Author: Isabella Rohrbacher
Company: Glendale Elementary School Dist #40

Instructional Design - Two-Step Addition Word Problems

Isabella Rohrbacher
Bowling Green State University

Rationale
At this time in a second graders math career they have had exposure to addition, subtraction, place value, shapes, comparing numbers and many other math concepts.  Students will have also had some exposure to one step word problems.  As students continue to advance through their math career word problems will continue to show up and two-step word problems will become more relevant.  Students will need to be able to pick apart the problem to find the questions, relevant information as well as unneeded information.  This makes this unit on two-step addition word problems very important because it is a skill that students will be expected to use throughout their entire time in school and possibly after.  This unit will focus specifically on identifying the questions asked in a two-step addition word problem and using that information to correctly answer the questions.  Lessons within this subunit will follow the same basic sequence, with questions getting a little more challenging during every lesson, in order to get students as comfortable with two-step word problems and the different ways to solve them as possible.
	This unit will also focus on moving away from manipulatives, to pictures and finally abstract ways (such as algorithms or mental math) that students have been exposed to in order them to work as efficiently as possible.  More exposure to both word problems as well as abstract problem solving will greatly benefit the students and continue to strengthen their mathematical foundation. 
	This unit will follow a 5-E instructional planning model, as seen in chapter 8 of Designing Instruction for Contextual Teaching and Learning by Chiarelott.  It is very important that students have the opportunity to engage and explore two-step word problems through discussions and working with manipulatives.  As we continue to explore students will transition into pictures and algorithm methods to solve problems.  Due to the amount of time that students spend exploring these different methods and discussing word problems they will easily understand what is expected of them and the explanation phase of the 5-E will be done by students, in my district we moved away from teacher modeling so this is a very important component of the 5-E cycle that tells a teacher whether or not a student understands a topic.  We will then use extension activities and a post-assessment to really gauge how well a student picked up on the unit concepts.
	The classroom itself will be a mix of traditional and constructivist teaching throughout this unit.  There will not be teacher modeling, as previously mentioned.  Instead there will be a lot of student discussions and exploration in order to learn the new concepts.  The teacher will act as a facilitator and prompt with questions and assist as needed.  With that being said there will still be some work sheets with this unit in order for the teacher to see how well students are progressing with the skills.

Unit Outcomes
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
o	Students will be able to apply their skills in order understand and solve a variety of multi-step word problems in which the unknown number can be either a part or a whole (Comprehnsion, Application, Synthesis)
o	Students will be able to justify their thinking about how the problem was solved in order to make a conclusion that they have arrived at the right answer (Evaluate)
•	Students will be able to analyze word problems in order to find the question being asked
•	Use given information to solve two-step addition word problems
•	Use previously learned strategies to solve problems and check answers

Pre-Assessment
The pre-assessment for this subunit will be given in two parts.  The first part will test student’s addition skills with one-digit and two-digit numbers as well as problems where there is no regrouping and some with regrouping.  This part of the assessment will be taken individually by the students.  It is important to continually check students’ progress with their addition skill because if they don’t have those basic skills mastered then there is no way that they will be able to apply them to word problems.
The second part of the pre-assessment will be given in small groups based on the student’s reading levels.  This pre-assessment is testing the student’s math skills and there are many kids who are struggling readers, by testing them in a small group and reading word problems aloud I will be able to know whether or not a student can figure out what the word problem is asking and if they are able to solve it, not that they can’t read the words.  By doing it this way I can already eliminate one barrier for the students.  Students will be tested in small group by reading ability because not all students need as much help and it is important that they are as independent as possible.  During this part of the assessment there will be one-step word problems to make sure the students have mastered that concept before trying to move them onto two-step problems.  There will also be a couple of two-step word problems so that I know which students will need enrichment beyond the lessons.

