Numbers Just keep Changing!

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Objective

4.NBT.A.1 SWBAT recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Big Idea

Students are use to numbers changing, working with a variety of skills students will be able to determine that a digit in the ones place represent ten times the digit in the tens place, and how to understand the concept of numbers altogether.

Warm-up

20 minutes

Interactive Base Tens

In this lesson I want my students to be able to explain the value of each digit as ten times the value to the right (connection to bundles of 10).

 To get a better understanding of what my students know about place value.  I write a single digit number on the board. 4. I ask students can anyone tell me what place this number is in? Ones What if I added a zero to this number,  Can anyone figure out what 10 times this number is? 

If you add a 0 to 4 the it would be 40, so 10 times 4 equals 40.  Yes! I draw a large place value chart on the board. I enter in the 4 first, and then I enter in 40, so that students can see I moved one space to the left.  I review a bit longer using different two and three digit numbers. I call on student volunteers to explain what would happen to a single digit number if they add ten times the number.  As students are working I encourage them to look for obvious patterns, and use them to reason  I do this until students recognize the repeated process. As students identify patterns I ask them to explain the pattern. For instance, one student notice how the place of the digit determines the value.  

For struggling students:  I have them represent the numbers using ten rods.. I ask how many groups of tens do we have. (4) If there are 4 groups of tens, then there are 4 tens. Where should you place the 4 in 40 on the place value chart. ( In the tens place)

MP-8 Look for and express regularity in repeated reasoning.

Students should see that adding a zero would give them the answer. However, I want to spend some time exploring what the class knows about place value. I repeat this pattern using numbers up to 5 digits, but always starting in the ones place. 

Modeling

Sharpening Skills

15 minutes

Materials: index cards, timer, pencils, Place value chart, base-ten materials, glue sticks

Skills: adding, estimating, making sense of and reasoning.

 

In this portion of the lesson I want my students to get in shape a bit! Well not literally! However, I want them to be able to move around a bit.  To do this I ask students to place their index cards and pencils on their desks. Then, I ask everyone to stand beside their seats.  I tell students we are going to record how many times we can do jumping jacks in 20 seconds.  Write that number down on your index card. Next, we are going to record how many times you guy can hop in 20 seconds. Write that number down on your paper. Of course students will come up with different numbers, however, they can be used if they have additional time.

After they have recorded their numbers, I ask students to pair up with their assigned partners.  What if we wanted to know how many times you can jump or hop in 40 seconds? How could we solve this using our 20 seconds numbers? How do you know? Explain? They should work together to look for structure within mathematics to help them solve problems efficiently. I explain, when say ten times a number we are composing numbers, how does this concept relate to place value and the value of digits.  Students that can change the value of a number by saying ten times a number. 

For struggling students: I give them base-ten materials to work with.  It helps them determine the value of a digit in relation to its place in a number, and recognize the distance between the numbers.

As students are working, I will circle the room to reinforce the idea of place value.  I might say can you record your twenty second number on your place value chart.  What happens if you wanted to know 10 times the number you recorded for 20-seconds number?  What do you notice about the place of the digits? How did it change? What if you wanted to know 10 times the number you just recorded?   What will happen to the value of the digit? MP8-Look for and express regularity in repeated reasoning.

(e.g., I can take the number 4, and add a zero to it to make 40, or I can say 10 x 4 = 40. I can see how this concept is preparing me for more complex skills like multiplication...)

Student sample of place value chart

Index card sample

Base tens example

Show Off!

15 minutes

 Materials:  place value chart, base ten material, pencil

Skills: adding, subtracting, multiplying 10 times a number, reasoning and comparing the value of the digits.

Now that students have worked with their partners some and in groups, I want them to return to their original seat. I write 260 on the board. I ask students to represent the number in the tens place by pasting the correct amount of tens on their place value chart.  I write 2600 on the board. I ask students to represent the number in the hundreds place by pasting the correct amount of hundreds on their chart.  Now let’s see who can tell me what number is 10 times 260.  I allow students to respond with guesses. (2600) some students noticed the answer by looking at their place value chart.  What if we take 260 and multiply it by 10? Again, I allow students to guess. Then, I ask them to represent 260 on their chart. After that, I ask them to represent 2600 on their charts.  How many spaces do 260 move to the left.  Students notice that each number move over once, and they added on 1 zero.   What if we took 2600 and multiplied it by 10? (26000) Students noticed that each number moved over once and they added on 1 zero.

To help them determine the difference between the numbers I ask them to add and subtract the two numbers.  2600- 260 = 2340     2600 + 260 = 2860. Then I ask them to represent the product and the difference on their place value charts.

Extension: Have students who are grasping the concept to compare two of the numbers using <, =, >.  

For struggling students: have them to work with the base-ten materials to help them recognize the difference between the numbers they are using.

 I repeat this process a couple times more to make sure each student does some kind of addition, subtraction, and comparing the values of the digits.  I continue to ask what’s happening with place value.  I provide guidance when needed.

Journal It!

10 minutes

To end this lesson student will write their own multi-digit number in their math journals.  They will have about ten minutes or so to answer the following questions about the number.

Questions:

How many tens are in this number?

Choose another number. Which number is bigger the number you chose, or the number you just wrote? Explain.

Add the two numbers together. What is 10 times the product?

As students are working, I circle the room to reinforce the standards addressed in this lesson For instance, did you notice a pattern. Can it be used to help you understand larger concepts? Explain? Did you explain mathematically? Can you illustrate, or represent your number? 

(Some students are able to determine the value of each digit, and others were able to express and show how numbers changed by show how ten times a number can change one/two/ and three digit numbers.) 

I use students’ responses to determine if they fully understand the concepts, or to decide if additional strategies should be given.