Mathematics
Advanced
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+60 XP
Teacher-led from the board — pupils need no device
What you need:
IWB/Projector/Large Screen
Multilink cubes

Investigation: the Staircase Pattern

Investigate how a staircase pattern grows by examining how each size is built from the one before, then use the rule to predict cube counts for staircases you haven't constructed.

Teacher Class Feed

Load previous activity
    Your turn
    Your teacher is running this lesson on the board. Here is the part you can try yourself.
    Your written work is on page 110
    Target number

    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is a staircase built from cubes. Look at how many cubes each size needs:

    • Size 1 → 1 cube
    • Size 2 → 3 cubes
    • Size 3 → 6 cubes
    • Size 4 → 10 cubes

    Roughly how many cubes do you think the size-5 staircase needs, before we work it out?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~8 mins

    Illustration for Watch and NoticeThe staircase grows in a special way. Let's look at the counts side by side and work out what gets added each time.

    • Size 1 → 1
    • Size 2 → 3
    • Size 3 → 6
    • Size 4 → 10
    Key pattern

    Look at the jumps between the counts. What gets added each time, and how do the jumps change? What do you think we add to a size-4 staircase to reach the next size?

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Sketch the Staircases in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, sketch staircases of size 1, 2, 3 and 4 and write the cube count underneath each one:

    • 1
    • 3
    • 6
    • 10

    Underline the pattern you see in the four counts, then write in words the rule that gives the next staircase.

    +10 XP

    4 - Try It Together ~9 mins

    Key point

    Now we extend the staircase table together on the board. We already have 1, 3, 6, 10 and 15. Predict the count for size 7 first, then size 8, then size 10. Each time you add the next counting number, so write the new total in the table and say which number you added before we agree on it.

    Illustration for Try It TogetherCheck size 7 with your hands: at your desk, build seven columns with cubes from the tub, then count. If your group has no cubes, sketch the seven columns on squared paper and count the squares.

    +10 XP

    5 - Class Challenge ~8 mins

    Key point

    First, predict the cube count for a staircase of size 12 using the rule, adding the next counting number each time. Write out the running steps from a size you already know so that size 12 is easy to reach.

    Then we play a target round on the board. The numbers you start with are the staircase counts 1, 3, 6, 10, 15 and 21, and each one may be used only once in a round. Join them with +, −, × and ÷ until the answer is exactly the target we are chasing: 13, then 24, then 34, then 40, and finally 49 as a stretch.

    Hit the target from staircase numbers

    +15 XP
    Pupil practice
    Module 8 · Algebra: Patterns, Expressions and Equations Algebra
    Lesson 117 · Investigation: the Staircase Pattern
    Download Activity Book page (PDF)
    123learn · Online learning platform

    Unlock the full learning experience

    You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.

    Hundreds of curriculum-aligned lessons
    Interactive activities in every lesson
    Printable resources & progress tracking
    Get started
    Copyright Notice
    This lesson is copyright of 123Learn.ie 2017 - 2025. Unauthorised use, copying or distribution is not allowed.
    🍪 Our website uses cookies to make your browsing experience better. By using our website you agree to our use of cookies. Learn more