How many oranges were there in the morning?

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  • Thread starter anemone
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In summary, the Singapore model method is a visual and concrete approach to solving arithmetic and algebraic word problems that focuses on using appropriately sized rectangles to represent information and unknown quantities. It is designed to develop students' understanding of fundamental math concepts and proficiency in solving word problems.
  • #1
anemone
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There was a total of 748 oranges and apples at a fruit stall in the morning. By afternoon, the number of oranges sold was thrice the number of apples sold. The number of apples left was twice the number of oranges left. There were 22 more apples left than the apples sold.

How many oranges were there in the morning?

This primary math problem (as usual) can be solved without setting up equations and solve the simultaneous system of equations.

I welcome members to give it a try but nevertheless, I will post the solution tomorrow to showcase how Singapore model method works well in this kind of problem.
 
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  • #2
We can draw the following model based on the given information, and the top bar and lower bar are equal after we added another 5 units and 4 of 22 into them and this makes the sum of both bars becomes 748+5 units + 4(22).

[TIKZ]
\filldraw [fill=cyan, thick, draw=black] foreach \i in {-4,...,-3} { ({\i*1.8},0) rectangle ({(\i+2)*1.8},0.8) };
\filldraw [fill=cyan, thick, dotted, draw=black] foreach \i in {-1,...,2} { ({\i*1.8},0) rectangle ({(\i+2)*1.8},0.8) };
\filldraw [fill=magenta, thick, draw=black] (-7.2,-1) rectangle (-4.8,-0.2);
\draw[thick, dotted] (-4.8,0) -- (-4.8,-0.2);
\filldraw [fill=magenta, thick, draw=black] (-3.6,-1) rectangle (-1.2,-0.2);
\draw[thick, dotted] (-1.2,0) -- (-1.2,-0.2);
\filldraw [fill=magenta, thick, draw=black] (0,-1) rectangle (2.4,-0.2);
\draw[thick, dotted] (2.4,0) -- (2.4,-0.2);
\filldraw [fill=magenta, thick, draw=black] (3.6,-1) rectangle (6,-0.2);
\draw[thick, dotted] (6,0) -- (6,-0.2);
\draw[thick, dotted] (7.2,-1) -- (7.2,-0.2);
\draw[<->] (7.5,0.9) -- (7.5,-1);
\node at (9.4,-0) {748+5 units+4(22)};
\draw [<->] (6, -0.5) -- (7.2, -0.5);
\node at (6.6,-0.69) {22};
\draw [<->] (2.4, -0.5) -- (3.6, -0.5);
\node at (3,-0.69) {22};
\draw [<->] (-1.2, -0.5) -- (0, -0.5);
\node at (-0.6,-0.69) {22};
\draw [<->] (-4.8, -0.5) -- (-3.6, -0.5);
\node at (-4.2,-0.69) {22};
\node at (-6.3,0.5) {\small apple left};
\node at (-4.5,0.5) {\small apple left};
\node at (-2.7,0.5) {\small orange left};
\node at (-6,-0.6) {\small apple sold};
\node at (-2.4,-0.6) {\small orange sold};
\node at (1.2,-0.6) {\small orange sold};
\node at (4.8,-0.6) {\small orange sold};
\node at (-6.3,1.6) {\small 1 unit};
\draw [<->] (-7.2, 1.1) -- (-5.4, 1.1);
\node at (-6.1,-1.6) {\small 1 part};
\draw [<->] (-7.2,-1.4) -- (-4.8, -1.4);
[/TIKZ]

The problem is asking to find the sum of 1 unit and 3 parts, hence we have

$\begin{align*} 8\text{units}&=\dfrac{748+5\text{units}+4(22)}{2}\\&=\dfrac{836+5\text{units}}{2}\\16\text{unit}&=836+5\text{units}\\ 11\text{units}&=836\\1\text{unit}&=76\end{align*}$

$\begin{align*} 1\text{part}+22&=2(76)\\1\text{part}&=130\end{align*}$

Therefore there were $76+3(130)=466$ oranges in the morning.
 
