How to Explain Decimals to Sixth Graders

By sixth grade, students have encountered decimals, but now they need to master all four operations with them. This guide helps you explain decimal concepts clearly and build computational fluency that lasts.

Why Decimals Matter for Sixth Graders

Decimals are everywhere in daily life:

• Money: Every price and transaction uses decimals ($4.99)
• Measurement: Precise lengths, weights, volumes (5.25 inches)
• Sports: Statistics and times (batting average .325, 100m in 9.58 seconds)
• Science: Lab measurements require decimal precision
• Technology: Digital data often uses decimal representations

Mastering decimals prepares students for:

• Percentages and financial literacy
• Scientific notation
• Algebra with decimal coefficients
• Statistics and data analysis
• Real-world problem solving

Key Concepts Broken Down Simply

Decimal Place Value Review

┌─────────────────────────────────────────────────────────────────┐
│                    DECIMAL PLACE VALUE                          │
├──────┬──────┬──────┬──────┬──────┬──────┬──────┬──────┬────────┤
│ 100s │ 10s  │  1s  │  .   │ 10ths│100ths│1000ths│10000ths│     │
├──────┼──────┼──────┼──────┼──────┼──────┼──────┼──────┼────────┤
│      │  4   │  7   │  .   │  3   │  8   │  5   │  2   │        │
└──────┴──────┴──────┴──────┴──────┴──────┴──────┴──────┴────────┘

47.3852 = 40 + 7 + 0.3 + 0.08 + 0.005 + 0.0002
        = 40 + 7 + 3/10 + 8/100 + 5/1000 + 2/10000

Key pattern: Each place is 10 times smaller as you move right.

Comparing Decimals

Step 1: Line up decimal points
Step 2: Compare from left to right

Compare: 0.305 and 0.35

    0.305
    0.35  → 0.350 (add zero placeholder)

Compare place by place:
    0.305    Both have 0 ones ✓
    0.350    Both have 3 tenths ✓
             0 hundredths vs 5 hundredths
             0 < 5, so 0.305 < 0.35

Common mistake: Thinking more digits means larger number!

0.9 > 0.123  (9 tenths is more than 1 tenth)

Adding and Subtracting Decimals

The golden rule: LINE UP THE DECIMAL POINTS!

Example: 12.5 + 3.847

  WRONG          RIGHT
    12.5         12.500
  + 3.847       + 3.847
  -------       -------
                 16.347

Add placeholder zeros so columns line up.

Subtraction example: 5 - 2.73

    5.00
  - 2.73
  ------
    2.27

Rewrite 5 as 5.00, then subtract.

Multiplying Decimals

Method 1: Count decimal places

Example: 3.4 × 2.5

Step 1: Ignore decimals, multiply whole numbers
        34 × 25 = 850

Step 2: Count total decimal places in factors
        3.4 has 1 decimal place
        2.5 has 1 decimal place
        Total: 2 decimal places

Step 3: Place decimal in answer
        850 → 8.50 = 8.5

Answer: 3.4 × 2.5 = 8.5

Why this works: Think fractions!

3.4 × 2.5 = 34/10 × 25/10 = 850/100 = 8.50

Method 2: Estimation check

3.4 × 2.5 ≈ 3 × 3 = 9

Our answer (8.5) is close to 9 ✓
(If we got 85 or 0.85, we'd know something was wrong!)

Dividing Decimals

Case 1: Dividing by a whole number

Example: 15.6 ÷ 3

     5.2
    -----
3 ) 15.6
    15
    --
     0.6
     0.6
     ---
       0

Answer: 5.2

Just bring the decimal straight up into the quotient.

Case 2: Dividing by a decimal

Example: 4.5 ÷ 0.9

Step 1: Make divisor a whole number by multiplying by power of 10
        0.9 × 10 = 9

Step 2: Multiply dividend by same amount
        4.5 × 10 = 45

Step 3: Divide
        45 ÷ 9 = 5

Answer: 4.5 ÷ 0.9 = 5

Visual representation:

