Transcript Exploring How Meanings are Made in Mathematics: Unpacking

EXPLORING HOW
MEANINGS ARE MADE IN
MATHEMATICS
Jockey Club Ti-I College
Kwan Po Man
BACKGROUND INFORMATION

Class Level:
Secondary Two Students
(Visual Arts Stream)

Topic:
Applications of simultaneous
linear equations
QUESTION

Patrick spends $36 to buy some apples and
oranges. Each apple and orange costs $2 and
$2.5 respectively. The number of apples that he
buys is 9 more than that of oranges. How many
apples and oranges does he buy?
(New Trend Mathematics S2B, Classwork 7.11)
STRATEGY USED


Change the written text into a more spoken-like
text.
By asking students questions in order to “unpack”
information of the problem.
DIALOGUES (SCAFFOLDING)
Teacher: Can you tell me the difference between oranges and apples?
Student: Apples are 9 more than the oranges.
Teacher: Let x be the number of apples and y be the number of oranges.
What is the relation between apples and oranges?
Student: x = y + 9?
Teacher: How much did Patrick pay for the oranges?
Student: y + 2.5?
Teacher: Well! One orange costs $2.5. How much for 10 oranges?
Student: $25.
Teacher: Why?
Student: 2.5 times 10.
Teacher: How much for y oranges?
Student: 2.5 times y. That is 2.5 y.
……
TABULATION OF THE PROBLEM
Numbers
Cost ($)
Apple
x
2
Orange
y
2.5
SET UP EQUATIONS
...... (1)
x  y  9

2 x  2.5 y  36 ...... (2)
CLASSWORK
Question

A sum of money is divided between Amy and Bob
in the ratio 7 : 4. If Amy gives $600 to Bob, the
new ratio is 5 : 6.
(a) How much do Amy and Bob get originally?
(b) What is the sum of money?
(New Trend Mathematics S2B, Ex7D)
STUDENT'S WORK (I)
STUDENT'S WORK (II)