A Story of Numbers
Class 8 · Mathematics
4 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Counting and Number Systems
To count, we match each object with one item of a fixed sequence, such as pebbles, sticks, spoken names or written symbols. This is one-to-one matching. A list of only 26 letters runs out after 26 objects, while sticks never run out but need as many sticks as objects. Counting in groups, such as 2s, 5s or 10s, makes larger counts shorter.
Why it matters. Knowing why number systems were invented helps children see why place value and zero matter. It also shows that counting is a way of matching and comparing, not only reciting names.
Try it in two minutes
- Give your child a handful of pebbles and ask them to count your spoons by placing one pebble for each spoon.
- Take away one spoon and ask how the pebbles tell you something is missing.
- Ask them to count 23 pebbles in groups of 5 and say how many groups and how many are left.
Try at home. Ask your child to invent their own names for the numbers 1 to 6 by counting in twos, like a made-up language.
Roman Numerals and Landmark Numbers
The Roman system uses landmark numbers: I is 1, V is 5, X is 10, L is 50, C is 100, D is 500 and M is 1000. To write a number, take as many of the biggest landmark as possible, then the next, and so on. For example 2367 is MMCCCLXVII. It is efficient, but there is no end to the symbols needed for very big numbers, and multiplying is hard.
Why it matters. Seeing how another system works helps children appreciate place value and understand what a landmark number is. It also gives practice in grouping and adding.
Try it in two minutes
- Write the Roman symbols on a card: I V X L C D M and their values.
- Ask your child to write 38 using the largest symbols first (XXXVIII).
- Ask what happens if you try to write 4000 with the symbols you have.
Try at home. Ask your child to find Roman numerals on a clock or a book chapter heading and read their values.
The Idea of a Base
In the Egyptian system the landmark numbers are 1, 10, 100, 1000 and so on, each 10 times the one before. A system whose landmark numbers are 1, n, n², n³ ... is called base n. In base 5 the landmarks are 1, 5, 25, 125 and so on. A number is built by using each landmark as many times as needed, up to n minus 1 times, because n copies make the next landmark.
Why it matters. A base makes it easy to add and multiply, since the product of two landmark numbers is another landmark number. This idea is the foundation of our own number system.
Try it in two minutes
- Make piles of 1, 5, 25 and 125 beans (or draw them) and list the landmark numbers.
- Ask your child to build 38 with the fewest piles. (25 + 5 + 5 + 1 + 1 + 1)
- Ask what happens when you have 5 piles of 5: they become one pile of 25.
Try at home. Ask your child to build a base 4 system with landmark numbers 1, 4, 16, 64 and write 50 with them.
Place Value Systems and the Role of Zero
In a place value system the position of a symbol shows which landmark number it counts. The Mesopotamians used base 60, so a numeral with groups 2, 5 and 30 stands for 2 × 3600 + 5 × 60 + 30. The Mayans used 1, 20, 360 and so on. The Hindu system is base 10 with ten digits, and the digit 0 shows an empty place so that 305 is not read as 35.
Why it matters. Place value is the idea behind every number we write. Understanding why zero is needed explains why 305 and 35 are different and helps in arithmetic.
Try it in two minutes
- Write 305 and 35 and ask your child how the numbers differ and what the 0 does.
- Ask what the 3 is worth in 305 and in 35.
- Tell them that time is counted in 60s and ask how many seconds are in 2 minutes and 15 seconds (135).
Try at home. Ask your child to write their age in seconds roughly, or the number of seconds in an hour.
What your child will practise
- Counting and Number Systems: Desert Quick Fire (Quick Fire)
- Counting and Number Systems: Mission Control Quest (Collect the Answer)
- Place Value Systems and the Role of Zero: Space Quick Fire (Quick Fire)
- Roman Numerals and Landmark Numbers: Number Quest (Match It Up)
- The Idea of a Base: Space Puzzle (Clue Puzzle)
- Quiz: Counting and Number Systems (8 questions)
- Quiz: Place Value Systems and the Role of Zero (8 questions)
- Quiz: Roman Numerals and Landmark Numbers (8 questions)
- Quiz: The Idea of a Base (8 questions)