Mathematical Reasoning Problems Justifications
Without doing the calculations, decide whether each answer lies between 500 and
550. In each case, explain how you decided.
a 3 x 149
b 500 x 1.21
c Half of 1073
d 93 x 6
e 4000 &divide; 9
f 220 &divide; 0.42
Decoding
The class you are going to watch is the upper of two sets in a city school in Birmingham.
25% of the pupils in the school are eligible for free school meals. The pupils are decoding
these tables. Mary, their teacher, starts with table Y.
Table V
H
H
H
H
H
H
H
H
H
x
x
x
x
x
x
x
x
x
A
F
G
C
H
J
D
I
B
Table W
=
=
=
=
=
=
=
=
=
A
F
G
C
H
J
D
I
B
H
H
H
H
H
H
H
H
H
x
x
x
x
x
x
x
x
x
J
F
B
I
H
G
D
C
A
=
=
=
=
=
=
=
=
=
Table Y
GJ
BI
D
BG
F
H
GA
GB
BC
C
C
C
C
C
C
C
C
C
x
x
x
x
x
x
x
x
x
G
J
H
I
B
C
E
A
D
Table Z
=
=
=
=
=
=
=
=
=
BG
AF
JD
DG
C
AC
DE
BE
GD
D
D
D
D
D
D
D
D
D
x
x
x
x
x
x
x
x
x
F
A
D
C
I
H
J
G
B
Consider and make notes on these questions as you watch the video.
1 What words and phrases do pupils use to link one part of their reasoning to
another?
2 Are there any examples of the pupils or teacher using a counter-example to
disprove a conjecture about a multiplication table?
3 What prompts does Mary use to guide pupils’ reasoning?
Handout 10.2
=
=
=
=
=
=
=
=
=
BG
D
JA
IH
AJ
FC
HI
CF
GB