Basic 6 · Mathematics · Counting, Representation and Cardinality
Numbers Around a Given Number on a Number Chart
In this topic you will identify numbers in different positions around a given number on a number chart and describe the patterns.
By the end of these notes you should be able to:
- Read a number chart and its patterns
- Find the numbers above, below, left and right of a given number
- Use patterns to fill missing numbers
What you already know
- Modelling numbers up to 1,000,000
Copy everything that has a blue line on its left into your notebook. The other parts are for reading.
- Strand
- Number
- Sub-strand
- Counting, Representation and Cardinality
- Indicator
- B6.1.1.1.2-3 – Identify numbers in different positions around a given number in a number chart
Introduction
A number chart is like a map. If you know where you are, you can find your neighbours above, below and on each side by following simple rules.
1. The Rules of a Number Chart
In a chart that counts in ones with 10 numbers in each row, moving right adds 1, moving left subtracts 1, moving down adds 10 and moving up subtracts 10.
| Move | Change |
|---|---|
| right → | + 1 |
| left ← | − 1 |
| down ↓ | + 10 |
| up ↑ | − 10 |
| diagonally down-right ↘ | + 11 |
| diagonally down-left ↙ | + 9 |
| diagonally up-right ↗ | − 9 |
| diagonally up-left ↖ | − 11 |
2. Charts with Bigger Steps
Number charts can count in tens, hundreds or thousands. In a chart counting in hundreds with 10 columns, moving right adds 100 and moving down adds 1,000. Always look at the first row to find the step size.
Example 1
In a chart counting in ones with 10 columns, find the neighbours of 45,327.
- Left: 45,327 − 1 = 45,326; Right: 45,327 + 1 = 45,328
- Above: 45,327 − 10 = 45,317; Below: 45,327 + 10 = 45,337
- Up-left: 45,316; Up-right: 45,318; Down-left: 45,336; Down-right: 45,338
Answer: The eight neighbours of 45,327
Example 2
A chart counts in hundreds with 10 columns. What number is directly below 230,400?
- Moving right adds 100, so one row has 10 × 100 = 1,000.
- Moving down adds 1,000.
Answer: 230,400 + 1,000 = 231,400
3. Filling Missing Numbers
To fill a gap, find a number you know in the same row or column and apply the rule. Check your answer using another direction.
Tip: Find the step size first by looking at two side-by-side numbers.
New words
- number chart
- A grid of numbers arranged in order.
- row
- A line going across.
- column
- A line going down.
- diagonal
- A slanting line from corner to corner.
- pattern
- A regular arrangement that repeats.
- step size
- The amount added each time.
Summary
- On a 10-column chart in ones: right +1, left −1, down +10, up −10.
- Diagonal moves combine these rules.
- Find the step size before working out missing numbers.
- Check answers using another direction.
Class activity: Chart Detectives
- Draw a 5 × 5 part of a number chart starting at any 5-digit number.
- Remove six numbers.
- Your partner fills them in and explains the rule used.
You need: Locally made number chart, Locally made number cards, Place-value chart on manila card
Exercises
Answer in your exercise book first, then check your answers.
1. On a 10-column chart in ones, the number below 3,456 is…
- A. 3,466
- B. 3,457
- C. 3,446
- D. 3,556
Show answer
Answer: 3,466Add 10.2. The number up-left of 52,330 is…
- A. 52,319
- B. 52,321
- C. 52,341
- D. 52,339
Show answer
Answer: 52,319Subtract 11.3. In a chart of hundreds (10 columns), moving down adds…
- A. 1,000
- B. 100
- C. 10
- D. 10,000
Show answer
Answer: 1,00010 × 100.4. Moving left on the chart subtracts 1.
- A. True
- B. False
Show answer
Answer: TrueIn a chart of ones.5. Moving down-left adds 11.
- A. True
- B. False
Show answer
Answer: FalseIt adds 9.6. The number to the right of 99,999 on a chart of ones is ______.
Show answer
Answer: 100,000Add 1.7. Find the numbers above and below 640,215 on a 10-column chart of ones.
Show answer
Answer: Above 640,205; below 640,225±10.8. A chart counts in tens with 10 columns. What is directly above 18,750?
Show answer
Answer: 18,650One row = 100, so subtract 100.
Homework
- Make a 4 × 4 number chart in thousands starting at 250,000.