year 8 maths

52 Chapter 1 Algebraic techniques 2 and indices
Card pyramids
Using a deck of playing cards, build some pyramids on your desk like the ones illustrated below.
Investigation
Pyramid 1
(One-triangle pyramid)
(Two cards)
Pyramid 2
(Three-triangle pyramids)
(Seven cards)
Pyramid 3
(Six-triangle pyramids)
(Fifteen cards)
1 Copy and complete this table.
Number of triangle pyramids on base 1 2 3 5
Total number of triangle pyramids 1 3 45 55
Total number of cards required 2 15 100
2 Describe the number of pyramids in, and the number of cards required for, pyramid 20 ( 20 pyramids
on the base). How did you get your answer?
3 If you had 10 decks of playing cards, what is the largest tower you could make? Describe how you
obtained your answer.
Number pyramids
Number pyramids with a base of three consecutive numbers
1 Can you explain how this number pyramid is constructed?
16
7
9
3
4
5
2 Draw a similar number pyramid starting with the number 4 on the left of the base.
3 Draw a similar number pyramid that has 44 as its top number. Remember the base of the pyramid
must be consecutive numbers.
4 Can you draw a similar number pyramid that has 48 as its top number? Explain your answer.
5 Draw several of these pyramids to investigate how the top number is related to the starting value.
• Set up a table showing starting values and top numbers.
• Can you work out an algebraic rule that calculates the top number when given the starting number?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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