NC.4.oa.3

Solve two-step word problems involving the four operations with whole numbers.

Use estimation strategies to assess reasonableness of answers.
Interpret remainders in word problems.
Represent problems using equations with a letter standing for the unknown quantity.

Step 1: Lesson Standards & Learning Goals

Unpacking Clarification

The focus of this standard is to have students use and discuss various strategies for solving word problems using all four operations. Students should build on the problem-solving strategies developed in earlier grades and apply those strategies to multi-step problems. Students should also use a variety of estimation strategies.

Estimation strategies include:

identifying when estimation is appropriate,
determining the level of accuracy needed,
selecting the appropriate method of estimation,
- - front-end estimation with adjusting
  - rounding and adjusting
  - using friendly or compatible numbers such as factors
  - using benchmark numbers that are easy to compute
verifying solutions or determining the reasonableness of situations using various estimation strategies.

NOTE: Problems should be structured so that all acceptable estimation strategies will arrive at a reasonable answer. The assessment of estimation strategies should only have one reasonable answer (500 or 530), or a range (between 500 and 550).

In this standard, students are required to solve division tasks and interpret remainders. All problems involving remainders should be in a real-world context that influences how the remainder should be interpreted. In both Grades 4 and 5 here are ways that students are expected to interpret remainders:

Sample Essential Questions

How do you solve problems using addition, subtraction, multiplication, or division in real-world situations?
What are some strategies for solving unknowns in open sentences and equations?
How can addition, subtraction, multiplication and division situations be represented in equations using a symbol for the unknown?
What are strategies for assessing the reasonableness of answers?
What are ways to represent problems using equations with letters standing for the unknown in any place?
What strategies are most helpful for solving particular problems?

Vocabulary

Addition
Difference
Division
Equation
Multiplication
Operation
Quotient
Reasonable
Remainder
Round
Subtraction
Sum
Whole number

Students will be able to...

Solve multi-step word problems using the four operations, including problems in which remainders must be interpreted.
Represent word problems using equations with a letter standing for the unknown quantity.
Use a variety of estimation strategies.
Assess for reasonableness using computation and estimation strategies including rounding.

Students will know...

There is more than one way to estimate a sum, difference, product, or quotient.
Each estimation technique gives a way to replace numbers with other numbers that are close and easy to compute mentally.
Rounding is one way to estimate answers. It involves replacing numbers with the closest multiple (or power, if appropriate) of 10 or 100.
Mathematical situations can be represented with equations using letters for the unknown quantity which may appear in any position. In division, the remainder must be less than the divisor.
The nature of the question asked determines how to interpret and use the remainder in a division problem.

Step 2: Assessment