Ten Times More

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SWBAT explore patterns in the base ten system and build numbers using base ten blocks to find ten times a number.

Big Idea

In this lesson, students will use place value reasoning, manipulatives, or proof drawings to understand a digit in the ones place represents ten times what it represents in the place to its right.

Warm Up

5 minutes

I begin this warm up by directing students to play one round of  "I have Who Has- Place Value". I Have Who Has Place Value 2 Thousands

 I only allow five minutes for this activity because this is a familiar game for my students and they can play this very quickly. 

The basic idea of this game is to distribute one problem (CARD) to each student.  If there are extra cards, some students may get 2 cards.  The first student reads his/her card.  The student with the correct answer on his/her card reads the answer along with the next question.   Play continues until all cards have been read.


One managment strategy I use is a classroom challenge.  In this challenge, I time students the first time they read and play one round of the I Have Who Has game.  Then, students particpate in the same activity the next day for warm up trying to read all cards faster than they did the day before. I record the times on the board so students can see progress in their time!

Concept Development

40 minutes

For this lesson, students work in table groups. One helpful tip is to have a "ready cue" to call students attention after an adequate amount of building time.  One ready cure I like to say is Hocus Pocus. Students respond with, "everybody focus." Prior to this lesson, I have placed an ample amount of base ten manipulatives at each table.  

To begin this lesson, I give my students 7 minutes of  "free building" time so students can experiment with the base ten blocks before using them for today's math task. I set a timer on www.timeme.com for 7 minutes and allow students to build what they wish to during this free building time.  When the timer goes off, my expectation is that "student time" is over and "instructional time" has begun.

Students need to use blocks to be successful with this lesson. Next, I ask students to make a two- digit number like 46 using the base ten manipulatives. I then pose this problem to students: “Imagine there are ten students and they each have 46 books. How would you show this with your base ten blocks?"

I direct students to model their thinking using the base ten manipulative and explain how they would model 10 groups of 46.  Students respond by saying they would build 46 ten times.  I ask students how they know how many books there are all together.  I  help guide students by asking them how many total tens they have.  They responded with 40.  I then ask how many total ones they have and students respond with 60.

Note: Some students are likely to have a symbolic algorithm, such as “add a zero,” that enables them to get an answer of 460.  I encourage students to build numbers with base ten blocks in their group in order to explain the use of zero as a placeholder. 

I pose several other similar problems where students build numbers with base ten blocks and look at the combined product.

Once students seem to be successful with the base ten manipulatives, I show them how to model with proof drawings.  I direct students to show a proof drawing of the ten groups of 46. An example of a proof drawing would be ten sets of 46 separated into tens and ones. Ten sets of 46 becomes 40 tens and 60 ones or 400 and 60 or 460.  

See the photograph below as an example of a proof drawing.  

Note: My students are very familiar with these proof drawings from prior work in second and third grade.  

I pose several more problems for students to model with proof drawings.  As students create their drawings, I circulate around the room and assist students as necessary. They work on the problems 10 x 36, and 10 x 78.

I observe students to see that they are able to solve and reason about products using place value understanding.  Next, I use a place value chart to connect 10 x 78 ( the last problem students solved) and show students what is happening on the place value chart. 7 tens x 10 would end up being 70 tens or 700 just like in the photograph above, 4 tens x 10 becomes 40 tens or 4 hundreds. 

I guide students to see and explain that the digits in 78 move one place to the left when creating ten groups of 78 or 10 x 78.   

For the remainder of the lesson, students work on the practice problems, creating proof drawings or models for each - place value sample problems. As students work, I circulate around the room and assist as necessary and guide students thinking through questioning. I clear up any misunderstandings as they occur. 

Student Debrief - Wrap Up

10 minutes

I instruct students to put all materials away. Then I lead a brief discussion about students findings, discoveries, or realizations.

I pose questions such as:

What happens to the value of the digit in the ones place when the number is multiplied by

10? by 100?

What happens to the value of the digit in the tens place when the number is multiplied by 10? by 100?


Then, I direct students to explain to their learning partner what he/she learned about the value of a digit's place as the digit moves one position to the left. 

I listen to see that students are beginning to articulate that each time the digit moves to left, the value of that digit increase by ten times.

Last, I give students an Exit Ticket to complete before they leave for the day. The Exit Ticket for this lesson is:

1 ten is ______ times as many as 1 one.

1hundred is __________ times as many as 1 ten.


Note: I will then group the exit tickets into two piles, a correct answer pile and incorrect answer pile which will also include tickets that were left blank.  I then present re-teaching opportunities for students with incorrect answers and not answered tickets at another time set aside during the day for re-teaching and extra support.  My colleagues and I have built in a half an hour time slot four days a week for math re-teaching outside of the math class.