Lesson 3.3: Two-Step Word Problems

Overview and Background Information
Mathematical By the end of the lesson (the lesson will be repeated many times) students will:
Goals • Accurately solve two-step story problems with numbers within 100.
• Communicate their strategies used to solve problems
Common Operations and Algebraic Thinking
Core State Represent and solve problems involving addition and subtraction.
Standards 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word
problems involving situations of adding to, taking from, puttinsg 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
1
See Glossary, Table 1.
Number and Operations in Base Ten
Use place value understanding and properties of operations to
add and subtract.
2.NBT.5 Fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and
properties of operations.
Emphasized 1. Make sense of problems and persevere in solving them
Standards for 2. Reason abstractly and quantitatively.
Mathematical 3. Construct viable arguments and critique the reasoning of others.
Practices 4. Model with mathematics
Prior Solving one-step addition and subtraction problems within 100
Knowledge
Needed
Vocabulary Tens, ones, two-step problems
Materials ten strips, worksheets of story problems, Beat the Calculator sheet, Beat the
Calculator cards, calculators
 
 
Tasks in the Lesson
Engage 25-30 minutes
Adding with Tens Strips and Dots
Place 4 tens strips and 5 dots (ones) on the overhead projector or document camera. Ask, “How many
dots?” (45).
Now add 2 ten strips and 3 ones.
Ask, “How many total dots?” (68)
The goal is for students to use the tens strips and ones to find the answer, so you do not need to
record the numerals.
“How did you find your answer?”

Possible student responses:

I added all the tens and then the ones.
I counted on 45, 55, 65 and then three more.

Ask students to write a story problem that matches these numbers and the action (adding more dots).
They should write the story problem in their notebook and then tell their story to a partner.

Grade 2: Two- and Three-Digit Addition and Subtraction

82  
 
  
An example would be:
There were 45 students on the playground. 23 students joined them. How many students are now on
the playground?

After most students have shared a story with a partner, ask 2-3 students to share their story.

Ask, “How could I represent this story with an equation?” 45 + 23 = ___.

There should still be 68 dots on the overhead projector. Next take away 35 dots.
Ask students to determine the total. (33).
Have students add onto their story in their journal and share their story with a partner to include the act
of removing 35 dots.
Example: There were 45 students on the playground. 23 students joined them. Then 35 students went
inside. How many students are still on the playground?

Have 2-3 students share their story.

Ask, “How could I represent this story with an equation?” 45 + 23 – 33 = __
Note: Teachers can leave the equation until the end of the discussion after students had written story
problems with the dots. The equation is an essential part of the Common Core Standards and should
be included for each task.

Put 2-3 equations on the board.

47 + 21 – 31 = ___, 47 - 21 + 31 = ___, 47 + 21 + 35 = ___

Have students choose an equation and create a story problem in their notebook. Students should then
share with their partner.

When the class comes back together have a few students share their story problems. The class needs
to listen to the story problem and choose which equation matches the story problem.

Tell the class that these stories have been two-step stories. Ask, “What do you think this means?”
(There are two steps in the problem or two actions.)

Two-step problems require two steps to solve. For these types of problems, it can be especially useful
for children to read and rephrase the story problem and to ask themselves what the problem is asking.
Children use drawings, manipulatives and equations to help solve the problems.

Ask, “How is solving this type of problem different from solving a one-step problem?”
• The equation will have + and – or + + or - -.
• You have to read it carefully to make sure you don’t miss the 2nd step

Ask, “How is solving this type of problem the same as solving a one step problem?”
• Read story problems carefully and rephrase them in their own language.
• Analyze what information is given and what is being asked.
• Represent the story problems
• Solve the problem

Next, give students problems that have a variable missing. Use the attached table of Addition and
Subtraction Situations to help you create story problems.

