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Place Value &MathLine

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builds the foundation for all elementary math! Place Value

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Research shows: Students who understand Place Value tend to understand elementary math Students who struggle with Place Value tend to struggle with elementary math Place Value

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Place Value is demonstrated many ways in curriculum, including: Place Value Expansion of numbers Explanation of numbers within their different place Understanding Ones, Tens, Hundreds and up

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Place Value It is important to first understand on MathLine… blue rings indicate 5’s… red rings indicate 10’s

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Place Value Here are some examples of Place Value exercises Starting with expansion of numbers…

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Simple Expansion of 17? Place Value – Expansion

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How many tens and how many ones in 17? 10 1234567

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Simple Expansion of 46? Place Value – Expansion

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Note the number of red rings Place Value – Expansion

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How many tens and how many ones in 46? 10

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Place Value – Expansion How many tens and how many ones in 46? 10

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Place Value – Expansion 10 RULE – if we begin a group on one bar, it continues on the next. RULE – if we begin a group on one bar, it continues on the next. 10

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Place Value – Expansion 10 RULE – if we begin a group on one bar, it continues on the next. RULE – if we begin a group on one bar, it continues on the next. 10

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Place Value – Expansion 10 How many ones in 46? 265431

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Place Value – Expansion Students struggle with understanding the values for similar numbers, example: 15 & 51

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Show the relationship between 15 and 51 Place Value – Expansion Put 2 MathLines front to back

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Students can see the difference. Place Value – Expansion 15 51

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First, identify the “1” in 51 Place Value – Expansion 15 51515151

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Next, identify the “1” in 15 15151515 51

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Place Value – Expansion See how the “1’s” in each relate Students can see that the “1” in 15 is a ten, versus the “1” in 51 is a one 15151515 51515151

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Place Value – Expansion 12 3 3 45 Now, look at the “5’s”, what is the “5” in 51? It is 5 tens 15 51515151

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Place Value – Expansion 1 What about the “5” in 15? 2345 15151515 51

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Place Value – Expansion 12 3 3 45 We can see the 5 in “51” represent 10’s 15 51515151

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Place Value – Expansion 1 Where as the “5” in 15 is only 5 ones 2345 15151515 51

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Place Value – Expansion MathLine builds a concrete picture so students who struggle with switching numbers like 15 and 51… can now understand their value.

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Place Value – Expansion Now use MathLine to teach Place Value of 3-digit numbers

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Place Value – Expansion 236 100 200 300 100 200 36 62 Using multiple MathLine’s show relationship between 362

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Place Value – Expansion How do the “2’s” relate in both numbers? 236 362

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Place Value – Expansion 2 236 100 200 The “2” in “236” is two groups of 100. 362

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Place Value – Expansion 100 62 236 100 200 300 62 200 362 While the “2” in “362” is two “ones” 6262

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Place Value – Expansion How do the “3’s” relate in both numbers? 236362 236236236236 362

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Place Value – Expansion 236236236236362 The “3” in “236” is three groups of 10. 1 2 3 3

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Place Value – Expansion 236362 362 The “3” in “362” is three groups of 100. 100 200 300

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Place Value – Expansion 236 362362362362 How do the “6’s” relate in both numbers?

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Place Value – Expansion 236 362 The “6” in “236” is six ones

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Place Value – Expansion 236 362362362362 The “6” in “362” is six tens 1 2 3 3 4 5 6

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Place Value – Expansion On MathLine, students clearly see what the 2, 6, and 3 represent to each of these numbers. Teachers use many MathLine’s in sequence to teach value of numbers up to 1000.

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Place Value – Expansion MathLine allows for a concise yet clear strategy to model large numbers. Students who struggle with Place Value need a concrete picture to understand the abstract symbols and the place values of each digit.

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Place Value – Expansion Teachers are very creative with MathLine & Place Value exercises … As MathLine fulfills a unique need in such a fundamental concept in elementary math.

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