Introduction to solving patterns in T-tables and equations

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Intros

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Lessons

Finding one-step relationships between columns in a T-table
Writing equations for T-table relationships (one-step)
Writing equations for T-table relationships (two-step)
How to isolate variables in two-step equations (solving algebra equations)

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Examples

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Lessons

T-tables and one-step equations
Write the equation for the relationship between the two variables. Follow the pattern to complete the T-table.

variables

a

and

b

a	b
1	14
2	15
3	16
4
20

variables

f

and

g

f	g
50	28
49	27
48	26
47
25

variables

q

and

r

q	r
8	32
9	36
10	40
11
1

variables

v

and

w

v	w
27	9
24	8
21	7
18
3

T-tables and two-step equations
Write the equation for the relationship between the two variables. Follow the pattern to complete the T-table.

variables

i

and

j

i	j
1	3
2	5
3	7
4
10

variables

d

and

e

d	e
5	13
6	16
7	19
8
1

variables

x

and

y

x	y
20	13
18	12
16	11
14
100

variables

x

and

y

x	y
24	4
21	3
18	2
15
300

T-tables and equations: word problem - 1
It costs $8 to rent a bicycle for the first hour. It costs $2 every hour after that.

Fill out a T-table for the cost of the first five hours.

*hour*	*cost*

Write an equation with variables for the relationship between hours ( $h$ ) and the cost ( $C$ ).
How much would it cost to rent a bicycle for 24 hours?
If someone paid a total of $26, how many hours did they rent a bicycle for?

T-tables and equations: word problem - 2
After the first month, seed A grew into a 2cm plant and continued to grow 5cm each month after that. Seed B grew to 6cm and continued to grow 3 cm each month after that.

Fill out a T-table for the cost of the first three months for both seeds.

*month*	*height_A*

*month*	*height_B*

Write an equation for each seed's growth, relating the number of months ( $m$ _A, $m$ _B) and the height ( $H$ _A, $H$ _B).
After 1 year, what is the height difference between the two plants?
When will each plant reach 42cm in height?