Word problems with two step equations are difficult for students. These problems have so much information that students get confused about where to start. In addition, we are not only asking them to solve two computation problems but to interpret what is happening and what operations to use. How do you break down these problems to make them more accessible to students?
Providing opportunities to do math puzzles daily is one way to help students practice their math facts and make math fun. In addition, this will better prepare them to solve word problems. So get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students.
Students who feel successful in math class are happier and more engaged in learning. Check out The Bonus Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys for students to use in your classroom to cultivate a positive classroom community in mathematics. You can also sign up for other freebies from me Here at Easternshoremathteacher.com.
Teaching word problems is hard, especially those with missing addends. For example, I have some cookies. I eat 5 cookies. Now I have 9 cookies. How many did I have at the start? I always have students model these problems with counters first to build their conceptual understanding. Then, we ask ourselves if our answer makes sense by going back to the information in the problem.
Then, we take it to another level with 2 step word problems in 2nd grade. Students must have a solid foundation with 1 step problems before moving to 2 step problems. Students need to think about what is happening in the problem, what steps they need to take, and what operations they need to use. At first, it is overwhelming, so using small numbers is critical so students can model the problem and focus on what is happening and not the computation. Otherwise, students are too focused on “doing something” to the numbers… usually, they add them all up!
What are Word Problems?
A word problem is a few sentences describing a ‘real-life’ scenario where a problem needs to be solved through a mathematical calculation.
A one-step equation is an algebraic equation you can solve in only one step. The common core lists several problem situations that are taught beginning in Kindergarten.
Word Problem Example
Paula has 16 tickets for the raffle. She has 8 fewer than Mark. How many tickets does Paula have?
Word Problem Standards
K.OA.A.2 Solve addition and subtraction word problems and add and subtract within 10.
1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions.
Resources for Teaching Word Problems
Taking the time to unpack the problems and then modeling the word problem with counters is essential. This will build the foundation for 2 step word problems.
I like to teach my students a process for solving process. Check out this Problem Solving Steps in Math Resource for ideas.
Kindergarten Word Problem Resources:
1st Grade Word Problem Resources:
- Make a 10 to Add Word Problems
- Word Problems to 10
- Word Problems to 20
- Subtraction Word Problems to 20
- 3 Addend Word Problems
2nd Grade Word Problem Resources:
Word Problem Structures
Link to Addition and Subtraction Problem Structure Table
What are Two Step Word Problems?
Two-step word problems are problems in which two separate calculations (usually different operations) are required to reach the answer. Operations are addition, subtraction, multiplication, or division.
What is an example of a multi-step problem?
Robert had 16 marbles. His brother gave him 3 more bags of marbles. If each bag contained 5 marbles, how many marbles does Robert have now?
Two Step Word Problems Addition and Subtraction
This standard extends the Kindergarten and Grade 1 one-step word problem standards. Students should continue to use linking cubes place value blocks, ten frames, and counters to model problems. When solving problems, some students may be ready to move from the concrete stage to the representational stage. Students may use materials or draw pictures to determine a strategy for solving a problem.
Represent and solve problems involving addition and subtraction.
CCSS.MATH.CONTENT.2.OA.A.1
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
- Numbers range up to a total (sum) of 100.
- Begin with problems in which the operation is the same in both steps.
- Progress to two-step problems that call for different operations.
- Keep the numbers small enough so the focus stays on understanding the problem situations and finding strategies to solve the problem instead of extending computational skills.
- By the end of Grade 2, students should be able to determine the unknown in all positions (result unknown, change unknown, and start unknown), using a variety of strategies that make sense to them.
- Concrete and pictorial representations should be used to explain their reasoning.
- Connections to written equations.
Two Step Word Problems All Operations
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
CCSS.MATH.CONTENT.3.OA.D.8
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Then, assess the reasonableness of answers using mental computation and estimation strategies, including rounding.
- Students solve two-step problems that include more than one operation by representing the information using concrete models, pictures including bar models, and number lines.
- They connect the concrete and pictorial representations to abstract representations (equations).
- Order of operation is not formally taught in Grade 3; however, thinking about the order should be a part of determining if answers are reasonable. For example, Kevin bought a toy car for $.25 and 3 cookies for $.50 each. How much did Kevin spend? Students need to realize they need to determine the cost of the cookies first.
- Determining reasonableness and if an answer makes sense is essential.
- Using a letter standing for an unknown quantity can be connected to identifying missing information represented by a box or another symbol.
Use the four operations with whole numbers to solve problems.
CCSS.MATH.CONTENT.4.OA.A.3
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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 continue to work with problem situations to build fluency with all four operations.
- Begin to interpret remainders. Using models, identifying information in the problem, and discussing the reasonableness of the answer will help students interpret the remainder.
How to Teach 2 Step Word Problems
Students who struggle with knowing what to do to solve problems will find it helpful to restate the problem in their own words. They should identify and underline the important information in the problem and determine what other information they might need to solve it. When they explain what the problem is asking, students will find that it will help them determine whether their answer makes sense.
How to Teach Two-Step Problems in 2nd Grade
Teachers should continue to provide students with experiences using all the problem structures. Students should solve problems using various materials such as part-part-whole mats, ten frames, cubes, counters, or place value blocks.
