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## Modeling Decimals with Base 10 Blocks

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**Modeling Decimals with Base 10 Blocks**Joyce Bishop**Using Familiar Base 10 Blocks to Model Decimal Numbers**• flat = 1 • long = 0.1 • small cube = 0.01 • small flat = 0.001**Representing Decimal Numbers**Base 10 blocks Decimal Fraction Representation Representation 2.6**Representing Decimal Numbers**Base 10 blocks Decimal Fraction Representation Representation 3.217**Comparing Decimals**Represent each of the following numbers with base 10 blocks and put them in order from smallest to greatest: 2.1 1.96 2**Comparing Decimals**1.96 2 2.1**Model Space Ship**Ethan is constructing a model of a space ship. The first stage is 2.34 meter tall. The second stage is 1.031 meters tall. What is the total height? Model the solution with base 10 blocks.**Model Space Ship - Addition**Add 2.34 + 1.031: 2.34 1.031 = (3 x 1) + (3 x 0.1) + (7 x 0.01) + (1 x 0.001)= 3.371**Representing Two Ways**Use your understanding of place value to show two ways to represent 0.18 with base 10 blocks.**Representing Two Ways**Use your understanding of place value to show two ways to represent 0.18. or √**Storing a Model Space Ship**Ethan has another model space ship that is 1.62 meters tall. If he stores it in a cabinet that is 2.18 meters tall, how much taller is the cabinet than the model space ship? Model your solution with base 10 blocks.**Storing a Model Space Ship - Subtraction**Subtract 2.18 – 1.62 2.18 Rename 1 as 10 x 0.1**Storing a Model Space Ship - Subtraction**Subtract 2.18 – 1.62 2.18**Storing a Model Space Ship - Subtraction**Subtract 2.18 – 1.62 2.18 2.18 m – 1.62 m = 0.56 m**Multiplying Decimals Using an Understanding of Place Value**Using Place Value Materials (With Renaming) 1.6 x 2 2 groups of 1.6**Multiplying Decimals Using an Understanding of Place Value**Using Place Value Materials (With Renaming) 1.6 x 2 Trade to make another unit. 1.6 x 2 = 3.2**Multiplying a Decimal by a Decimal**1.6 x .2 Find two tenths of each part.**Multiplying a Decimal by a Decimal**1.6 x .2 Find two tenths of each part (not drawn proportionally.) xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx**Multiplying a Decimal by a Decimal**1.6 x 0.2 1.6 x 0.2 = (2 x 0.1) + (12 x 0.01) xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx**Multiplying a Decimal by a Decimal**1.6 x 0.2 1.6 x 0.2 = (3 x 0.1) + (2 x 0.01) = 0.32 xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx**One Multiplicative Situation: Two Division Types**Aeisha is cutting ribbon for a hair bow. She has 1.2 meters of ribbon. Each piece of ribbon must be 0.3 meters long. She can cut 4 pieces of ribbon. Two division questions: • You know how long each piece of ribbon must be. How many pieces can you cut? (Measurement Division) • You know how many pieces of ribbon you need. How long is each piece? (Partitive or Sharing Division)**Measurement Division**Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut? Rename 1.0 as (10 x 0.1)**Measurement Division**Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut? Count groups of (3 x 0.1).**Measurement Division**Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut? One group of (3 x 0.1).**Measurement Division**Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut? Two groups of (3 x 0.1).**Measurement Division**Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut? Three groups of (3 x 0.1).**Measurement Division**Aeisha has 1.2 meters of ribbon to use for a hair bow. Each piece of ribbon must be 0.3 meters long. How many pieces can she cut? Four groups of (3 x 0.1). 1.2 meters ÷ by 0.3 = 4**Partitive (Sharing) Division**Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be? Rename 1.0 as (10 x 0.1)**Partitive (Sharing) Division**Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be? Arrange the blocks in four equal groups.**Partitive (Sharing) Division**Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be? Four groups of 0.1 m with 0.8 m left.**Partitive (Sharing) Division**Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be? Four groups of 0.2 m with 0.4 m left.**Partititve (Sharing) Division**Aeisha has 1.2 meters of ribbon to make into a hair bow. If she wants to cut it into 4 pieces, how long will each piece be? There are four groups with 0.3 meter in each. 1.2 meters ÷ by 4 = 0.3