Quiz Answer Explanations

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📚 Part 1: Multiple Choice — Answers & Explanations

1. Which number sentence shows the correct sum using models for $3.45 + $2.60?

$5.95

$6.05 — Correct

$6.15

$5.55

Explanation: Align decimal places and add. 3.45 + 2.60 = 5 ones and 0.05 left: 3.45 + 2.60 = 6.05. Using place-value blocks, hundredths add to 5 hundredths, tenths sum to 0 with a carry to the ones.

2. Subtract using a place-value model: 5.00 − 3.27 = ?

1.63

1.73 — Correct

2.73

1.07

Explanation: Borrow from the ones: 5.00 − 3.27 = (4.100) − 3.27 = 1.73. Show borrowing in tenths and hundredths on a place-value chart.

3. Which description matches the decimal 2.34 when shown by place value blocks?

2 ones, 3 tenths, 4 hundredths — Correct

23 ones, 4 tenths

2 tens, 3 ones, 4 tenths

2 ones, 34 tenths

Explanation: 2.34 is 2 ones + 0.3 (three tenths) + 0.04 (four hundredths). Place-value labels must match tenths and hundredths, not combine them incorrectly.

4. Estimate and check all that apply: 4.76 + 3.29 ≈ _____

8.05 — Correct

8.1 — Correct

8.0 — Correct

7.9

Explanation: Exact sum is 8.05. Rounding to the nearest tenth gives 8.1. Rounding to the nearest whole number gives 8.0. 7.9 is not a reasonable estimate for this sum.

✏️ Part 2: Short Answers & Models — Solutions with Steps

5. Use a place-value model to find 3.58 + 1.47. Show any regrouping and write the sum.

Hundredths: 8 + 7 = 15 → write 5 hundredths, carry 1 tenth.
Tenths: 5 + 4 + 1(carry) = 10 → write 0 tenths, carry 1 one.
Ones: 3 + 1 + 1(carry) = 5.

Answer: 5.05. Explanation: Regrouping shown in the steps above; align decimal points when using columns or grids.

6. Subtract using a model or step-by-step work: 6.00 − 2.58 = _______

Start with 6.00. Borrow 1 from ones → 5 ones = 4 tenths + 10 tenths etc.
Hundredths: 00 − 58 → borrow from tenths: (10 hundredths) − 8 = 2 hundredths.
Tenths after borrowing: (9 tenths) − 5 = 4 tenths. Ones: 5 − 2 = 3.

Answer: 3.42. Explanation: Show borrowing in place-value columns; label units (ones, tenths, hundredths).

7. Word problem: A runner completed 2.35 miles on Monday and 1.48 miles on Tuesday. How many miles did they run in total?

Align decimals:
2.35
+1.48
----
Hundredths: 5 + 8 = 13 → 3 hundredths, carry 1 tenth.
Tenths: 3 + 4 + 1 = 8 tenths.
Ones: 2 + 1 = 3.

Answer: 3.83 miles. Explanation: Always label units (miles) and show regrouping in hundredths and tenths.

8. Word problem: The temperature rose from 32.5°F to 35.2°F. What was the change in temperature?

Subtract: 35.2 − 32.5
Align decimals:
35.2
−32.5
----
Tenths: 2 − 5 → borrow 1 from ones: becomes 12 − 5 = 7 tenths.
Ones: 4 − 2 = 2.

Answer: 2.7°F. Explanation: Align decimal points and show borrowing in the tenths place; include unit °F.

🧭 Teacher Notes — Lesson Support & Extensions

I can: Add and subtract decimals using place-value and area models.

Success criteria: Align decimal points, use place-value columns or 10x/100x models, show regrouping/borrowing, and label units (dollars, miles, °F).

Differentiation strategies: Provide a partially filled place-value chart or base-ten blocks image for students who need support; allow calculators for checking only; use one-step problems before two-step; pair students for peer modeling.

Extension activities: Create and solve a two-step word problem using both addition and subtraction of decimals (include money and distance). Convert a decimal sum into fraction form and compare models.

Dyslexia-friendly options: Use larger spacing and color-coded columns, read problems aloud, and provide audio or a partially completed place-value chart.