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Fractions, Decimals, and Percents.notebook 1 March 07, 2011 Sep 2911:57 AM Fractions, Decimals, and Percents Sep 2911:57 AM Fraction Riddles Draw a rectangle to represent the following scenarios A rectangle is 1/2 red, 1/5 green, 1/10 blue, and the rest yellow. How much of the rectangle is yellow? A rectangle is 3/5 red. The rest is blue and yellow but not in equal amounts. What could the rectangle look like? A rectangle is 1/2 red and 1/3 blue. It also has green and yellow in equal amounts. What could the rectangle look like? Sep 2911:57 AM 1. Students must experience fractions in many ways including parts of wholes, ratios, and division 2. Three types of models exist: area, length, and part of a set. 3. Partitioning and iterating are ways to understand. 4. Students need to have many experiences estimating with fractions 5. Understanding equivalence is critical. Computation 1. The meaning of each operation with fractions is the same as the meaning of each operation with whole numbers. 2. Estimation is tied to the concept of the operations. Fraction Big Ideas Sep 2911:57 AM Math Activity: Thinking about Fractional Amounts Sep 2911:57 AM What is a Fraction? Sharing 10 brownies shared with 4 children 5 pizzas shared with 3 children Ratios Division Sep 2911:57 AM What is the Whole? Why does the Whole matter? Measurement wholes Geometric wholes Part of a set If xxx if 1/3, what is the whole? If xxxxxx is 3/8, what is the whole?

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Page 1: Fractions, Decimals, and Percents.notebookfaculty.weber.edu/kristinhadley/med6312/Fractions... · Fractions and Number Sense •Comparing and ordering fractions •Order the following

Fractions, Decimals, and Percents.notebook

1

March 07, 2011

Sep 29­11:57 AM

Fractions, Decimals, and Percents

Sep 29­11:57 AM

Fraction RiddlesDraw a rectangle to represent the following scenarios

• A rectangle is 1/2 red, 1/5 green, 1/10 blue, and the rest yellow. How much of the rectangle is yellow? • A rectangle is 3/5 red. The rest is blue and yellow but not in equal amounts. What could the rectangle look like?• A rectangle is 1/2 red and 1/3 blue. It also has green and yellow in equal amounts. What could the rectangle look like?

Sep 29­11:57 AM

1. Students must experience fractions in many ways including parts of wholes, ratios, and division

2. Three types of models exist: area, length, and part of a set.

3. Partitioning and iterating are ways to understand.4. Students need to have many experiences estimating 

with fractions5. Understanding equivalence is critical.

Computation

1. The meaning of each operation with fractions is the same as the  meaning of each operation with whole numbers.

2. Estimation is tied to the concept of the operations. 

Fraction Big Ideas

Sep 29­11:57 AM

• Math Activity:  Thinking about Fractional Amounts

Sep 29­11:57 AM

What is a Fraction?

• Sharing• 10 brownies shared with 4 children• 5 pizzas shared with 3 children

• Ratios

• Division

Sep 29­11:57 AM

What is the Whole?Why does the Whole matter?• Measurement wholes• Geometric wholes• Part of a set• If xxx if 1/3, what is the whole?• If xxxxxx is 3/8, what is the whole?

Page 2: Fractions, Decimals, and Percents.notebookfaculty.weber.edu/kristinhadley/med6312/Fractions... · Fractions and Number Sense •Comparing and ordering fractions •Order the following

Fractions, Decimals, and Percents.notebook

2

March 07, 2011

Sep 29­11:57 AM

What is the Whole?• Geometric Wholes

• Tangrams• Pattern blocks• Geoboards• Fraction circles• Graph paper• Fraction bars / Cuisenaire rods• Fraction plates

Sep 29­11:57 AM

Fractions and Number Sense

• Comparing and ordering fractions• Order the following set of fractions from smallest to largest value in your journal without using computation. Explain to a partner how you know the fractions are in the right order.     1/8     3/7 1/2 3/5 1/4 3/2 5/9    2/3 2/9 7/12 5/6 8/11 7/10 7/4

Sep 29­11:57 AM

Review of the Meaning of Addition and Subtraction• What is addition?

• What is subtraction?

What doe

s the com

mon den

ominator

 

have to d

o with an

ything?

Number Sense ASR Activity• Closer to 0, 1/2 or 1

Sep 29­11:57 AM

Multiple StripsNLVM ­ Factor Tree ­­ Venn Diagram

Sep 29­11:57 AM

Review of the Meaning of Multiplication and Division• What is multiplication?

• What is division?

• Rectangular array• Multiplying and Dividing with Fractions (MMO p. 63)

Sep 29­11:57 AM

Draw a picture in your journal representing the following problems

• Wanda really likes cake. She decides that a serving should be 3/5 of a cake. She has 4 cakes. How many servings does she have?

• I put 2 2/3 gallons of gas into my empty lawn mower. I notice that it is now 2/3 filled. What is the capacity of my gas tank?

Write an equation for each problem.

Page 3: Fractions, Decimals, and Percents.notebookfaculty.weber.edu/kristinhadley/med6312/Fractions... · Fractions and Number Sense •Comparing and ordering fractions •Order the following

Fractions, Decimals, and Percents.notebook

3

March 07, 2011

Sep 29­11:57 AM

Decimals and Percents In the textbook, the authors discussed not directly teaching procedures for decimal operations, but instead to rely on the number sense developed about number systems and estimation to guide their strategies. What does this mean for the teacher?

Sep 29­11:57 AM

Decimals and Percents Big Ideas• Decimal numbers are another way of writing fractions.• The base‐ten place‐value system extends infinitely in both directions.• The decimal point is a convention to indicate units position.• Percents are hundredths and another way to express fractions and decimals.• Addition and subtraction with decimals are a simple extension of whole numbers.• Multiplication and division of two numbers will produce the same digits, regardless of the positions of the decimal points.

Sep 29­11:57 AM

Rational NumbersRational number line

Number systems

Connections between fractions, decimals, and percents

Walking a decimal number line

Decimal estimation activities

What about the decimal point

Base Blocks decimals

Place value number line

Sep 29­11:57 AM

Percents

• Use problem‐based activities• Use real problems• Use friendly percents