Page 47 - 01-Yr5_Front cover-ccp.indd

• Prism patterns • • • • • • •••••••••••••

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m Copy this table.
Complete it for the six prisms shown at the top of these two pages.
Start with a and finish with f.
Handle real shapes to help you, if you want.
• Draw a table showing your answers.
---- _ _!~~--- ----- ----- ---- How many edges does each end face of a prism hove if it has:
~----~~e_C}_~'!~~~~---- ----- ---- ----- A heptagon is a 42 vertices b 18 faces?
a closed shape
--- __ !!_~'!!~--- ----- ----- ---- wlth7straightsides.
_!_ ---~'-"-'!!.~°!___ _.!_ -- - / CHALLENGE '
___ _ __!:!~ondl _ _ _____________ _ • For each prism in your tables from lfij and (]].compare the number
of edges with the number of faces and vertices added together.
octago11a/
• Try to spot a pattern and explain it in words.
• Try to write the pattern as a formula.
[E'.I Explain any patterns in your results.
m
[I]

letter prism name number of number of number of letter prism name number of number of number of
faces vertices edges faces vertices edges
d triangular 5 6 q a nonagonal 11 18 27
b rectangular 6 8 12 b decagonal 12 20 30

f pentagonal 7 10 15 c undecagonal 13 22 33
a hexagonal 8 12 18 d duodecagonal 15 24 36
c heptagonal q 14 21 e icosagonal 22 40 60

e octagonal 10 16 24

a 21 b 16
The number of faces, plus the number of vertices, is 2 more than the Challenge
number of edges. The number of vertices increases by 2 each time. The
number of edges increases by 3. The number of faces, plus the number of vertices is 2 more than the
number of edges.
F+V=E+2