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CBSE Class 6 · Mathematics

Patterns in Mathematics

Official NCERT chapter from Ganita Prakash (book code fegp1). ExamMaster notes are original teaching at CBSE Class 6 depth.

This lesson follows the official chapter “Patterns in Mathematics” in Ganita Prakash. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 6
  • Easy level
  • 8 concepts

1What is Mathematics?

Mathematics is the work of naming a rule you can check: a count, a shape test, a pattern that restarts. A pretty drawing without a rule is not yet mathematics.

Calling every calculation “maths” without a checkable rule is a slogan.

Figure. Mathematics here is noticing a chunk that comes again. Name A-B before you guess the next tile.

How it works

  1. Name what you will checkA count, a shape, a sequence.
  2. Say the ruleA sentence you can rerun.
  3. Run it onceIf it fails, it was not the rule.

2Patterns in Numbers

A number pattern is a sequence with a rule: add 3, double, alternate. The next term comes from the rule, not from a favourite digit.

A list with no restarting or growing rule is just a list.

Figure. The list 2, 4, 6, 8, 10 is the rule +2, not five pretty marks. Say the rule, then the next mark is 12.

How it works

  1. Read the first few termsEvidence.
  2. Say a candidate ruleAdd 4, or ×2.
  3. Check it on the next term you already haveThen predict.

3Visualising Number Sequences

Dots, steps, or a number line can show the same rule the digits hide. 2, 5, 8 as hops of +3 is a picture of the rule.

A picture that does not match the digits is a different sequence.

Figure. Triangular numbers are stacked rows: 1, then 1+2, then 1+2+3. T3 is 6 because the picture has six boxes, not because 6 is pretty.

How it works

  1. Write the terms2, 5, 8.
  2. Draw the hop+3 each time.
  3. Demand the picture and the digits agreeOne rule.

Hops of +3

A sequence reads 4, 7, 10. What is the hop, and what is the next term?

  • Hop+3
  • Next13
  • Check10+3=13

Pro tip. The picture is the hop. The next term is the hop applied once more.

4Relations among Number Sequences

Two sequences can share a relation: one is double the other, or one is the running total of the other. Name the relation; do not stare at two pretty lists.

A relation you cannot say is not a relation yet.

Figure. Two neighbouring triangular numbers make a square: 3 + 6 = 9 = 3². The picture of T2 beside T3 is the 3-by-3 square.

How it works

  1. Write sequence A and BSide by side.
  2. Try a sentenceB is 2×A, or B is A plus 5.
  3. Check every pair you haveOne miss kills the claim.

5Patterns in Shapes

A shape pattern is a unit that repeats or grows: square-circle, or 1 tile then 3 then 5. The unit or add-on is the rule.

Almost the same tile is a new pattern or a break.

Figure. Growing squares: 1 by 1, 2 by 2, 3 by 3. The side grows by 1; the count of unit squares is 1, 4, 9.

How it works

  1. Find the unit or the add-onThe rule.
  2. Copy it to the next placeA check.
  3. If a tile differs, name a new rule or a stopDo not force the old unit.

6Relation to Number Sequences

A growing shape pattern often hides a number sequence: 1, 3, 5 squares. The shape is a costume; the sequence is the count of tiles.

Admiring the drawing without counting is not the relation.

Figure. The shape count is the number sequence. After 1, 4, 9 the rule n² says 16, whether or not you draw the 4-by-4 square.

How it works

  1. Count the tiles in each figureA sequence.
  2. Name the number-rule+2 each time.
  3. Predict the next figure’s countThen build it if you can.

7A sequence is a rule you can say, not a pretty list

If you cannot say the next term’s reason, you do not yet have a sequence — you have a list.

A beautiful arrangement of digits is not a rule.

Figure. A sequence is a rule you can say. +3 takes 5 to 8 to 11 to 14. The next mark is 17 because the rule says so, not because the list looks tidy.

How it works

  1. Ask “why the next?”A reason.
  2. If there is no reason, stop calling it a sequenceIt is a list.
  3. If there is a reason, write it as a sentenceThat is the maths.

8A miss: treating the picture as the number

Five dots arranged as a pentagon is still 5. The picture is a view; the number is the count.

Changing the arrangement does not change how many.

Figure. The six boxes are a picture of a count. The number is 6. Treating the drawing as if it were the number is the miss this chapter names.

How it works

  1. CountThe number.
  2. Allow a new picture of the same countA view.
  3. Do not add 1 because the picture looks biggerCount again.
2, 5, 8, 11 is best named by
  1. The rule “add 3 each time”
  2. A pretty list with no rule
  3. The picture of a pentagon

A sequence is a rule you can say and check.

Notes

  • The official chapter title is “Patterns in Mathematics”. Teach the school test for that title, not a contest shortcut.
  • If a step needs a later class, stop. The next official chapter will pick it up.

Formulas

  • Next term = the named rule applied once more.
  • A shape-count sequence: count tiles, then name the hop.

Recap

Hold these pegs from the official chapter “Patterns in Mathematics”. The wording is ExamMaster’s teaching, not a textbook recap.

What is Mathematics?
Mathematics is the work of naming a rule you can check: a count, a shape test, a pattern that restarts.
Patterns in Numbers
A number pattern is a sequence with a rule: add 3, double, alternate.
Visualising Number Sequences
Dots, steps, or a number line can show the same rule the digits hide.
Relations among Number Sequences
Two sequences can share a relation: one is double the other, or one is the running total of the other.
Patterns in Shapes
A shape pattern is a unit that repeats or grows: square-circle, or 1 tile then 3 then 5.
Relation to Number Sequences
A growing shape pattern often hides a number sequence: 1, 3, 5 squares.

Practise Patterns in Mathematics

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