Tell this story or have it written on the board and read it.
There were 15 frogs in the pond. Some frogs jumped out. Then 8 frogs jumped in the pond. Now
there are 20 frogs in the pond. How many frogs jumped out?
Grade 2: Two- and Three-Digit Addition and Subtraction
83  
 
  
Have students come to the front of the room and act out the problem.
Ask, “What do we have to find?” (how many frogs jumped out).
“How can we find the answer?”

Possible student responses:

Some students may say to put 15 and 8 in the pond and then see how many need to jump out so the
total is 20.
Some may suggest trying different numbers in the blank to see what works.

After students have acted out the problem, have students write an equation to represent what
happened in the problem. 15 - ___ + 8 = 20.

As you do this make sure to use the action language in the problem to help.
• “When frogs jump in, what operation should we use?”
• “When frogs jump out, what operation should we use?”
Do 2-3 other 2-step problems together.
Explore 15 minutes
The students will solve the story problems on one of the worksheets.
There are two different sheets of story problems. Each of these sheets has numbers appropriate for
the 2nd nine weeks of school. The next sheet has the same problems with smaller numbers.

Give the students a copy of the story problems. Have them read problem 1 with a partner. Say, “Talk
with your partner about what you know and need to know?” After 1-2 minutes ask for comments.
Students can:
• Retell the story.
• Act out the problem.
• Write an equation.
• Solve the problem with a partner.
The students can solve the rest of the problems individually or with a partner. Students need multiple
experiences solving multi-step problems. The problems on the worksheets are examples. The teacher
can create additional problems to be used. As the students are working on the problems observe their
strategies. Choose several students with strategies you want shared to share during the “explain” time
of the lesson.
Explain 15 minutes
After most students have solved the problems on one worksheet, bring the students together to discuss
their work. Choose the problem you want to discuss. Their attention span will probably not allow
discussion of all the problems. The teacher can record strategies on the board to save time and have
the students explain their strategies. Questions to ask:
• What do you notice about how this strategy uses place value?
• How are these two strategies alike/different?
• Why did you choose this strategy?
• Why did you start with this number?
• What’s hard about this problem?

Grade 2: Two- and Three-Digit Addition and Subtraction

84  
 
  
 

Elaborate 20 minutes
Introduce the game, “Beat the Calculator.” The rules and cards are attached to this game.
Students solve the problems mentally and with a calculator. Play the game with the class. One side of
the class can solve the problem mentally and the other side solves the problem with a calculator. Do
this several times, switching sides for using the calculator and mentally solving the problems.

After several rounds ask, “What does this game help you do?” :
• Solve problems mentally.
• Practice using a calculator.
• Find easy numbers to solve first. Example in 8 + 6 + 2 the students may see that adding 8 + 2
first makes a 10 and then adding the 6 is easier.

Ask, “How do these problems relate to two-step story problems?”

After the class has worked together to solve the problems tell them that they will play the game with a
partner tomorrow. This game should be played repeatedly during class time.
Evaluation of Students
Formative: As the students are working observe whether students can: write an equation, solve for an
unknown, and solve two-step problems.

Summative: Use the story problem worksheet to assess student understanding.

Plans for Individual Differences
Intervention: Students who have difficulty solving the two-step problems may need to use smaller
numbers so they can concentrate on the structure of the problem rather than the numbers. You can
change the numbers to one digit numbers or numbers less than 20. Example: There were 5 students
on the playground. 3 students joined them. Then 2 students went inside. How many students are now
on the playground?
There are two versions of each worksheet. The second worksheet has the same word problems with
smaller numbers.

Extension: Have students write two-step problems and have classmates solve the problems. Have
students solve start unknown problems—refer to Table 1 of common addition and subtraction
situations. An example: There were some students on the playground. 36 children joined them. In a
few minutes 16 students went inside. Now there are 75 students on the playground. How many
students were on the playground at the start? (_____ + 36 – 16 = 75). Start unknown problems are
harder for students to solve.
Repeating this Lesson
It is recommended that similar lessons be taught over the 2nd nine weeks. As assessment information
is gathered on student understanding meet with groups of students with similar needs. Have them
solve two-step problems adjusting the numbers according to their needs.