Name_________________________________________________________________________

Individual Pre-Assessment
Solve each problem.  If needed use a place value disk drawing.
	      8                              9                           10
	    + 6                            + 4                           + 7  

            22
	    + 6   

            92
	    + 7   

            47
	    + 5   
            84
	    + 9   

            98
	    + 3   

           158
	    + 6   

           589
	   + 23   

Name_________________________________________________________________________

Small Group Pre-Assessment
Read each problem and circle the question or questions being asked. Then solve each problem.  If needed use a place value disk drawing.

1.	Alyssa has 37 gummy worms.  Arlin has 58 gummy worms.  How many gummy worms do they have all together?

2.	Farmer Joe picked 97 apples in the morning.  In the afternoon he picked 67 more.  How many apples did Farmer Joe pick in all?  

3.	Julian has 46 red Legos and 38 blue Legos.  How many Legos does he have in all?  If his mom buys him 27 green Legos how many Legos will he have?

4.	Lauren and Gina's mother told her daughters they can swim in the pool for 20 minutes. First, they swam laps in the pool for 7 minutes.  Then they swam underwater for one minute. Then they played water polo for 8 minutes. How much longer can they stay in the pool?

Lesson Plan #1
2 Step word Problems with Concrete Manipulatives

Concept/Skill To Be Learned:
Identifying the questions in a two-step word problem.  Solving the problem with concrete manipulatives.

Unit Outcomes:
Students will be able to analyze word problems in order to find the question being asked.
Students will be able to use given information to solve two-step addition word problems with 90% accuracy.
Students will use previously learned strategies to solve problems and check answers

Lesson Objectives:
To identify the question being asked.
To correctly solve two-step word problems with 90% accuracy.
To use manipulatives to show how the problem was solved.

Time Allotment:  45 – 55 minutes

Materials/Resources Needed:
Personal Dry Erase Boards
Dry Erase Markers
Day 1 Worksheet
Place Value Disks

Procedures:
1.	Call students to the carpet- 5 Minutes
a.	“Who can remind me what we have been working on in math?”
b.	Students may give responses such as addition and subtraction strategies and word problems.
c.	Tell students that they are correct and that we will be using those skills today when we look at something brand new, two-step word problems.
d.	Talk to students about the importance of really reading the question and looking for what it is asking
2.	After talking to the students about what we are going to do ask them to go back to their seats- 25 minutes
a.	Put the following problem on the board: Erica has 14 pieces of gum and 35 pieces of licorice. How much candy does she have in all?  If she gets 8 Reeses how much candy does she have now?
b.	Read the question aloud to the students and ask them to find the question or questions that are being asked and raise their hand when they know.
c.	Give students a minute and then call on somebody to say the questions, make sure that they say both questions and circle them on the board.
d.	After questions have been identified pass out place value disks and ask students to take out their dry erase boards and markers.
e.	Tell students that they need to use the place value disks to solve the questions and write both of their answers on their white boards.
f.	Give them 5 minutes to work.
g.	At the end of 5 minutes go over the question, having students lead the discussion and scaffolding when appropriate.
h.	Repeat these whole group steps for the following 2 questions.
i.	     Pencils come in boxes of 10.  Victor has 14 boxes and Gabby has 5 boxes.  How many pencils do each of them have? How many pencils do they have altogether if they add ones more box?
j.	     Maria invited 4 of her friends over for a water balloon fight in the backyard.  At the start of the game, Maria gave each of her friends 2 water balloons.  She had one water balloon for herself.  How many water balloons did they have altogether?
k.	During the guided practice make sure that students are able to model their answers with their place value disks.
3.	After guided practice pass out Day 1 worksheet, instruct students to circle the questions that are being asked and use place value disks in order to help them solve the problems.- 15 Minutes

Assessment/Evaluation Strategy: Observation, Worksheet
Day 1 worksheet
Observation during guided practice

Day 1 Worksheet
Name_____________________________________________________
Circle the questions in each problem. Solve using place value disks, in the box draw what your disks look like.

1.	 Angela spent the day at the beach. She saw 12 children swimming in the ocean. 15 children were playing in the sand. 20 children were splashing in the wading pool. How many children did Angela see at the beach?

2.	 Laurie had 24 pumpkin seeds and 35 apple seeds. How many seeds did she have? If she gets 42 sunflower seeds how many seeds will she have now?

