6.03 Writing rules for relationships
Yvonne has constructed the first three triangles of a pattern using matchsticks:
Find the number of matchsticks that are used to make each new triangle.
Describe the relationship between the number of triangles and the number of matchsticks Yvonne will need for his pattern.
Write the algebraic rule for the number of matchsticks, M, in terms of the number of triangles, T, for this pattern.
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 number | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Matchsticks | 5 | 6 |
Complete the table for the above pattern.
Describe the relationship between the figure number and the number of matchsticks used to make it.
Write the algebraic rule for the number of matchsticks, M, in terms of the Figure number, F, for this pattern.
Dave is constructing a continuing pattern of squares using matchsticks:
If Dave wanted to continue the pattern, determine the number of matchsticks he would need for each square he adds.
Dave made a table comparing the figure number to the number of matchsticks required. Describe any patterns that you notice.
| Figure no. | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Matchsticks | 4 | 7 | 10 | 13 |
Describe the relationship between the figure number and the number of matchsticks it requires.
Write the algebraic rule for the number of matchsticks, M, in terms of the Figure number, S, for this pattern.
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) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| \text{No. of tiles used }(T) | 1 |
Complete the table of values.
Describe a rule that Vanessa could use to find the number of tiles required for each entry.
Write the algebraic rule for the number of tiles, T, in terms of the entry number, E, for this pattern.
Write an equation for y in terms of x for the following rules:
"The value of y is six less than the value of x".
"The value of y is three times the value of x".
"The value of y is five more than two times x".
For each of the following tables:
Describe the relationship between x and y.
Write an equation for y in terms of x.
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 9 | 10 | 11 | 12 | 13 |
| x | 3 | 6 | 9 | 12 | 15 |
|---|---|---|---|---|---|
| y | 1 | 2 | 3 | 4 | 5 |
| x | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|
| y | 1 | 2 | 3 | 4 | 5 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 7 | 14 | 21 | 28 | 35 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 7 | 12 | 17 | 22 | 27 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 14 | 11 | 8 | 5 | 2 |
For each table of values below, write an equation for y in terms of x:
| x | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|
| y | 3 | 4 | 5 | 6 | 7 |
| x | 10 | 11 | 12 | 13 | 14 |
|---|---|---|---|---|---|
| y | 50 | 55 | 60 | 65 | 70 |
| x | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|
| y | 13 | 14 | 15 | 16 | 17 |
| x | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|
| y | 12 | 14 | 16 | 18 | 20 |
| x | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|
| y | 2 | 4 | 6 | 8 | 10 |
| x | 72 | 81 | 90 | 99 | 108 |
|---|---|---|---|---|---|
| y | 8 | 9 | 10 | 11 | 12 |
For each equation below, complete a table of values of the form:
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y |
Gwen sells bananas in bunches of 4.
Complete the following table:
| \text{Bunches}, x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| \text{Bananas},y |
Describe the relationship between the number of bunches and the number of bananas.
Write an equation for the number of bananas, y, in terms of the number of bunches, x.
Quentin buys some decks of playing cards that contain 52 cards each.
Complete the following table:
| \text{Decks}, d | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| \text{Cards},c |
Describe the relationship between the number of decks and the number of cards.
Write an equation for the number of cards, c, in terms of the number of decks, d.
Vanessa opens a bank account and deposits \$300. At the end of each week she adds \$10 to her account.
Complete the following table which shows the balance of Vanessa's account over the first four weeks:
| \text{Week }(W) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{Account total }(A) | \$300 | \$310 |
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.
Quentin already owns 5 marbles. He then buys some bags of marbles containing 4 marbles each.
Describe the relationship between the number of marbles Quentin will have in total and the number of bags of marbles he buys.
Write the algebraic rule for the number of marbles Quentin will own, y, in terms of the number of bags he buys, x.