4.5 ÷ 0.9 = 4.5/0.9 = 4.5 × 10 / 0.9 × 10 = 45/9 = 5

More complex example: 2.76 ÷ 0.12

Move decimal 2 places (to make 0.12 become 12):
2.76 ÷ 0.12 = 276 ÷ 12 = 23

Check: 23 × 0.12 = 2.76 ✓

Visual Examples and Diagrams

Place Value Blocks

ONE           TENTH         HUNDREDTH
┌─────────┐   ┌─┐           ┌┐
│         │   │ │           ││
│         │   │ │           └┘
│         │   │ │          (tiny
│         │   └─┘           square)
└─────────┘  (strip)
(large
 square)

Representing 1.35:
┌─────────┐ ┌─┐┌─┐┌─┐ ┌┐┌┐┌┐┌┐┌┐
│    1    │ │ ││ ││ │ │││││││││
│  whole  │ │ ││ ││ │ └┘└┘└┘└┘└┘
└─────────┘ └─┘└─┘└─┘ 5 hundredths
            3 tenths

Number Line for Decimals

Zooming in on decimals between 0 and 1:

0    0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9   1.0
├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤

Zooming further (between 0.3 and 0.4):

0.30  0.31  0.32  0.33  0.34  0.35  0.36  0.37  0.38  0.39  0.40
├─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┤
                              ↑
                           0.35 is here

Area Model for Multiplication

2.3 × 1.4 = ?

        2       +     0.3
    ┌───────────┬───────────┐
    │           │           │
1   │    2      │    0.3    │   1 × 2 = 2
    │           │           │   1 × 0.3 = 0.3
    ├───────────┼───────────┤
    │           │           │
0.4 │    0.8    │   0.12    │   0.4 × 2 = 0.8
    │           │           │   0.4 × 0.3 = 0.12
    └───────────┴───────────┘

Total: 2 + 0.3 + 0.8 + 0.12 = 3.22

Answer: 2.3 × 1.4 = 3.22

Hands-On Activities

Activity 1: Decimal Grocery Shopping

Materials: Grocery ads or receipts, calculator

Instructions:

1. Give student a "budget" of $20.00
2. Have them "shop" from ads, adding prices
3. Calculate how much they spent and what's left
4. Find the cost per item for multi-packs

Activity 2: Measurement Practice

Materials: Ruler with centimeters/millimeters, various objects

Instructions:

1. Measure objects to the nearest tenth of a centimeter
2. Add measurements of several objects
3. Find the difference between longest and shortest
4. Calculate the average length

Activity 3: Decimal Card Games

Materials: Deck with decimal cards (0.1 to 0.99)

Games:

1. Decimal War: Higher decimal wins
2. Make 1: Draw cards and add to get as close to 1.00 as possible without going over
3. Decimal Sums: Draw two cards, multiply them mentally

Activity 4: Recipe Scaling

Materials: A recipe with decimal measurements

Tasks:

1. Double the recipe (multiply all by 2)
2. Make 1.5 batches (multiply by 1.5)
3. Make half a batch (multiply by 0.5)

Activity 5: Sports Statistics

Materials: Sports statistics from newspapers/websites

Tasks:

1. Compare batting averages or completion percentages
2. Add up game statistics
3. Calculate averages over multiple games

Common Mistakes and How to Fix Them

Mistake 1: Misaligning Decimal Points When Adding

Wrong:

    12.5
  + 3.847
  -------
    16.347  ← Actually calculated 12.5 + 3847!

Correct:

    12.500
  +  3.847
  --------
    16.347

Fix: Always rewrite problems with decimals aligned. Add zeros as placeholders.

Mistake 2: Placing Decimal Wrong in Multiplication

Wrong: 2.4 × 3.5 = 84.0 (just multiplied 24 × 35 and placed decimal randomly)

Correct: 2.4 × 3.5 = 8.40 = 8.4

Fix: Count decimal places in factors (1 + 1 = 2), then count that many places from the right in the answer.

Verification: 2.4 × 3.5 ≈ 2 × 4 = 8 (Estimate confirms 8.4 is reasonable)

Mistake 3: Comparing Decimals by Number of Digits

Wrong thinking: "0.125 > 0.2 because 125 > 2"

Correct: 0.2 > 0.125 (2 tenths > 1 tenth)

Fix: Line up decimals and compare place by place from left to right:

0.200
0.125
  ↑ Compare tenths first: 2 > 1, so 0.2 > 0.125

Mistake 4: Forgetting to Move Both Decimals in Division

Wrong: 4.5 ÷ 0.9 → Just do 4.5 ÷ 9 = 0.5

Correct: 4.5 ÷ 0.9 → Move both: 45 ÷ 9 = 5

Fix: Remember you're multiplying BOTH by the same power of 10 to keep the division equivalent.

