Learn on PengiEureka Math, Grade 4Chapter 35: Problem Solving with Measurement

Lesson 3: Solve problems involving mixed units of weight.

In this Grade 4 Eureka Math lesson from Chapter 35, students solve addition and subtraction problems involving mixed units of weight, converting between pounds and ounces and applying multiple strategies such as making a whole pound or decomposing sums. Students practice converting weight units (for example, expressing 1 pound 3 ounces as 19 ounces) and use those skills to solve multi-step word problems. The lesson builds directly on prior work with mixed units of length and fraction concepts to strengthen fluency with customary measurement.

Section 1

Adding Mixed Weights Using Multiple Strategies

Property

To add mixed units of weight, you can use various strategies. Three common methods for a problem are:

  1. Regrouping: Add pounds and ounces separately, then convert any sum of 16 or more ounces into pounds.
  2. Making the Next Pound: Decompose one addend to make the other a whole pound, then add the remainder.
  3. Compensation: Round one addend up to the next whole pound, add, and then subtract the amount you rounded up by.

Examples

Let''s solve 5 lb 12 oz+3 lb 7 oz5 \text{ lb } 12 \text{ oz} + 3 \text{ lb } 7 \text{ oz}. The conversion is 1 lb=16 oz1 \text{ lb} = 16 \text{ oz}.

  • Strategy 1: Regrouping

Add pounds: 5 lb +3 lb =8 lb5 \text{ lb } + 3 \text{ lb } = 8 \text{ lb}. Add ounces: 12 oz +7 oz =19 oz12 \text{ oz } + 7 \text{ oz } = 19 \text{ oz}.
Combine and regroup: 8 lb 19 oz=8 lb +(16 oz +3 oz)=8 lb +1 lb +3 oz=9 lb 3 oz8 \text{ lb } 19 \text{ oz} = 8 \text{ lb } + (16 \text{ oz } + 3 \text{ oz}) = 8 \text{ lb } + 1 \text{ lb } + 3 \text{ oz} = 9 \text{ lb } 3 \text{ oz}.

  • Strategy 2: Making the Next Pound

Start with 5 lb 12 oz5 \text{ lb } 12 \text{ oz}. You need 4 oz4 \text{ oz} to make 6 lb6 \text{ lb}. Decompose 3 lb 7 oz3 \text{ lb } 7 \text{ oz} into 4 oz4 \text{ oz} and 3 lb 3 oz3 \text{ lb } 3 \text{ oz}.
5 lb 12 oz+4 oz=6 lb5 \text{ lb } 12 \text{ oz} + 4 \text{ oz} = 6 \text{ lb}. Then, 6 lb+3 lb 3 oz=9 lb 3 oz6 \text{ lb} + 3 \text{ lb } 3 \text{ oz} = 9 \text{ lb } 3 \text{ oz}.

  • Strategy 3: Compensation

Round 3 lb 7 oz3 \text{ lb } 7 \text{ oz} up to 4 lb4 \text{ lb} by adding 9 oz9 \text{ oz}.
Add: 5 lb 12 oz+4 lb=9 lb 12 oz5 \text{ lb } 12 \text{ oz} + 4 \text{ lb} = 9 \text{ lb } 12 \text{ oz}.
Compensate by subtracting the 9 oz9 \text{ oz} you added: 9 lb 12 oz−9 oz=9 lb 3 oz9 \text{ lb } 12 \text{ oz} - 9 \text{ oz} = 9 \text{ lb } 3 \text{ oz}.

Explanation

This skill demonstrates three different mental math strategies for adding mixed units of weight. The regrouping method is a standard algorithm, while making the next pound and compensation are flexible number-based strategies. Making the next pound is useful when one addend is close to a whole pound. Compensation works well when you can easily round one number up and subtract later.

Section 2

Subtracting Mixed Weights Using Multiple Strategies

Property

To subtract mixed units of weight, you can use various strategies.

  • Decompose a Pound
  • Subtract from a Whole Unit
  • Add Up to Find the Difference

Examples

Problem: 5 lb 2 oz−2 lb 8 oz5 \text{ lb } 2 \text{ oz} - 2 \text{ lb } 8 \text{ oz}.
Strategy 1: Decompose a Pound
5 lb 2 oz→4 lb 18 oz5 \text{ lb } 2 \text{ oz} \rightarrow 4 \text{ lb } 18 \text{ oz}
4 lb 18 oz−2 lb 8 oz=2 lb 10 oz4 \text{ lb } 18 \text{ oz} - 2 \text{ lb } 8 \text{ oz} = 2 \text{ lb } 10 \text{ oz}
Strategy 2: Subtract from a Whole Unit
5 lb−2 lb 8 oz=2 lb 8 oz5 \text{ lb} - 2 \text{ lb } 8 \text{ oz} = 2 \text{ lb } 8 \text{ oz}
2 lb 8 oz+2 oz=2 lb 10 oz2 \text{ lb } 8 \text{ oz} + 2 \text{ oz} = 2 \text{ lb } 10 \text{ oz}
Strategy 3: Add Up to Find the Difference
2 lb 8 oz→+8 oz3 lb→+2 lb5 lb→+2 oz5 lb 2 oz2 \text{ lb } 8 \text{ oz} \xrightarrow{+8 \text{ oz}} 3 \text{ lb} \xrightarrow{+2 \text{ lb}} 5 \text{ lb} \xrightarrow{+2 \text{ oz}} 5 \text{ lb } 2 \text{ oz}
Total added: 8 oz+2 lb+2 oz=2 lb 10 oz8 \text{ oz} + 2 \text{ lb} + 2 \text{ oz} = 2 \text{ lb } 10 \text{ oz}

Explanation

There are multiple ways to subtract mixed units of weight like pounds and ounces. You can decompose a larger unit into smaller units, such as converting 1 pound into 16 ounces, to make subtraction possible. Another method is to subtract from a whole number and then add back the remaining part. A third strategy, often used for mental math, is to "add up" from the smaller weight to find the difference between the two amounts.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Adding Mixed Weights Using Multiple Strategies

Property

To add mixed units of weight, you can use various strategies. Three common methods for a problem are:

  1. Regrouping: Add pounds and ounces separately, then convert any sum of 16 or more ounces into pounds.
  2. Making the Next Pound: Decompose one addend to make the other a whole pound, then add the remainder.
  3. Compensation: Round one addend up to the next whole pound, add, and then subtract the amount you rounded up by.

