Why this matters for FAST: Decimal division is essential for real-world problem solving involving money, measurement, and data. Students must understand how to place the decimal point correctly and verify their answers make sense.
Students calculate 7.2 / 4 = 18 instead of 1.8. They perform the division correctly but forget or misplace the decimal point.
"Always estimate first! 7.2 / 4 should be close to 8 / 4 = 2. So our answer should be close to 2, not 18. The decimal point goes directly above where it is in the dividend."
When dividing by a decimal like 0.5, students aren't sure which way to move the decimal or how many places.
"To divide by a decimal, make the divisor a whole number by moving the decimal right. Then move the decimal in the dividend the SAME number of places. Example: 12 / 0.5 becomes 120 / 5 = 24."
Students believe 12 / 0.5 should be less than 12 because "division makes things smaller."
"When you divide by a number less than 1, you get a LARGER answer. Think: How many halves are in 12? There are 24 halves in 12, so 12 / 0.5 = 24."
Review: "What is 72 / 4?" (18) "Now, what do you think 7.2 / 4 might be?" Discuss how the decimal changes the answer. Connect to place value.
"When dividing a decimal by a whole number, set up the division like normal. The key is to bring the decimal point straight up into the quotient, directly above where it sits in the dividend."
Example: 8.4 / 3 = ?
The decimal in 2.8 is directly above the decimal in 8.4
Explain: "When the divisor is a decimal, we need to make it a whole number first. Move the decimal point to the right until it's a whole number, then move the decimal in the dividend the same number of places."
Example: 6 / 0.3 = ?
Step 1: Move decimal in 0.3 one place right: 0.3 becomes 3
Step 2: Move decimal in 6 one place right: 6 becomes 60
Step 3: Now divide: 60 / 3 = 20
Answer: 6 / 0.3 = 20
"Check: Does 20 make sense? How many groups of 0.3 fit into 6? If each group is less than 1, we'll have MORE than 6 groups. 20 groups of 0.3 = 6. Yes!"
Always estimate before calculating to check if the answer is reasonable:
Work through these together:
"What is 12.6 / 3?"
A) 42 B) 4.2 C) 0.42 D) 420
Correct answer: B) 4.2 (12.6 is close to 12, and 12/3 = 4, so 4.2 makes sense)
For struggling students: Use money examples (dividing $8.40 among 4 friends) and base-ten blocks to visualize. Start with divisors of 2, 4, and 5 before moving to other numbers.
For advanced students: Challenge with multi-step problems: "A rope is 15.75 meters long. If you cut it into pieces that are 0.25 meters each, how many pieces will you have?" (63 pieces)
For home: Send Parent Activity sheet. Families can practice with money - dividing costs equally or calculating unit prices.