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# Fractions and Decimals Grades 2-5 - PowerPoint PPT Presentation

Fractions and Decimals Grades 2-5. MSP Nov. 16 and 18 KCS. Decimal Work. Opening Task. Represent each decimal grid as a: Fraction (in simplest form) Decimal Percent. Approaches- How and why…. Easiest…. Hardest… What did you need to know to be successful?.

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## Fractions and Decimals Grades 2-5

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Presentation Transcript

MSP Nov. 16 and 18

KCS

### Decimal Work

• Represent each decimal grid as a:
• Fraction (in simplest form)
• Decimal
• Percent

### Approaches- How and why…

• Easiest….
• Hardest…
• What did you need to know to be successful?

### Connecting the grid to the answer

• Teacher: “So what was Natalie’s answer as a percentage?”
• Sam: “42.5 percent.”
• Teacher: “How much percent is in one square?”
• Sam: “1.25 percent.”
• Teacher: “So if 34 boxes are squared what percent is shaded?”
• Sam (uses overhead calculator): 34 * 1.25 = 42.5
• Sam: “42.5 percent”

### Examining the Teacher Moves

• How has the teacher “leveraged” student responses during this discussion?
• Discuss the mathematical focus in each of the three stages.
• Was it on computations, representations, connecting mathematical ideas or a combination?

• Shade 3/8 of a 12x8 grid (12 across, 8 tall)
• Show it 3 different ways
• What is the decimal number, fraction and percent for the shaded region?

### Student work- Devon

• Here is Devon’s progression of shading 3/8.
• What did he do?
• What concepts does he understand based on his representations?

### Student work- Devon

• “I broke the rectangle into four parts. There would be six columns in each half and then three columns in each fourth. “
• “Then, I split the fourths into eighths. There are 1 ½ columns in each eighth. Then I shaded in 3 of the 8ths.”
• T: “Why are you not sure? What do you know about how you shaded the rectangle?”
• D: “I broke it into eighths. Fourths are 25% and eighths are half of that (uses calculator to divide 25 by 2). Each eighth is 12.5% so it would be 12.5+12.5+12.5 which is 37.5 percent.
• T: “How would we write that as a decimal?”
• D: “I know 37.5% is less than one so it’s 0.375.”
• Based on Devon’s comments above what mathematics does he know?
• How did the teacher moves help Devon connect his strategy to the mathematical concepts?
• What would you do next with Devon to make sure he understood the concept?

### Great White Shark Ratio

• A great white shark is 6 meters long (average)
• A great white shark’s tooth is 8 cm long
• Find the proportion(ratio) of the great white shark’s body length to tooth length
• Using the great white shark ratio above, find the “expected” length of your tooth
• Compare you and your partner?

### Shark

• 8 cm/ 600 cm = 1 cm / 75 cm
• 1 cm of tooth for every 75 cm of body
• 129 cm human body
• 129-75 = 54, 1 r 54…. 1.4
• 129/75

### Equivalent Fractions

• Find equivalent fractions for
• 1/2
• 2/3
• 3/7

### Equivalent Fractions

• How did you do to find equivalent fractions?
• How can you prove that they are equivalent?
• With manipulatives?
• With an area model (circle or rectangle)
• With an equation?
• With words?

### Comparing Fractions

• Two pizzas are on the counter. The pepperoni pizza is cut into 5 slices. The cheese pizza is cut into 8 slices.
• If you take two pieces from the pepperoni pizza and four pieces from the cheese pizza, which pizza has more left?
• How do you know?

### Comparing Fractions

• What did you to solve the task?
• A circular shaped pizza
• A rectangular shaped pizza
• Individual pieces of pizza
• Cross multiplication (butterfly  )
• Finding equivalent fractions with common denominators

### Comparing Fractions

• Let’s look at student work
• What strategy does the student use?
• What do they know?
• What misconceptions do they have?
• Ideas for interventions?

### Fractions on a Number Line

• Let’s count around the class by 3/8
• What number do you think we will land on?
• Why?
• As we count, write down your number.
• Where did we end up?
• How close was our estimation?

### Fractions on a Number Line

• Stand if your fraction can be simplified to a whole number
• Stand if your fraction can be simplified to ½
• Stand if your fraction can be simplified to ¼ or ¾
• Stand if your fraction cannot be simplified at all

### Fractions on a Number Line

• Mark the following fractions
• 1/12, 13/12, 9/8, 15/8, 7/4, 9/6, 7/13

### Fractions on a Number Line

• In Between
• What strategies did you use as you played?

### Fractions on a Number Line

• In Between
• What mathematical concepts are embedded in the task?

### Fractions of a group

• In a basket there are 24 apples. 1/3 of them are red. ½ of them green. The rest are yellow. How many of each color are there?

### True or false

• 2/5 of 50 = 20% of 100
• Prove this using a picture and an equation.

### True or false

• 2/5 of 50 = 20% of 100
• Approaches?

### True or false

• 2/5 of 50 = 20% of 100
• Explanations?

### Comparing Fractions of a Group Tasks

• Look at these two tasks
• 1) 2/5 of 50 = 20% of 100
• 2) In a basket there are 24 apples. 1/3 of them are red. ½ of them green. The rest are yellow. How many of each color are there?
• How are they similar?
• How are they different?
• What are the different issues and struggles students have?

### Proportional Squares

• If the smallest square is 1 unit by 1 unit, what is the area of each square? The entire unit?

### Proportions

• Make a pattern block picture that includes at least 10 shapes and is ½ blue.
• How can you prove that it is ½ blue?
• Make a pattern block picture that is ¾ blue. How can you prove that it is ¾ blue?

### What does this look like in Grades 3-5?

• It takes you 45 minutes to drive 30 miles. How long will it take to travel 120 miles?
• How would we expect students to solve this task?
• Where would they struggle?

### Proportional Reasoning in 5th Grade

• How much oatmeal and flour for 120 cookies?

### Condominium Demographics

• In a condominium, 9/17 of the people are married and 3/5 of the men are single.
• How many people are:
• Married men?
• Married women?
• Single men?
• Single women?
• Extension: Find more possible answers (there are many)