Mistake 5: Dropping Trailing Zeros That Matter

Wrong: 5.00 - 2.73 = 2.27, so 5 - 2.73 = 2.7 (dropped the final 7)

Correct: Always use placeholders to maintain place value.

Fix: Rewrite whole numbers with appropriate decimal places before computing.

Practice Ideas for Home

Money Math Practice

1. Making Change: Practice making change from various amounts
2. Budget Planning: Plan a meal with a budget, calculating totals
3. Price Comparison: Find unit prices to compare deals
4. Tip Calculation: Calculate 15% or 20% tips at restaurants

Measurement Activities

1. Measure height in meters (with decimals)
2. Track temperature changes over a week
3. Measure and calculate perimeters of rooms in meters

Daily Practice Problems

Level 1: Addition/Subtraction

4.5 + 3.27 = ?
10 - 3.45 = ?
12.6 + 0.847 = ?

Level 2: Multiplication

3.4 × 5 = ?
2.5 × 2.5 = ?
0.7 × 0.8 = ?

Level 3: Division

15.6 ÷ 4 = ?
8.4 ÷ 0.7 = ?
2.56 ÷ 0.8 = ?

Level 4: Mixed Operations

3.5 × 2 + 1.75 = ?
10 - 2.4 × 3 = ?
(4.5 + 3.5) ÷ 2 = ?

Estimation Practice

For each problem, estimate first, then calculate:

1. 4.8 × 3.2 ≈ ? (estimate: 5 × 3 = 15, actual: 15.36)
2. 19.6 ÷ 4.1 ≈ ? (estimate: 20 ÷ 4 = 5, actual: 4.78...)
3. 12.3 + 8.75 ≈ ? (estimate: 12 + 9 = 21, actual: 21.05)

Connection to Future Math Concepts

Percentages

Decimals and percentages are interchangeable:
0.25 = 25%
0.075 = 7.5%

To find 15% of 80:
0.15 × 80 = 12

Scientific Notation

Very small decimals become scientific notation:
0.00045 = 4.5 × 10⁻⁴

Decimal skills are essential for this!

Algebra

Solve: 2.5x + 1.3 = 8.8
       2.5x = 7.5
       x = 3

Same decimal operations!

Statistics

Mean = Sum ÷ Count

Data: 3.5, 4.2, 2.8, 5.1, 4.4
Sum: 20.0
Mean: 20.0 ÷ 5 = 4.0

Finance and Real World

Interest: $1000 × 0.035 = $35 (3.5% interest)
Tax: $45.99 × 0.08 = $3.68 (8% tax)
Discount: $79.99 × 0.25 = $20.00 (25% off)

Quick Reference

┌────────────────────────────────────────────────────┐
│            DECIMAL QUICK REFERENCE                 │
├────────────────────────────────────────────────────┤
│ COMPARING: Line up decimals, compare left to right │
│                                                    │
│ ADD/SUBTRACT: Line up decimal points, use zeros   │
│   as placeholders                                  │
│                                                    │
│ MULTIPLY:                                         │
│   1. Multiply as whole numbers                    │
│   2. Count total decimal places in factors        │
│   3. Place decimal that many places from right    │
│                                                    │
│ DIVIDE BY DECIMAL:                                │
│   1. Move decimal in divisor to make whole number │
│   2. Move decimal in dividend same number of places│
│   3. Divide normally                              │
│                                                    │
│ ALWAYS ESTIMATE to check if answer is reasonable! │
└────────────────────────────────────────────────────┘

Tips for Teaching Success

1. Start with money: Most students already understand $3.50
2. Use estimation: Before calculating, estimate to check reasonableness
3. Emphasize place value: Understanding why operations work builds lasting skills
4. Connect to fractions: 0.5 = 1/2, 0.25 = 1/4 helps build number sense
5. Practice regularly: Short daily practice beats occasional long sessions

Decimal fluency is a foundational skill that students will use throughout their lives—in math class, in their careers, and in everyday situations. With consistent practice and real-world connections, your sixth grader will develop the confidence and competence they need.