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Maths • Base Ten & Decimals

Decimal Detective Lab

Compare, round, add, subtract, multiply, and divide decimals in real-world measurement and money problems.

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Activities

Learning Goals

  • ✓Compare decimals to the thousandths place.
  • ✓Round decimals to a given place value.
  • ✓Add and subtract decimals by lining up decimal points.
  • ✓Multiply decimals and place the decimal correctly.
  • ✓Divide decimals by whole numbers.

Mini Lesson

  1. 1Decimals must be lined up by place value before adding or subtracting.
  2. 2Placeholder zeros help keep digits in the correct columns.
  3. 3When comparing decimals, line up the decimal points and compare from left to right.
  4. 4When rounding, check the digit to the right of the target place.
  5. 5When dividing a decimal by a whole number, move the decimal point straight up into the quotient.
decimaltenthshundredthsthousandthsplaceholder zeroroundingcompare

Interactive Activities

Tap an answer choice. The card will show feedback, the correct answer, visual model, and step-by-step explanation.

🏎️
Activity 1Compare Decimalsdecimal-place-value

Race Car Decimal Comparison

Question

Race car A finished a lap in 4.205 seconds. Race car B finished in 4.25 seconds. Which car had the faster time?

Instruction

The faster car has the smaller time. Line up the decimal points and compare place values.

💡 Teacher Hint

Write 4.25 as 4.250 so both numbers have thousandths.

👁️ Show Visual Model: Place Value Chart
Model Type: place-value-chart
Ones . Tenths  Hundredths  Thousandths
  4  .    2        0            5   ← Car A
  4  .    2        5            0   ← Car B

Compare left to right.
Hundredths: 0 < 5
Therefore: 4.205 < 4.250
Car A is faster.
✅ Show Step-by-Step Answer
  1. 1Write Car B's time as 4.250.
  2. 2Compare the ones: both have 4.
  3. 3Compare the tenths: both have 2.
  4. 4Compare the hundredths: Car A has 0, Car B has 5.
  5. 5Since 0 < 5, 4.205 < 4.250.
  6. 6The smaller time is faster, so Car A is faster.
CCSS 5.NBT.A.3
🔬
Activity 2Round Decimalsdecimal-place-value

Round the Wire Weight

Question

A science experiment requires a piece of wire that weighs 18.367 grams. Round this weight to the nearest hundredth.

Instruction

Find the hundredths place, then look at the thousandths digit to decide whether to round up.

💡 Teacher Hint

The hundredths digit is 6. The thousandths digit is 7.

👁️ Show Visual Model: Number Line Model
Model Type: number-line
18.360       18.365       18.370
  └────────────┴────────────┘
                  ↑
               18.367

18.367 is closer to 18.370 than 18.360.
Rounded answer: 18.37 grams
✅ Show Step-by-Step Answer
  1. 1Locate the hundredths digit in 18.367. It is 6.
  2. 2Look to the digit on the right, the thousandths digit. It is 7.
  3. 3Since 7 is 5 or greater, round the hundredths digit up.
  4. 418.367 becomes 18.37 grams.
CCSS 5.NBT.A.4
📚
Activity 3Add Decimalsquiz

Bookstore Decimal Addition

Question

Maya bought a book for $24.56 and a bookmark for $8.90. How much did she spend in total?

Instruction

Line up the decimal points and add. Use a placeholder zero when needed.

💡 Teacher Hint

Add 24.56 + 8.90.

👁️ Show Visual Model: Decimal Alignment
Model Type: decimal-alignment
2 4 . 5 6
+    8 . 9 0
────────────
   3 3 . 4 6

Total spent: $33.46
✅ Show Step-by-Step Answer
  1. 1Write 24.56.
  2. 2Write 8.90 underneath it with decimal points aligned.
  3. 3Add hundredths: 6 + 0 = 6.
  4. 4Add tenths: 5 + 9 = 14, write 4 and carry 1.
  5. 5Add ones and tens carefully.
  6. 6The total is $33.46.
CCSS 5.NBT.B.7
🪢
Activity 4Subtract Decimalsquiz

Rope Decimal Subtraction

Question

A rope is exactly 14.0 meters long. Ben cuts off a piece that is 5.32 meters long. How much rope is left?

Instruction

Write 14.0 as 14.00, line up the decimals, regroup, and subtract.

💡 Teacher Hint

Use 14.00 - 5.32.

👁️ Show Visual Model: Regrouping Decimal Subtraction
Model Type: regrouping
1 3   9   10
   1 4 . 0   0
-    5 . 3   2
──────────────
     8 . 6   8

Rope left: 8.68 meters
✅ Show Step-by-Step Answer
  1. 1Rewrite 14.0 as 14.00.
  2. 2Line up the decimal points.
  3. 3Regroup because 0 hundredths cannot subtract 2 hundredths.
  4. 4After regrouping, subtract hundredths, tenths, ones, and tens.
  5. 5The remaining rope is 8.68 meters.
CCSS 5.NBT.B.7
🧃
Activity 5Multiply Decimalsquiz

Juice Bottle Cost

Question

A small bottle of juice costs $4.25. If Leo buys 3 bottles, how much will it cost?

Instruction

Multiply 4.25 by 3. Think of it as repeated addition or multiply as whole numbers and place the decimal.

💡 Teacher Hint

425 × 3 = 1,275. Then place the decimal two spots from the right.

👁️ Show Visual Model: Decimal Multiplication Model
Model Type: decimal-alignment
4.25   → 2 decimal places
×    3
──────
 12.75   → decimal placed 2 spots from the right

Total cost: $12.75
✅ Show Step-by-Step Answer
  1. 1Ignore the decimal first and multiply 425 × 3.
  2. 2425 × 3 = 1,275.
  3. 3The original number 4.25 has two decimal places.
  4. 4Place the decimal two digits from the right.
  5. 5The total is $12.75.
CCSS 5.NBT.B.7
🎀
Activity 6Divide Decimals by Whole Numbersquiz

Ribbon Division

Question

A 15.5-inch piece of ribbon needs to be cut into 5 equal pieces. How long will each piece be?

Instruction

Divide 15.5 by 5. Move the decimal point straight up into the quotient.

💡 Teacher Hint

5 goes into 15 three times. Then divide the 0.5.

👁️ Show Visual Model: Long Division with Decimal
Model Type: long-division
3 . 1
    ┌───────
5   │ 1 5 . 5
     -1 5
     ────
        0   5
           -5
           ──
            0

Each piece is 3.1 inches.
✅ Show Step-by-Step Answer
  1. 1Set up 15.5 ÷ 5.
  2. 2Move the decimal straight up into the quotient.
  3. 35 goes into 15 three times.
  4. 4Subtract 15 from 15 to get 0.
  5. 5Bring down 5 tenths.
  6. 65 goes into 5 one time.
  7. 7The quotient is 3.1 inches.
CCSS 5.NBT.B.7

Exit Ticket

Why should decimal points be lined up when adding or subtracting decimals?

Show Suggested Answer

Decimal points must be lined up so each digit is added or subtracted with the same place value.

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