Project: Yellow, Red, Green trinomials -

In this project you are to make red/yellow/green counter array patterns using given quantities of each colour. The objective of this project is to explore the factored form (product) and the standard form (sum) of a trinomial.

red yellow green counters in a 3 by 3 array

You will need a set of about 50 red/yellow/green counters (any three colours), or use the virtual set at the end of this page.

Page Structure

Title page with your name, date, project title and an introduction that states the objective of the project in your own words. Perhaps also a picture.
Table 1, photo 1, answers to 1 d, 1e, 1f.
Table 2, photo 2, answers to 2d, 2e, 2f.
Table 3, photo 3, answers to 3d, 3e, 3f

The task details

(a) Copy and complete table 1. Use the formula given in the last row to complete each column.

TABLE 1
$n$	Yellow	Red	Green	Total
$1$
$2$
$3$	9	6	1	16
$10$
	$y(n)=n^2$	$r(n)=2n$	$g(n)=1$	$t(n)=\quad$

(b) Create a rectangular array pattern with the red, yellow, green counters with the numerical pattern in the table. You need to construct shape #1, shape #2, shape #3. The pattern for table#1 is already constructed on the applet below.

(d) Verify that the expression for total counters is $t(n)=n^2+2n+1$

(To verify the formula, substitute the numbers 1, 2, 3 into the formula. See if the answers from your formula are the same as the total number of counters in the shapes in your photo.)

(e) Factor the trinomial in part (d).

(f) Explain:

(i) how does the factored form of the trinomial relate to the picture of each square in the shape pattern?

(i) how does the sum form of the trinomial relate to the picture of each squaer in the shape pattern?

(g) Repeat (a) – (f) with table 2.

TABLE 2
$n$	Yellow	Red	Green	Total
$1$	1
$2$		8
$3$			3
$10$
	$y(n)=n^2$	$r(n)=4n$	$g(n)=3$	$t(n)=\quad.$

(h) Choose one of the formulas below. Construct a TABLE 3 with your formula Repeat (a) – (f) using your third table:

CHOOSE:	Yellow	Red	Green
(i)	$n^2$	$4n$	$4$
(ii)	$n^2$	$5n$	$4$
(iii)	$(n+1)^2$	$3n$	$3$
(iv)	$(n+1)^2$	$4n$	$7$
(v)	$2n^2$	$3n$	$1$

Red, Yellow, Green counters

applet link