Grade 2: Two- and Three-Digit Addition and Subtraction

85  
 
  

Glossary, Table 1. Common addition and subtraction situations.1

  Result Unknown Change Unknown Start Unknown
Two  bunnies  sat  on  the  grass.   Two  bunnies  were  sitting  on   Some  bunnies  were  sitting  on  
Three  more  bunnies  hopped   the  grass.  Some  more   the  grass.  Three  more  
there.  How  many  bunnies  are   bunnies  hopped  there.  Then   bunnies  hopped  there.  Then  
Add to on  the  grass  now?   there  were  five  bunnies.   there  were  five  bunnies.  How  
2  +  3  =  ?   How  many  bunnies  hopped   many  bunnies  were  on  the  
  over  to  the  first  two?   grass  before?  
2  +  ?  =  5   ?  +  3  =  5  
Five  apples  were  on  the  table.   Five  apples  were  on  the   Some  apples  were  on  the  
I  ate  two  apples.  How  many   table.  I  ate  some  apples.   table.  I  ate  two  apples.  Then  
apples  are  on  the  table  now?   Then  there  were  three   there  were  three  apples.  
Take from
5  –  2  =  ?   apples.  How  many  apples  did   How  many  apples  were  on  
I  eat?   the  table  before?  
5  –  ?  =  3   ?  –  2  =  3  
2
Total Unknown Addend Unknown Both Addends Unknown
Three  red  apples  and  two   Five  apples  are  on  the  table.   Grandma  has  five  flowers.  
green  apples  are  on  the  table.   Three  are  red  and  the  rest   How  many  can  she  put  in  her  
How  many  apples  are  on  the   are  green.  How  many  apples   red  vase  and  how  many  in  
Put Together/
3 table?   are  green?   her  blue  vase?  
Take Apart
3  +  2  =  ?   3  +  ?  =  5,  5  –  3  =  ?   5  =  0  +  5,  5  =  5  +  0  
5  =  1  +  4,  5  =  4  +  1  
5  =  2  +  3,  5  =  3  +  2  
Difference Unknown Bigger Unknown Smaller Unknown
(“How  many  more?”  version):   (Version  with  “more”):   (Version  with  “more”):  
Lucy  has  two  apples.  Julie  has   Julie  has  three  more  apples   Julie  has  three  more  apples  
five  apples.  How  many  more   than  Lucy.  Lucy  has  two   than  Lucy.  Julie  has  five  
apples  does  Julie  have  than   apples.  How  many  apples   apples.  How  many  apples  
Lucy?   does  Julie  have?   does  Lucy  have?  
4      
Compare
(“How  many  fewer?”  version):   (Version  with  “fewer”):   (Version  with  “fewer”):  
Lucy  has  two  apples.  Julie  has   Lucy  has  3  fewer  apples  than   Lucy  has  3  fewer  apples  than  
five  apples.  How  many  fewer   Julie.  Lucy  has  two  apples.   Julie.  Julie  has  five  apples.  
apples  does  Lucy  have  than   How  many  apples  does  Julie   How  many  apples  does  Lucy  
Julie?   have?   have?  
2  +  ?  =  5,  5  –  2  =  ?   2  +  3  =  ?,  3  +  2  =  ?   5  –  3  =  ?,  ?  +  3  =  5  
 
2
These  take  apart  situations  can  be  used  to  show  all  the  decompositions  of  a  given  number.  The  associated  equations,  
which  have  the  total  on  the  left  of  the  equal  sign,  help  children  understand  that  the  =  sign  does  not  always  mean  makes  or  
results  in  but  always  does  mean  is  the  same  number  as.  
3
Either  addend  can  be  unknown,  so  there  are  three  variations  of  these  problem  situations.  Both  Addends  Unknown  is  a  
productive  extension  of  this  basic  situation,  especially  for  small  numbers  less  than  or  equal  to  10.  
4
For  the  Bigger  Unknown  or  Smaller  Unknown  situations,  one  version  directs  the  correct  operation  (the  version  using  more  
for  the  bigger  unknown  and  using  less  for  the  smaller  unknown).  The  other  versions  are  more  difficult.  
 
