Where's the Value in Place Value?

I have a love-hate relationship with the New Math TEKS, as I'm sure many of you Math Educators can probably understand. Although, if I truly took your pulse, I'm willing to bet 'hate' would be the more dominant beat than love.

Well I love that the TEKS address the foundational and conceptual basis of Math (which in fact are NOT new at all, just new to us). I hate that there are little to no resources that really instruct teachers on how to disseminate the information to their students. But with the latter, I find it fun (call it the geek in me) to study different strategies and create in my mind the perfect classroom situation and centers for students to engage in to assist with their discovery of these understandings.

Big shout out to my 3rd grade teachers who are now helping students understand value of numbers to the hundred thousands place. Here's a few strategy and center ideas to help you out next school year! And if you happen to teach 4th grade, you may benefit from this as well.

The NEW TEK states:
3.2A (similar 4th grade TEK is 4.2A) -  Compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate.

3.2B (similar 4th grade TEK is 4.2B)- Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place.

*Note the only difference in the 3rd and 4th grade TEKS are verbs and the place value focus.

STRATEGY IDEA: So, during your 15-20 minute mini-lesson, have your students sit in cooperative groups and work with a set of Base Ten Blocks (distribute up to 1 thousand block, 3 hundred flats, 5 ten longs and 10 units per group/pair-this should help you keep the numbers you compose/decompose within a certain range).

1. Give your students the task of creating a ten long using only unit cubes. Have them verbally express how we could write this in a number sentence. [They may say 1 + 1 + 1... = 10] Assist them in creating a multiplication number sentence (because up to this point they've only covered multiplication in the contextual sense, the multiplication symbol hasn't been introduced formally).

 

 

Verbal sentence: "1 group of 10 units = a 10 long" 

Number sentence: 1 x 10 = 10

 

 

2. Repeat facilitation of this task by having them line up the ten longs to see how many it takes to create a hundred flat; how many hundred flats stacked create a thousand block. Again, have them create a verbal sentence and corresponding number sentence.

 

3. Students can have a place value chart drawn in their journals. They can draw an arrow from the ones place to the tens place and label the arrow "10 times". Then draw an arrow from the tens place to the hundreds place labeled "10 times" and so on; to show that the progression from right to left across the place value chart is based on multiples of 10. Allow them to extend the pattern to the hundred thousands place.

 

 

4. Finally, demonstrate how to build a number (such as 324) and trade one of the hundred flats for 10 ten longs. Have them count to see if the value remains the same:

 

Say: "One hundred, two hundred, two hundred ten, twenty, thirty..., three hundred, three hundred ten, three hundred twenty, three hundred twenty-one, ....three hundred twenty-four)."

 

*This will help them grasp the concept of 'regrouping' when subtraction!!!

 

**Then see if they can discover other relationships; can they determine a relationship between the units and the hundred flat?

 

Verbal sentence: "10 groups of 10 units = a 100 flat"

Number sentence: 10 x 10 = 100

 

 

CENTER IDEA:

Materials: Number generators (dice), index cards with different numbers written on them, Place value disks.

 

Place value disks

 

Create numbers on index cards (or let students generate numbers using dice) in standard form up to the hundred thousand place. Have students build that number using place value disks or place value blocks.

 

 

 

 

Students can then write the number in expanded notation.

(1 x 1,000) + (2 x 100) + (4 x 10) + 3 x 1)

 

What many don't know is that the standard implies that students must be able to represent the number in other ways. So have students trade out a place value (for its x 10 value equivalent) and rewrite the same numeral a different way.

 

 

Notice here how the thousand block has been traded for 10 hundred flats.

This makes a combination (total) of 12 (10 and 2) hundred flats.

So the new expanded form & notation, respectively, would be as follows:

 12 hundreds + 4 tens + 3 ones

(12 x 100) + (4 x 10) + (3 x 1)

 

OR

 

Notice here how one of the ten longs has been traded for 10 units.

This makes for a combination of 13 total units, which doesn't change the value of the number but does affect how its written:

1 thousand + 2 hundreds + 3 tens + 13 ones

(1 x 1,000) + (2 x 100) + (3 x 10) + (13 x 1)

 

 

Now ordinarily, I would advise one to use a center sheet so students can record their findings. Something like what you see below (but of course for larger numbers):

 





 





No disrespect for those types of sheets, I often use them! But I'm a bit of a "tree hugger" (I like to protect the number of copies I make) so I prefer dry erase boards (unless of course I'm collecting it for a grade). Then in that case, I would put to use the construction paper in my room and have students create a foldable and record their work on it, in chart form.

 

Can't wait for the Fall to roll around again so you guys can try this out and let me know how it works for your students! Happy Educating!