1.What are Word Problems?
Word problems are mathematical problems that are presented in the form of a real-life situation or scenario. They often require students to use their critical thinking skills to analyze and interpret the information given in the problem and apply their mathematical knowledge to find a solution. Word problems can involve a range of mathematical concepts such as addition, subtraction, multiplication, division, fractions, percentages, ratios, and more. They are commonly used in math textbooks, tests, and exams to test students' understanding of mathematical concepts and their ability to apply them in real-life situations.
1.1 Vocabulary used in Word Problems
Children must be aware about the vocabulary associated while solving word problems:
Look at the table below to understand the logic of how to analyse a word problem:
1.2 What sort of Word Problems may you encounter in your 11 plus exam?
You may encounter Word Problems from the following nine strands in your 11 plus exams:
- Number and Place Value
- Calculations
- Fractions, Decimals & Percentages
- Ratio and Proportion
- Algebra
- Measurement
- Geometry: Properties of Shapes
- Geometry: Position & Direction
- Statistics
1.3 Solved Examples
Example 1:
Jessica has 5 cards with the digits 9, 5, 7, 1 and 8 written on them.
| 9 | 5 | 7 | 1 | 8 |
Write down the smallest number Jessica can make using all of these cards:
Solution:
The cards given are: 9, 5, 7, 1, 8
Arranging the cards in ascending order: 1, 5, 7, 8, 9
Smallest five digit number formed is: 15789
Example 2:
Six friends shared the cost of a tennis court (priced at 3 million pounds) equally. How much did each of them pay?
Solution:
3 million pounds = £3,000,000
£3,000,000 ÷ 6 = £500,000
Each of the friends have to pay £500000.
Example 3:
Sam spends 1/3 of his money. He then spends 1/3 of what he has left. What fraction of his money did he spend altogether?
Solution:
First time, Sam spends = 1/3 of his money
Remaining money = 1 - 1/3 = 2/3 of his money
Second time, Sam spends = 1/3 of his remaining money
= 1/3 × 2/3 of his money
= 2/9 of his money
Total spending = 1/3 of his money + 2/9 of his money
= 1/3 + 2/9
= 3/9 + 2/9
= 5/9
Sam spends 5/9 of his money altogether.
Example 4:
A drink is made by mixing fruit juice with water. 39 ml of fruit juice is needed to make 600 ml of the drink. How much water is needed to make 800 ml of the drink?
Solution:
39 ml of fruit juice is required to make 600 ml of the drink.
(600 - 39) = 561 ml of water required to make 600 ml of drink
Required water to make 200 ml of the drink = 561 ÷ 3 = 187 ml
Required water to make 800 ml of the drink = 187 x 4 = 748 ml
Example 5:
Miley and Seema are collecting money for charity. Miley collects £10 more than Seema. Altogether they collect £240. How much did Seema collect?
Solution:
Let Seema collect = £x
Then, Miley collected = £(x + 10)
Total money = £240
x + x + 10 = 240
2x + 10 = 240
2x = 240 - 10
2x = 230
x = 230 ÷ 2
x = £115
Seema collected £115.
Example 6:
Add together 5 metres, 5 centimetres and 5 millimetres. Give your answer in millimetres.
Solution:
5 m = 5000 mm & 5 cm = 50 mm
5 m+ 5 cm + 5 mm
= 5000 mm + 50 mm + 5 mm
= 5055 mm
Example 7:
Saif puts five dots on a piece of paper in such a way that no three dots are in a straight line. He joins every dot to every other dot with a straight line. How many lines does he draw?
Solution:
Saif draws 5 dots such that no three dots are in a straight line.
The dots represent the vertices of a pentagon Thus, the number of lines can be found using,
Thus, 10 lines can be drawn.
Example 8:
Give the size of the obtuse angle between the compass directions NE and S.
Solution:
The angle between Northeast to East = 45°
The angle between East to South = 90°
The obtuse angle between NE and S = 45° + 90° = 135°
Example 9:
The bar graph below shows the number of pet sets in each house in a street.
(a) How many houses have 1 pet?
(b) How many houses are there in the street?
(c) How many pets are there in the street?
Solution:
(a) 14 houses have 1 pet.
(b) 9 + 14 + 4 + 3 = 30
There are 30 houses in the street.
(c) (9 x 0) + (14 x 1) + (2 x 4) + (3 x 3)
= 0 + 14 + 8 + 9
= 31
There are 31 pets in the street.
