Singapore Math: Drawing Models Method

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Learn to apply the Singapore Math drawing models method.

Page: 1, 2, 3

Question 1

Solution

More Explanations

This question involves a comparison of 2 numbers. Help your child understand that Maths is all about the concepts 'more than', 'less than' and 'equal'.  Teach him to think in terms of these concepts.

Before we start drawing the models we need to collect our thoughts. This is the information we can infer from the question:

  • the total of the 2 numbers is 7467
  • the difference of the 2 numbers is 1351
  • we need to draw 2 boxes, one longer than the other

Now we are ready to draw.

Things to note:

  • add color so the difference is easy to see
  • the same color refers to the same number
  • write the total at the side to differentiate from the difference
  • we can also write the difference inside the green box

From our model, we can see that if we take away the green box, we will have 2 yellow boxes representing 2 equal numbers.

So the first step is to use subtraction:

7467 - 1351 = 6116

Now we use division to find out the number represented by the yellow box.

We now know the smaller of the 2 numbers.

To find the bigger number we use addition:

3058 + 1351 = 4409

The 2 numbers are 3058 and 4409.

Remember to check your work by working out the total of 3058 and 4409 to make sure it equals 7467.


Here's an easy worksheet for you to use with your child:


Question 2

Marty loves reading. He goes to the library every week. He borrowed 25 more books in June than in May. In July he borrowed half as many books as he did in May. How many books did he borrow in May if he had borrowed a total of 120 books for May, June and July?

This question involves the comparison of 3 numbers. There is a 'more than' comparison as well as a 'as many as' comparison.

Before we start drawing, we make the following deductions:

  • Marty borrowed the least number of books in July (always try to start with the smallest number and build from there)
  • the next bigger number is in May
  • the biggest number is in June

We start with July:

We draw May below July. Since the July number is half as many as May, this means that the May number is twice as many as July.

Remember to draw the boxes of equal size to help you understand the relationship at a glance.

Now we add in the June portion.

  • Add in the numbers in the correct place.
  • Add colour to make the 'more than' bit stand out.
  • Remember to draw the 'more than' bit either bigger or smaller than the rest.
  • Do not draw the 'more than' box the same size as the rest or else you will make the mistake of thinking that every box represents 25 books.

From the picture, we can see that every box is the same size except the '25' box. This means that if we remove the '25' from the total, we would have 5 equal boxes.

The secret to solving complex questions easily is to make use of the concept of equal as much as possible.

We use subtraction to find the total of 5 equal boxes:

120 - 25 = 95

To find the number of books Marty borrowed in July (one white box) we use division:

So now we know that Marty borrowed 19 books in July.

He borrowed twice as many books in May so we use multiplication to find the answer:

19 x 2 = 38

Marty borrowed 38 books in May.

Do you know how to find out the number of books borrowed in June?


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