Playing With Place Value - Manipulatives

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Students will be able to see that each time a digit is moved to another place value column it is 10 times greater or 10 times less.

Big Idea

Seeing is believing - especially in place value.


In the Common Core Standards, place value is no longer just the value of a digit because of the place it is in.  We now need to make sure students also understand that "in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left."  (5.NBT.A.1) 

Your students will be using manipulatives to model with mathematics the exchange of increasing 10 times or decreasing 1/10 the value as a digit moves through place value in this lesson.


30 minutes

I start my lessons with a question for students to discuss that will get them feeling included into the lesson and link their prior knowledge or experiences to the lesson.  For this lesson I asked my students to talk for a minute or so about what they would like to have 10 more of.  This activates students interest and gives real life examples - If I was to give my own example it may not relate to what my students know.  

I overheard students talking about they would like ten times more recess, ten times more dessert, ten times more gaming time, ten times more allowance.  

The next step is to review what the base 10 blocks mean.  The small cube = 1 unit, the bar is 10 units, the flat is 100 units and the large cube is 1000 units.   This is directly related to MP4 or modeling with mathematics and MP5, using appropriate tools strategically. I do this by holding up the manipulative and tossing a koosh ball to one student to answer.  They then toss the koosh to another student who has their hands raised to tell the class what the next manipulative is. 

I then start to put the blocks under my document camera and have students tell me the name of the number.  If you have a Smart Board you could find these pieces in Smart Exchange.  If you don't have the manipulatives or Smart Board you can have your students cut out pieces from  centimeter graph paper.  I would recommend gluing envelopes into Math Journals to save these for future use. 

 Once you feel your students are able to read the numbers from the blocks, or enough are to become your helpers, its time for a collaborative activity.  Review your procedures for group work and give these instructions to your students.

1. Make a number with your blocks (MP4,5)

2. Your partner will read the number and then multiply one of the digits by 10 and change the blocks to represent the new number. (MP7 - look for and make use of structure, MP8 Look for and express regularity in repeated reasoning.)

3.  Write a number sentence in your Math Journal. 


10 minutes

To extend this lesson I looked up Place Value in my district required textbook and assigned the pages for my students to work on independently. You can see some of their work pages in the resources below.

Because my students are 4th and 5th graders I need to meet a range of abilities - which I am sure you have in your classroom also.  The fourth grade workbook did not have place value with decimals but the 5th grade did.  I was okay with my 5th graders taking the information in the activity and transferring it to decimals.  This way I could assess where they are and if they need extra support. The 5th grade students who were struggling I did not move them back to whole number place value - I continued to teach place value with decimals in combination.  I am comfortable with the 4th grade not including decimals because it is not required in the 4th grade standards and I could really focus on place value with whole numbers for them.  The ones that wanted to do the 5th grade work I found an extra book for them to work out of but did not let them write in the book or they partnered up with a 5th grader.  This way I have a clean copy. 

I also believe productive struggle is good - the students who struggled a little with place value read the text to give them a different input of information and then had them work with someone else.  If needed (really struggling) I would have pulled a group together and work with small groups but I didn't need to this time. 

When your students are done have them thank their partners.  Appreciations build classroom collaboration which equals more time on task! 


5 minutes

After teaching a lesson always have your students reflect on the lesson - academics and behavior.  Reflection increases retention 50%. 

For this lesson I wanted to make sure one of my content reflection questions specifically asked what happens to a digit when it is moved one column up or down in place value.  When discussion is opened up so is MP3 - construct viable arguments and critique the reasoning of others. 

1.  What happens when a digit is moved one column up?

The value increases 10 times.

2. What happens when a digit is moved one column down?

The value decreases 10 times.

3. Was there anything else you noticed? 

I do not always have a answer in mind for this questions because I am assessing their understanding of the lesson.

If you don't have time to do the last two questions whole group, have your students tell their answers to their partner.  It is a built in appreciation!

4.  What went well with you and your partner?  

5.  What did you do to help your group?