# Pattern Charts Years 2 - 6

This investigation has several levels of challenge. You don't have to do it all. Do as much as you can then stop. If you keep good journal notes you can come back any time and know what you were up to.

### Preparation

• Print this Professor Morris Poster. (Artist: Rob Mullarvey)
• If you are a teacher using a Poster Problem Clinic you will also need this Professor Morris Slide.
Allow full screen when asked by the slide. Use Esc to return to menu view.
• Write the title of this challenge and today's date on a fresh page in your maths journal.

### Patterns In The Puzzle

• Professor Morris has hidden some numbers. Write in the missing numbers.
• If your numbers are correct there will be pattern.
• Stick the puzzle sheet in your journal. You can colour it first if you want to.
• There's lots of patterns in this puzzle.
- Show someone else the patterns you see.
- Can they see any others?
- Write and draw about the patterns you find.

### Numbers In The Puzzle

• Make a list of the numbers Professor Morris used. Just write each number once.
• Make a list of the numbers you used. Just write each number once.
• One of you used Odd numbers and one of you used Even numbers.
- Who used which numbers?
- How do you know?
• Pretend Professor Morris has drawn the chart on the driveway with chalk.
Choose any odd number on the chart and pretend to stand on it.
- If you jump left or right one square, what sort of number do you land on?
- If you jump forward or backward one square, what sort of number do you land on?
- If you jump diagonally forward or backward one square, what sort of number do you land on?
• It doesn't matter which odd number you stand on, the same thing always happens. Can you explain why?
• What happens if you start on an even number?

### Send A Text

Professor Morris loved the patterns in his chart and he wanted to share it with his friend Mini. He sent her this text.
To make my puzzle you draw 5 rows of 6 squares.
Start with number 1 in the bottom right corner.
To fill in the rest of the numbers you ...
Uh oh! The text went off the screen. What did Professor Morris write next? Write what you think in your journal.

Have fun exploring Pattern Charts.

### Walking On The Puzzle

Suppose six (6) children were in the driveway with one person in each box of the bottom row.
They start with the number they are standing on and walk to the top adding each number they step on.
• Calculate and record each total.
Hint: look for ways to group each person's numbers to help you add them quickly.
• What is the pattern in the totals?
Try to explain the pattern?
• Mini-Challenge: Find the total of the totals WITHOUT adding them all up
In your journal record how you did it.

Suppose five (5) children were in the driveway with one person in each box of the right hand column.
They start with the number they are standing on and walk to the left side adding each number they step on.

• Calculate and record each total.
Hint: can you use knowledge you already have?
• What is the pattern in the totals?
Try to explain the pattern?
• Mini-Challenge: Find the total of the totals WITHOUT adding them all up
Professor Morris got a surprise when he first did this.
Why do think he was surprised?

In your journal explain why both 'totals of totals' get the same answer.
Use diagrams to explain if you want to.

Then Ali noticed something:

Look. If I stand on this 6 and I walk this way, then this way, I get to ten. That means its 6 + 1 + 3 = 10 and I did it in two moves.
When Ali says 'move' she means she walks in a straight line until she turns a corner or reaches her finish square.
• Where did Ali stand and how did she walk?
• Find another place Ali could start and do two (2) moves to get to 10. Write its equation.
• Find five (5) more.
• One of the kids said they did this three (3) move walk: 1 + 3 + 4 + 2 =10. Show how they walked.
• Make up your own three move walk without looking at the chart. Does it work?
Then Ali said:
Okay, let's try getting to 1 in two moves. Suppose I start on 6 again. I can do this: 6 - 2 - 3 = 1
• How did Ali walk?
• Find all the ways Ali could walk to 1 from a 6 and record them.
• One 6 is special. Why?
• Explore more two move and three move walks to get to 1.

Another kid came up with a new game.

Hey guys. I know. I'll give you a total and you have to walk a straight line from edge to edge horizontally, vertically or diagonally to make that total. First to get it wins a point.
Try these questions and write the answers in your journal.
• One of the totals was 20. How would you do that one?
• Is there another way?
• How many solutions are there?
• How do you know when you have found them all?
A mathematician might ask these questions:
• What is the lowest total I can walk in this game?
• What is the highest total I can walk in this game?
• Can I make all the totals between the highest and the lowest?

### Frames On The Chart

 The children found an old picture frame in the garage. It exactly fitted around two (2) squares. They put it around lots of pairs of numbers on the board. Use the frame horizontally or vertically. Explore. Report on what you discover with this frame.

1 row of 3

1 row of 4

2 rows of 2

### Extra Challenges

1. Choose one of the other frames on the left.
See what you can find out about the numbers inside.

2. Print these two Extra Challenges.
Professor Morris has made his chart bigger and you have to fill in ALL of it.
Extra Challenge 1 (could be a bit easy) ... Extra Challenge 2 (could be a bit hard)

3. Print this Chart Paper and create your own Professor Morris puzzle.
• You choose the size.
• You choose the starting point.
• You choose the starting number.
• You choose the pattern to build the chart.

Investigate your own puzzle and report.

### Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
• How did you work like a mathematician today? Record 2 ways.
• What do you know now that you didn't know when you started Pattern Charts?

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

Maths At Home is a division of Mathematics Centre