Mushroom Hunt
Years 4 - 10

This investigation has several levels of challenge. You don't have to do it all. Like a video game, you can stop at any level then return later for the next level. Keep good journal notes so you know the level you reached.

Preparation

  • You need to collect at least 64 small objects to use as pretend mushrooms.
    You could use pasta, plastic screw caps, pebbles, Smarties (don't eat them until the activity is finished) or...
  • You at least 6 paper plates or pieces of A4 paper to use as pretend baskets.
    The mushrooms have to fit on the basket.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.
When the activity is over your recording sheets should be put into your journal beside any other notes you make.

Pretend mushrooms and baskets.

Investigating Mushroom Hunt

  • Open this Mushroom Hunt Starter.
    You can read it on screen or print it.
  • Investigate Mushroom Hunt using the questions on the Starter.
    You can work with a partner if you wish.

    When you find the right way to sort the mushrooms there will be a pattern.

  • In your journal explain the pattern and the things that helped you find it.
Have fun exploring Mushroom Hunt.

Extending The Pattern

Print Mushroom Hunt Investigation Guide A
  • Fill in the pattern of six (6) basket numbers that solves the Starter problem.
    The highest number goes in the left hand basket.
  • Fill in all the rows to show how to make the totals on the sheet.
Suppose one little pig had stayed home, but the others collected baskets of mushrooms with the same pattern.
  • What would be the largest basket number?
  • What would be the smallest basket number?
  • These five (5) mushroom hunters would be able to make totals up to ...?
Suppose Goldilocks joined the three (3) pigs and three bears and they collected baskets of mushrooms with the same pattern.
  • What would be the largest basket number?
  • What would be the smallest basket number?
  • These seven (7) mushroom hunters would be able to make totals up to ...?

Picturing The Pattern

Print Mushroom Hunt Investigation Guide B
  • When you have finished the sheet stick it in your journal.

Write the Pattern like a Mathematician

The pattern in this investigation is very important. You learnt it when you were in Year 1 or 2. It was called doubling then.

Mathematicians have invented a new way to write the numbers in the pattern. For example they would write:

16 = 2 x 2 x 2 x 2 = 24
8 = 23
4 = 22
and all their basket numbers like this:
Mathematicians call numbers like this index or power numbers:  
  • Discuss with someone else and write in your journal what you think the base number tells you to do.
  • Discuss with someone else and write in your journal what you think the index number tells you to do.
  • What do you think a mathematician would write in the last box? Why?
  • How would a mathematician write the basket number for the extra basket gathered on the day Goldilocks went out with the others?
What happens if we change the base number? Calculate:
  • 34 =
  • 53 =
Make up a power number of your own and calculate it.

Binary in the Background

You can make any number up to 63 with the baskets.
BUT you don't use every basket to make each number.
A basket is either used ... or it is not used.
It's In or it's Out.

Print Mushroom Hunt Investigation Guide C and fill it in.
You will discover that every mushroom number can be written using only zeros (0s) and ones (1s).

  • When you have finished the sheet stick it in your journal.
  • Write these numbers in zeros and ones:
    68 ... 83 ... 127

Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
  • What do you know now that you didn't know when you started this investigation?
  • In your journal, finish this paragraph:
    I was working like a mathematician when I...

 

Answers & Discussion

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

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

 

Maths At Home is a division of Mathematics Centre