Lesson Plan #2
2 Step word Problems Moving from Concrete to Pictorial

Concept/Skill To Be Learned:
Identifying the questions in a two-step word problem.  Solve the problems with pictorial representations.

Unit Outcomes:
Students will be able to analyze word problems in order to find the question being asked.
Students will be able to use given information to solve two-step addition word problems with 90% accuracy.
Students will use previously learned strategies to solve problems and check answers

Lesson Objectives:
To identify the question being asked.
To correctly solve two-step word problems with 90% accuracy.
To use pictures to show how the problem is solved.

Time Allotment:  45 - 55 minutes

Materials/Resources Needed:
Personal Dry Erase Boards
Dry Erase Markers
Day 2 Worksheet

Procedures:
1.	Call students to the carpet- 5 Minutes
a.	“Who remembers the new math skill that we started working on yesterday?”
b.	Students will give answers about 2-step word problems, finding the questions and using the place value disks to solve the problem
c.	Tell students that today we are going to continue working on two-step problems but we are going to go back to our addition strategy of drawing a math picture to solve
d.	Remind students that whenever they work with word problems they need to read very carefully in order to make sure that they know what they are trying to solve.
2.	After talking to the students about what we are going to do ask them to go back to their seats- 25 minutes
a.	Put the following problem on the board: Anna's team scored 5 runs in the first inning of the kickball game. They scored 6 more runs in the second inning and 3 runs in the last inning. How many runs did Anna's team score in all?
b.	Read the question aloud to the students and ask them to find the question or questions that are being asked and raise their hand when they know.
c.	Give students a minute and then call on somebody to say the questions, make sure that they say both questions and circle them on the board.
d.	After questions have been identified ask the students to get out their dry erase board and markers.
e.	Tell students that they need to use our drawing a math picture strategy in order to solve the problems today.
f.	Give them 5 minutes to work.
g.	At the end of 5 minutes go over the question, having students lead the discussion and scaffolding when appropriate.
h.	Repeat these whole group steps for the following 2 questions.
i.	The book store is very busy today.  There are 25 children listening to a story.
36 people are shopping for books.  How many people are there?  If there are 16 people at the checkout how many people are in the store altogether?
j.	Crayons come in packs of 10.  If Sara has 26 packs and Alex has 12 packs how many crayons do they each have?  How many crayons do they have altogether? 
k.	During the guided practice make sure that students are able to model their answers with a math picture.
l.	After guided practice pass out Day 2 worksheet, instruct students to circle the questions that are being asked and use math drawings in order to help them solve the problems.

Assessment/Evaluation Strategy: Observation, Worksheet
Day 2 worksheet
Observation during guided practice

Day 2 Worksheet
Name_____________________________________________________
Circle the questions in each problem. Solve using a math picture, show your work.

3.	Trevor did his math homework for 19 minutes. He did his spelling homework for 15 minutes. How long did he do his homework for? He then practiced the piano for 23 minutes. How much time did he spend doing things altogether?

4.	Kelly did 124 addition math problems in 5 minutes. David did 37 more problems than Kelly. How many problems did David do? How many problems did the two do altogether?

Lesson Plan #3
2 Step word Problems with Algorithms and Mental Math

Concept/Skill To Be Learned:
Identifying the questions in a two-step word problem.  Solve the problems with pictorial representations.

Unit Outcomes:
Students will be able to analyze word problems in order to find the question being asked.
Students will be able to use given information to solve two-step addition word problems with 90% accuracy.
Students will use previously learned strategies to solve problems and check answers

Lesson Objectives:
To identify the question being asked.
To correctly solve two-step word problems with 90% accuracy.
To use the addition algorithm and mental math in order to solve the problems.

