Castle Douglas Primary and Early Learning and Childcare Centre

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Pattern and Relationships

As well as the activities below you can have fun with pattern online at https://www.mathsisfun.com/algebra/patterns.html

Activity 1 – Make snakes. 

Focus – I have explored a range of patterns using the same steps.

Resources – pens and paper.

Working together – draw three snakes, split into many sections, and to write a sequence in each snake, e.g. by counting on or back in steps of the same size. For more of a challenge you could state that the fifth number in each sequence must be a particular number, e.g. 27 or 54, and say that at least one sequence must be descending (going down).

 

 

Activity 2 – Trail Puzzles

Focus – I have explored a range of patterns using the same steps.

Resources –  squared paper (from school).

Using a small piece of squared paper each, write a wiggly number sequence from adjacent square to adjacent square. Sequences can be counting on or back in constant steps of any size from any number. Several different sequences could be written from side to side across the page or from top to bottom. The remaining squares are randomly filled with numbers. Swop your puzzles and see if the other person can follow the sequence.

 

Activity 3 – What’s the Rule?

Focus – I have explored a range of patterns using the same steps.

Resources – paper and pens

Copy the sequences below and work together to work out the rule
e.g.  6, 7, 9, 12, 16, 21, 27, …      The rule is  start at 6, then add 1, 2, 3, 4, 5, …   What would the tenth number be?

Try these …

a) 20, 25, 30, 35, …    b) 1, 2, 4, 8, 16, 32, …    c)  50, 49, 46, 41, 34, 25, …

d) 1, 3, 9, 27, 81, 243, …    e) 1, 3, 6, 10, 15, 21, 28, 36, 45 ….

Challenge your family with your own sequences.

 

Activity 4 – True or False

Focus – I have explored a range of patterns using different steps.

Resources – Paper and pens

Investigate this puzzle is it True or false? 

A sequence starts at 3. The terms grow by adding 2, 4, 6, 8, 10 and so on.  i.e. 3 (+2)  5 (+4)   9 (+6)   15 (+8) , …..

Every number in the sequence will have a units digit of 3, 5 or 9. Do you think the statement is true or false?

 

 

 

 

Activity 5 – Get Stacking

Focus – I have explored a range of patterns using different steps.

Resources – Paper and pens

Imagine a stack of tins, with one tin on the top level, two on the second, three on the third, etc. with 10 levels altogether. Investigate the total number of tins in the stack and to make notes on how the relationship between number and visual patterns can be used to help find the answer.

 

 

 

Activity 6 – True or False?

Focus – I can describe and continue a range of different number sequences.

Resources – pencil and paper

Solve the following problem:
A sequence starts at 5. The terms grow by adding 2, 4, 6, 8, 10, etc.  i.e.  5, 7, 11, 17

Every number in the sequence will have the units digit 5, 7 or 1. Do you think the statement is true or false? How do you know?

 

 

Activity 7 – Try Triangles.

Focus – I can solve word problems by creating and solving equations.
Resources – pencil and paper

Solve the following word problem: A scalene triangle has angles of sizes a, 6a and 5a. What is the size of each angle? Use your knowledge of the sum of angles in a triangle (180°) to make an equation and solve it to find the size of each angle.

Hint is at the bottom of this page.

 

 

 

 

 

 

 

 

 

Activity 3 Answer

a) 20, 25, 30, 35, …   Start at 20 and add 5 to each new number.

b) 1, 2, 4, 8, 16, 32, …   Start a 1 then double each new answer.

c)  50, 49, 46, 41, 34, 25, …  Start at 50 then subtract  1, 3, 5, 7, 9 …..

d) 1, 3, 9, 27, 81, 243, …     Start at 1 then multiply each answer by 3

e) 1, 3, 6, 10, 15, 21, 28, 36, 45 ….     Start at 1 then add 2, 3, 4, 5, 6, 7, …

 

Activity 4 Answer

True    3, 5, 9, 15, 23, 33, 45, 59, 75, 93, 113, …

 

Activity 5 – Answer = 55     (1+2+3+4 …….)

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Activity 7 – Hint

a + 6a + 5a = 180   or   12a = 180  (12 x ? = 180  or 180 divided by 12? = 15)  Check your answer  15 + (6×15) + (5×15) = 180

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