Learn on PengiEureka Math, Grade 4Chapter 5: Multi-Digit Whole Number Subtraction

Lesson 4: Solve two-step word problems using the standard subtraction algorithm fluently modeled with tape diagrams, and assess the reasonableness of answers using rounding.

In this Grade 4 Eureka Math lesson from Chapter 5, students practice solving two-step word problems by applying the standard subtraction algorithm and modeling solutions with tape diagrams. They work with multi-digit numbers up to one million, learning to assess the reasonableness of their answers by rounding to the nearest ten thousand. Real-world contexts such as employee counts and website visitor data help students connect multi-digit subtraction to practical problem-solving situations.

Section 1

Modeling Two-Step Word Problems with Tape Diagrams

Property

In a two-step word problem involving parts and a whole, a tape diagram represents the total amount (the whole) and its components (the parts). To find an unknown part, you often first find the sum of the known parts, then subtract that sum from the whole. This relationship can be shown as:

Unknown=Whole(Part1+Part2)Unknown = Whole - (Part_{1} + Part_{2})

Examples

Section 2

Check: Using Estimation to Assess Reasonableness

Property

To assess the reasonableness of a precise answer, compare it to an estimate made by rounding the numbers in the problem.
If the precise answer is close to the estimated answer, it is likely reasonable.
This can be represented as:

AnswerpreciseAnswerestimateAnswer_{precise} \approx Answer_{estimate}

Examples

Section 3

Finding a Missing Part by Adding Known Parts

Property

In a two-step problem where a whole is broken into multiple parts, you can find a missing part by first adding the known parts together and then subtracting that sum from the whole.

Whole(Part1+Part2)=MissingPartWhole - (Part_{1} + Part_{2}) = Missing Part

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Modeling Two-Step Word Problems with Tape Diagrams

Property

In a two-step word problem involving parts and a whole, a tape diagram represents the total amount (the whole) and its components (the parts). To find an unknown part, you often first find the sum of the known parts, then subtract that sum from the whole. This relationship can be shown as:

Unknown=Whole(Part1+Part2)Unknown = Whole - (Part_{1} + Part_{2})

Examples

Section 2

Check: Using Estimation to Assess Reasonableness

Property

To assess the reasonableness of a precise answer, compare it to an estimate made by rounding the numbers in the problem.
If the precise answer is close to the estimated answer, it is likely reasonable.
This can be represented as:

AnswerpreciseAnswerestimateAnswer_{precise} \approx Answer_{estimate}

Examples

Section 3

Finding a Missing Part by Adding Known Parts

Property

In a two-step problem where a whole is broken into multiple parts, you can find a missing part by first adding the known parts together and then subtracting that sum from the whole.

Whole(Part1+Part2)=MissingPartWhole - (Part_{1} + Part_{2}) = Missing Part