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Algebra Play

What a term is built from

Add the four dates in a 2 by 2 calendar square. If a is the top-left date, the sum is 4a + 16. It has two terms — the pieces that are added. The term 4a has two parts.

Term: 5a², written whole.
Step 1 of 4
  1. Term: 5a², written whole.
  2. Split it: coefficient 5, letter part a².
  3. A bare letter hides a 1: a = 1 × a.
  4. A minus belongs to the number: −4b has coefficient −4.

Coefficient — the number part of a term. The letters of the term are its letter part.

Rule: every term has a coefficient. A term with letters also has a letter part. A bare letter, one with no number, has coefficient 1. A minus sign in front belongs to the number, not the letters.

Because −4b means −4 × b, the minus goes with the 4.

Four terms split into their parts
TermCoefficientLetter part
5a²5a²
a1a
−4b−4b
1212none

A puzzle gives 50k + 20 + n. The coefficient of k is 50. The coefficient of n is 1.

Slide the chip to the coefficient of each term.

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This track

  1. 0 Start here
  2. 1 What a term is built from
  3. 2 Joining terms of one kind
  4. 3 One term times another
  5. 4 Multiplying a bracket by one term
  6. 5 Every term of one meets every term of the other
  7. 6 Checkpoint: parts, joining and multiplying
  8. 7 A square cut into four pieces
  9. 8 The easy way round an awkward product
  10. 9 Taking out what every term shares
  11. 10 Putting a number in to find out
  12. 11 From a situation to a line
  13. 12 Checkpoint: patterns, factors and checking
  14. 13 The big picture
  15. 14 Track quiz

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