Finding the Unknown: Solving Problems with Unknown Change

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SWBAT use strategies to solve story problems with unknown change or starting number. SWBAT use numbers and standard notation to record answers.

Big Idea

Students will dive into problems that require them to solve story problems with unknown changes. The idea will be explored as a class and then applied in individual tasks.

Warm Up

10 minutes

I start this part of the lesson by asking all of the students to face the white board easel and hand them each a small clock.  

"I want to spend a few minutes using clocks to read and set the time?.  It has been a few weeks since we have worked with our clocks and I just want to check in with you about it"

"Who can remind me the names of each hand?  Who can tell me which numbers are the hour numbers and which numbers are the minute numbers?  (I am using a big demonstration clock as I ask these questions).  

"I am going to call out a time.  Your job will be to set your clock for the time I say and then hold the clock up so that i can see it. Once everyone is down, I will set my clock to the time and then you can check your clock with mine."   

I do this for a few hour times and then I jump to half hour times.  Then I switch it up by writing digital times on the board (half hours and hours) and have them read the time in their head and then set their clocks to the written time.

The Core Standards expect that 1st graders can "tell and write time in hours and half-hours using analog and digital clocks (CCSS.Math.Content.1.MD.B.3)."  I am asking the students to use clocks to read times and placing hour and minute hands to represent set times. I am also asking them to read digital notation and represent that time with an analog clock. The students are using a mathematical tool to solve a problem and are becoming familiar with clocks (CCSS.Math.Practice.MP5).

I find this warm up routine to be a very crucial moment in my lessons.  This time allows me to continue to hit upon skills that have been introduced throughout the year but might not necessarily be the main focus at this time.  This way I can reiterate concepts that need multiple exposure points and continued review.   

Exploring the Conceptual Idea of Unknown Change Problems

20 minutes

I start this part of the lesson off by reviewing with the students the steps that we have used to solve a story problem.  There is a video in the section resource that captures this discussion and review.

I then move into the following discussion:

"I want you to use the approach we just discussed to solve a story problem that I am going to tell you."  

My daughter, Abby, was putting books on her bookshelf.  At first, she put three books on the top shelf.  She put some more books on the bottom shelf.  Then, she had 5 books on her bookshelf.

"Who can retell that story to me in your own words?  What happened in the story?  What are we trying to find out?  Will our number be more or less than three?  Why?" "How many did use have at the end?  What do you think we need to find out?"

After a discussion about this, I want to model how to notate what we are thinking.  I have mixed in the idea of missing addends throughout the year.  If this is a new concept for your kids, it will take a much richer conversation for the majority of your students to grasp this idea.  

"I am going to write down the number that you said we started with.  You said that she got some more so I am going to write a '+' sign next to the three and then a blank line to represent the number of books that she added to the other shelf.  I know that she has 5 books at the end of the problem, so I ma going to write =5."  There is a photo in the section resource that models this part of the discussion.  

"I now want you to work with someone next to you to solve this problem.  How many books did she put on the 2nd shelf? You can use connecting cubes to help with your thinking."

I then ask students to share how they solved the problem.  I am looking for students to model how they used cubes to find the missing part.  This way everyone can not only see their thinking but also have a visual to relate to.  

Note:  Some kids will use addition and add up from 3 to 5.  Some kids will use subtraction and know that taking 3 from 5 will yield the answer.  You want to make sure that the addition and subtraction models are modeled, even if this means that you show it as your example.

In this case the students are using quantitative reasoning by creating a representation of the problem, understanding the meanings of the quantities and using different operations to solve the task (CCSS.MATH.PRACTICE.MP2)


Applying the Concept in Story Problems

25 minutes

*Advanced Preparation:  You will need to make enough copies, of the story problems (section resource), for each of your students.

Note:  I am using small numbers with these problems because students find unknown change problems difficult.  By keeping the numbers small, They are working with familiar numbers and focusing on the hard part of the problem.

"You are now going to solve some problems on your own.  I will read the first one to you.  Then you will get to work.  Again, you can use connecting cubes to help solve the problem.  Remember, I want you to show your thinking and write an equation to represent it.  If you need help reading the next problem or would like a problem reread, please let me know."  The students are
solving problems using addition and subtraction within 20 and using a symbol for the unknown number to represent the problem (CCSS.MATH.CONTENT.1.OA.A.1 & CCSS.MATH.CONTENT.1.OA.D.8).  This is an end of the year CCSS expectation for each first grader.

As students are working, you will want to circulate to help students and make sure that everyone truly understands what he/she is solving for.  You will also want to know what strategy that students are using to solve the problem.   Some will model with cubes/pictures.  Some will use counting on or back, and some will use known facts. 

It is expected that the students can analyze relationships mathematically and draw conclusions as well model their thinking with mathematics (CCSS.MATH.PRACTICE.MP4).

There is a video in the section resource that has a student explaining who she solved one of the problems.  She is modeling how she counted on and then created an equation.  There is also a copy of her page int he section resource (Lucy).  I also included Matthew's who used known facts.  

Lesson Wrap Up

15 minutes

I will wrap up today's lesson with a discussion about problems one and two from the story problem packet.  I will reread each problem (one at a time) and ask the group to help me write an equation to represent what is going on in the problem.  

I will then ask students to share who they solved each problem.  I will call on specific students (based on strategies that they used in solving the problems not heir own).  This way I can make sure that a variety of strategies represented.  I have included a video of one student's (the girls who explained her answer in the previous section) presentation.


Continued Practice

5 minutes

I will end today's lesson with a skill sheet that reinforces the concept of the "unknown."  This sheet should be done individually and some students may not finish in the remaining time.  If that is the case, you could ask students to complete two liens from each section.  This way you could get a sample of the addition and subtraction problems.  The sheet is located in the section resource.