Teacher Guide: Multiplying Decimals

@ Learning Objective 5-10 min lesson

Students will: Multiply multi-digit numbers with decimals to the hundredths, including using a standard algorithm with procedural fluency. Students will understand how to place the decimal point in the product by counting decimal places in the factors.

Why this matters for FAST: Multiplying decimals appears frequently on the FAST assessment, often in real-world contexts like calculating costs, areas, and measurements. Students must demonstrate procedural fluency with the standard algorithm.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Place value chart
Graph paper (optional)
Calculator (for checking)
Colored pencils

! Common Misconceptions to Address

Misconception #1: Lining Up Decimals When Multiplying

Students try to line up decimal points when multiplying (like they do with addition). This leads to incorrect alignment and wrong answers.

How to Address:

"When multiplying decimals, IGNORE the decimal points at first! Line up the numbers on the right side like whole numbers. Multiply normally, THEN count decimal places to place the decimal in your answer."

Misconception #2: Miscounting Decimal Places

Students count decimal places incorrectly or forget to count places in both factors. For example, 2.3 x 4.5 - they might only count 1 decimal place instead of 2.

How to Address:

"Count the decimal places in BOTH numbers you're multiplying. 2.3 has 1 decimal place. 4.5 has 1 decimal place. 1 + 1 = 2 decimal places in the answer. 23 x 45 = 1035, so 2.3 x 4.5 = 10.35"

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Review multiplying whole numbers. Ask: "What is 23 x 4?" (92). "Good! We're going to use this same skill to multiply decimals!"

2

Introduce Decimal x Whole Number (2 min)

SAY THIS:

"When multiplying decimals, we use THREE steps: 1) Ignore the decimal and multiply like whole numbers, 2) Count decimal places in BOTH factors, 3) Put that many decimal places in your answer."

Example: 2.3 x 4

23

x 4

92

2.3 has 1 decimal place. 4 has 0 decimal places.

Total: 1 + 0 = 1 decimal place. Answer: 9.2

3

Teach Decimal x Decimal (2 min)

Example: 3.4 x 2.5

34

x 25

170

680

850

3.4 has 1 decimal place. 2.5 has 1 decimal place.

Total: 1 + 1 = 2 decimal places. Answer: 8.50 or 8.5

4

Teach the Rule for Placing Decimals (2 min)

THE DECIMAL RULE

Count decimal places in Factor 1 + Factor 2 = Decimal places in Product

0.5 x 3 = 1.5 (1 decimal place + 0 = 1 decimal place)
0.6 x 0.4 = 0.24 (1 + 1 = 2 decimal places)
1.25 x 0.3 = 0.375 (2 + 1 = 3 decimal places)

5

Guided Practice (2-3 min)

Work through these together:

4.5 x 6 = ?
2.4 x 3.2 = ?
0.8 x 0.7 = ?
12.5 x 4 = ?

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"What is 0.6 x 0.8?"

A) 4.8 B) 0.48 C) 48 D) 0.048

Correct answer: B) 0.48 (6 x 8 = 48, 1 + 1 = 2 decimal places)

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Multiply a decimal by a one-digit whole number Multiply a decimal by a multi-digit whole number Multiply decimals Multiply decimals: word problems Estimate products of decimals

^ Differentiation & Extension

For struggling students: Start with money contexts ($2.50 x 3 = how much for 3 items?). Use graph paper to keep digits aligned. Practice counting decimal places with highlighting.

For advanced students: Challenge with three-factor multiplication (0.5 x 0.4 x 2) and problems requiring estimation to check reasonableness.

For home: Send Parent Activity sheet. Families can practice calculating total costs when buying multiple items at the grocery store.