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CBSE Class 7 · Mathematics

Connecting the Dots...

Official NCERT chapter from Ganita Prakash Part II (book code gegp2). ExamMaster notes are original teaching at CBSE Class 7 depth.

This lesson follows the official chapter “Connecting the Dots...” in Ganita Prakash Part II. 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 7
  • Easy level
  • 8 concepts

1Of Questions and Statements

A question asks; a statement reports. “How many students chose tea?” is a question. “12 chose tea” is a statement. Data work starts by knowing which you have.

A heading on a chart is not automatically a question.

Figure. A question asks for a number you do not yet hold. A statement offers a number you can test against the tally. “How many visits?” is the question; “16 visits here” is the statement you check.

How it works

  1. Read the sentenceThis one.
  2. Ask: does it request a number, or give one?Question, or statement.
  3. Sort itThen collect or read.

2Representative Values

A representative value is a single number standing for a list: mean (fair share), or a middle, or a most-often, as taught. It is not every value in the list.

The biggest value is not automatically the representative.

Figure. Counts 7, 7 and 2. Sum 16, mean 16÷3 = 5.33 (dashed rule). Ordered 2, 7, 7 so the middle is 7. The most frequent value is also 7. Mean, median and mode are three tests on the same pile.

How it works

  1. Write the listThe given.
  2. Name which representative you were askedMean, or another taught one.
  3. Compute that oneOne number for the list.

3Visualising Data

A bar graph or pictograph is a picture of counts. Visualising means the bar-height or picture-count matches the table. A pretty colour that disagrees with the table is a lie.

The tallest bar is not a decoration contest — it is the largest count.

Figure. A bar’s height is the count. Monday 7, Tuesday 7, Wednesday 2. Changing the scale mid-chart would silently double a day. One key, one grid.

How it works

  1. Read the key or scaleWhat one picture or one grid is worth.
  2. Read a bar or a row of picturesA count.
  3. Demand it agrees with the tableOne data set.

4Data Detective

A data detective checks agreement: table, graph, and a statement about “most” or “least”. If they disagree, the statement fails. Detective work is the check, not a new story.

A caption that ignores the tallest bar is a miss you should catch.

Figure. A data detective reads the chart instead of guessing. Two days sit at 7 and one at 2, so the mode is the pair of 7s — Monday and Tuesday — not the shortest bar.

How it works

  1. Read the graph or tableEvidence.
  2. Read the claim“Most chose tea.”
  3. Keep or kill the claimDetective.

5A definition is a test you can run

A representative is a test: you can recompute it from the list. A definition that is only the word “average” without a method is a poster.

Calling the first number the mean is not the test.

Figure. A definition is a test you can run on the figure. The small square sits on the axis-aligned corner, so the right angle is earned by the legs, not by a tidy look.

How it works

  1. Write the listThe object.
  2. Run the taught methodThe test.
  3. If you cannot run it, you do not yet have the representativeName the method.

6Name the given before the unknown

The given is the table or the list. The unknown is a count, a representative, or whether a claim matches. Read the given counts first.

Inventing a 20 because the graph “looks tall” is a silent given.

Figure. Write the given counts before the unknown. Here the given pile is 7, 7 and 2; the unknown is the mean. Swapping those labels makes a sum you cannot check.

How it works

  1. Copy the numbers you were givenThe given.
  2. Name what is askedThe unknown.
  3. Then compute or compareGiven first.

7One worked case is enough at this class

One list (or one graph) is enough. A page of the same 12, 8, 5 clone does not add a new representative.

Ten twins of the same bar graph are still one case.

Figure. One worked case is enough at this class: 7 + 7 + 2 = 16, then 16 ÷ 3 = 5.33. The same three counts, one mean. No second invented pile.

How it works

  1. Read one table or graphThe case.
  2. A second only as a checkOptional.
  3. StopThis class.

8A miss: swapping the school name for the picture

A class-survey photo is a setting. The maths is the table. Counting smiling faces in the photo and skipping the key is the swap-miss.

A group photograph is not a bar graph.

Figure. A pictograph key must name what one picture is worth. Four pictures at “\blacksquare = 2 visits” is 8 visits. Swapping the school name into the key (“\blacksquare = school”) turns the picture into a label and the count vanishes.

How it works

  1. Keep the photo as a storyA setting.
  2. Read the table or the keyThe maths.
  3. Answer from those countsDo not swap.
A bar that disagrees with its table is
  1. A lie — picture and table must match
  2. Fine if the colour is nice
  3. A crore

Visualising is agreement, not decoration.

Notes

  • The official chapter title is “Connecting the Dots...”. 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.

Recap

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

Of Questions and Statements
A question asks; a statement reports. “How many students chose tea?” is a question. “12 chose tea” is a statement. Data work starts by knowing which you have.
Representative Values
A representative value is a single number standing for a list: mean (fair share), or a middle, or a most-often, as taught.
Visualising Data
A bar graph or pictograph is a picture of counts.
Data Detective
A data detective checks agreement: table, graph, and a statement about “most” or “least”.
A definition is a test you can run
A representative is a test: you can recompute it from the list.
Name the given before the unknown
The given is the table or the list. The unknown is a count, a representative, or whether a claim matches. Read the given counts first.

Practise Connecting the Dots...

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
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