Making the connection:
My students understand certain things can be represent in different ways. I ask them to view the picture of the dove. What can it represent? (peace, to be free) Right! Today we are going to learn how to represent numbers in a variety of ways.
In this portion of the lesson I am going to demonstrate how to read and write multi-digit numbers in a variety of ways. MP4-Model with mathematics.
In order for students to work flexibly with numbers, they need to understand different representation of numbers, including standard form, expanded form, and word form. Understanding multiple representations of numbers sets the stage for multiplication and division of numbers as well as understanding and comparing fractions and decimals.
To start students off, I say there are various ways to write numbers can anyone think of a way to write 385. I want to start with a smaller number, so that students can quickly grasp the concept.
Students recall expanded form. 300+ 80 + 5
Can you represent this number using base-tens, or other drawings?
What number is in the ones, tens, and hundred place?
How many hundreds do we have? 3 hundreds
How many tens do we have? 8 tens
How many ones do we have? 5 ones
I tell students you guys are exactly right, these are all ways to write and identify numbers.
Another way to write and identify number is by writing the number in word form. Let's look at the number 385 again. Can anyone tell me how to write that number?
(three hundred eighty five) You guys are awesome! You have 3 hundreds eight tens, and five ones.
I point out that using models to represent and solve a problem can help you explain your ideas by relying on the model that represents your answer. You guys are doing a great job so far!
I will continue this pattern gradually working students up to four and five digit numbers. I am careful to guide students only when needed, so that they gain a deeper understanding of representing numbers.
Are you guys ready to represent?
In this portion of the lesson I want my students to practice reading, writing, and modeling numbers! This activity will give them time to explore a bit on their own, hopefully to gain understanding.
To begin I ask students how did you show 1,456 using the base-tens blocks. Students took their time modeling with base ten material. As they were creating their models, I ask them to describe the blocks they used.
For instance, one student used 10 hundred blocks to represent 1 thousand, and another student used tens to represent 4 hundred.
I probe student who represented 4 hundred with 10 rods, just to see if he can come up with another way to represent 4 hundred. It took him a minute, but he eventually used 4 hundred blocks.
Allowing them to represent different numbers through base-ten models will help them better understand the value of the digits. I ask students can you show me how to write this number in expanded form. I ask students to write their representation down on their record sheet. I explain that they will compare their number forms by writing them on their recording sheets.
Can someone explain how to separate the different parts of 1,456 when written in expanded form? 1000 + 400 + 50 + 6
Because some students are unable to explain, I discuss how determine the value of each digit by placing them into the correct place on the place value mat.
Have students to share their findings with the rest of the class. As students are sharing, I encourage students to ask question is they need to!
Can you explain what you have done so far? What else is there to do? Why did you decide to use this method? Can you think of another method that might have worked? Is there a more efficient strategy? What did you notice?
MP2- Reason abstractly and quantitatively.
In this fun activity students will get a chance to do what they love best. DANCE... They will dance their way into understanding how to represent a number in four different ways.
Mrs. Redfield’s class is putting on a step-show to represent the special number of the day. Each group of students has to represent a number in at least four different ways with an arrhythmic step beat. Today it is time for all groups to present their Steps by representing the number 2,143. Each group has to figure out how to represent the number in four ways? After that, create a jazzy step-dance to present your representations of their number.
I ask students to record and discuss their representation on large chart paper. As for their beats ask them to be prepared to show their creativity with the class.
In the video below, students represent their numbers in four different unique ways. For instance, they use based-tens, hand movement to represent standard form, and their written form was on classic white paper incorporated into a unique beat.
MP4-Model with mathematics.
After each group has presented their work, I invite students to the carpet. I want to open up a brief discussion, so that I can gauge what they know so far.
How many ways did we represent numbers? Can someone describe one way? How do you know? Are their other ways to represent this number? Explain? Why is it important for us to learn how numbers can be represent? Can this skill be used to solve problems? Explain?
Students eagerly explain four ways numbers can be represented. One student point out that they can identify the number in many forms, and know that it has the same value.
We continue discussing until the last group has presented.