5.NBT.7: Operations with Decimals

Visual Models for Decimal Operations

1. Decimal Grids

Use 10×10 grids where the whole grid = 1, each row = 0.1, and each small square = 0.01. Shade areas to represent decimal values and show operations visually. This helps children understand the place value concepts behind decimal operations.

2. Number Lines

Use number lines to show decimal addition and subtraction. For 3.45 + 2.67, start at 3.45 and move 2.67 units to the right to reach 6.12. For subtraction, move to the left. This visual representation helps children see the magnitude of decimal numbers.

3. Area Models for Multiplication

Draw rectangles to show decimal multiplication. For 2.5 × 1.8, create a rectangle with sides 2.5 and 1.8, then find the area (4.5). This connects to previous learning about area models for whole number multiplication.

4. Money Models

Use dollars and cents to model decimal operations. For example, $3.45 + $2.67 = $6.12, or $7.56 ÷ 1.2 = $6.30. This connects decimal operations to the familiar context of money.

Everyday Activities

1. Shopping Math

When shopping, have your child calculate totals, discounts, or change. "If this shirt costs $12.99 and is 25% off, what's the sale price?" or "If we buy 3 items at $4.25 each, what's our total?" These real-world calculations provide meaningful practice with decimal operations.

2. Recipe Scaling

When cooking, have your child help scale a recipe. "This recipe calls for 1.5 cups of flour, but we want to make 2.5 times the amount. How much flour do we need?" This requires multiplying decimals in a practical context.

3. Measurement Activities

Measure items around the house using a ruler with centimeters and millimeters. Convert between units and perform calculations with the measurements. "This book is 1.25 cm thick. If we stack 8 books, how tall will the stack be?" This connects decimals to measurement.

4. Budget Game

Give your child a pretend budget and have them plan purchases, calculate totals, and determine how much money they have left. This provides practice with all four operations using decimals in a financial context.

Strategies When Your Child Struggles

1. Decimal Point Alignment

For addition and subtraction, use graph paper or draw vertical lines to align decimal points. Say "decimal points always line up" as a reminder. This visual organization helps prevent place value errors.

2. Decimal Multiplication Rule

Teach the rule: "Count the total number of decimal places in the factors, then count that many places from the right in the product." For 2.5 × 1.8: one decimal place plus one decimal place equals two decimal places in the answer.

3. Division Decimal Placement

For division, move the decimal point in both numbers the same number of places to create a whole number divisor. For 7.56 ÷ 1.2, rewrite as 75.6 ÷ 12. This simplifies the division process while maintaining the correct relationship.

4. Estimation Check

Before calculating, round the decimals to estimate the answer. This helps catch major errors in decimal point placement. For example, 3.45 + 2.67 is about 3.5 + 2.7 = 6.2, so the exact answer should be close to this.

5. Money Connection

If your child understands money, relate decimal problems to dollars and cents to make them more concrete. This familiar context can help bridge understanding of abstract decimal concepts.

5-Minute Activities

Activity 1: Decimal War

Play with a deck of cards (face cards = 0, aces = 1). Each player draws two cards to create a decimal (first card.second card). Players can choose to add, subtract, multiply, or divide their decimals, and the highest result wins.

Activity 2: Estimation Challenge

Give your child a decimal operation and ask them to estimate the answer by rounding. Then have them solve it exactly and compare. This builds number sense and helps catch calculation errors.

Activity 3: Error Hunt

Show your child a decimal calculation with an intentional error (usually in decimal point placement). Ask them to find and fix the mistake. This develops critical thinking and reinforces proper procedures.

Activity 4: Real-World Problems

Create quick word problems using decimals: "If one gallon of gas costs $3.45 and you need 5.2 gallons, how much will you pay?" This connects decimal operations to practical applications.

Mid-Year Expectations

By the middle of 5th grade, your child should be able to:

• Add and subtract decimals to the hundredths place with proper alignment
• Multiply a decimal by a whole number
• Use estimation to check if answers are reasonable
• Explain their reasoning for decimal point placement

End-of-Year Expectations

By the end of 5th grade, your child should be able to:

• Add and subtract decimals fluently with proper alignment
• Multiply decimals by decimals and correctly place the decimal point
• Divide decimals using an appropriate strategy
• Solve multi-step word problems involving decimal operations

Mastery Signs

Your child has mastered this standard when they can:

• Add and subtract decimals with proper alignment consistently
• Multiply decimals and correctly place the decimal point
• Divide decimals using an appropriate strategy
• Explain their reasoning for each operation
• Apply decimal operations to solve real-world problems
• Estimate to check if answers are reasonable

Questions to Ask:

Ask your child to solve these problems and explain their process:

• 3.45 + 2.67 = ?
• 7.56 - 3.29 = ?
• 2.5 × 1.8 = ?
• 7.56 ÷ 1.2 = ?

Ask them to explain why the decimal point is placed where it is in each answer.

Below Grade Level

Practice problems focusing on single decimal place operations with visual supports and step-by-step guidance.

📥 Download Practice Worksheet

At Grade Level

Standard practice with all four operations using decimals to the hundredths place in various contexts.

📥 Download Grade Level Worksheet

Above Grade Level

Advanced problems involving multiple operations, thousandths place decimals, and complex real-world applications.

📥 Download Challenge Worksheet