PrepShorts · Teaching notes · Class 6 Mathematics · Chapter 3, Number PlayPrepShorts

Chapter 3 · Number Play

Placing a large number on the number line by feel

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10 min.

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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.

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What to assume they know

  • Supercells: a number's status comes from its neighbours: comparing large numbers, and reading a printed row of cells as data
  • Number lines with small whole numbers, from earlier classes
  • Reading and writing numbers up to five digits, with the comma after the thousands digit
  • Knowing that 1000 comes after 999, and that the digit count jumps there

What they should be able to do

  • Read the step of a number line from two labelled marks
  • Label the remaining marks on a line once the step is known
  • Place a given whole number between the two thousands marks it falls between
  • Judge, without computing, whether a number sits near the start, the middle or the end of its interval
  • Order a set of large numbers by placing them on one line
  • Distinguish pairs that share digits but not order — 9590 and 9950, 5030 and 5300
  • Circle the smallest and box the largest number in a labelled sequence
  • Explain why a line whose marks are one apart looks identical to a line whose marks are a thousand apart

Where it usually goes wrong

  • "Numbers with the same digits sit close together." 9590 and 9950 use the same four digits and land in different thousands. So do 5030 and 5300. Placing them on one line is the cheapest demonstration a student will ever get that order of digits is the whole story.
  • "A number goes in the middle of its gap unless it is obviously at one end." 2180 is not near the middle. Students default to the midpoint because the midpoint is easy to find; make them ask how far through instead.
  • "Every number line steps by one." Line (d) steps by a thousand and looks identical to line (b), which steps by one. Nothing about the drawing says which — only the labels do.
  • "You only need one label to read a line." One label fixes where you are; it does not fix how fast the line moves. Two are the minimum.
  • "After 9999 the line stops." Line (b) walks straight through 9999 into 10,000 and keeps going. The digit count changes; the spacing does not.
  • **"The lines in Figure it Out start at 0."** None of them do. Their left-hand ends are unlabelled and must be worked back to from the labels that are given.

Questions to check understanding

  • Identify the numbers at marked positions on a partly labelled line, and fill in the rest
  • Place a given list of numbers on a supplied line
  • Circle the smallest and box the largest in a labelled sequence
  • "What is the step of this line?" given two labels
  • Order four large numbers, with the line as the working
  • Items built on digit-order confusion: which of 9590 and 9950 is larger, and how far apart are they
  • Items where the line crosses a digit-count boundary, such as 9998 to 10,002

Examples worth working on the board

  • The printed line (§3.3, p.59). A single line marked 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 10,000. Two curved pointers run to positions between the 2000 and 3000 marks, one labelled 2180 above the line and one labelled 2754 below it. The pointers are drawn artwork.
  • The numbers to be placed (§3.3, p.59). 2180, 2754, 1500, 3600, 9950, 9590, 1050, 3050, 5030, 5300 and 8400. Eleven numbers, of which only the first two are placed for you. Useful structure: they arrive in near-pairs that share an interval — 1050 with 1500, 3050 with 3600, 5030 with 5300 — and one pair, 9590 and 9950, sits in two different intervals despite using the same four digits.
  • The four lines to be identified (§3.3, p.59, Figure it Out). Each has ten marks and exactly two or three of them labelled:
    • (a) 2010 and 2020, two marks apart
    • (b) 9996 and 9997, next to each other
    • (c) 15,077 and 15,078 next to each other, and 15,083 five marks further on
    • (d) 86,705 and 87,705, next to each other The steps are therefore 5, 1, 1 and 1000. The third labelled mark in (c) is a free consistency check and should be shown being used as one.
  • The closing instruction (§3.3, p.59). Circle the smallest number and draw a box round the largest, on each of the four lines.
  • Where inside an interval. 2180 is 180 of the way through a gap 1000 wide, so it sits just clear of the left-hand mark; 2754 is three-quarters of the way across. These two fractions are the whole content of sections 4 and 5.

Figures to have open

  • The printed number line from §3.3, p.59, with all ten thousands marks and the two curved pointers to 2180 and 2754. Standard schematic; redraw, but keep both pointers, since the fact that both numbers land in one gap is section 3.
  • The four Figure it Out lines (§3.3, p.59), each with ten marks and only the printed labels shown. They must start blank — a pre-filled version has no exercise in it.
  • A blown-up single interval, 2000 to 3000, wide enough to place a number to the nearest ten. Standard schematic, not in the textbook.
  • No table, dataset or photograph is required.

Where this sits in the book

The book

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