Determine whether the following patterns are increasing, decreasing or neither:
7, 6, 11, 3, 9
25, 22, 19, 16, 13
5, 4, 9, 1, 7
21, 20, 19, 18, 17
For each of the following patterns:
State whether the pattern is increasing or decreasing.
Determine by how much the pattern is increasing or decreasing each time.
31, 25, 19, 13
15, 21, 27, 33
5, 12, 19, 26
34, 28, 22, 16
17, 23, 29, 35
9, 16, 23, 30
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 |
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.
Explain how to write the algebraic rule for the number of marbles Quentin will own, m, in terms of the number of bags he buys, b.
Find the next number in the following patterns:
2,4, 6, 8
7, 9, 11, 13
65, 58, 51, 44
16, 36, 64, 100, 144
Explain how to find the next number in the pattern 48, 24, 12, 6.
Consider the rule: "The starting number, N, is doubled, then 4 is subtracted to get the answer A."
Write the algebraic rule for A in terms of N.
Use the rule to complete the table of values:
| \text{Starting Number }(N) | 12 | 13 | 14 | 15 |
|---|---|---|---|---|
| \text{Answer }(A) |
Consider the rule: "The starting number, N, has 9 added to it. The sum is then multiplied by 5 to get the answer A."
Write the algebraic rule for A in terms of N.
Use the rule to complete the table of values:
| \text{Starting Number }(N) | 4 | 5 | 6 | 7 |
|---|---|---|---|---|
| \text{Answer }(A) |
Each of the patterns below was created in steps using matchsticks.
Write a formula that describes the relationship between the number of matches, m, and the step number, t.
Complete the following table of values using the formula:
| \text{Step number} \left(t\right) | 1 | 2 | 3 | 4 | 5 | 10 |
|---|---|---|---|---|---|---|
| \text{Number of matchsticks}\left(m\right) |
Vanessa is making a pattern of shapes out of tiles. She creates a table comparing the pattern number of a shape to the number of tiles needed to make it:
| \text{pattern} \\ \text{number } \left(n\right) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| \text{Number of} \\ \text{tiles } \left(T\right) | 3 | 5 | 7 |
How many new tiles are added at each step?
Find how many tiles Vanessa will need to make the next three shapes in the pattern by completing the table of values.
Write the equation for T in terms of n.
Find how many tiles Vanessa will need to make the 20th shape in the pattern.
James is making snowflakes out of hexagonal tiles:
James creates a table comparing the width of a snowflake to the number of tiles needed to make it:
| \text{Width } (W) | 1 | 3 | 5 | 7 | 9 | 11 | 13 |
|---|---|---|---|---|---|---|---|
| \text{No. tiles } (T) | 1 | 7 | 13 | 19 |
Write an algebraic rule for the number of tiles, T, in terms of the snowflake's width, W.
Use your rule to complete the table of values.