Time Allotment:  45 - 55 minutes

Materials/Resources Needed:
Personal Dry Erase Boards
Dry Erase Markers
Day 3 Worksheet

Procedures:
1.	Call students to the carpet- 5 Minutes
a.	“What addition strategy did we focus on yesterday?”
b.	Students will give answers that involve drawing a math picture to find an answer
c.	Ask students to tell you things that they should do when they are solving two-step word problems
d.	Students will talk about reading carefully, using addition methods and circling the questions that you need to answer
e.	Tell students that today we are going to try using the addition algorithm we learned to try to solve two-step word problems. 
2.	After talking to the students about what we are going to do ask them to go back to their seats- 25 minutes
a.	Put the following problem on the board: Suzy had 143 teddy bears and Bobby had 267 toy cars.  How many toys do they have altogether? James came over for a playdate and brought 53 dinosaurs.  How many toys do they have now?
b.	Read the question aloud to the students and ask them to find the question or questions that are being asked and raise their hand when they know.
c.	Give students a minute and then call on somebody to say the questions, make sure that they say both questions and circle them on the board.
d.	After questions have been identified ask the students to get out their dry erase board and markers.
e.	Tell students that they need to use the addition algorithm to solve the problems today.
f.	Give them 5 minutes to work.
g.	At the end of 5 minutes go over the question, having students lead the discussion and scaffolding when appropriate.
h.	Repeat these whole group steps for the following 2 questions.
i.	Alexa is reading a Nancy Drew mystery. She read 18 pages the first day. The next day, Alexa just couldn't stop reading.
She read 58 pages. How many pages did she read in all?  The third day she finished the book. She read 26 pages that day.  How many pages were in the book?
j.	Jake has 36 comic books. His brother has 15 more comic books than Jake.
How many comic books do they have altogether?
k.	During the guided practice make sure that students are able to show the algorithm and how they solved the problems.
l.	After guided practice pass out Day 3 worksheet, instruct students to circle the questions that are being asked and use place value disks in order to help them solve the problems.

Assessment/Evaluation Strategy: Observation, Worksheet
Day 3 worksheet
Observation during guided practice

Day 3 Worksheet
Name_____________________________________________________
Circle the questions in each problem. Solve using the algorithm, show your work.
1.	 Jeff had 58 stickers. Lisa had 16 stickers. How many stickers did they have in all?
Their friend Ed had 75 stickers.  How many stickers are there altogether?

2.	There are 10 M&Ms in each bag. Jack has 7 bags and Terry has 4 bags.  How many M&Ms do they have in all?
If they buy 8 more bags how many M&Ms do they have now?

Post- Assessment
	I am using the same assessment that was used for my pre-assessment as my post-assessment.  I have been taught that using the same assessment is important so that you can really see the growth that students have made over the course of the unit.  I will be able to compare the data side-by-side to see where students have made growth and where they are still struggling.  The assessment will still be given in two parts with the first part being individually taken by the student and the second part being a small group administered assessment.

Name_________________________________________________________________________

Individual Pre-Assessment
Solve each problem.  If needed use a place value disk drawing.
	      8                              9                           10
	    + 6                            + 4                           + 7  

            22
	    + 6   

            92
	    + 7   

            47
	    + 5   
            84
	    + 9   

            98
	    + 3   

           158
	    + 6   

           589
	   + 23   
Name_________________________________________________________________________

Small Group Pre-Assessment
Read each problem and circle the question or questions being asked. Then solve each problem.  If needed use a place value disk drawing.

1.	Alyssa has 37 gummy worms.  Arlin has 58 gummy worms.  How many gummy worms do they have all together?

2.	Farmer Joe picked 97 apples in the morning.  In the afternoon he picked 67 more.  How many apples did Farmer Joe pick in all?  

3.	Julian has 46 red Legos and 38 blue Legos.  How many Legos does he have in all?  If his mom buys him 27 green Legos how many Legos will he have?

4.	Lauren and Gina's mother told her daughters they can swim in the pool for 20 minutes. First, they swam laps in the pool for 7 minutes.  Then they swam underwater for one minute. Then they played water polo for 8 minutes. How much longer can they stay in the pool?

References
Chiarelott, L. (2006). Curriculum in context: Designing curriculum and instruction for teaching 
and learning in context. Belmont, CA: Thomson Wadsworth