_________________
1
Adapted  from  Box  2-­‐4  of  Mathematics  Learning  in  Early  Childhood,  National  Research  Council  (2009,  pp.  32,  33).  

Grade 2: Two- and Three-Digit Addition and Subtraction

86  
 
  

Ten Strips

Grade 2: Two- and Three-Digit Addition and Subtraction

87  
 
  

Name ___________________________

Solve each story problem. Use numbers, pictures or words to explain how you solved the problems.
Write an equation.

1. In the morning there are 35 students in the cafeteria. 16 more students come in. After a few
minutes, some students leave. If there are 31 students still in the cafeteria, how many students
left the cafeteria?

2. Mr. Brown’s class was studying the life cycle of toads. Tom brought 41 tadpoles to class. Sara
brought 15 to class. They put them all in an aquarium. After a few days 19 tadpoles changed
into toads. How many tadpoles are still in the aquarium?

3. There are 29 students on the playground. 15 students went inside to get water. Then Mrs.
Jones brought her students outside to play. Now there are 40 students on the playground.
How many students did Mrs. Jones bring to the playground?

Grade 2: Two- and Three-Digit Addition and Subtraction

88  
 
  

Name ___________________________

Solve each story problem. Use numbers, pictures or words to explain how you solved the problems.
Write an equation.

1. In the morning there are 15 students in the cafeteria. 6 more students come in. After a few
minutes, some students leave. If there are 10 students still in the cafeteria, how many students
left the cafeteria?

2. Mr. Brown’s class was studying the life cycle of toads. Tom brought 14 tadpoles to class. Sara
brought 5 to class. They put them all in an aquarium. After a few days 11 tadpoles changed
into toads. How many tadpoles are still in the aquarium?

3. There are 19 students on the playground. 11 students went inside to get water. Then Mrs.
Jones brought her students outside to play. Now there are 20 students on the playground.
How many students did Mrs. Jones bring to the playground?

Grade 2: Two- and Three-Digit Addition and Subtraction

89  
 
  

Name ___________________________

Solve each story problem. Use numbers, pictures or words to explain how you solved the problems.
Write an equation.

1. At the first stop, 25 people got on the school bus. At the second stop, 13 people got off. At the
third stop, 17 people got on. How many people were on the school bus then?

2. Robin invited 12 girls and 9 boys to her party. Her mom said she could invite 25 friends in all.
How many more friends could Robin invite?

3. Tasha has 44 books. She put 16 books on a shelf. She put 12 books in her book bag and the
rest on her desk. How many books did she put on the desk?

4. There were 18 carrots and 15 potatoes in the garden. The rest of the plants were tomato
plants. There were 51 plants in the garden. How many tomato plants were in the garden?

Grade 2: Two- and Three-Digit Addition and Subtraction

90  
 
  

Name ___________________________

Solve each story problem. Use numbers, pictures or words to explain how you solved the problems.
Write an equation.

1. At the first stop, 12 people got on the school bus. At the second stop, 6 people got off. At the
third stop, 7 people got on. How many people were on the school bus then?

2. Robin invited 6 girls and 3 boys to her party. Her mom said she could invite 15 friends in all.
How many more friends could Robin invite?

3. Tasha has 14 books. She put 6 books on a shelf. She put 2 books in her book bag and the rest
on her desk. How many books did she put on the desk?

4. There were 8 carrots and 5 potatoes in the garden. The rest of the plants were tomato plants.
There were 20 plants in the garden. How many tomato plants were in the garden?

Grade 2: Two- and Three-Digit Addition and Subtraction

91