Page 30 - 新思维数学学生用书9 样章

2.2 Constructing expressions

Think like a mathematician

6 Work with a partner to answer these questions.
Alicia and Razi have rods of four different colours.

The blue rods have a length of x + 1.
The red rods have a length of x + 2.
The green rods have a length of 2x + 1.
The yellow rods have a length of 3x.

x + 1 x + 2 2x + 1 3x

Alicia shows Razi that the total length of 3 red rods and 5 yellow rods is the
same as 6 green rods and 2 yellow rods, like this.

3 red + 5 yellow = 3(x + 2) 6 green + 2 yellow = 6(2x + 1)
+ 5(3x) + 2(3x)
= 3x + 6 + 15x = 12x + 6 + 6x
= 18x + 6 = 18x + 6

a Show that
i the total length of 2 red rods and 2 yellow rods is the same as 4 green rods

ii the total length of 3 red rods and 3 yellow rods is the same as 6 green rods
iii the total length of 4 red rods and 4 yellow rods is the same as 8 green
rods.
b What do your answers to part a tell you about the connection between the

number of red and yellow rods and the number of green rods?
c Show that
i the total length of 6 red rods and 2 yellow rods is the same as 12 blue rods
ii the total length of 9 red rods and 3 yellow rods is the same as 18 blue rods

iii the total length of 12 red rods and 4 yellow rods is the same as 24 blue
rods.
d What do your answers to part c tell you about the connection between the
number of red and yellow rods and the number of blue rods?

e Discuss your answers to parts b and d with other learners in your class.

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