Examples

Let''s solve 5 lb 12 oz+3 lb 7 oz5 \text{ lb } 12 \text{ oz} + 3 \text{ lb } 7 \text{ oz}. The conversion is 1 lb=16 oz1 \text{ lb} = 16 \text{ oz}.

  • Strategy 1: Regrouping

Add pounds: 5 lb +3 lb =8 lb5 \text{ lb } + 3 \text{ lb } = 8 \text{ lb}. Add ounces: 12 oz +7 oz =19 oz12 \text{ oz } + 7 \text{ oz } = 19 \text{ oz}.
Combine and regroup: 8 lb 19 oz=8 lb +(16 oz +3 oz)=8 lb +1 lb +3 oz=9 lb 3 oz8 \text{ lb } 19 \text{ oz} = 8 \text{ lb } + (16 \text{ oz } + 3 \text{ oz}) = 8 \text{ lb } + 1 \text{ lb } + 3 \text{ oz} = 9 \text{ lb } 3 \text{ oz}.

  • Strategy 2: Making the Next Pound

Start with 5 lb 12 oz5 \text{ lb } 12 \text{ oz}. You need 4 oz4 \text{ oz} to make 6 lb6 \text{ lb}. Decompose 3 lb 7 oz3 \text{ lb } 7 \text{ oz} into 4 oz4 \text{ oz} and 3 lb 3 oz3 \text{ lb } 3 \text{ oz}.
5 lb 12 oz+4 oz=6 lb5 \text{ lb } 12 \text{ oz} + 4 \text{ oz} = 6 \text{ lb}. Then, 6 lb+3 lb 3 oz=9 lb 3 oz6 \text{ lb} + 3 \text{ lb } 3 \text{ oz} = 9 \text{ lb } 3 \text{ oz}.

  • Strategy 3: Compensation

Round 3 lb 7 oz3 \text{ lb } 7 \text{ oz} up to 4 lb4 \text{ lb} by adding 9 oz9 \text{ oz}.
Add: 5 lb 12 oz+4 lb=9 lb 12 oz5 \text{ lb } 12 \text{ oz} + 4 \text{ lb} = 9 \text{ lb } 12 \text{ oz}.
Compensate by subtracting the 9 oz9 \text{ oz} you added: 9 lb 12 oz−9 oz=9 lb 3 oz9 \text{ lb } 12 \text{ oz} - 9 \text{ oz} = 9 \text{ lb } 3 \text{ oz}.

Explanation

This skill demonstrates three different mental math strategies for adding mixed units of weight. The regrouping method is a standard algorithm, while making the next pound and compensation are flexible number-based strategies. Making the next pound is useful when one addend is close to a whole pound. Compensation works well when you can easily round one number up and subtract later.

Section 2

Subtracting Mixed Weights Using Multiple Strategies

Property

To subtract mixed units of weight, you can use various strategies.

  • Decompose a Pound
  • Subtract from a Whole Unit
  • Add Up to Find the Difference

Examples

Problem: 5 lb 2 oz−2 lb 8 oz5 \text{ lb } 2 \text{ oz} - 2 \text{ lb } 8 \text{ oz}.
Strategy 1: Decompose a Pound
5 lb 2 oz→4 lb 18 oz5 \text{ lb } 2 \text{ oz} \rightarrow 4 \text{ lb } 18 \text{ oz}
4 lb 18 oz−2 lb 8 oz=2 lb 10 oz4 \text{ lb } 18 \text{ oz} - 2 \text{ lb } 8 \text{ oz} = 2 \text{ lb } 10 \text{ oz}
Strategy 2: Subtract from a Whole Unit
5 lb−2 lb 8 oz=2 lb 8 oz5 \text{ lb} - 2 \text{ lb } 8 \text{ oz} = 2 \text{ lb } 8 \text{ oz}
2 lb 8 oz+2 oz=2 lb 10 oz2 \text{ lb } 8 \text{ oz} + 2 \text{ oz} = 2 \text{ lb } 10 \text{ oz}
Strategy 3: Add Up to Find the Difference
2 lb 8 oz→+8 oz3 lb→+2 lb5 lb→+2 oz5 lb 2 oz2 \text{ lb } 8 \text{ oz} \xrightarrow{+8 \text{ oz}} 3 \text{ lb} \xrightarrow{+2 \text{ lb}} 5 \text{ lb} \xrightarrow{+2 \text{ oz}} 5 \text{ lb } 2 \text{ oz}
Total added: 8 oz+2 lb+2 oz=2 lb 10 oz8 \text{ oz} + 2 \text{ lb} + 2 \text{ oz} = 2 \text{ lb } 10 \text{ oz}

Explanation

There are multiple ways to subtract mixed units of weight like pounds and ounces. You can decompose a larger unit into smaller units, such as converting 1 pound into 16 ounces, to make subtraction possible. Another method is to subtract from a whole number and then add back the remaining part. A third strategy, often used for mental math, is to "add up" from the smaller weight to find the difference between the two amounts.