Lesson 1 Checkerboard Borders Develop Understanding

Ready

Evaluate each of the expressions below using the given value.

1.

$3 n + 7$ , $n = 12$

2.

$w^{2} - 3$ , $w = 4$

3.

$5 (t - 9) + 12$ , $t = 20$

4.

$\frac{2 (x + 13)}{3}$ , $x = 5$

5.

$3 (6 m - 17)$ , $m = 5$

6.

$\frac{2 a}{3} + 13$ , $a = 15$

Set

For each set of figures, show how the green colored tiles in the border can be grouped to allow for quick calculation. Each set of figures has two figures of different sizes for you to work with; use a different grouping method on each and provide a mathematical expression that connects with your grouping method.

7.

a.

Grouping method 1

Figure Size 3

b.

Create a mathematical expression to represent your grouping strategy.

c.

Grouping method 2

Figure Size 4

d.

Create a mathematical expression to represent your grouping strategy.

e.

Find the number of green tiles in figure size 8.

f.

Turn one of your expressions into an equation that can be used to find the figure size number for a shape with $72$ green colored tiles.

8.

a.

Grouping method 1

Figure Size 1

b.

Create a mathematical expression to represent your grouping strategy.

c.

Grouping method 2

Figure Size 2

d.

Create a mathematical expression to represent your grouping strategy.

e.

Find the number of green tiles in a figure size 11.

f.

Turn one of your expressions into an equation that can be used to find the figure size number for a shape with $219$ green colored tiles.

Go

Graph the ordered pairs from the tables on the given graphs.

9.

$x$	$y$
$0$	$4$
$2$	$8$
$3$	$10$
$5$	$14$

10.

$x$	$y$
$0$	$12$
$4$	$8$
$7$	$5$
$9$	$3$

11.

$x$	$y$
$2$	$13$
$4$	$12$
$6$	$11$
$8$	$10$

12.

$x$	$y$
$1$	$6$
$2$	$9$
$3$	$12$
$4$	$15$