3rd Grade - Expand Using Place Value

 
     
 
     
 
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3rd
Numbers
Expand Using Place Value
Use expanded notation to represent numbers (e.g., 3,206 is written as 3,000 + 200 + 6 in expanded form).
Number Sense: Expanded notation, expanded form. The ability to stretch out numbers to reflect the value in each place of the number.
 

Sample Problems

(1)

How are numbers written? Numbers can be written in different ways. (standard and expanded)

(2)

What do the terms standard notation and expanded notation mean? (Standard numbers are written with numerals and commas like you see in everyday life. Expanded notation numbers are pulled apart into parts and reflect the number value of each place—just like when figuring out place value.)

(3)

How do you write the number 823 in expanded notation? (800 + 20 + 3)

(4)

Write in standard notation: 6000 + 500 + 8

(6,508)

(5)

Write this in standard notation. 9,000 + 300 + 20 + 6 (9,326)

Learning Tips

(1)

If children are to really “understand” math, they need to understand how we create larger numbers. Remind them that we can never put more than 9 units into one place-value slot; when we add one more (counting is the same as adding one) we must move over to the next place-value column. For example, to represent the number 32, we place 3 counters in the 10s spot and 2 counters in the ones spot. Another way to say this is that we have a value of 30 in the tens column and if we add the value in the ones column to it (30+2) we have represented the same number in a different way.

(2)

Children who understand how to write numbers in this format (called “expanded notation) will have learned an important mathematical representation form that they will need later for algebra. It’s worth making sure that your child is capable of this skill and understands what he/she is doing, as opposed to memorizing a few specific problems. Students who have only memorized it will forget it without constant reinforcement of additional problems; those who understand it will remember it later with very little review.

(3)

Reading the number aloud will help children to write an expanded notation form correctly because reading the number reminds them of what an expanded notation actually means. For example, to expand 3,284, when your child says “three-thousand,” it is obvious that the largest place value is thousands, so that one should be written first. When your child says “two-hundred,” it is obvious that the next largest place-value is the hundreds. Continuing, when your child says, “eighty” and then “four” the rest of the expanded notation is clear: 3,000+200+80+4.

(4)

If your child has difficulty in rewriting a number in expanded notation form back into standard form, use the place value rectangle mats from the lesson on place value and have children place manipulatives on the mat to express number. For example, 345 will show three tokens in the hundreds compartment, four tokens in the tens space and five in the ones. Children can then recite the amount in each space. Since the place value columns have replaced the 0s in the expanded notation (the number of 0s show the place value in a different way) your child should see how to write the standard form. If the place value column is empty then a 0 goes in that space; i.e., for the number 406, there are 4 manipulatives in the hundreds column, and six in the ones column, but nothing in the tens column. Therefore the tens column must be written as a 0 since there are no manipulative pieces there.

(5)

Use base ten blocks to visually show expanded notation. 123=one 100 flat, two ten rods and 3 ones.

Extra Help Problems

(1)

How do you write the number 508 in expanded notation? (500 + 8; since there are no tens to represent there is nothing to write in that space)

(2)

How do you write this expanded number in standard notation? 9,000 + 700 + 50 + 3 (5,753)

(3)

How do you write this expanded number in standard notation? 5,000 + 200 + 50 + 5 (5,255)

(4)

How do you write the number 1,008 in expanded notation? (1000+8)

(5)

How do you write the expanded number in standard notation? 10,000 + 800 + 30 + 1 (10,831)

(6)

How do you write the number 999 in expanded notation? (900 + 90 + 9)

(7)

How do you write the expanded number in standard notation? 6,000 + 600 + 20 (6,620)

(8)

How do you write the number 23 in expanded notation? (20 + 3)

(9)

How do you write the expanded number in standard notation? 10,000 + 900 + 70 + 9 (10,979)

(10)

How do you write the number 200 in expanded notation? (200)

(11)

How do you write the expanded number in standard notation? 300 + 3 (303)

(12)

How do you write the number 842 in expanded notation? (800 + 40 + 2)

(13)

How do you write the expanded number in standard notation? 8,000 + 400 + 3 (8,403)

(14)

How do you write the number 250 in expanded notation? (200 + 50)

(15)

How do you write the expanded number in standard notation? 600 + 90 + 9 (699)

(16)

In problems 16-25, decide if the number has been written in expanded notation or standard form. If the number is in expanded notation, write it in standard form. If the number is in standard form, write it in expanded notation.

(17)

8,000 + 400 + 30 + 0 (8,430)

(18)

8925

(8,000+900+20+5)

(19)

6000 +200 + 40 + 4

(6,244)

(20)

5334

(5000 + 300 + 30 + 4)

(21)

4541

(4000 + 500 + 40 + 1)

(22)

5000 + 300 + 6

(5,306)

(23)

3073

(3000 + 70 + 3)

(24)

759

(700 + 50 + 9)

(25)

3000 + 100 + 4

(3,104)

(26)

1411

(1000 + 400 + 10 + 1)

 

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