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Class 7 Maths · Chapter 3 · NCERT (gegp103)

A Peek Beyond the Point: common misconceptions

See the tempting mistake students make in A Peek Beyond the Point, why it feels right at first glance, and a worked visual example that shows the right idea.

The tempting mistake & worked visual

Which decimal is larger?

Wrong

0.35 is greater than 0.4 because 35 is greater than 4.

Why it feels right. I compare the digits after the point as whole numbers.

Right

Compare tenths with tenths and hundredths with hundredths.

Worked example

0.35 · 35 squares
0.4 = 0.40 · 40 squares
Both grids have 100 equal squares. The grid for 0.40 has five more shaded squares than the grid for 0.35.
  1. Write 0.4 as 0.40.
  2. On a hundred-square, 40 squares cover more than 35 squares.

If your child says… (8 concept checks in this chapter)

As you work through A Peek Beyond the Point, listen for these everyday misunderstandings and use the prompt alongside each one.

If your child says… “I only count the three tenths left over.”

Ask together
How many tenths cover the length before your leftover part?
What’s true
The complete unit contributes another ten tenths.
2. A Hundredth Part See how to teach this step →

If your child says… “Hundredths are bigger because a hundred is bigger than ten.”

Ask together
How many little squares fit inside the shaded tenth?
What’s true
Dividing the same whole into more equal pieces makes each piece smaller.
3. Decimal Place Value See how to teach this step →

If your child says… “I can leave out the zero and write 1.5.”

Ask together
Without the zero, which heading would the five sit under?
What’s true
Removing this zero moves five from hundredths into tenths.
4. Decimal Place Value See how to teach this step →

If your child says… “Twelve tenths is 0.12.”

Ask together
After ten tenths fill a whole, how many tenths remain?
What’s true
Twelve tenths exceed a whole, so the whole-number part cannot be zero.
5. Units of Measurement See how to teach this step →

If your child says… “Every unit change moves the point one place.”

Ask together
How many centimetres fill this whole metre?
What’s true
The conversion depends on how many smaller units fill the larger unit.
6. Locating and Comparing Decimals — There is Zero Dilemma! See how to teach this step →

If your child says… “0.50 must be different because it has another digit.”

Ask together
Where do five tenths and fifty hundredths land on the tape?
What’s true
The five still counts tenths, and the final zero adds no hundredths.
7. Addition and Subtraction of Decimals See how to teach this step →

If your child says… “Five wholes and twelve tenths make 5.12.”

Ask together
How many of those twelve tenths can become another whole?
What’s true
Twelve tenths contain another whole and two remaining tenths.
8. Deceptive Decimal Notation See how to teach this step →

If your child says… “4.5 hours after noon means five minutes past four.”

Ask together
How many minutes did the half-turn cover?
What’s true
Five tenths of an hour is half an hour, which contains thirty minutes.

Use this chapter three ways