Year 6 Maths: Index Number

What is an Index Number?

An index number is a way to show how much something has changed over time. Think of it like a special number that helps us compare things easily.

Why Do We Use Index Numbers?

We use index numbers to:

• See changes in prices over time (like how much things cost)
• Compare different things (like the price of apples this year vs last year)
• Understand how things are getting better or worse (like weather, prices, or even your school grades!)

How Does It Work?

Imagine you have a basket of apples. Last year, a single apple cost £1. If this year, the price of an apple is £1.20, we can use an index number to show how much the price has changed.

To find the index number, we use this formula:

$$

\text{Index Number} = \left( \frac{\text{New Value}}{\text{Old Value}} \right) \times 100

$$

Example

1. Last Year: 1 apple = £1 (Old Value)
2. This Year: 1 apple = £1.20 (New Value)

Now, let’s plug in the values:

$$

\text{Index Number} = \left( \frac{1.20}{1} \right) \times 100 = 120

$$

This means the index number is 120. Since it’s over 100, it means the price has gone up!

Key Rules for Index Numbers

1. Base Year: The first year you compare is called the base year. The index number for that year is always 100.
2. New Value and Old Value: Always identify which is the new value (current year) and which is the old value (previous year).
3. Multiplication by 100: Always multiply by 100 to express the index number as a percentage.

Tips and Tricks

• If the index number is over 100, it means things have gotten more expensive.
• If the index number is under 100, it means things have gotten cheaper.
• Remember to always keep your numbers clear and double-check your calculations!

Questions

Easy Level Questions (1-20)

1. What do we call the year we start comparing prices?
2. What is the index number for the base year?
3. If last year an apple was £2 and this year it is £2.50, what is the old value?
4. What is the new value if the old value is £1 and the index number is 150?
5. Calculate the index number if the old value is 4 and the new value is 8.
6. If the index number is 120 and the old value is £5, what is the new value?
7. What does it mean if the index number is less than 100?
8. If the price of a toy was £10 last year and £12 this year, what is the index number?
9. Is an index number of 90 considered an increase or decrease in price?
10. If an old value is 20 and the new value is 30, what is the index number?
11. What happens to the index number if the new value is the same as the old value?
12. Calculate the index number if the old value is 30 and the new value is 45.
13. What does an index number of 100 mean?
14. If you bought a book for £8 last year and £10 this year, what is the index number?
15. What is the index number if an old value is £15 and the new value is £12?
16. How would you show a price increase using an index number?
17. If the old value is £50 and the new value is £60, what is the index number?
18. What is the formula to calculate the index number?
19. If the price of a sandwich was £3 last year and £2 this year, what is the index number?
20. Is an index number of 110 a good sign for prices?

Medium Level Questions (21-40)

21. If an old value is £25 and the new value is £30, calculate the index number.
22. The index number is 130, and the old value is £20. What is the new value?
23. If the price of a bike was £200 last year and £250 this year, what is the index number?
24. Calculate the index number if the old value is 60 and the new value is 45.
25. What does an index number of 80 indicate about price changes?
26. If the old value is £35 and the new value is £42, what is the index number?
27. If the index number is 150 and the old price is £30, what is the new price?
28. Calculate the index number for a shirt that cost £15 last year and £18 this year.
29. If the price of a game was £25 last year and is £22 this year, what is the index number?
30. What does it mean when the index number is exactly 100?
31. If an old value is 80 and the new value is 64, what is the index number?
32. Calculate the index number if the old value is £10 and the new value is £15.
33. If the price of shoes increased from £50 to £60, what is the index number?
34. What happens to the index number if the new value is lower than the old value?
35. If the old value is £12 and the new value is £15, what is the index number?
36. Calculate the index number if an old value is 20 and the new value is 10.
37. If the index number is 90, what does that tell us about the prices?
38. What is the new price if the old price was £40 and the index number is 125?
39. If the price of a bus ticket was £2 last year and £2.50 this year, calculate the index number.
40. What does an index number of 200 signify?

Hard Level Questions (41-60)

41. If an old value is £100 and the new value is £150, find the index number.
42. The index number is 200, and the old value is £50. What is the new value?
43. If a textbook cost £30 last year and £42 this year, what is the index number?
44. Calculate the index number if the old value is £80 and the new value is £64.
45. If the index number is 75, what does that tell us about the value?
46. If the old value is 90 and the new value is 108, what is the index number?
47. Calculate the index number for a laptop that cost £400 last year and £500 this year.
48. If the price of a coffee was £3 last year and £3.60 this year, what is the index number?
49. What is the new value if the index number is 140 and the old value is £200?
50. If a bike cost £150 last year and £120 this year, what is the index number?
51. How do you find the percentage increase using the index number?
52. If an old value is 75 and the new value is 90, calculate the index number.
53. If the index number is 110 and the old value is £20, what is the new value?
54. Calculate the index number if the old value is £15 and the new value is £18.75.
55. If the price of a meal was £25 last year and is £30 this year, what is the index number?
56. What does an index number of 50 indicate about price changes?
57. If the old price of a concert ticket was £40 and it is now £50, find the index number.
58. If the index number is 180 and the old value is £70, what is the new value?
59. What happens to the index number when the new value is the same as the old?
60. If the old value is £90 and the new value is £81, what is the index number?

Answers

Easy Level Answers

1. Base Year
2. 100
3. £2
4. £1.50
5. 200
6. £6
7. It means prices have decreased.
8. 120
9. Decrease in price.
10. 150
11. The index number remains 100.
12. 150
13. It means there is no change in price.
14. 125
15. 80
16. By showing a number over 100.
17. 120
18. $$\text{Index Number} = \left( \frac{\text{New Value}}{\text{Old Value}} \right) \times 100$$
19. 66.67
20. Yes, it shows an increase.

Medium Level Answers

21. 120
22. £26
23. 125
24. 75
25. Prices have decreased.
26. 120
27. £45
28. 120
29. 88
30. No change in price.
31. 80
32. 150
33. 120
34. Prices have decreased.
35. 125
36. 50
37. Prices have decreased.
38. £50
39. 125
40. Prices have doubled.

Hard Level Answers

41. 150
42. £100
43. 140
44. 80
45. Prices have decreased.
46. 120
47. 125
48. 120
49. £280
50. 80
51. Subtract the old value from the new, then divide by the old value.
52. 120
53. £22
54. 125
55. 120
56. Prices have significantly decreased.
57. 125
58. £126
59. The index number stays at 100.
60. 90

Feel free to ask more questions or practice with these topics! Remember, index numbers help us understand how prices and values change over time. Happy learning!