Change Unknown Word Problems

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SWBAT solve change unknown word problems using addition and subtraction strategies.

Big Idea

Students identify, develop, use, and share their own strategies for solving change unknown word problems.


10 minutes

 I start today's lesson with a problem of the day which I post on the board: 

At the seashore there were 65 shells. A big wave came and then there were only 19 shells. How many shells were washed away by the wave. 

 I start by asking students to help me draw a picture of this problem.   On the board, I have a volunteer draw a picture of the seashells at the seashore. Since it is tedious to draw 65 seashells, I ask students: 

How can we represent these seashells easily? 

Students may suggest drawing groups of tens and ones or building an array.  I ask a volunteer to come up and draw groups of tens and ones to represent the problem. 

Now, I give students white boards and ask them to solve this problem using the picture to help them.  As students work, circulate to determine what strategies students are using and what common mistakes are being made. 

Introduction to New Material

10 minutes

I would like for three students to share HOW they solved this problem.  As you share, I am going to draw and record your strategy on this chart so that everyone can see how you solved the problem. 

I ask three students who solved the problem accurately in different ways to come  and share.  Some students might have solved the problem by subtracting (65-19= _____).   Others might add (19 + ______= 65).  All strategies are appropriate as long as students can conceptually understand the problem and accurately solve. 

NOTE: Even if students have set up the problem the same way, students might have SOLVED it differently.

 For instance, one student might solve 65-19 like this:




Another student might solve it like this:



These different strategies can be recorded as above, or open number lines and should be discussed in the class as viable and different strategies for solving the problem. 

Guided Practice

15 minutes

Now you are going to have a chance to work with a partner to solve one of these problems.  Use the strategies that we have discussed to solve this problem accurately. In order to determine what the best number sentence is, you can draw a picture of the problem just like we did as a whole group. 

I hand out the guided practice worksheets to students.  I have students work in heterogeneous pairs so that they can support each other in answering the question and finding appropriate strategies.

When students have finished,  I bring them back together and have them share out their strategies (ask 2-3 pairs to share, esp. pairs who have chosen different strategies).  AS students present, ask them: Why did you choose that strategy?  Explain to your classmates how that strategy works.  Why did you choose to ___________ in this problem?

If students are all struggling with one component (regrouping, choosing an appropriate strategy or operation), use this time for necessary re-teaching.  If not, release students to the independent practice.  

This guided practice allows students to use the tools we have learned (addition, subtraction, invented algorithms, open number lines, hundreds, tens, and ones) in strategic ways.  Students should feel comfortable to use a variety of strategies to solve each of these problems. (MP5) 

Independent Practice

15 minutes

Independent Practice is differentiated based on student understanding of this concept. 

Group A: In need of intervention

Students will work with teacher to solve change unknown problems that do not require regrouping.  This group will mostly focus on drawing a picture to describe the problem and then setting the problem up correctly.  (Students in this group  may need more concrete modeling to understand how to set up the problem) 

Group B: Right on Track!

Students in group B will work independently to solve change unknown problems with numbers 1-100 that require regrouping.  

Group C: Extension

Students in group C will work independently to solve change unknown problems with numbers 1-300  that require regrouping. 


5 minutes

Now that you have worked alone to solve problems, I want you to share your work on the first independent practice problem with a partner.  As you share, explain how you used your strategy and how you made sure that your work was accurate. 

 Give students the following sentence starters if necessary: 

I solved the problem using this strategy....

My picture helped me to make this number sentence...

I chose this number sentence because...

I checked my work by...

As students share, circulate to gauge their understanding and confidence with change unknown problems.  

When students are finished sharing, ask one student from each group (A/B/C) to share their work and the strategies that they used.