Steps
Years 2 - 10

 

Preparation

  • Tear a piece of paper into nine (9) pieces and number them 1 to 9, or, print and cut this set of digit cards.
    Keep your pieces in an envelope or press-seal bag.
    You will use them in other activities.
    (You don't use zero (0) in this activity.)
  • Write the title of this challenge and today's date on a fresh page in your maths journal.

Getting Started

  • Arrange the digits in a step shape.
  • Each of the two (2) horizontal lines and the two vertical lines must add to the same number.

The layout in the photo is correct, but someone put stickers over four of the numbers.
You have to find out what digits are under the stickers.

  • When you find out record the solution in your journal.
  • Explain your thinking in words and pictures.

The Next Challenge

  • Find two (2) more ways to arrange the nine digits as steps so the four (4) lines each add to the same number.
  • Record and explain your thinking.

Have fun exploring Steps.

The Big Challenge

So far you have found three (3) ways to make the steps.
Do they all have the same total for each line?
  • Open this Steps Starter. You can read it on screen or print it.
  • You have already done the first part of the Starter.
    Your challenge now is to try Question 2.
  • Keep good notes in your journal because it might take you a few days to find the four line totals.

Note: If your school is a member of Maths300, your teacher can provide software that will help you explore Steps.

Digging Deeper

At this point a mathematician would ask:
  • How many different solutions are there?
  • How will I know when I have found them all?
Look at the strategies on your working like a mathematician page.
  • Which strategy do you think your mathematician might choose to try to find more solutions?
Before getting started a mathematician would also ask:
  • What do I know about this problem already?
  • What do I know about the numbers from 1 to 9 that might help?
Have you noticed something about the corner numbers?
Have you realised that this problem is really only adding up the numbers 1 to 9
    ... but the corner numbers change that a little. How?
Do you know what the answer is if you do add the numbers 1 to 9?
So, your challenge now, if you choose to accept it, is to find all twelve (12) unique solutions.
  • Are your solutions unique so far, or are some variations of others?
  • There are 12 unique solutions, but each one is part of a family with 8 variations, so there are actually ninety-six (96) sets of steps that work.

Just Before You Finish

Read your Working Like A Mathematician page again and identify the things you did in this activity that prove you worked like a mathematician.

 

Answers & Discussion

Click the image to remove the stickers.

The journal on the right shows two solutions found by Jasmin in Year 3.

These notes were originally written for teachers. We have included them to support parents to help their child learn from Steps.

 

Send any comments or photos about this activity and we can start a gallery here.

 

Maths At Home is a division of Mathematics Centre