Working Memory (Supplementary) 1

Appendix A

Questions used in the overall accuracy task and their classification

Questions / Content / Classification
1 / Abdul and Betty shared $454. Betty received $98 more than Abdul. How much money did Abdul receive? / ·  2 protagonists
·  Utilising the relative term more than
2 / Ali and Peter have $240 altogether. Peter has $56 less than Ali. How much money does Ali have? / ·  2 protagonists
·  Utilising the relative term less than
3 / Mr Ram sold a total of 540 rotis, chapattis, and puris at a food sale. He sold 50 more chapattis than rotis. He sold 80 more puris than chapattis. How many chapattis did he sell? / ·  3 protagonists
·  Utilising the relative term more than
4 / A walkman costs $160 more than a badminton racquet. A radio costs $140 less than a walkman. The three items cost $450 altogether. How much is a walkman? / ·  3 protagonists
·  More than and less than
5 / A total of 450 boys and girls went to the zoo. There were two times as many boys as girls. How many girls went to the zoo? / ·  2 protagonists
·  Twice as many
6 / Mary and Peng have 380 picture cards altogether. Mary has one-third as many cards as Peng. How many cards does Peng have? / ·  2 protagonists
·  Multiplicative relationships in terms of fractions
7 / There are a total of 561 red, blue, and green marbles. There are 2 times as many blue marbles as green marbles. There are 3 times as many blue marbles as red marbles. How many red marbles are there? / ·  3 protagonists
·  Multiplicative relationships involving whole numbers.
8 / 280 kg of flour is divided into bags A, B and C. Bag B has two times as much flour as bag A. Bag C has as much flour as bag B How much flour is in bag B? / ·  3 protagonists
·  Relative in terms of multiplications
·  Whole number and fractional relationship
9 / Mr Ling bought some T-shirts and 5 times as many caps. A T-shirt costs $13 while a cap costs $9. Mr. Ling spent $464 altogether. How many caps did Mr Ling buy? / ·  Simultaneous equations
·  Multiplicative relationship
10 / Mrs Tan is 30 years older than her daughter, Jane. In 4 years’ time, Jane will be her mother’s age. How old is Jane now? / ·  2 protagonists
·  Relative in terms of more than and multiplicative relationship involving fraction


Appendix B

Questions used in the Representation Formation tasks and their classification

Questions / Content / Classification
1 / John and Peter have $298.
John has $92 more than Peter.
How much money does Peter have?

Total amount of money John and Peter has.
Amount of money John has.
Amount of money Peter has.
This question asks you to find: amount of money Peter has. / ·  2 protagonists
·  Utilising the relative term more than
2 / David travelled 210 miles around Singapore.
He travelled 35 miles more by car than on foot.
He travelled 25 miles less on foot than on bicycle.
How many miles did David travel on foot?

Total distance travelled by David.
Distance travelled by David on car.
Distance travelled by David on bicycle.
Distance travelled by David on foot.
This question asks you to find: distance travelled by David on foot. / ·  3 protagonists
·  More than and less than
3 / There are 154 flowers in the garden.
There areas many roses as tulips.
How many roses are there?
Number of flowers in the garden.
Number of tulips.
Number of roses.
This question asks you to find: number of roses in the garden. / ·  2 protagonists
·  Multiplicative relationships in terms of fractions
4 / Siti bought 207 pies altogether.
She bought three times as many chicken pies as vegetable pies.
She also bought as many apple pies as chicken pies.
How many chicken pies did she buy?

Total number of pies Siti bought.
Number of chicken pies.
Number of apple pies.
Number of vegetable pies.
This question asks you to find: the number of chicken pies Siti bought. / ·  3 protagonists
·  Relative in terms of multiplications
·  Whole number and fractional relationship
5 / Ali is 38 years younger than his grandfather.
In 7 years time, Ali will be of his grandfather’s age.
How old is Ali now?
The difference in age between Ali and his
Grandfather.
Ali’s age.
Ali’s grandfather’s age.
This question asks you to find: Ali’s age. / ·  2 protagonists
·  Relative in terms of less than and multiplicative relationship involving fraction


Appendix C

Questions used in the Solution Formation task and their classification

Questions / Content / Classification
1 / A school has 359 rackets
There are 65 more badminton rackets than tennis rackets.
How many tennis rackets are there?
Number of badminton rackets ( ? )
Number of tennis rackets ( ? )
Total number of rackets ( 359 )
The question asks you to find: the number of tennis rackets in the school.

There are ______tennis rackets. / ·  2 protagonists
·  Utilising the relative term more than
2. / The total length of three ribbons A, B and C is 970 metres.
Ribbon B is 130 metres longer than Ribbon C.
Ribbon C is 150 metres shorter than Ribbon A.
What is the length of ribbon C?
Length of ribbon A ( ? )
Length of ribbon B ( ? )
Length of ribbon C ( ? )
Total length of ribbons A, B and C ( 970 )
This question asks you to find: the length of ribbon C.

