Tales by Dots and Lines
Class 8 · Mathematics
5 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
The Mean as a Balance Point
Part of: Averages and graphs
The mean is the sum of all values divided by the number of values. On a number line the mean is the balance point: the total distance of the values below it equals the total distance of the values above it. For two numbers, the mean is exactly halfway between them. For more numbers, the mean is not always halfway between the smallest and largest. There is only one such balance point.
Why it matters. Seeing the mean as a balance point helps children understand why it changes when values change, and not just how to calculate it.
Try it in two minutes
- Write the numbers 2, 5 and 11 on a number line. Find the mean (6).
- Measure how far each number is from 6. Add the distances below and above.
- Ask your child why the two totals match and what would happen if the centre moved to 7.
Try at home. Use coins or small stones on a ruler as a seesaw and find where it balances for different weights.
How Mean and Median Change
Part of: Averages and graphs
Adding a value greater than the mean raises the mean, adding a smaller value lowers it, and adding a value equal to the mean leaves it unchanged. If every value is increased by a fixed number, the mean increases by that number. If every value is multiplied by a number, the mean is multiplied by it too. The median can also move: including a value above the median pushes the median up.
Why it matters. Knowing how a measure reacts to change lets children spot errors and reason about data without recalculating from scratch.
Try it in two minutes
- Take marks 4, 8 and 12 (mean 8). Add another mark of 8 and ask what happens to the mean.
- Now add a mark of 20 instead and ask whether the mean goes up or down.
- Ask what happens to the mean if every mark is increased by 5.
Try at home. Ask your child to predict the new mean after adding 10 marks to each score in a quiz.
Finding Missing and Wrong Values
Part of: Averages and graphs
Because the mean is the total divided by the number of values, the total is the mean multiplied by the count. If one value is missing, find the total from the mean and subtract the known values. If a value was written wrongly, adjust the total by the error and divide again. To get a target mean, work out the total needed and subtract what is already there.
Why it matters. These ideas are used in marks, targets and averages. They also show children how to go backwards from the mean to the original numbers.
Try it in two minutes
- Say that the mean of 4 test marks is 15 and three marks are 12, 14 and 18. Ask for the fourth.
- Ask your child to find the total first by multiplying the mean by 4.
- Ask what changes if one of the marks was noted 3 too high.
Try at home. Ask your child to find the mark needed in the next test to bring their average up to a chosen number.
Mean and Median from a Frequency Table
Part of: Averages and graphs
A frequency table shows how many times each value occurs. To find the mean, multiply each value by its frequency, add the products and divide by the total frequency. To find the median, add the frequencies from the smallest value until you reach the middle position. Simply averaging the listed values gives a wrong answer unless all the frequencies are equal.
Why it matters. Surveys and class data are often written as a table, not a long list. Children must know how to read each row as repeated values.
Try it in two minutes
- Make a table of the number of siblings that five friends have, using tally marks.
- Ask your child to multiply each value by its tally count and add the products.
- Ask your child to divide by the total number of friends.
Try at home. Do a quick survey in the family of how many books each person read this month and make a frequency table.
Spreadsheets and Line Graphs
Part of: Averages and graphs
A spreadsheet is a grid of cells. Columns are named A, B, C and so on, and rows are numbered 1, 2, 3. A cell name such as E5 means column E, row 5. A range such as B3:G3 means all cells from B3 to G3. The formula SUM(B3:G3) adds that row of cells, and AVERAGE finds their mean. A line graph joins points with lines to show how something changes over time, and a steeper line means a faster change.
Why it matters. Computers do the adding and averaging for large amounts of data. Reading graphs well helps children understand news, weather and other data in daily life.
Try it in two minutes
- Draw a small table on paper with columns A, B and C and rows 1 to 4. Ask your child to name a cell, like B3.
- Write a few numbers and ask which range of cells they occupy.
- Draw a line graph of the temperature at 3 times of the day and ask where it rose fastest.
Try at home. Make a simple table of how many steps you each walked on 5 days and use a spreadsheet to find totals and averages.
What your child will practise
- Finding Missing and Wrong Values: Jungle Quick Fire (Quick Fire)
- How Mean and Median Change: Number Quest (Collect the Answer)
- Mean and Median from a Frequency Table: Space Puzzle (Clue Puzzle)
- Spreadsheets and Line Graphs: Space Quick Fire (Quick Fire)
- The Mean as a Balance Point: Mission Control Quest (Match It Up)
- Quiz: Finding Missing and Wrong Values (8 questions)
- Quiz: How Mean and Median Change (8 questions)
- Quiz: Mean and Median from a Frequency Table (8 questions)
- Quiz: Spreadsheets and Line Graphs (8 questions)