This is the third part of the Solving Math Word Problem Solving Series on Numbers for Grade 6 – 8 students. The first part was on solving number problems mentally by working backward. The second part discussed on solving number problems using the model method. In this post, we are going to discuss how to solve word problems using Algebra if the mental and model methods fail. We will start with simple problems and will continue to solve more complicated problems later. We will use the problems we discussed in the first two parts of this series. Note that the discussion in this post is quite detailed because it is designed for beginners particularly middle school and high school students.
Example 1 One number is 1 more than the other. Their sum is 47. What are the numbers?
First Sentence: One number is 1 more than the other.
If there are two numbers and the other one is 1 bigger than the number, then if the smaller number is 5, the other is 5 + 1 or 6. So, since we don’t know what the number is, we let the number n. This means that the larger number is n + 1. Continue reading
This is the second part of the Word Problem Solving Series on Numbers. In the previous post, I have shown you ways on how to solve number problems mentally by working backward. In this post, I am going to teach you how to use models, rectangles in particular, to solve the problems in the previous post. This representation is called the model method. The model method is very popular in Singapore.
One number is 1 more than the other. Their sum is 47. What are the numbers? Solution
Let us represent numbers using rectangles. The first rectangle is the smaller number, and the second rectangle is the larger which is 1 more than the smaller. Clearly, if take away 1 from the larger number, the two numbers will be equal.
In addition, if we take away 1 from the larger number, then, we also have to take away 1 from the sum which gives us 46 after subtraction. Since the two rectangles have the same size, they will have to split 46 equally. This gives each large rectangle 23 each. This means that the smaller number is 23 and the larger number is 23 + 1 = 24. Continue reading
This is the first part of the Solving Number Problems Series for Grade 6-8 students, a-sub series of the Math Word Problem Solving Series.
Some of you probably need paper and pencil to solve number problems. You will be surprised that if you think harder and work backward, you can actually solve these problems in your head. Consider the following examples.
One number is 1 more than the other. Their sum is 47. What are the numbers?
Explanation and Solution
First, one number is 1 more than the other. That means that if we subtract 1 from the larger number the two numbers will be equal. That’s our first clue.
Second, if we subtract 1 from the larger number, then we should also subtract 1 from the sum (Can you see why?). That makes the sum 46. Now, since the two numbers are equal, we can divide 46 by 2. That gives us 23 which is the smaller number. Now, since the other number is 1 larger than 23, then it is 24.
Answers: 23 and 24 Continue reading
Did you know that out of 6 people, either 3 are friends or 3 are strangers? Three are friends in the question means mutual friends: A and B are friends, B and C are friends, and A and C are friends. Three are strangers also mean that out of three persons, none of whom know each other.
In the mathematical proof below, we represent the individuals by vertices and the relationships by edges. As we can see, we can form triangles. In the triangles below, a green edge connecting two vertices means that the persons represented by two vertices are friends and a red edge connecting two vertices means that the persons represented by two vertices are strangers. A triangle formed by edges of the same color represents three mutual friends or three mutual strangers. We highlight this relationship by filling the interior of the triangle with the appropriate color. Continue reading
I have shared quite a lot of sites in this blog about places where you can find challenging math problems for your intellectual satisfaction. In this post, I am going to introduce a website called Brilliant.org, a problem solving website which provides different levels of physics, computer science, and math problems depending on solver’s ability.
Brilliant.org provides different levels of physics and math problems, from practice to Olympiad level. Recently, it has also added problems in computer science particularly on data structures and algorithm. Math problems include challenges in algebra, number theory, geometry, and combinatorics. Physics problems include challenges in mechanics, electricity and magnetism.
Just like in other challenges and games, problem solved at Brilliant.org have corresponding points. Players can exchange points for corresponding prizes. Players can also discuss problems within the website.