How to Teach Arithmetic Sequences

1Why is it important?

Spotting patterns is one of the most basic thinking skills, far beyond arithmetic. Sequences teach a child to look at a run of numbers, ask what repeats here, and put a rule into words. That is exactly the thinking that will serve them in algebra, in coding, and in problem solving generally. Sequences are also fun, because they hold a moment of discovery, when a child suddenly catches the pattern and feels like a detective who cracked the case. That enjoyment is worth nurturing, since it is a strong engine for learning.

2How to teach?

• Start with simple rising sequences like 2, 4, 6, 8, and let your child feel the rhythm.
• Encourage them to find the rule themselves, asking what you do to get from one number to the next.
• Practice descending sequences too, such as 20, 17, 14, so they do not assume a sequence always goes up.
• Introduce multiplication sequences only after adding and subtracting sequences are solid, otherwise it gets confusing.
• Ask your child to state the rule in words, because anyone who can explain the pattern has truly understood it.

3Detailed examples

4Common mistakes

• Looking for a complicated rule when it is actually simple, and missing the steady amount sitting right in front of them.
• Mixing up an adding sequence with a multiplying one, and trying to add when they should multiply.
• Finding the rule correctly but slipping on the final calculation.
• Assuming a sequence always goes up, and not noticing that the numbers are going down.

5Tips for parents

• Always start with the question, what is the difference between the numbers, since that points to the rule.
• Encourage your child to explain the pattern in their own words.
• Make up your own sequences and let your child find the rule, then swap roles.
• Bring in sequences from life, like house numbers down the street or counting by jumps.
• When a sequence is hard, remind them to start simple, because most sequences are a constant add or subtract.