Ganita Prakash, period by period — fitted to your timetable.
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Place Value Unpacked: Reading Decimals Aloud
A Quick Recap of Decimals · Inductive
Watch for students who place the decimal point one position off when dividing by 10 — a common slip when the dividend has no existing decimal point. Use 123 ÷ 10 = 12.3 and 24 ÷ 100 = 0.24 side by side to show that counting zeroes in the divisor tells exactly how many places to shift.
0–8Students read 27.53 aloud and break it into place-value parts — 2 tens, 7 units, 5 tenths, 3 hundredths — on a chart drawn in their notebooks, internalising how the decimal point separates whole parts from fractional parts.
8–20Using the spice-buying context from section 12.1, students express 50 g, 100 g, 25 g, and 250 g as fractions of 1 kg, then rewrite each as a decimal, discovering that denominators of 10, 100, and 1000 map directly to tenths, hundredths, and thousandths columns.
20–32A class-wide fraction–decimal game (mirroring the Jonali–Pallabi game in section 12.1): teacher calls a fraction, pairs race to write the decimal and say the place-value reading aloud, reinforcing the connection between denominator size and decimal depth.
32–40Students derive the divide-by-power-of-ten rule from the pattern 123 ÷ 10 = 12.3, 24 ÷ 100 = 0.24, 12 ÷ 1000 = 0.012, then practise Example 1, section 12.2 p.69 ("Arshad buys 5 pens at ₹9.5 each….") as a preview of how this rule carries into multiplication.
Example 1, section 12.2 p.69 — Arshad buys 5 pens at ₹9.5 each. Cost = 9.5 × 5 = (95/10) × (5/1) = 475/10 = ₹47.5.
Which of the following correctly expresses the decimal 4.307 in expanded place-value form?
- A 4 ones + 3 tenths + 0 hundredths + 7 thousandths
- B 4 tens + 3 ones + 0 tenths + 7 hundredths
- C 4 ones + 3 hundredths + 0 tenths + 7 thousandths
- D 4 ones + 30 tenths + 7 thousandths
A. 4 ones + 3 tenths + 0 hundredths + 7 thousandths
What each wrong option reveals
- B The student has shifted the place-value columns one position left, treating the digit before the decimal point as tens rather than ones.
- C The student has swapped the tenths and hundredths columns, placing 3 in the hundredths position instead of the tenths position.
- D The student has regrouped 3 tenths as 30 tenths, showing confusion between place value and digit face value.
Also saved as 7 periods or 10 periods.
- 2Shifting the Point: Powers of Ten in Practice
A Quick Recap of Decimals - 3Fraction Bridges: Multiplying Decimals Through Fractions
Decimal Multiplication - 4Count the Places: The Decimal Multiplication Rule
Decimal Multiplication - 5Bigger or Smaller? Reasoning About Products
Decimal Multiplication - 6Dividing by Powers of Ten and Equivalent Fractions
Decimal Division - 7Long Division Extended: Decimal Quotients Step by Step
Decimal Division - 8Decimal Divisors and Word Problems
Decimal Division - 9When Does Division Ever End? Cycles and Conjectures
Decimal Division - 10Leap Years by Decimal: Accumulating the Extra Hours
Look Before You Leap! - 11Why Do Some Decimals Terminate? Denominators of 2s and 5s
Look Before You Leap! - 12Decimals at Work: A Chapter Closing
Synthesis
- 1. Large Numbers Around Us
- 2. Arithmetic Expressions
- 3. A Peek Beyond the Point
- 4. Expressions Using Letter-Numbers
- 5. Parallel and Intersecting Lines
- 6. Number Play
- 7. A Tale of Three Intersecting Lines
- 8. Working with Fractions
- 9. Geometric Twins
- 10. Operations with Integers
- 11. Finding Common Ground
- 12. Another Peek Beyond the Point
- 13. Connecting the Dots
- 14. Constructions and Tilings
- 15. Finding the Unknown
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