# Solve two-step contextual problems using the four operations. Represent these problems using ### Cluster

Solve problems involving the four operations and identify and explain patterns in arithmetic.

Wilbur has 400 stickers.

• He gives 9 stickers each to 8 of his friends.
• He keeps the remaining stickers for himself.

Which is the best estimate of the number of stickers that Wilbur keeps for himself?

Evidence of Learning Statements

 Students with a level 1 understanding of this standard will most likely be able to: Students with a level 2 understanding of this standard will most likely be able to: Students with a level 3 understanding of this standard will most likely be able to: Students with a level 4 understanding of this standard will most likely be able to: Solve one- and two-step contextual problems, with unknowns in all positions, involving a wide variety of common addition and subtraction situations. Solve one-step multiplication or division contextual problems, with unknowns in all positions, involving Equal Groups, Arrays, and Area situations. Represent one-step contextual problems with an equation using a letter to represent the unknown quantity. Choose a reasonable answer to a given one-step contextual problem without working the problem. Solve two-step contextual problems using the four operations involving both addition/subtraction and multiplication/division situations with unknowns in a wide variety of positions. Represent two-step contextual problems using a series of equations with a letter standing in for the unknown quantity. Choose a reasonable answer to a given two-step contextual problem involving multiple operations without working the problem. Use mental computation and estimation strategies to present a reasonable solution to a given contextual two-step problem. Solve the contextual problem including a representation using equations with a letter standing in for the unknown quantity and compare the original estimation with the actual answer, providing mathematical justification for any discrepancies. Create a contextual problem that represents a given two-step equation (e.g., 2 x 5 + 1= x or m + 4 – 9 =20).

Instructional Focus Statements

Level 3:

In grade 2, students solved one- and two-step addition and subtraction contextual problems with a focus on common addition and subtraction situations with unknowns in all positions. In grade 3, standard 3.OA.A.3 students were first introduced to solving one-step multiplication and division contextual problems.  It is important that standard 3.OA.D.8 build on these experiences to extend student thinking as they solve two-step contextual problems using all four operations.

In transitioning all students to working with two-step, multi-operation contextual problems, instruction should initially focus on problems involving smaller, familiar numbers allowing students to focus on the conceptual understanding of multiple operations within the problem as opposed to focusing on computation with less familiar numbers. Additionally, it is easier for students to begin with problems that call for commonly paired operations (i.e., addition/subtraction, multiplication/division) within the problem and then move to working with two-step problems that involve less common pairings (e.g., addition and division). It is important to call out that students should continue to use manipulatives, multiple strategies, and written equations when solving two-step contextual problems. To demonstrate their understanding, they should be able to explain the connections between the visual representation and the equation(s) that represents the problem. Additionally, students should be encouraged to use multiple strategies and make connections between each strategy. For example, students may write individual equations for each step in a two-step problem or write both steps in one equation. This is a good opportunity for students to compare their work to others and explain why both are correct or in some cases incorrect and explain the connection between the two strategies. The instructional focus should be more on students understanding two-step problems and sense making as opposed to simply getting a correct answer.

Teaching key words to associate with addition, subtraction, multiplication, and division should not be an instructional focus. Instruction should focus on developing an understanding of what operation is needed to solve the problem rather than focusing on key words that sometimes, but not always, associate with the operation.

Instruction should also focus on encouraging students to assess the reasonableness of their answers. Students should use estimation strategies and mental computations as they consider reasonableness. One beneficial instructional strategy is for students to estimate a solution prior to solving the problem.

Level 4:

As students deepen their understanding of two-step contextual problems, they should be able to represent these problems with a mathematical drawing, diagram, and an equation with a letter for the unknown number. They should be able to explain their thinking using multiple representations and make connections between the visual representations and their equations. Students should be able to use mental computation and estimation strategies to present a reasonable solution, solve the problem, and then compare the original estimation and the actual answer providing mathematical justification for any discrepancies.

Additionally, students should be able to create their own two-step contextual problem and explain the solution. When doing so, students should use visual representations, equations, and precise mathematical vocabulary.