place value &mathline. builds the foundation for all elementary math! place value
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Place Value
Place Value Place Value &&
MathLineMathLine
Place Value Place Value builds the foundation for all builds the foundation for all
elementary math!elementary math!
Place Value
Research shows:Research shows:Students who understand Students who understand
Place Value tend to understand Place Value tend to understand elementary mathelementary math
Students who struggle with Students who struggle with Place Value tend to struggle with Place Value tend to struggle with
elementary math elementary math
Place Value
Place Value is demonstratedPlace Value is demonstrated many ways in curriculum, many ways in curriculum,
including:including:
Place Value
Expansion of numbersExpansion of numbers
Explanation of numbers within their different placeExplanation of numbers within their different place
Understanding Ones, Tens, Hundreds and upUnderstanding Ones, Tens, Hundreds and up
Place Value
It is important to first It is important to first understand on MathLine…understand on MathLine…
blue rings indicate 5’s…blue rings indicate 5’s…red rings indicate 10’sred rings indicate 10’s
Place Value
Here are some examples Here are some examples of Place Value exercises of Place Value exercises
Starting with expansion of numbers…Starting with expansion of numbers…
Simple Expansion of 17?Simple Expansion of 17?
Place Value – Expansion
Place Value – Expansion
How many tens and how many ones in 17?How many tens and how many ones in 17?
10 1 2 3 4 5 6 7
Simple Expansion of 46?Simple Expansion of 46?
Place Value – Expansion
Note the number of red ringsNote the number of red rings
Place Value – Expansion
Place Value – Expansion
How many tens and how many ones in 46?How many tens and how many ones in 46?
10
Place Value – Expansion
How many tens and how many ones in 46?How many tens and how many ones in 46?
10 10
Place Value – Expansion
10 10
RULE – if we begin a group on one bar, RULE – if we begin a group on one bar, it continues on the next.it continues on the next.
10
Place Value – Expansion
10 10
RULE – if we begin a group on one bar, RULE – if we begin a group on one bar, it continues on the next.it continues on the next.
10 10
Place Value – Expansion
10 10
10 10
How many ones in 46?How many ones in 46?
2 65431
Place Value – Expansion
Students struggle Students struggle with understanding the values for with understanding the values for
similar numbers, example:similar numbers, example:
15 & 5115 & 51
Show the relationship between 15 and 51Show the relationship between 15 and 51
Place Value – Expansion
Put 2 MathLines front to backPut 2 MathLines front to back
Students can see the difference.Students can see the difference.
Place Value – Expansion
1515
5151
First, identify the “1” in 51First, identify the “1” in 51
Place Value – Expansion
1515
5511
Place Value – Expansion
Next, identify the “1” in 15Next, identify the “1” in 15
1155
5151
Place Value – Expansion
See how the “1’s” in each relateSee how the “1’s” in each relateStudents can see that the “1” in 15 is a ten, Students can see that the “1” in 15 is a ten, versus the “1” in 51 is a oneversus the “1” in 51 is a one
1155
5511
Place Value – Expansion
11 22 33
33 44 55
Now, look at the “5’s”, what is the “5” in 51?Now, look at the “5’s”, what is the “5” in 51?It is 5 tensIt is 5 tens
1515
5511
Place Value – Expansion
11
What about the “5” in 15?What about the “5” in 15?
22 33 44 551155
5151
Place Value – Expansion
11 22 33
33 44 55
We can see the 5 in “51” represent 10’sWe can see the 5 in “51” represent 10’s
1515
5511
Place Value – Expansion
11
Where as the “5” in 15 is only 5 onesWhere as the “5” in 15 is only 5 ones
22 33 44 551155
5151
Place Value – Expansion
MathLine builds a concrete picture MathLine builds a concrete picture so students who struggle so students who struggle with switching numbers with switching numbers
like 15 and 51… like 15 and 51…
can now understand their value.can now understand their value.
Place Value – Expansion
Now use MathLine to teach Now use MathLine to teach Place Value of 3-digit numbersPlace Value of 3-digit numbers
Place Value – Expansion
236236
100
200
300
100
200
36
62
Using multiple MathLine’s Using multiple MathLine’s show relationship betweenshow relationship between
362362
Place Value – Expansion
How do the “How do the “22’s” relate in both numbers?’s” relate in both numbers?
223636 363622
Place Value – Expansion
2
223636
100
200
The “The “22” in” in ““2236” is two groups of 100.36” is two groups of 100.
362362
Place Value – Expansion
100
62
236236
100
200
300
62
200
363622
While the “While the “22” in “36” in “3622” is two “ones”” is two “ones”
62
Place Value – Expansion
How do the “3’s” relate in both numbers?How do the “3’s” relate in both numbers?
236236 362362223366 336262
Place Value – Expansion
223366 362362
The “The “33” in “2” in “2336” is three groups of 10.6” is three groups of 10.
1 2 3
3
Place Value – Expansion
236236 362362336262
The “The “33” in “” in “3362” is three groups of 100.62” is three groups of 100.
100
200
300
Place Value – Expansion
232366 336622
How do theHow do the ““66’s” relate in both numbers?’s” relate in both numbers?
Place Value – Expansion
232366 362362
The “The “66” in “23” in “2366” is six ones” is six ones
Place Value – Expansion
236236 336622
The “The “66” in “3” in “3662” is six tens2” is six tens
1 2 33 4 5
6
Place Value – Expansion
On MathLine, students clearly On MathLine, students clearly see what the 2, 6, and 3 represent to each of see what the 2, 6, and 3 represent to each of
these numbers.these numbers.
Teachers use many MathLine’s in sequence to Teachers use many MathLine’s in sequence to teach value of numbers up to 1000. teach value of numbers up to 1000.
Place Value – Expansion
MathLine allows for a concise yet clear MathLine allows for a concise yet clear strategy to model large numbers.strategy to model large numbers.
Students who struggle with Place Value need Students who struggle with Place Value need a concrete picture to understand the abstract a concrete picture to understand the abstract symbols and the place values of each digit.symbols and the place values of each digit.
Place Value – Expansion
Teachers are very creative with MathLine & Teachers are very creative with MathLine & Place Value exercises …Place Value exercises …
As MathLine fulfills a unique need in such a As MathLine fulfills a unique need in such a fundamental concept in elementary math.fundamental concept in elementary math.