Page 19 - 新思维数学活动用书9 样章

2 Expressions and formulae

Challenge

11 Jake and Razi have four different types of rod. a + 2 a + 3
The length of each grey rod is a + 2.
The length of each black rod is a + 3. 2a + 2 3a + 1
The length of each white rod is 2a + 2.

The length of each striped rod is 3a + 1.
Jake shows Razi that the total length of two black rods and four striped rods is the same as the
total length of four white rods and two striped rods, as shown.

2 black + 4 striped = 2(a + 3) + 4(3a + 1)
= 2a + 6 + 12a + 4
= 14a + 10

4 white + 2 striped = 4(2a + 2) + 2(3a + 1)
= 8a + 8 + 6a + 2
= 14a + 10

a Show that
i the total length of 2 black rods and 2 striped rods is the same as the total length of 4

white rods
ii the total length of 3 black rods and 3 striped rods is the same as the total length of 6
white rods
iii the total length of 5 black rods and 5 striped rods is the same as the total length of 10

white rods.
b What do your answers to part a tell you about the connection between the number of black
and striped rods and the number of white rods?

c Show that
i the total length of 4 black rods and 2 white rods is the same as the total length of 8 grey
rods
ii the total length of 6 black rods and 3 white rods is the same as the total length of 12 grey
rods

iii the total length of 8 black rods and 4 white rods is the same as the total length of 16 grey
rods.
d What do your answers to part c tell you about the connection between the number of black

and white rods and the number of grey rods?

18