This problem solving activity has an algebra focus.
Manu was singing a song. It went "one, two, three, one, two, …"
What are the next three numbers?
What is the tenth number he’ll sing?
- Describe and continue a repeating number pattern.
- Use ordinal numbers (i.e. numbers used to represent order).
- Devise and use problem solving strategies to explore situations mathematically (guess and check, make a drawing, use equipment).
This problem is about recognising number sequences and then being able to use the sequences in some way. In this question the number sequence is 1, 2, 3, 1, 2, 3, …. The students have to recognise this sequence before using it to find the tenth number in Manu's song. To succeed in this lesson your students will need to be able to read and count with numbers up to 10.
- Copymaster of the problem (English)
- Counters (3 colours)
- Number tiles (many 1's, 2's, 3's)
- Copymaster of the problem (Māori)
The Problem
Manu was singing a song. It went "one, two, three, one, two, …" What are the next three numbers? What is the tenth number he’ll sing?
Teaching Sequence
- Start the following pattern: snap, clap, snap, clap....Join my pattern when you know how it goes.
- After all of the students can follow the pattern ask them if they can use counters (2 colours) to show the pattern. You could use a digital tool to show this pattern (search for interactive pattern blocks).
Ask if they can use numbers to show this pattern: 1, 2, 1, 2... - Read the problem to the class.
- As the students work on the problem ask questions that focus on their description of patterns:
What number comes next? How do you know?
How will you find the tenth number? (ways of keeping track) - Share solutions.
Extension
Find other ways to show the pattern (counters, actions ...) or increase the difficulty of the sequence.
Solution
The next three numbers are 3, 1, and 2 in that order.
To find the tenth number Manu will sing it may be easiest to write out all the numbers. (It can be done by drawing or by using counters numbered 1, 2, 3.) We have listed the first ten numbers with their ‘number’ underneath.
1, 2, 3, 1, 2, 3, 1, 2, 3, 1
1 2 3 4 5 6 7 8 9 10
So the tenth number that Manu sings is one!
Solution to the Extension
Other ways to represent this repeating triplet include:
blue red yellow blue red yellow ...
click slap clap click slap clap