Ribbon C is ______metres long. / ·  3 protagonists
·  More than and less than
3. / Container A and container B contain a total of 165kg of flour.
Container B contains as much flour as Container A.
How much flour has Container B?
Amount of flour in Container A ( ? )
Amount of flour in Container B ( ? )
Total amount of flour in Container A and B ( 165 )
This question asks you to find: the amount of flour in Container B.

Container B has ______kg of flour. / ·  2 protagonists
·  Multiplicative relationships in terms of fractions
4. / There are altogether 207 animals in the pet shop.
There are three times as many hamsters as kittens.
There are as many puppies as hamsters.
How many hamsters are there?
Number of hamsters in the pet shop ( ? )
Number of kittens in the pet shop ( ? )
Number of puppies in the pet shop ( ? )
Total number of pets in the pet shop ( 207 )
This question asks you to find: the number of hamsters in the pet shop.

There are ______hamsters in the pet shop. / ·  3 protagonists
·  Relative in terms of multiplications
·  Whole number and fractional relationships
5. / Alice is 27 years younger than her mother.
In 4 years time, Alice will be of her mother’s age.
How old is Alice now?
Alice’s age ( ? )
Alice’s mother’s age ( ? )
Difference between Alice and her mother’s age ( 27 )
This question asks you to find: Alice’s present age.

Alice is ______years old now. / ·  2 protagonists
·  Relative in terms of less than and multiplicative relationship involving fractions


Appendix D

Sample questions used in the Componential tasks

Questions / Tasks/Content / Classification
Question Understanding
1 / Joe and Mark have 341 marbles altogether. Joe has 174 marbles. How many marbles does Mark have?
(a)  Answer each statement. For those statements to which you have no answers, put a “?”.
The number of marbles Joe has. ( )
The number of marbles Mark has. ( )
The total number of marbles Joe and Mark have. ( )
(b)  What are you asked to find? Circle your response.
(A) The total number of marbles Joe and Mark have.
(B)  The number of marbles Mark has.
(C)  The number of marbles Joe has. / ·  2 protagonists
·  Arithmetic – end unknown
2 / Jane and Mary have 268 beads. Jane has 88 more beads than Mary. How many beads does Mary have?
(a)  Answer each statement. For those statements to which you have no answers, put a “?”.
The total number of beads Jane and Mary has. ( )
The number of beads Jane has. ( )
The number of beads Mary has. ( )
(b)  What are you asked to find? Circle your response.
(A) The number of beads Jane has.
(B)  The total number of beads Jane and Mary has.
(C)  The number of beads Mary has. / ·  2 protagonists
·  Utilising the relative term more than
3 / There were 184 vehicles in the parking lot. There were five times as many cars as lorries. There were as many motorbikes as cars. How many cars were there?
(a)  Answer each statement. For those statements to which you have no answers, put a “?”.
The number of cars in the parking lot ( )
The number of vehicles in the parking lot. ( )
The number of motorbikes in the parking lot. ( ) / ·  3 protagonists
·  Relative in terms of multiplications
·  Whole number and fractional relationship
Relational A
1 / Mr Ravi drove 88 miles less than Mr Goh. Mr Ravi drove for 48 miles. How many miles did Mr Goh drive?
Mr Goh drove for ______miles. / ·  Addition
·  Inconsistent
2 / May has $78. June has $25 lesser than May. How much money does June have?
June has $______. / ·  Subtraction
·  Consistent
3 / Li Peng watched 15 movies in a year. She watched as many movies as Hui Ling. How many movies did Hui Ling watch in a year?
Hui Ling watched ______movies in a year. / ·  Multiplication
·  Inconsistent
4 / Siti is the age of her mother. Siti’s mother is 36 years old. How old is Siti?
Siti is ______years old. / ·  Division
·  Consistent
Relational B
1 / Heng Heng, Sukey and Lily have some stamps. Sukey has 68 stamps more than Heng Heng. Lily has 55 stamps more than Sukey.
A.  Lily has more stamps than Heng Heng.
B.  Lily has fewer stamps than Heng Heng. / ·  3 protagonists
·  Utilising the relative term more than
2 / Mrs Lim bought some plates and four times as many cups. A plate costs $7 while a cup costs $3. She spent $95 altogether.
A.  Mrs. Lim bought more plates than cups.
B.  Mrs. Lim bought fewer plates than cups. / ·  Simultaneous equations
·  Multiplicative relationships
3 / A school has some badminton and tennis rackets. There are 65 fewer badminton rackets than tennis rackets.
A.  There are more tennis rackets than badminton rackets.
B.  There are fewer tennis rackets than badminton rackets. / ·  2 protagonists
·  Utilising the relative term less than
Computation
1 / 234 568 + 562 431 = / ·  Addition with whole numbers
2 / / ·  Addition with fractions
3 / 524 367 – 279 588 = / ·  Subtraction with whole numbers
4 / 4325 x 12 = / ·  Multiplication with whole numbers
5 / 8911 11 = / ·  Division with whole numbers
6 / of 12 = / ·  Division with fractions