A focused Grade 4 learning session for Comparing Decimals using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can compare decimals to the hundredths place and justify my answer.
Comparing Decimals means choosing a model, naming what each number means, and explaining the strategy.
Question: Look at the number line below. What decimal is shown by the arrow?
Why it works: The arrow points exactly halfway between \(0.6\) and \(0.7\). The midpoint is \(0.65\).
Answer: \(0.65\)
Question: Look at the place-value table below. What decimal has \(6\) tenths and \(2\) hundredths?
| Tenths | Hundredths | Decimal |
|---|---|---|
| \(6\) | \(0\) | \(0.60\) |
| \(6\) | \(2\) | ? |
Answer: \(0.62\)
Question: Look at the number line. What decimal is marked by the dot?
Answer: \(0.38\)
Question: Kai is at a lemonade stand. Pitcher A holds \(0.75\) liters. Pitcher B holds \(0.57\) liters. Which pitcher holds more lemonade?
Why it works: Compare the tenths place: \(7 > 5\), so \(0.75 > 0.57\). Pitcher A holds more lemonade.
Answer: Pitcher A holds more at \(0.75\) liters
Comparing Decimals 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.
Which comparison is true?
Answer C: \(0.6>0.59\)
Compare place by place: Write \(0.6\) as \(0.60\). Now both have the same number of decimal places. Since \(60 > 59\) hundredths, we have \(0.6 > 0.59\).
Which decimal is the smallest?
Answer A: \(0.35\)
When comparing decimals, look at the tenths place first---it has the most weight. \(0.35\) has \(3\) tenths; the others (\(0.53, 0.50, 0.55\)) all have \(5\) tenths. Since \(3 < 5\), the number with fewer tenths is automatically the smallest, no matter what's in the hundredths place. So \(\mathbf{0.35}\) is the smallest. \checkmark
How does \(0.4\) compare to \(0.40\)?
Answer C: \(0.4=0.40\)
A trailing zero doesn't change the value. Both \(0.4\) and \(0.40\) represent the same amount: \(4\) tenths, or \(40\) hundredths.
Order these decimals from least to greatest: \(0.72\), \(0.27\), \(0.70\), \(0.07\).
Answer A: \(0.07, 0.27, 0.70, 0.72\)
Compare the tenths place first: \(0 < 2 < 7\). For the two decimals with tenths \(= 7\), compare hundredths: \(0 < 2\), so \(0.70 < 0.72\).
Look at the number line below. What decimal is shown by the arrow?
Answer B: \(0.65\)
The arrow points exactly halfway between \(0.6\) and \(0.7\). The midpoint is \(0.65\).
Which shows the correct comparison?
Answer B: \(0.8<0.81\)
Rewrite \(0.8\) as \(0.80\) to see it clearly. Comparing: \(80 < 81\) hundredths, so \(0.8 < 0.81\).
Which decimal is greatest?
Answer B: \(0.84\)
Look at the tenths place: \(0.84\) has \(8\) tenths while the others have \(4\) tenths. Since \(8 > 4\), \(0.84\) is the largest.
Ava is comparing two running times. Her first race was \(0.55\) seconds and her second race was \(0.50\) seconds. Which time was faster?
Answer B: \(0.50\) seconds (second race)
Smaller numbers are faster! Since \(0.50 < 0.55\), the second race at \(0.50\) seconds is the faster time.
What is the correct way to order \(0.91\), \(0.19\), \(0.99\), and \(0.11\) from greatest to least?
Answer A: \(0.99, 0.91, 0.19, 0.11\)
Start with tenths: \(9 > 1\). Among the two with tenths \(= 9\), compare hundredths: \(9 > 1\), so \(0.99 > 0.91\). Among the two with tenths \(= 1\), compare hundredths: \(9 > 1\), so \(0.19 > 0.11\).
Look at the grid below with hundredths shaded. What decimal is shown?
Answer C: \(0.73\)
Count the shaded squares: \(7\) full columns (that's \(70\) squares) plus \(3\) extra squares make \(73\) squares total. So the decimal is \(73\) hundredths \(= 0.73\).
Which decimal is between \(0.3\) and \(0.4\)?
Answer B: \(0.35\)
\(0.35\) fits perfectly between \(0.3\) and \(0.4\). The other options fall outside this range.
