6 in the number 4,365?
2.) Which inequality sign fits in the between these equations: 65 +10 ___ 95.
3.) How do you write 2,356 in explanded form?
4.) How many groups of ten are in 457? How many ones are left over?
5.) There are 145 first graders and 138 second graders in the dining room. How many students are there in all?
6.) There are 336 marbles in a jar. The marbles are either red or blue. There are 245 blue marbles. How many red marbles are there?

Answer three of these questions in a comment by Tuesday (10/11) and you will earn extra class money! Don't forget to sign your first name only when you leave a comment.