As students work with concrete materials to solve problems, teachers should help students see the connection between pictorial representations and abstract (equations) representations.
In addition, opportunities for students to explain their strategies for solving problems and make connections between strategies are essential. This allows students to extend their thinking and decide if they are using the most efficient strategy.
Begin with using problems with small numbers, so the focus stays on understanding the problem situations and finding strategies to solve the problem instead of extending computational skills. Eventually, increase the range of numbers in the problem to a total (sum) of 100.
As part of determining if a solution is reasonable, expect students to label the answer to a problem with the unit. For example, 25 apples.
How to Teach Two-Step Problems in 3rd Grade
Teachers should provide scaffold problems that use all four operations, including two-step problems that call for different operations. Again, focus on using smaller numbers initially, so students focus on the process and not the computation.
Additional support for interpreting problems, including identifying the information given, needed, and wanted, should be provided. Students should use a variety of problem-solving strategies. In addition, opportunities for students to explain their strategies and justify why their solution makes sense using precise mathematical language.
How to Teach Two-Step Problems in 4th Grade
Teachers provide two and three-step problems with all four operations. In addition, division problems which include remainders. Students need to think about the question and determine what to do with the remainder. Finally, students solve the problems using models or pictures, and numbers.
Opportunities for discussion where students show and explain their strategies and compare the different methods of solving the problem allow students to extend their thinking.
Common Errors in Teaching 2 Step Word Problems
Teaching keywords does not help students to develop an understanding of problem situations. Instead, students can understand the problems by using concrete models and drawing pictures.
Students will determine what operation makes the most sense to them in missing addend cases. For example, addition/subtraction or multiplication/division. Teachers should not tell students what operations they should use.
If students do not know their math facts, they are more focused on the computation than on understanding the word problem. Providing opportunities to do math puzzles daily is one way to help students be more successful with word problems. If students know their facts, they can focus on understanding the problem and not on the computation. So get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students.
Two Step Word Problems Practice
Once your students are ready to move to two step word problems, begin with teaching students how to read and think about the problem. Then, model the problem with ten frames or part-part-whole mats and counters. Eventually, move to drawing pictures and equations to represent the word problems 2 step. Solving problems together will help students build their understanding and expose them to different strategies.
Try out this bundle which includes 120 two step word problems addition and subtraction practice problems in digital and print form. Teach Addition and Subtraction 2 step word problems within 100 with different word problem structures.
Using Ten Frames and Double Ten Frames
A ten frame is a rectangle with ten equal spaces. It has five spaces on top and five on the bottom. You often find the ten frames positioned horizontally and filled with counters placed from left to right and top to bottom. A double ten frame is 2 ten frames put together to show up to 20.
Ten frames are a fantastic tool used in kindergarten and first grade to help build an understanding of counting, place value, adding, subtracting, and more. You use counters or math manipulatives to represent word problems on the frame. Check out this link to find a free Ten Frames Template. Ten Frames Free Printable.
Read more about using ten frames here…Why Using Ten Frames for Math to Develop Understanding is Effective?
Using Part-Part-Whole Mats with Word Problems 2 Step
The part-part-whole model is a pictorial representation of a problem that helps students see the relationship between a “whole” and its components.
The part- part- whole diagram shows that you know some information but still need to find additional information. The bar can be split into as many parts as you need, depending on the amount of information you’ve been given. The whole or any of the parts can be missing.
Children using this model will see the relationship between the whole number and its parts, helping learners to make the connections between addition and subtraction.
This is another valuable tool in modeling word problems. Check out this link to find a free Part-Part-Whole Template. Part- Part-Whole Mat
Read more about using the part-part-whole strategy here…How to Use the Powerful Part-Part-Whole Strategy to Improve Number Sense.
Real-World Connections
Using real-world situations or situations from literature books will help students visualize what is happening in the word problems. Then, students can act out the problem or use counters to model what is happening.
Two Step Equation Problems
Two Step Word Problems Grade 2 Resources
Two Step Word Problems Grade 3 & 4 Resources
- Two Step Word Problems – 3rd Grade Math Videos
- Solving 2-step Word Problems | MightyOwl Math | 3rd Grade
Additional Resources
- 5 Best Strategies for Engaging Students to Learn in Mathematics Class
- 5 Simple and Effective Ways to Practice Doubles Facts in Math
- Math Playground
Word Problems for Two Step Equations
Taking your time to build the foundation with 1 step word problems and helping students understand the problem and make a plan will make students more successful. Students need to act out or model the problem before drawing pictures and writing equations. Working through one or two problems is beneficial for students and helps them build conceptual understanding.
Providing opportunities to do math puzzles daily is one way to help students be more successful with word problems. If students know their facts, they can focus on understanding the problem and not on the computation. So get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students. You can also sign up to receive other freebies from me Here at Easternshoremathteacher.com.
Check out The Free Ultimate Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys to use in your classroom.
Word problems that connect to real-world experiences are essential so students see the importance of learning the skill. Guided practice with building models is the best way to teach word problems with two step equations.
4 Responses