Teacher Guide: Adding & Subtracting Decimals

@ Learning Objective 5-10 min lesson

Students will: Explore the addition and subtraction of multi-digit numbers with decimals to the thousandths, using strategies based on place value, properties of operations, and the relationship between addition and subtraction.

Why this matters for FAST: Adding and subtracting decimals appears frequently on the FAST assessment, often in real-world contexts like money and measurement. Students must correctly align decimal points and handle different numbers of decimal places.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Place value chart
Graph paper (optional)
Base-ten blocks (optional)
Colored pencils

! Common Misconceptions to Address

Misconception #1: Lining Up the Last Digits Instead of Decimal Points

Students write 5.6 + 3.48 as: 5.60 + 3.48, but some align the 6 with the 8, getting 5.6 + 348 or other incorrect arrangements.

How to Address:

"Always line up the decimal points FIRST! Then fill in zeros as placeholders if needed. The decimal points must be in a straight vertical line."

Misconception #2: Forgetting to Regroup (Borrow/Carry)

Students subtract 5.2 - 3.8 and get 2.6 (subtracting 2-8 as 8-2), forgetting they need to regroup from the ones place.

How to Address:

"Just like with whole numbers, when the top digit is smaller than the bottom digit, we need to regroup from the next place to the left. 5.2 - 3.8: Regroup to get 4.12, then 12-8=4 and 4-3=1. Answer: 1.4"

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Review adding and subtracting whole numbers using the standard algorithm. Ask: "What do we always line up when adding whole numbers?" (The ones place - the right side). Connect this to decimals: "With decimals, we line up the decimal points instead!"

2

Introduce Decimal Addition (2 min)

SAY THIS:

"When adding or subtracting decimals, the most important rule is: LINE UP THE DECIMAL POINTS! This ensures we're adding tenths to tenths, hundredths to hundredths, and so on."

Example: 4.5 + 2.38

4.50

+ 2.38

6.88

Add a zero placeholder: 4.5 = 4.50, then add normally

3

Teach Decimal Subtraction with Regrouping (2 min)

Example: 7.2 - 4.85

7.20

- 4.85

2.35

Add zero: 7.2 = 7.20. Regroup: can't do 0-5, so borrow from tenths.

SAY THIS:

"When subtracting, if the top digit is smaller than the bottom digit, regroup just like with whole numbers. Borrow 1 from the next place to the left, which gives you 10 more in the current place."

4

Show Different Place Values (2 min)

Demonstrate adding/subtracting when numbers have different numbers of decimal places:

12.5 + 3.478: Write as 12.500 + 3.478 = 15.978
8 - 2.75: Write as 8.00 - 2.75 = 5.25

Emphasize: "Adding zeros to the right of a decimal doesn't change the value!"

5

Guided Practice (2-3 min)

Work through these together:

6.7 + 8.45 = ?
10.3 - 4.67 = ?
15 - 8.246 = ?
2.5 + 0.375 + 1.25 = ?

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"What is 8.4 - 3.67?"

A) 5.27 B) 4.73 C) 4.27 D) 5.73

Correct answer: B) 4.73 (8.40 - 3.67, regrouping required)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Add decimal numbers Subtract decimal numbers Add and subtract decimals: word problems Estimate sums and differences of decimals Maps with decimal distances

^ Differentiation & Extension

For struggling students: Use graph paper to help with alignment - one digit per box, with the decimal point in its own box. Start with problems that have the same number of decimal places.

For advanced students: Challenge with multi-step word problems and problems requiring estimation to check reasonableness. Introduce adding 3+ decimals at once.

For home: Send Parent Activity sheet. Families can practice with shopping receipts and making change.