CBSE Class 4 · Mathematics
Sharing and Measuring
Official NCERT chapter from Math-Mela (book code demm1). ExamMaster notes are original teaching at CBSE Class 4 depth.
This lesson follows the official chapter “Sharing and Measuring” in Math-Mela. 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 4
- Easy level
- 8 concepts
2Parts and wholes: a half is one of two equal parts
Halves are two matching pieces of one whole. Each is \frac{1}{2}.
Two pieces that do not match are not halves.
Figure. A half is one of two parts that have the same width. Colouring one part names the half. The empty part is the other half, not leftover scrap.
How it works
- Split into two equal partsSame size.
- Take oneOne half.
- Check the leftoverThe other half must match.
3A quarter is one of four equal parts
Quarters are four matching pieces. Each is \frac{1}{4}. Two quarters make one half of the same whole.
Four unequal wedges are not quarters.
Figure. A quarter is one of four matching parts. The coloured strip is the numerator 1; the four strips together are the denominator 4.
How it works
- Split into four equal partsSame amount.
- Take one\frac{1}{4}.
- Two such parts\frac{2}{4} = \frac{1}{2} of that whole.
4Numerator counts the coloured parts
In \frac{3}{4}, 3 is how many equal parts you coloured. 4 is how many equal parts the whole was cut into.
Swapping them names a different share.
Figure. The denominator is how many equal parts the whole was cut into. The numerator is how many of those parts are coloured. Here three of four fourths are coloured, so the amount is 3/4.
How it works
- Count equal parts of the wholeDenominator.
- Count the coloured onesNumerator.
- Write coloured over total partsThat is the fraction.
Three of four equal strips
A ribbon is 4 equal strips. You colour 3. What fraction is coloured?
- Equal parts4
- Coloured3
- Fraction3/4
Pro tip. Numerator is the coloured count. Denominator is the equal-part count of the whole.
5Same amount, new writing
\frac{2}{4} and \frac{1}{2} can name the same share of one sheet. The writing changed; the paper did not grow.
New writing is not a new extra piece.
Figure. The coloured length is the same on both bars: one half, or two fourths. A dashed line marks that shared end. New writing does not change the amount.
How it works
- Fix the wholeSame sheet.
- See two writings2 of 4, or 1 of 2.
- Check they cover the same regionThen they are the same share.
7Adding only when the parts match
You can add \frac{1}{4} + \frac{1}{4} of the same sheet. That is \frac{2}{4}.
Adding a half of one sheet to a quarter of another is two wholes mixed.
Figure. Addition waits until both amounts are written in the same part-size. Here every strip is a fourth, so one fourth plus two fourths is three fourths. Different part-sizes cannot be stacked.
How it works
- Same wholeDo not swap the sheet.
- Same kind of part, or rewrite firstQuarters with quarters.
- Add the numeratorsDenominator stays the part-size.
8A leftover sliver means the parts were not equal
If four “quarters” leave a sliver unused, those pieces were not quarters of this whole.
Do not hide the sliver and still say fourths.
Figure. A leftover sliver after a share means the parts were not equal. Two matching halves leave no sliver. A big piece and a small piece leave a scrap that is not a half.
How it works
- See a leftover sliverUnused paper.
- Ask if the four pieces matchedIf not, not quarters.
- Redo the splitEqual first.
\frac{2}{4} of one sheet is the same share as
- \frac{1}{2} of that sheet
- \frac{1}{4} of that sheet
- Two whole sheets
Same region, new writing.
Notes
- The official chapter title is “Sharing and Measuring”. 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
- One half = \frac{1}{2}; one quarter = \frac{1}{4}.
- \frac{2}{4} = \frac{1}{2} of the same whole.
- Share of a length = (fraction) \times (whole length in one unit).
Recap
Hold these pegs from the official chapter “Sharing and Measuring”. The wording is ExamMaster’s teaching, not a textbook recap.
- One sheet shared is equal parts first
- Fair share of one sheet means parts that match.
- Parts and wholes: a half is one of two equal parts
- Halves are two matching pieces of one whole.
- A quarter is one of four equal parts
- Quarters are four matching pieces. Each is \frac{1}{4}. Two quarters make one half of the same whole.
- Numerator counts the coloured parts
- In \frac{3}{4}, 3 is how many equal parts you coloured.
- Same amount, new writing
- \frac{2}{4} and \frac{1}{2} can name the same share of one sheet.
- Measure a share of a length with the same unit
- Half of a 12-span rope is 6 spans only if you used the same span end to end.
Practise Sharing and Measuring
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