Strategies for Adding Mixed Units of Length
Grade 4 Eureka Math students add mixed units of length such as yards, feet, and inches using two main strategies. The add-and-regroup strategy adds like units first, then converts: 4 yd 2 ft + 3 yd 2 ft = 7 yd 4 ft = 8 yd 1 ft. The make-the-next-whole-unit strategy decomposes one measurement to complete a whole unit before adding the rest. Both strategies reinforce unit conversion relationships (3 ft = 1 yd, 12 in = 1 ft) and develop fluency with measurement in the U.S. customary system.
Key Concepts
Property To add mixed units of length, you can use various strategies. 1. Add and Regroup: Add like units, then convert smaller units to larger ones.
2. Make the Next Whole Unit: Decompose one addend to make a whole unit with the other.
3. Compensation: Add then Subtract.
Common Questions
How does the add-and-regroup strategy work for mixed units?
Add like units separately (yards with yards, feet with feet), then convert any sum that exceeds the unit threshold, such as 4 ft converting to 1 yd 1 ft.
How does the make-the-next-whole-unit strategy work?
Decompose one addend's smaller unit to complete the next whole unit in the other addend, then add the remaining amount.
What conversion facts are needed for adding mixed length units?
Key facts: 12 inches = 1 foot, 3 feet = 1 yard. Sums exceeding these thresholds must be regrouped into larger units.
How do you add 4 yd 2 ft and 3 yd 2 ft?
Add yards: 4 + 3 = 7 yd. Add feet: 2 + 2 = 4 ft. Since 4 ft exceeds 3 ft per yard, convert: 4 ft = 1 yd 1 ft. Total: 8 yd 1 ft.
Why are two strategies taught instead of one?
Different problem structures favor different strategies. Offering both develops flexible problem-solving and number sense with measurement.