
Plate Triangles
Years 4  8

This activity is really two activities. They have been put together because they use the same equipment.
Part 1: Exploring Triangle Numbers
Preparation
 Find thirtysix (36) paper plates.
They usually come in packs of fifty (50) or one hundred (100), so there might be some in the house.
Paper patty pans for cup cakes would work too, especially if you don't have much floor space.
 If you can't find paper plates, 36 paper squares (not rectangles) will do.
 Write the title Plate Triangles Part 1 and today's date on a fresh page in your maths journal.
Investigating Plate Triangles
 Open this Plate Triangles Starter.
You can read it on screen or print it.
 Investigate Plate Triangles using Questions 1  5 on the Starter.
You can work with a partner if you wish.
 Pause after Question 5 and look back at your journal notes for a pattern. It might help to organise your data a different way.
For example:
Building to Row 1 uses 1 plate.
Building to Row 2 uses 3 plates in total.
Building to Row 3 uses 6 plates in total.
Building to Row 4 uses ...
What will be the total of plates for Row 9?
How do you know?
Can you check it another way?
What will be the total of plates for Row 11?
How do you know?
Can you check it another way?


If you can't find paper plates or squares, click this image and print the page.
 Cut on the line. Save the number tiles until Part 2.
 In Part 1 begin with only the first two (2) rows of the triangle uncovered. Cover the rest with a piece of paper.

The big mathematician's question is:
If I tell you any Row Number, can you tell me the total number of plates to make the triangle to that row?
This Investigation Guide will help you. It can be printed, or you can read it on screen. Keep good notes in journal or on the Guide.
Have fun exploring Triangle Numbers.
Just Before You Finish
For this part you need your maths journal and your Working Like A Mathematician page.
Luke & Dylan thought the triangle of circles above looked like a Christmas Tree. It reminded them of the song The Twelve Days of Christmas.
They investigated the numbers in the song and wrote a report.
 Print Luke & Dylan's Report and stick it in your journal.
 Pretend you are their teacher and they have handed in for assessment. You want all your students to feel that they work like a mathematician.
 At the end of their report, write them a paragraph telling them what you see that proves they are working like mathematicians.
Part 2: Exploring Triangle Teasers

Preparation
 Print and cut out these 36 number tiles. or use if you are using the Triangle Sheet, above, use the number tiles you cut off before.
 Write the title Plate Triangles Part 2 and today's date on a fresh page in your maths journal.
Investigating Triangle Teasers
 Open this Plate Triangles Starter.
You can read it on screen or print it.
 Investigate Triangle Teasers using Questions 6  9 and the Challenge on the Starter.
You can work with a partner if you wish.
 Keep notes in your journal about anything you discover.
Have fun exploring Triangle Teasers
Just Before You Finish
In real life, mathematicians are always working on something no one else has done. So there is no one to tell them if they are right or wrong. So we are not telling you any answers to these teasers. However, we do want you to:
 Prepare a report  written or poster or slide show or any other way  explaining to someone else:
What you did.
What you found out.
How you checked your work.
What new questions it made you think about.
You can use Luke and Dylan's report above to give you ideas about how to prepare a report.

Answers & Discussion
These notes were originally written for teachers. We have included them to support parents to help their child learn from Plate Triangles.
Send any comments or photos about this activity and we can start a gallery here.
Maths At Home is a division of Mathematics Centre
