A focused Grade 6 learning session for Decimal Operations using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving decimal operations.
Decimal Operations means choosing a model, naming what each number means, and explaining the strategy.
Question: The place-value chart shows a decimal. What is the digit in the hundredths place?
| Ones | Tenths | Hundredths | Thousandths |
|---|---|---|---|
| \(3\) | \(2\) | \(7\) | \(5\) |
Why it works: Reading the chart: the digit in the hundredths place is in the third column, which is \(7\).
Answer: \(7\)
Question: Place-value chart of a decimal is shown. What is the number in standard form?
| Ones | Tenths | Hundredths |
|---|---|---|
| \(5\) | \(4\) | \(8\) |
Answer: \(5.48\)
Question: A jogger runs \(2.25\) km in the morning and \(3.75\) km in the evening. What is the total distance?
Answer: \(6.0\) km
Question: A recipe calls for \(3.5\) cups of flour. If you are making double the recipe, how much flour do you need?
Why it works: Double means multiply by \(2\): \(3.5 \times 2 = 7\) cups.
Answer: \(7\) cups
Decimal Operations becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is \(4.6\times0.8\)?
Answer A: \(3.68\)
Treat it like whole numbers first: \(46\times8=368\). Together the factors tuck in two decimal places, so the "real" answer is cozy at \(3.68\).
Compute: \(12.7+8.45\)
Answer D: \(21.15\)
Align decimal points: \(12.70 + 8.45 = 21.15\). Stack and add, carrying as needed.
What is \(25.6 - 13.8\)?
Answer A: \(11.8\)
Align the decimal points. In the tenths place, \(6\) is smaller than \(8\), so regroup one whole as ten tenths: the \(5\) becomes \(4\) and the tenths become \(16\). Then \(16 - 8 = 8\) tenths, \(4 - 3 = 1\) one, and \(2 - 1 = 1\) ten, so the result is \(11.8\).
Estimate the product: \(7.9 \times 4.2\). Which is closest?
Answer A: \(32\)
Roughly, \(8 \times 4 = 32\) since \(7.9\) is near \(8\) and \(4.2\) is near \(4\). That ballpark is what estimation is for---save the exact digits for when you need them.
A receipt shows three items: $5.25, $12.99, and $8.50. What is the total?
Answer A: $26.74
Add: $5.25 + $12.99 + $8.50 = $26.74. Align decimal points for money.
Divide: \(18.4 \div 4\)
Answer A: \(4.6\)
Sharing \(18.4\) across four equal groups yields \(4.6\). Multiply back cheerfully: \(4 \times 4.6 = 18.4\) feels just right.
Which multiplication has the decimal point in the correct place?
Answer C: \(2.3 \times 5.1 = 11.73\)
\(23 \times 51 = 1173\). We have \(1 + 1 = 2\) decimal places total, so \(11.73\) is correct.
A recipe calls for \(3.5\) cups of flour. If you are making double the recipe, how much flour do you need?
Answer C: \(7\) cups
Double means multiply by \(2\): \(3.5 \times 2 = 7\) cups.
Find the sum: \(0.75 + 1.4 + 2.1\)
Answer B: \(4.25\)
Add: \(0.75 + 1.40 + 2.10 = 4.25\). Align all decimal points first.
What is \(0.06 \times 0.8\)?
Answer A: \(0.048\)
\(6 \times 8 = 48\). We have \(2 + 1 = 3\) decimal places total, so \(0.048\) is correct.
A pencil is \(0.15\) meters long. A pen is \(0.08\) meters long. How much longer is the pencil?
Answer A: \(0.07\) meters
Subtract: \(0.15 - 0.08 = 0.07\) meters. Align decimal points.
