Multi-Step Word Problems and Addition

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SWBAT use tape diagrams to solve multi-step word problems using the standard addition algorithm.

Big Idea

In this lesson, students will utilize their knowledge of rounding and addition and practice using tape diagrams to solve word problems.

Number Hook - Magic Trick

7 minutes

I performed a magic trick today called 21.  You can see how it works in the video below.  The man in the video does it slightly different than I do, but you'll get the gist. 


My students were, as usual, happy, in awe, and amazed. Thee magic tricks truly captivate my students instantly.  The tricks are turning out to be great help with transition as well because students are entering in quickly and quietly in order to see the "next new trick."   

Note: When I perform this trick, I do not take nearly as long as the man in the above video.  I shorten mine down so I have enough time to deliver the content of my lesson.

Warm Up

10 minutes

I believe writing in math class supports learning because it requires students to organize, clarify, and reflect on their ideas—all useful processes for making sense of mathematics. In addition, when students write, their papers provide a window into their understandings, their misconceptions, and their feelings about the content they're learning.  Getting into the routine of the school year always seems to take some time, but writing in math is one component I want to make sure I do each day. Students begin using their math journals more to review skills taught, but in particular, practice writing about their math thinking. I use a resource from

I like these math prompts from this site because they are directly tied to the common core standards. While the prompts definitely don't cover a standard in it's entirety or to the full depth of a standard, they do provide helpful information for formative assessments and give my students opportunities to practice writing in math.  At the end of the fourth grade journal from this website, is a rubric for math writing.  I actually went through the rubric with my students during a writing block time.  They then glued them into the front of their math notebooks.  This gives them an idea of what I'm looking for in their math writing and a way for me to score their work. Just as in writing stories, or other work, students are always asked and encouraged to EDIT their math writing and increase their rubric score.

To begin this warm up, students answer a journal prompt:  

Due to copywrite issues, the following problem is similar but not exact to the problem my students solved. 

Eric thinks of a number. When rounded to the nearest ten, the number is rounded to 370. When rounded to the nearest hundred, the number is rounded to 400. What could the number be?  Explain your thinking.

The above prompt correlates to standard 4.NBT.3, use place value understanding to round multi-digit whole numbers to any place.

When I look at students' responses later not only will I be able quickly gauge which students are understanding rounding, I will be able to give feedback on their math writing.  I'm interested how they chose to write about what the number could be. 



Concept Development

40 minutes

To begin this lesson, I remind students about a previous lesson in which they learned about tape diagrams as tools and models to help visualize addition and subtraction. 

For this lesson problems,  I want my students to continue to use tape diagrams to help bridge or connect their concrete representations of addition to the abstract world of mathematical symbols.  This is especially important for word problems. Based on previous assessments, I know most of my students are successful with adding large numbers, however, many of my students struggle with making sense of an addition situation, especially when the  numbers are large.

I assign students word problem partners for today's practice. Before we begin I play this top tips for partners  song.


 This is a great reminder about working together and really tackles the issues that many students often struggle with. My students giggled and loved this song.  I even had a few students ask if we could make our own partner videos. So many of my students come to fourth grade with word problem anxieties.  Working with a partner eases some of this anxiety which is the reason I chose to have them work with partners for this assignment.

Next, I review how a tape diagram is helpful and model the first problem on the second page from the word problems page. (students worked on the first page in a previous lesson) Then students work with their partners to complete the rest of the page.  

As students work with their partner, I circulate around the room and guide students thinking.  I ask clarifying questions and help clear up misunderstandings. 

As seen in this video, a student is working through a word problem from the assignment using a tape diagram.  







Student Debrief

10 minutes

For todays wrap up, I gave students an index card. On their index card I ask them to write three things.  They write one way a tape diagram can be a useful tool, two numbers that are about 70,000 when rounding to the nearest ten thousand, and three things they know about addition.

When I look through their index cards I will be looking for several things.  As we head into adding and subtracting large numbers, I want to see what my students prior knowledge is about adding. Do they know words like addend, sum, and equal. I also want to find out who still needs more assistance with rounding to the nearest ten thousand.  Lastly, I want to see if introducing the tape diagram as a tool resonates with students about being a math tool they can use to solve problems and model situations.