Predicting What Comes Next: Exploring Sequences and Progressions: common misconceptions

If your child says… “The little 2 means the value is 2.”

Ask together

Before the swap, which value sits below position 2?

What’s true

The subscript chooses the position; the entry there supplies the value.

If your child says… “A number can be the 94.6th term.”

Ask together

Which entry would you point to when counting reaches 94.6?

What’s true

Positions count entries, so fractional positions cannot name terms.

If your child says… “For term three, I add 3 to the position number.”

Ask together

Which value did we find for the second term?

What’s true

The rule uses the previous term's value, starting from the given first value.

If your child says… “The fourth term needs four additions.”

Ask together

How many extensions did we make after building the first square?

What’s true

The first term is already present, so reaching the fourth takes three additions.

If your child says… “The booking fee is the first term.”

Ask together

Has the taxi covered a kilometre when we record the first term?

What’s true

The first listed fare already includes one kilometre's charge.

If your child says… “One triangle contains the whole rectangle's total.”

Ask together

How many copies of the original staircase fill the rectangle?

What’s true

The rectangle holds two equal triangular totals, so either triangle contains half.

If your child says… “I cube both the starting 3 and the multiplier 2.”

Ask together

How many times does 3 appear in the expanded first line?

What’s true

Only the multiplier repeats, so only it receives the power.

If your child says… “Enough halvings will make the value exactly zero.”

Ask together

What happens when you halve any positive value that still remains?

What’s true

Every finite number of exact halvings leaves a positive value.