Terminology[ edit ] Electronic symbol for an antenna The words antenna and aerial are used interchangeably. Occasionally the term "aerial" is used to mean a wire antenna. The origin of the word antenna relative to wireless apparatus is attributed to Italian radio pioneer Guglielmo Marconi.
She has been part of the NSF-funded Routines project upon which our perspective on early algebraic reasoning is based for several years. Thus, she has had extensive experience guiding elementary school students in making generalizations about arithmetic operations.
In our work with her last year, students were quite successful using the animation software to make statements about arithmetic equivalences, but never got to making arguments about generalizations about the way operations worked across "all numbers.
We were successful in our attempts; details of the results of this trial are included here. Students in this class had already used our software for several days, but had not encountered the animation system.
In one period of approximately an hour, almost all students in this class were successful in using the animation to show the equivalence of 3 X 4 and 2 X 6 by creating an array representation of 3 X 4 and modifying it to become an array representation of 2 X 6.
While we were in this third grade classroom for four days, two of the sessions were very short, so our total time working with these students was only about three hours.
A few of them successfully created an animation to show that 5 X 4 was equivalent to 5 X 2 X 2. While they were not able to create an animation to show the equivalence for "any number," it was clear that the students were basing their arguments on the examples they had just worked.
Students successfully made the crucial distinction between the parts of the equivalence that could change "it would be the same for any number"; "the first number could be either even or odd" and the parts of the equivalence that could NOT change "as long as the 4 and the 2X2 is the same"; "because 2 is half of 4, so you just double it".
Overall These three trials demonstrated that third and fourth grade students could learn to use the array tools and the animation system in a period or two and could quickly be meaningfully engaged in exploring equivalences among multiplicative structures.
Our research has indicated that with appropriate digital capabilities e. Furthermore, this pedagogical sequence can take place over just days; our work suggests that the digital representational tools we have provided allow students to understand the concepts more quickly and flexibly than they could without them.
Students in our field test classrooms were enthusiastically engaged in authentic mathematical reasoning; several of them participated more actively and energetically than they usually do in math class, according to their teachers.
The relatively ambitious goal of the 5-day trial was to have the students use the new "fuzzy array" tool to demonstrate a generalization about multiplication. In previous classroom trials in this project, we had worked with third and fourth grade students, so this was a bold choice, but we were encouraged by the math coach, who felt that this particular group of students was up to the challenge.
The coach participated in planning the trial and co-taught the lessons with one of the PIs. Curriculum Flow In order to have this class of second-graders reach our goal of creating a generalized representation-based proof using our new Fuzzy Array tool, we designed the following curriculum sequence: Introduction of array tool, reiteration of the relationships among multiplication, division and arrays.
Make all the arrays you can whose product is Introduction of the "cut" tool. Figure out 9x14 by cutting a 9x14 array into smaller arrays.
Introduction of the "snap" tool. Figure out 8x17 by creating smaller arrays and snapping them together. Introduction of animation tool. Discussion of why cutting and snapping an array without adding or deleting any squares shows equivalence.
Discussion of parenthesis notation. Next three pages are: Discussion of the pattern in these problems. Students chose a variety of numbers to create a problem similar to the first three: Challenge for tomorrow issued: Do you think that no matter what number we picked - odd, even, big, little - that this sentence is true: Introduction of "N" notation — the way that mathematicians say "any number.The Yale National Initiative to Strengthen Teaching in Public Schools, which builds upon the success of a four-year National Demonstration Project, promotes the establishment of new Teachers Institutes that adopt the approach to professional development that has been followed for more than twenty-five years by the Yale-New Haven Teachers Institute.
write a problem write a word problem involving the number of pages in a alphabetnyc.com write the numerical expression that you would need to use to solve your problem. Maths A large school in the UK offers its pupils the opportunity to learn several non-English languages.
alphabetnyc.com3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation .
I have an array of 4 columns or I have an array of 3 columns with 4 rows. with 3 rows in each column. This is where placement of the decimal comes in for division of decimals.
More situations like the one above will be needed for the students to get a good understanding of dividing decimals. If a group holds the cards -2, 4, 3, and Have a volunteer write the multiplication sentence on the board and label the numbers.
Say: Arrangements of objects in rows and columns are called arrays. Write “array” on the board. How many more squash plants than tomato plants did Jason plant?
Model with Arrays An array is a set of objects arranged in rows and columns. Write a multiplication sentence for each array.
This array has 2 rows and 5 columns. Count by fives. 2 rows of 5 are The multiplication sentence is Write a multiplication sentence for the model.