Patterns, tables & graphs

A growing pattern often follows a rule that connects the position (like the 1st, 2nd, 3rd shape) to the value (like the number of squares). You can record this in a table of values, then plot each pair as a point on the Cartesian plane to see the pattern visually — often forming a straight line if the pattern grows at a steady rate. Reading a graph the other way lets you predict values without continuing the pattern by hand.

Key terms

Table of values:

A table showing pairs of matching numbers, like position and value.

Rule:

A formula connecting one quantity to another, e.g. "matches = 3 × squares + 1".

Questions

1. 1. A table of values shows:

   • Only pictures
   • Pairs of matching numbers
   • Only colours
   • Random numbers

2. 2. A rule connects:

   • Two unrelated things
   • Position and value
   • Only colours
   • Only shapes

3. 3. In the pattern 2, 4, 6, 8..., what is the rule?

   • Add 1 each time
   • Add 2 each time
   • Multiply by 2 each time
   • Subtract 2 each time

4. 4. If a pattern follows "value = 2 × position", what is the value when position = 3?

   • 3
   • 5
   • 6
   • 9

5. 5. If a pattern follows "value = position + 5", what is the value when position = 2?

   • 2
   • 5
   • 7
   • 10

6. 6. A straight line on a graph usually shows:

   • No pattern
   • A steady rate of growth
   • Only negative numbers
   • A single point

7. 7. Plotting values from a table on a graph helps you:

   • Hide the pattern
   • See the pattern visually
   • Remove the numbers
   • Avoid maths

8. 8. A pattern uses 3 matches for 1 triangle, 5 for 2 triangles, 7 for 3 triangles. What is the rule?

   • matches = triangles + 2
   • matches = 2×triangles + 1
   • matches = 3×triangles
   • matches = triangles × 2

9. 9. Using the rule "matches = 2×triangles + 1", how many matches for 5 triangles?

   • 10
   • 11
   • 12
   • 15

10. 10. A table shows (1,3), (2,6), (3,9). What is the rule?

    • value = position + 2
    • value = 3 × position
    • value = position × position
    • value = position - 3

11. 11. Using the rule "value = 3 × position", what is the value when position = 7?

    • 10
    • 18
    • 21
    • 24

12. 12. If a graph of a pattern is a straight line, the pattern grows:

    • Randomly
    • At a steady rate
    • Not at all
    • Only sometimes

13. 13. A table shows (1,5), (2,8), (3,11). What is the rule?

    • value = position + 4
    • value = 3×position + 2
    • value = 5×position
    • value = position + 11

14. 14. Using the rule "value = 3×position + 2", predict the value when position = 10.

    • 30
    • 32
    • 35
    • 23

15. 15. A pattern has values (1,2), (2,5), (3,10). Is this pattern likely to form a straight line on a graph?

    • Yes, always
    • No, since it is not growing at a steady rate
    • Cannot be graphed
    • Only if reversed

16. 16. A table shows (1,7), (2,12), (3,17). What is the rule?

    • value = 5×position + 2
    • value = 5×position
    • value = position + 6
    • value = 7×position

17. 17. Using the rule "value = 5×position + 2", what position gives a value of 32?

    • 4
    • 5
    • 6
    • 7

18. 18. A pattern's table shows (0,3), (1,5), (2,7), following the rule value = 2×position + 3. What is the value when position = 10?

    • 20
    • 21
    • 23
    • 25

19. 19. Which pattern would NOT form a straight line when graphed?

    • 1,2,3,4 (add 1 each time)
    • 2,4,6,8 (add 2 each time)
    • 1,2,4,8 (double each time)
    • 5,10,15,20 (add 5 each time)

20. 20. A pattern rule is "value = 4×position - 1". What position gives a value of 19?

    • 4
    • 5
    • 6
    • 20