  • #3
I don't see any reason NOT to set up equations- they help to organize one' thoughts.
Let x be the number of oranges and let y be the number of apples in the fruit store in the morning. Let u be the number of oranges sold by afternoon and let v be the number of

anemone said:
There was a total of 748 oranges and apples at a fruit stall in the morning.
So x+ y= 748

By afternoon, the number of oranges sold was thrice the number of apples sold.
So u= 4v

The number of apples left was twice the number of oranges left.
The number of apples left was the number of apples in the morning minus the number of apples sold, y- v, and the number of oranges left is the number of oranges in the morning minus the number of oranges sold, x- u.

So y- v= 2(x- u) or 2x- y- 2u+ v= 0.

There were 22 more apples left than the apples sold.
So y- v= v+ 22 or y= 2v+ 22.

How many oranges were there in the morning?

This primary math problem (as usual) can be solved without setting up equations and solve the simultaneous system of equations.

I welcome members to give it a try but nevertheless, I will post the solution tomorrow to showcase how Singapore model method works well in this kind of problem.

We have four equations
x+ y= 748,
u= 4v,
2x- y- 2u+ v= 0, and
y= 2v+ 22

They can be solved for all of x, y, u, and v.
The problem is asking for the value of x.
 
  • #4
What is the Singapore model method?
 
  • #5
Fantini said:
What is the Singapore model method?
It's now six days after he said he would post it "tomorrow"!
 
  • #6
Country Boy said:
It's now six days after he said he would post it "tomorrow"!

She posted the solution using the cited method in the second post.
 
  • #7
Fantini said:
What is the Singapore model method?

Hello Fantini! (Wave)

Singapore model method is a child-friendly pictorial language designed to develop students' understanding of fundamental mathematics concepts and proficiency in solving basic mathematics word problems. The model method affords higher ability children without access to letter-symbolic algebra as a means to represent and solve algebraic word problems. In Singapore, primary school children are taught a visual and concrete approach to solve arithmetic and/or algebraic word problems involving whole numbers, fractions, ratios and percents.

The model method focuses on the importance of representation. It builds upon children's knowledge of part-whole relationships in numbers. Children are taught to use appropriately sized rectangles to represent the information presented in word problems. In arithmetic problems, the rectangles represent specific numbers. By changing the role of the rectangles and using them to represent unknown quantities, the model method also can be used to depict algebraic word problems. Such representations effectively serve as pictorial equations.

The model method has proved to be an effective teaching tool for helping elementary aged children solve more word problems successfully.
 
  • #8
Do you have references where I could learn more about this method?
 
  • #9
Of course!

You can explore these few links below to understand for more. Just so you know, if you find any problem that interests you and you want to figure out how to apply the model method on it, you can post it here and I will do my best (the hardest part for me comes of cranking out the code for TiKZ to display the model and that was why it took me more than a day to draw the model above) to guide you through it. :)

https://www.basic-math-explained.com/sg-math-drawing-models.html#.XxuOx-fLc2w

https://www.hmhco.com/~/media/sites.../math-in-focus/mif_model_drawing_lr.pdf?la=en
 

Related to How many oranges were there in the morning?

1. How do you determine the number of oranges in the morning?

The number of oranges in the morning can be determined by counting the total number of oranges present in the morning or by using a measuring tool such as a scale to weigh the oranges.

2. Why is it important to know the number of oranges in the morning?

Knowing the number of oranges in the morning can provide valuable information for farmers and suppliers to track crop production, estimate market demand, and make informed decisions about pricing and distribution.

3. Can the number of oranges in the morning change over time?

Yes, the number of oranges in the morning can change over time due to factors such as harvesting, consumption, and spoilage. It is important to regularly monitor and update the number of oranges to ensure accuracy.

4. How does the number of oranges in the morning affect the nutritional value of orange juice?

The number of oranges in the morning can affect the nutritional value of orange juice as it directly impacts the amount of juice produced. More oranges will result in a higher volume of juice and potentially higher levels of nutrients such as vitamin C.

5. Are there any methods to estimate the number of oranges in the morning without physically counting them?

Yes, there are methods such as using statistical sampling techniques or using images from drones or satellites to estimate the number of oranges in a large area. However, these methods may not be as accurate as physically counting the oranges.

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