Addition with word problems has several problem types, which can be challenging for students if we do not take the time to teach them the various problem structures. Students need to begin modeling problems with concrete materials and then move to more abstract methods of solving problems. Are you familiar with all the different problem types for addition word problems?
Engaging students to learn in math class will help students to love math. Unfortunately, children develop a dislike of math early on and end up resenting it into adult life. So how can teachers make math more interesting to engage 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.
Have you ever given students a word problem, and they just added the two numbers in the problem without even reading the context? This can be frustrating because you know they can do the math if they just thought about what was happening in the problem! Using problem solving steps in math helps my students to understand what is happening in the problem. In addition, this allows students to develop a process for solving word problems, and they are no longer just adding up the numbers in the problem without thinking about the context.
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 Problems in Addition and Subtraction
Word problems in addition and subtraction can be challenging for students if we do not take the time to model the steps in solving problems and teach them strategies.
Starting with acting out and using counters to act out various situations builds the foundation for more complex problems. Then, students are ready to do more complicated problem structures using concrete materials and eventually draw pictures and write equations. In addition, starting with smaller numbers helps students focus on the problems and not the computation at first.
Teaching Word Problems for Addition and Subtraction
Kindergarten Word Problems
K.OA.A.2 Solve addition and subtraction word problems and add and subtract within 10.
Students connect their work from K.OA.A.1 (representing addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations) to applying addition and subtraction to various word problem situations.
Students should first use concrete objects and later use drawings to represent what is happening in the problem.
In addition, Teachers should begin with smaller addends (up to 5) and then move to larger addends (with the total being 10 or less).
decomposing-in-math1st Grade Word Problems
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.
At the beginning of the first grade, review situations taught in kindergarten and increase the number to 20. Over time, introduce the other situations for students to model. Have students describe what is happening in the problem and make a plan for solving the problem. In addition, they should identify what they are looking for in each problem situation. For example, the number of apples.
Students solve problems using materials such as counters, five and ten frames, part-part-whole tables, and number lines to model various situations. In addition, they begin to use drawings to represent what is happening in the problem. Model writing equations that describe the student’s actions with the expectation that they will begin to use symbols to show their work when ready. Give students opportunities to say the equation orally and then in writing.
Eventually, move to the comparison situations. Students begin by modeling the problem with concrete materials and progress to drawing pictures. Furthermore, Emphasize the difference between more than and fewer than situations.
2nd Grade Word Problems
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.
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. As students work with concrete materials to solve problems, teachers should help students see the connection between pictorial representations and abstract (equations) representations.
Teachers should continue to provide students with experiences using all the problem structures. Eventually, move to two-step word problems with smaller numbers and both operations being the same. Then, use larger numbers and addition and subtraction within the same problem.
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.
To read more on 2 Step Word Problems….What’s the Best Proven Way to Teach Word Problems with Two Step Equations?
Adding Word Problem Structures
Students begin with 3 types of addition problem structures in Kindergarten, then move on to solving all 7 types of addition word problem structures by the end of 1st Grade. Therefore, it is essential to ensure you are modeling and having students practice all the different problem structures.
Kindergarten Word Problem Structures
- Add To- Result Unknown (7 add 3 equals a result: 7 + 3=?)
- Two frogs sat on the grass. Three more frogs hopped there. How many frogs are on the grass now? 2 + 3 = ?
- Put Together/Take Apart– total known (put together 7 and 3 and get a total: 7 + 3=?)
- Three red apples and two green apples are on the table. How many apples are on the table? 3 + 2 = ?
- Put Together/Take Apart- Both Addends Unknown (take 7 apart to make 2 groups: 7= ? + ?)
- Peter has 7 flowers. How many can she put in her red vase, and how many in her blue vase?
1st Grade Word Problem Structures
- Add To- Change Unknown (7 add some more equals 9: 7 + ? = 9)
- Two frogs were sitting on the grass. Some more frogs hopped there. Then there were five frogs. How many frogs hopped over to the first two? 2 + ? = 5
- Add To- Start Unknown (have some add 4 more equals 9: ? + 4= 9)
- Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before? ? + 3 =5
- Put Together/ Take Apart- Addend Unknown (take 7 apart: 7= 3 + ?)
- Five pears are on the table. Three are red, and the rest are green. How many pears are green? 3 + ? = 5, 5-3 = ?
- Comparison- Difference Unknown, Smaller Unknown, Bigger Unknown
- Difference unknown: Larry has 5 apples. James has 8 apples. How many more apples does Larry have than James? 5 + ? = 8 8 – 5 = ?
- Bigger unknown: Larry has 4 fewer oranges than James. Larry has 6 oranges. How many oranges does James have?
- Smaller unknown: Larry has 6 fewer apples than James. James has 9 apples. How many apples does Larry have?
2nd Grade Word Problem Structures
- Continue to provide students with experiences using all the problem situations.
Addition and Subtraction Problem Structure Table
Word Problems of Addition Strategies
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 from left to right. 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. Additionally, 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
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 information you’ve been given. The whole or any of the parts can be missing.
Furthermore, 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 & Math Literature
Using real-world situations or situations from literature books will help students visualize what is happening in word problems. Then, students can act out the problem or use counters to model what is happening.
Problem Solving Steps in Math
Students are more successful when using these 4 problem solving steps in math. This helps them think about the problem and make a plan before even solving the problem. Then, after solving the problem, check if their answer makes sense.
Step 1: Understand
- Read and think about the problem.
- Circle the needed information in the problem.
- Underline the question in the problem.
- Write an answer stem sentence. There are ____ pages left to read.
Step 2: Plan
- Make a plan to solve the problem.
- What strategy will you use? (draw a picture, work backward, look for a pattern, create a table, bar model)
- What math tools do you need?
Step 3: Do
- Solve the problem.
- Show your work to solve the problem.
Step 4: Check
- Answer the question and check your work.
- Write the answer into the answer stem.
- Does your answer make sense?
- Check your work using a different strategy.
Resources for Teaching Word Problems
Taking the time to unpack the problems and then modeling the word problem with counters is essential.
Composing and Decomposing Numbers Kindergarten Anchor Chart
Add To Word Problems- Result Unknown
Add To Change Unknown Word Problems
Word Problem Resources:
- Make a 10 to Add Word Problems
- Word Problems to 10
- Word Problems to 20
- 3 Addend Word Problems
- Word Problems to 100
- Two-Step Word Problems
How to Write Word Problems
First, decide which type of problem structure you would like to use. Then, we need to be relatable to the students. When crafting a word problem, we need to ensure the students can connect to or picture what’s happening.
This comes from knowing your students and their interests. So when we create word problems and use these topics, the students are interested in the story and can visualize what’s happening.
In addition, they especially love it when you use their names to make them the star of the word problem.
Additional Resources
Addition and Subtraction Problem Structure Table
How Do You Successfully Teach Word Problems in Addition and Subtraction?
What’s the Best Proven Way to Teach Word Problems with Two Step Equations?
Top 3 Ways for Improving As a Teacher and Growing Your Mindset
Types of Addition Problems
If we take the time to teach students the process and ask themselves, “Does this make sense?” we will better prepare them to solve more complex problems. Start by modeling and move to more abstract ways to solve problems.
In addition, make sure you include all types of addition problems for students to solve.
So how can teachers make math more interesting to engage students? Download 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. You can also sign up to receive other freebies from me Here at Easternshoremathteacher.com.
Teaching the process and teachers knowing the different addition and subtraction situations by grade level is critical when teaching word problems in addition and subtraction. What are some of your tips for teaching addition with word problems?
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