Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Students are able to… 

  • Solve problems using models, pictures, words and numbers.
  • Use a variety of problem solving strategies, including restating the problem in their own words, making models, and drawing pictures to represent their thinking.
  • Explain how they solved the problem using accurate mathematical vocabulary and why their answer makes sense.

Students are able to…because teachers:

  • Scaffold problems that use all four operations, including two-step problems that call for the use of different operations.
  • Support students in interpreting problems, including identifying given, needed, and wanted information.
  • Expect students to explain their solution strategies and to justify why their solution makes sense.

Questions to ask students:

Sample problem: Rita found 4 eggs.  Joe found 3 times as many eggs as Rita.  They put their eggs in the same basket.  How many eggs were in the basket?

  • Explain how you solved the scenario using precise mathematical vocabulary.
    • Sample answer that indicates understanding: I had to multiply 3 x 4 to get 12 eggs for Joe and add that to Rita’s 4 eggs for a total of 16 eggs.  I know my answer makes sense because if I subtract $2.25 from the total, $3.10, I get the cost of the apple which is 85 cents.
  • Explain how your model represents the problem.
    • Sample answer that indicates understanding: I made an array with 4 tiles to represent Rita’s eggs.  I made three of those same arrays of 4 to represent Joe’s eggs, which ended up being 12.  All of the tiles together give me the total 16 eggs in the basket.

FSA Notes:

Cognitive Complexity Level: 2 – Basic Application of Skills and Concepts

Achievement Level Descriptors:

2- solves two-step problems using addition and subtraction within 100 and multiplication and division using factors of 1,  2, or 5

3- solves two-step word problems using the four operations and using equations with a letter for the unknown quantity

4- assesses the reasonableness of answers using mental computation and estimation strategies including rounding

5- creates a two-step word problem from an equation with a variable

Assessment Limits:

Adding and subtracting is limited to whole numbers within 1,000.

All values in multiplication or division situations may not exceed whole number multiplication facts of 10 × 10 or the related division facts.

Students may not be required to perform rounding in isolation.

Equations may be provided in items.

Additional Resources:

Additional in depth content knowledge

LearnZillion Video: Solving Two-Step Problems Using a Model 

Kahn Academy Video:  Unknowns with Multiplication and Division

Sample Formative Assessment Tasks: 

Resources/Tasks to Help your Child at Home:

As your child is creating models to represent one- and two-step word problems, challenge them to write equations with variables to represent each step in their model. Students can then try to represent all of the steps in one equation.  *Students do not need to know the order of operations.

Provide real-world opportunities to estimate sums or differences, including two-step problems.  For example, rounding to estimate total cost of items at store and estimating change that will be received; or rounding to estimate nutritional information of ingredients. 

Khan Academy: Two-Step Estimation Problem – Marbles 

Khan Academy: Two-Step Problem – Truffles 

Math Playground: Thinking Blocks Modeling Tool

PBS Games: Estimation Contraption 

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