Q&A - PSLE Math
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Hi I have one Maths question but the answer kit used Algebra to solve, hence wld like to kw if anyone cld help with using Models.
Mr Tan had some apples and oranges in his shop. 30% of the fruits were oranges. He sold 70 apples and bought another 170 oranges. Then 65% of the fruits were oranges. How many apples did he have at first?
Thks in advance! -
N3SKiasu:
AfterHi I have one Maths question but the answer kit used Algebra to solve, hence wld like to kw if anyone cld help with using Models.
Mr Tan had some apples and oranges in his shop. 30% of the fruits were oranges. He sold 70 apples and bought another 170 oranges. Then 65% of the fruits were oranges. How many apples did he have at first?
Thks in advance!
-----
Oranges New -- 3 units + 170 (= 65% -- 13 small units)
Apples New -- 7 units - 70 (=35% -- 7 small units
Before
--------
Orange -- Draw 3 units
Apples -- Draw 7 units
Apples -- Shade out 10 in each of the 7 units (to represent 70 apples sold)
Orange -- Shade out 10 in each of the 3 units, then add 170 oranges. You get 3 small units + 3 x 10 + 170 = 13 small units
10 small units --> 3 x 10 + 170 = 200
1 small unit --> 200 / 10 = 20
Apples --> 20 x 7 + 70 = 210 apples. -
1). The average score of a mathematics test in a class is 5.2. One
student, who scored 7 in the test, transferred to another school. As a
result, the average score of the remaining students was 5. How many
students were there at first? (Ans : 10)
*(Note : pls do not use algebra method)
2). Alan, Bob & Carl ran at a speed of 5km/h, 6km/h & 7km/h
respectively. They ran along the same route and started at 6am,
630am & 7am respectively. When Bob passed Alan, he gave Alan a
message to pass to Carl. What time will Carl receive the message?
(Ans : 0.30am)
3). Mona has 60% more stamps than HuiLing. Katherine has 15% less
stamps than Mona. If the difference in the number of stamps that
Katherine & HuiLing is 216, how many stamps does Mona have?
(Ans : 600 but I get 960)
4). There were some 50-cent coins and one-dollar coins in a coin box. 12
50-cent coins were taken out and exchanged for one-dollar coins and
the money was put back into the coin box. The ratio of the number of
50-cent coins to one-dollar coins became 4:3. If all the coins in the
coin box added up to $75, what was the ratio of the number of
50-cent coins to one-dollar coins at first? (Ans 24:13) -
N3SKiasu:
Let's attempt this question using the shortest and best equalisation method.Hi I have one Maths question but the answer kit used Algebra to solve, hence wld like to kw if anyone cld help with using Models.
Mr Tan had some apples and oranges in his shop. 30% of the fruits were oranges. He sold 70 apples and bought another 170 oranges. Then 65% of the fruits were oranges. How many apples did he have at first?
Thks in advance!
A:O
7:3
-70 +170
7:13
equalising both sides
7x13:13x7
7ux13-70x13 = 3ux7+170x7
91u - 910 = 21u +1190
91u = 21u +2100
70u= 2100
1u = 30
7u = 210
There are 210 apples.
This equalisation method is found in school teachers' guide Unit 7.
ISBN : 9789810195649
Title : Challenging Maths Problems Made Easy (Upper Primary)
Author : Ammiel Wan Chee Hong
Specifications : 210mm x 296mm, 178pp, Perfect
Synopsis :
Recognising the frustrations that teachers, parents and pupils face in applying the heuristic approach to solving Maths problems, Ammiel Wan, an experienced Maths teacher, developed eleven concepts to help teachers, parents and pupils manage the wide range of challenging problems. Challenging maths Problems Made Easy contains concepts that have been tried by pupils who found them easy to understand and to apply, even with very challenging problems. Each of the eleven concepts is presented in a step-by-step manner. The comprehensive explanations and examples allow teachers and parents to guide their children and for pupils to pick up the concepts on their own. -
faith2u:
Hi,1).
2). Alan, Bob & Carl ran at a speed of 5km/h, 6km/h & 7km/h
respectively. They ran along the same route and started at 6am,
630am & 7am respectively. When Bob passed Alan, he gave Alan a
message to pass to Carl. What time will Carl receive the message?
(Ans : 0.30am)
This qns has been answered in Pg 33. The answer should be 9.30am -
faith2u:
Hui Ling : 100%1).
3). Mona has 60% more stamps than HuiLing. Katherine has 15% less
stamps than Mona. If the difference in the number of stamps that
Katherine & HuiLing is 216, how many stamps does Mona have?
(Ans : 600 but I get 960)
Mona : 160%
Katherine : 136%
36% = 216
1% = 6
Mona = 160 x 6 = 960
Mona has 960 stamps (You are right)[/img] -
James Ang:
Hi James, thanks for solving the prob so quickly, this method is good but I am not sure..may I kw is this method taught in sch or prob by private tutor/tution ctr only to tackle diff sum? is it possible to solve by model that the student can undertstand? Welcome others to try this as well.
Let's attempt this question using the shortest and best equalisation method.
This equalisation method is found in school teachers' guide Unit 7. -
faith2u:
At first
4). There were some 50-cent coins and one-dollar coins in a coin box. 12
50-cent coins were taken out and exchanged for one-dollar coins and
the money was put back into the coin box. The ratio of the number of
50-cent coins to one-dollar coins became 4:3. If all the coins in the
coin box added up to $75, what was the ratio of the number of
50-cent coins to one-dollar coins at first? (Ans 24:13)
50 cents = 1 unit
100 cents = 1 part
At last
50 cents = 1 unit -12
100 cents = 1 part +6
(1 unit -12) x 3 = (1 part + 6) x 4
3 units - 4 parts = 60
(50 units) cents + (100 parts) cents = 7500
1 unit + 2 parts = 150
5 units = 360
1 unit = 72
1 part = 39
Ratio of 50 cents to 1 dollar at first = 1 unit : 1 part = 72:39 = 24:13 -
N3SKiasu:
is it possible to solve by model that the student can undertstand? Welcome others to try this as well.
Sorry just realised Tang has solved using Model earlier, thanks Tang. -
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