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6.03 Writing rules for relationships

Worksheet
Geometric patterns
1

Yvonne has constructed the first three triangles of a pattern using matchsticks:

a

Find the number of matchsticks that are used to make each new triangle.

b

Describe the relationship between the number of triangles and the number of matchsticks Yvonne will need for his pattern.

c

Write the algebraic rule for the number of matchsticks, M, in terms of the number of triangles, T, for this pattern.

2

Peter is making a sequence of shapes out of matchsticks:

Peter makes a table comparing the figure number to the number of matchsticks needed to construct it as shown:

Figure number1234
Matchsticks56
a

Complete the table for the above pattern.

b

Describe the relationship between the figure number and the number of matchsticks used to make it.

c

Write the algebraic rule for the number of matchsticks, M, in terms of the Figure number, F, for this pattern.

3

Dave is constructing a continuing pattern of squares using matchsticks:

a

If Dave wanted to continue the pattern, determine the number of matchsticks he would need for each square he adds.

b

Dave made a table comparing the figure number to the number of matchsticks required. Describe any patterns that you notice.

Figure no.1234
Matchsticks471013
c

Describe the relationship between the figure number and the number of matchsticks it requires.

d

Write the algebraic rule for the number of matchsticks, M, in terms of the Figure number, S, for this pattern.

4

Vanessa makes the first four entries of a sequence out of coloured tiles and as shown:

She then creates a table to show the relationship between the entry number and the number of tiles used for that entry:

\text{Entry number }(E)1234
\text{No. of tiles used }(T)1
a

Complete the table of values.

b

Describe a rule that Vanessa could use to find the number of tiles required for each entry.

c

Write the algebraic rule for the number of tiles, T, in terms of the entry number, E, for this pattern.

Equations and tables
5

Write an equation for y in terms of x for the following rules:

a

"The value of y is six less than the value of x".

b

"The value of y is three times the value of x".

c

"The value of y is five more than two times x".

6

For each of the following tables:

i

Describe the relationship between x and y.

ii

Write an equation for y in terms of x.

a
x12345
y910111213
b
x3691215
y12345
c
x678910
y12345
d
x12345
y714212835
e
x12345
y712172227
f
x12345
y1411852
7

For each table of values below, write an equation for y in terms of x:

a
x678910
y34567
b
x1011121314
y5055606570
c
x678910
y1314151617
d
x56789
y1214161820
e
x56789
y246810
f
x72819099108
y89101112
8

For each equation below, complete a table of values of the form:

x1234
y
a
y = 7 x
b
y = x + 8
c
y = 2x - 6
d
y = \dfrac{x}{4}
e
y = 5x + 1
f
y = -3x
g
y = \dfrac{2x}{3}
h
y = 10 - 4x
Equations for relationships
9

Gwen sells bananas in bunches of 4.

a

Complete the following table:

\text{Bunches}, x1234
\text{Bananas},y
b

Describe the relationship between the number of bunches and the number of bananas.

c

Write an equation for the number of bananas, y, in terms of the number of bunches, x.

10

Quentin buys some decks of playing cards that contain 52 cards each.

a

Complete the following table:

\text{Decks}, d1234
\text{Cards},c
b

Describe the relationship between the number of decks and the number of cards.

c

Write an equation for the number of cards, c, in terms of the number of decks, d.

11

Vanessa opens a bank account and deposits \$300. At the end of each week she adds \$10 to her account.

a

Complete the following table which shows the balance of Vanessa's account over the first four weeks:

\text{Week }(W)01234
\text{Account total }(A)\$300\$310
b

Write the algebraic rule for Vanessa's account total, A, in terms of the number of weeks W, for which she has been adding to her account.

12

Quentin already owns 5 marbles. He then buys some bags of marbles containing 4 marbles each.

a

Describe the relationship between the number of marbles Quentin will have in total and the number of bags of marbles he buys.

b

Write the algebraic rule for the number of marbles Quentin will own, y, in terms of the number of bags he buys, x.

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