Answer to Question #123926 in Algebra for khomotso

Question

( a) give the meaning of each of the following: term , pattern , and function.
( b ) what is the difference between numerical patterns and geometrical patterns?
( c) (i) draw the first three terms of a simple ascending geometrical pattern with a constant difference.
( ii) describe the pattern in words .
( iii) write down the rule of the pattern.
( iv) using the rule ,extend the pattern to the fourth and the tenth term .
( v) describe the pattern in a flow diagram ( spider diagram) .
( vi) describe the pattern in a table.
( vii) describe the pattern in a graph.
( d) (i) the first three terms of my ascending geometrical pattern with a constant difference. Term 1 , term 2, term 3 ,term 4, term 10.
( ii) verbal description of the geometrical pattern.
( c) describe, using examples,how can a teacher use number lines and grids to represent number patterns.
( e)
( iii) the rule of the pattern.
( iv) using the rule, extend the pattern in term 4 and term 10.

Answer 1

(a)

Meaning of each of the following : terms, pattern and function

Term : In algebra a single variable or number multiplied together is termed as a term. They are seperated by + or - signs, or sometimes by divide.

Pattern : Patterns in algebra is important in the development in the early stages of algebraic thinking.

Functions: In an equation a function has only one answer for every x for y. A function assign to each input exactly one output of a specified type. A function is either named as f(x) or g(x).

(b)

Different between numeric and geometric patterns:

In a numeric sequence we find the number pattern with a constant difference or constant ratio.In numeric sequences we only add and subtract to get the next answer.

In geometric sequence we find the a number pattern with a constant ratio. In geometric sequence we multiply and divide to get the next answer.

(c) (i)

draw the first three terms of a simple ascending geometrical pattern with a constant difference.

Extending geometric patterns:

Square numbers:

  

Type 1                    Type 2                          Type 3

(C) (ii)

Describing patterns in words:

Sometimes the patterns are giben in tabular formats that means presentes in a table.

x     -1   0   1   22  4

y     -4   0   4  88  16

Here in the table we can see that y is 4 times more bigger than x. Therefore,the pattern is that the "y value is four times larger than the x value."

(C) (iii) Using the rule extending the fourth term to the tenth term:

Finding the 10th term:

                       4, 8, 12, 16, .....

The terms of the sequence can be obtained as:

                       1st term   = 1*4 = 4

                       2nd term  = 2*4 = 8

                       3rd term   = 3*4 = 12

                       4rth term  = 4*4 = 16

                       5th term   = 5*4 = 20

                       6th term   = 6*4 = 24

                       7th term   = 7*4 = 28

                       8th term   = 8*4 = 32

                       9th term   = 9*4 = 36

                       10th term  = 10*4 = 40

So the pattern extended to 10th term resulted as 40.

(C) (V) Describing patterns in a flow diagram

patterns in flow diagram :

 

decribing pattern in table

x  2  4  8  10  12  14  16

y  3  6  9  12  15  18   21

z  4  8  12  16  20  24   28

describing patterns in graph:

let x and y 2 values in the pattern sequence where y has value 2 times more than x

 

(d) (i) describing the first three terms of my ascending geometrical pattern with a constant difference.

3, 5, 7, 9,.....

                  3            5          7

                 term 1      term 2     term 3

here the first three terms 3, 5, 7 has constant difference of +2 between them.

(D) (ii) describing the verbal description of the geometrical pattern :

Verbal description of the patterns can be expressed or represented as equations and expressions. Geometrical concepts has been described in the arithmetic concepts done differently. In the geometrical concepts there are two main things that describes it which is understanding the problem and solving it. Geometric patterns consists of euations and graphs representing the solutions which make the user to understand the problem easily.

(C)

the following activities can help understanding the number pattern

Link the number line to skip counting.

• When counting repeating patterns, represent the numbers on a number track.

The equal spacing on the number track helps students to skip count (in this case, by threes).

Then move on to a number line (note the addition of zero at the beginning).

Gradually remove some of the labels, leaving numbers spaced by two, five or ten. In the following example, the numbers are spaced by two.

Later, remove the intermediate marks as well.

(E)

(iii) Rule of pattern:

A pattern is a group of numbers, shapes, or objects that follow a rule while repeating or changing. To extend a pattern you can use a table or a pattern rule that relates the term number to the pattern rule. A term number is the number that tells the position of an item in a pattern. Multiply 7 by the term number.

(iv)

Using the rule extending the fourth term to the tenth term:

Finding the 10th term:

                       4, 8, 12, 16, .....

The terms of the sequence can be obtained as:

                       1st term   = 1*4 = 4

                       2nd term  = 2*4 = 8

                       3rd term   = 3*4 = 12

                       4rth term  = 4*4 = 16

                       5th term   = 5*4 = 20

                       6th term   = 6*4 = 24

                       7th term   = 7*4 = 28

                       8th term   = 8*4 = 32

                       9th term   = 9*4 = 36

                       10th term  = 10*4 = 40

So the pattern extended to 10th term resulted as 40.