4.NF.7: Comparing Decimals

Visual Models for Comparing Decimals

1. Decimal Grids

Use 10×10 grids to represent decimals visually. Each grid represents one whole, each row represents one-tenth (0.1), and each small square represents one-hundredth (0.01). Shade the appropriate number of squares to compare decimals visually.

2. Number Lines

Place decimals on a number line to compare their values. Decimals closer to 1 are larger than decimals closer to 0. For example, place 0.75 and 0.8 on a number line to see that 0.8 is larger.

3. Place Value Charts

Create place value charts to compare decimals digit by digit, starting from the left. For example, when comparing 0.42 and 0.38, look at the tenths place first (4 > 3), so 0.42 > 0.38.

Strategies for Comparing Decimals

1. Compare Whole Numbers First

When comparing decimals, first look at the whole number part. If they're different, you can immediately determine which decimal is larger.

Example: Compare 3.45 and 2.78

• The whole number parts are 3 and 2
• Since 3 > 2, we know that 3.45 > 2.78

2. Compare Digit by Digit

If the whole number parts are the same, compare the digits in the tenths place. If those are the same, move to the hundredths place.

Example: Compare 0.63 and 0.67

• The whole number parts are both 0
• The tenths digits are both 6
• The hundredths digits are 3 and 7
• Since 3 < 7, we know that 0.63 < 0.67

3. Use Equivalent Decimals

Add zeros to the end of a decimal to make comparison easier. This doesn't change the value of the decimal.

Example: Compare 0.8 and 0.75

• Convert 0.8 to 0.80 (adding a zero doesn't change the value)
• Now compare 0.80 and 0.75
• Since 80 hundredths > 75 hundredths, we know that 0.8 > 0.75

Everyday Applications

1. Money

Compare prices when shopping:

• Which costs more: an item priced at $3.49 or one at $3.50?
• If you have $5.25, can you afford an item that costs $5.20?
• Which is the better deal: 16 oz for $2.89 or 20 oz for $3.45?

2. Measurements

Compare measurements in cooking, crafts, or sports:

• Which is longer: 4.25 inches or 4.3 inches?
• Who jumped farther: someone who jumped 3.85 meters or someone who jumped 3.9 meters?
• Which container holds more: one with 2.75 liters or one with 2.7 liters?

3. Weather

Compare temperatures or rainfall:

• Was it warmer on Tuesday (72.5°F) or Wednesday (72.45°F)?
• Did it rain more in April (3.25 inches) or May (3.2 inches)?

When Your Child Struggles

1. Use Money as a Familiar Context

If your child is having trouble comparing decimals, relate them to money. For example, 0.25 is like 25 cents, and 0.10 is like 10 cents. Ask, "Which would you rather have: 25 cents or 10 cents?"

2. Focus on Place Value

Make sure your child understands the place value system for decimals. Create a place value chart with columns for ones, tenths, and hundredths. Have your child place digits in the correct columns and compare values.

3. Use Visual Models

Draw decimal grids or number lines to help your child visualize the size of decimals. Seeing that 0.7 takes up more space on a number line than 0.5 can make the comparison more concrete.

4. Add Zeros for Clarity

Remind your child that adding zeros to the end of a decimal doesn't change its value. For example, 0.5 = 0.50 = 0.500. Adding zeros can make it easier to compare decimals with different numbers of decimal places.

5. Practice Reading Decimals Correctly

Make sure your child reads decimals correctly. For example, 0.45 is "forty-five hundredths" (not "point forty-five"). This helps reinforce the place value concept.

5-Minute Activities

Activity 1: Decimal War

Play a card game where each player draws cards to create a decimal (e.g., draw two cards for a decimal like 0.47). The player with the larger decimal wins the round. Use the comparison symbols to record each comparison.

Activity 2: Decimal Sort

Create cards with various decimals and have your child sort them from least to greatest. Start with 5-6 decimals and gradually increase the difficulty.

Activity 3: Decimal Number Line

Draw a number line from 0 to 1, marked in tenths. Give your child decimal cards and have them place each card in the correct position on the number line.

Activity 4: Price Comparison

Show your child two price tags (real or made-up) and ask which item costs more. For example, "Which costs more: a notebook for $2.59 or a folder for $2.65?"

Activity 5: Decimal Riddles

Give clues about a decimal, such as "I'm greater than 0.45 but less than 0.5" and have your child guess the decimal. Then switch roles.

Mid-Year Expectations

By the middle of the school year, your child should be able to:

• Understand that decimals represent parts of a whole
• Read and write decimals to the hundredths place
• Compare decimals with the same number of decimal places (e.g., 0.45 and 0.72)
• Correctly use the symbols <, >, and = when comparing decimals
• Represent decimals using visual models

End-of-Year Expectations

By the end of the school year, your child should be able to:

• Compare any two decimals to the hundredths place
• Compare decimals with different numbers of decimal places (e.g., 0.7 and 0.65)
• Justify their comparisons using place value reasoning
• Order three or more decimals from least to greatest or greatest to least
• Apply decimal comparison skills to solve real-world problems

Signs of Mastery

Your child has mastered this standard when they can:

• Consistently and accurately compare decimals to the hundredths place
• Choose appropriate strategies for different types of decimal comparisons
• Explain their reasoning when comparing decimals
• Use precise mathematical language and symbols when comparing decimals
• Apply decimal comparison skills to solve complex real-world problems
• Connect decimal comparisons to fraction comparisons (e.g., understanding that 0.25 = 1/4)

Questions to Check Understanding:

• "Which is greater, 0.38 or 0.4? How do you know?"
• "How can you use a number line to show that 0.75 is less than 0.8?"
• "If one runner finished in 12.45 seconds and another finished in 12.54 seconds, who was faster? How do you know?"
• "Place these decimals in order from least to greatest: 0.09, 0.9, 0.19, 0.91."

Below Grade Level

For students who need additional support with basic decimal concepts and simple decimal comparisons.

📥 Download Practice Worksheet

At Grade Level

For students who need practice with grade-level decimal comparison concepts.

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging decimal comparison concepts and applications.

📥 Download Challenge Worksheet