PrepShorts · Teaching notes · Class 6 Mathematics · Chapter 7, FractionsPrepShorts

Chapter 7 · Fractions

Every fraction has one place on the number line

Teaching notesNCERT10 min

This video could not be loaded. Reload the page to try again.

Sign in with Google

10 min.

These teaching notes are for members

What the video covers, what to say before it, where a class usually goes wrong, and what to set afterwards. An account is free, and it opens every chapter of every book.

What to assume they know

What they should be able to do

  • Divide the gap between two consecutive whole numbers into a stated number of equal parts and label every new mark
  • Read the length of a drawn bar on a number line as a fraction
  • Distinguish the length from zero from the tick it ends on, and use either to name the same fraction
  • Mark given fractions, including fractions past 1, on a line you draw yourself
  • Say how many fractions there are between 0 and 1, and justify the answer by subdividing
  • Explain why a fraction beyond 1 is still a length measured from 0
  • State, in one sentence, what the number line establishes about fractions that the sharing pictures did not

Where it usually goes wrong

  • "The tick marks are the fractions." The fraction is the length from 0. The tick is where that length ends. A student who reads ticks instead of lengths will count one third when the bar ends on the second tick, because the first tick is the one that was labelled.
  • "Fractions live between 0 and 1, and whole numbers live outside." The bars on p.160 run past 1 on purpose. Fractions are spread across the whole line, and some of them sit exactly on the whole-number marks.
  • "A number line can only be divided one way." The same 0-to-1 gap is cut in two, three, five and eight over a single page. The line does not change; only the choice of step does.
  • "There are as many fractions between 0 and 1 as there are ticks I can draw." This is the misconception the p.160 discussion question is aimed at. Answer it by halving a gap, then halving what is left, and refusing to stop.
  • "Between 0 and 1 there is a next fraction after one half." There is not. Whatever candidate a student names.
  • "A longer bar always means a bigger denominator." It means a bigger number of steps taken, not a smaller step. Keep the step size visible in every frame so that the two roles do not merge.

Questions to check understanding

  • Divide a unit gap into a stated number of equal parts and label every mark
  • Given a drawn bar on a number line, write its length as a fraction
  • Mark a list of fractions on a number line, including fractions greater than 1
  • Say how many fractions lie between two given fractions, and justify it
  • Given two fractions, produce a third that lies between them
  • Draw a line on which both a stated fraction and a stated fraction with a different denominator can be marked exactly
  • The solutions appendix bound with this chapter answers the §7.4 questions on its §7.4 pages, with the one exception noted below

Examples worth working on the board

  • The halved unit (§7.4, p.159). Checked against the printed page. A line runs 0, 1, 2 with the 0-to-1 gap split by one extra tick; an empty box sits under that tick; a blue bar drawn above the line starts at 0 and ends at the tick. The book states in words that the gap is one unit long and split into two equal parts, and reads the bar off as one half. This is the template every later picture reuses.
  • Thirds (§7.4, p.159). Checked against the printed page. The 0-to-1 gap carries two extra ticks; the first is printed as one third and the second has an empty box; the blue bar ends on the second tick. Inputs: three equal parts, bar ending on the second mark. The solutions appendix bound with this chapter records the answer as two thirds.
  • Fifths (§7.4, p.159). Checked against the printed page. The unit is cut five ways; the ticks at one fifth and three fifths are printed and the ticks between them and after them carry empty boxes; two blue bars are drawn, the shorter ending on the second tick and the longer on the fourth. Inputs: five equal parts, bars ending on the second and fourth marks. The appendix records two fifths and four fifths.
  • Eighths (§7.4, p.159). The unit is cut eight ways and the student is asked to write the fractions into a notebook rather than into the book. The appendix gives the opening of the run — one eighth, two eighths, three eighths — and then an ellipsis, which is the honest answer: the point is the pattern, not a list.
  • Draw-your-own (§7.4, p.160). Checked against the printed page. The Figure it Out set asks for bars of one tenth, three tenths and four fifths on one line, then for five fractions of the student's own choosing. Inputs only. Note that one tenth and four fifths cannot share a set of ticks unless the unit is cut into ten, which is the hidden lesson of the question.
  • The crowding question (§7.4, p.160). Printed as a Math Talk discussion question with no answer in the chapter. The honest answer at this level is that there is no end to them, and the reason is that any gap can be cut again. See Notes: the solutions appendix answers it with a word that is mathematically wrong.
  • The bar past 1 (§7.4, p.160). Checked against the printed page. The unit is halved, a blue bar ends at the half mark, and a black bar drawn above it runs past 1 and ends at the next half mark; an empty box sits under that mark. Inputs: unit halved, black bar ending one half beyond 1. The appendix records three halves.
  • Four bars past 1 (§7.4, p.160). Checked against the printed page. The unit is cut into fifths, the ticks up to four fifths are printed, and four black bars of increasing length end on the four ticks that lie beyond 1, each with an empty box. Inputs: fifths, four bars each one fifth longer than the last, the shortest ending one fifth past 1. The appendix records six fifths, seven fifths, eight fifths and nine fifths.
  • Teacher's Note (§7.4, p.160). A dashed panel asking that the figures be put up on the board, with the class writing answers in their notebooks. Worth knowing because it tells you the figures are meant to be reproduced by hand, which is a hint about how simple the figure should stay.

Figures to have open

  • A number line running 0 to 2 whose unit gap can be subdivided into any chosen number of equal parts, with bars drawn from 0. This single figure carries sections 1 to 9. Standard schematic.
  • A zoom device for section 7 that can keep halving a gap without the figure ever appearing to finish. This is an added construction; the textbook poses the question and prints no figure for it.
  • Bars in two visibly distinct colours, matching the book's convention that one colour stays under one unit and the other passes it, so that a student holding p.160 recognises the picture.
  • No photograph, table or data figure from the textbook is required.

Where this sits in the book

  • NCERT Ganita Prakash, Class 6, Chapter 7 "Fractions", §7.4 "Marking Fraction Lengths on the Number Line", pp.159–160 — the halved unit and the thirds, fifths and eighths (p.159); the Figure it Out set, the discussion question, the bars past 1 and the Teacher's Note (p.160)
  • §7.3, p.156, for the folded strip this section straightens into an axis
  • §7.5, p.161, which sorts the bars of p.160 into those under and over one unit
  • Summary, p.186, for the printed one-line statement that a fraction has a point on the number line
  • Solutions appendix bound with this chapter file, §7.4 pages

The book

Open in a new tab