Before

Teacher will mentally prepare students to

•understand the problem •think of ideas that will help them work on the task •understand their responsibilities in learning the material

by •reviewing what has already been learned •introducing new ideas in several ways •eliciting discussion of problem solving strategies

Teacher will interact with students and help them discover their learning patterns.

The top section of a fraction number is called the Numerator

Numerator comes from the Latin word enumerate.Enumerate means to count.

The numerator counts how many pieces.

This numerator is 1. 1 piece is how many we count.

This numerator is 2. We count 2 pieces.

The bottom section of a fraction number is called the Denominator

Denominator comes from the Latin word nomin.Nomin means to name

The denominator names how many pieces make

the whole.The denominator in both fractional

numbers is 4. It takes 4 pieces to make this a whole

number.

Fractions use equal parts like when we shared our sandwich with our friends.

We can also have one whole sandwich and half another sandwich!

During

• Teacher will guide students to

•understand the problem •think of ideas that will help them work on the task •Discuss their findings to better ascertain the concepts that are introduced

By•Modeling thinking•Rephrasing as necessary for better comprehension•Recommending strategies to try

Do you see a pattern in the parts?

1 whole

1 whole divided into 2 parts, each part is one half or

1 whole divided into 3 parts, each part is one third or

1 whole divided into 4 parts, each part is one fourth or

1 whole divided into 5 parts, each part is one fifth or

1 whole divided into 6 parts, each part is one sixth or

1 whole divided into 7 parts, each part is one seventh or

1 whole divided into 10 parts, each part is one tenth or

A fraction is part of a whole number-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Fraction numbers are the numbers in between whole numbers.

For example, between 0 and 3 we can count0, ½ ,1, 1 ½ , 2, 2 ½ , 3

I can have no sandwich, half of a sandwich, 1 whole sandwich, one and a half sandwiches

And so on…..

Fractions are part of a wholeNow matter how big or small the whole is, the

whole can be divided into smaller parts.

2 inches

1 inch 1 inch

Krill

A Blue whale is the same length as 2 Humpback whales.

The length of each Humpback whale is one part of the whole length of a Blue whale.

The whole length of a Blue whale was divided into two parts.

1 Humpback whale 2 Humpback whales make a whole Blue whale.

The length of a Humpback whale is 1 part of the whole length of a Blue whale.

The length of a Humpback whaleis 1 part.The Numerator counts the partwe want to know about.

The length of the Blue whale was divided into 2 parts.The Denominator names how many make the whole.

Fractions and Decimals represent the same number.

A decimal represents numbers in groups of tenths.

A tenth can be written as or 0.1 or one-tenth.

A Humpback whale is or 0.5 or five-tenths the length of a Blue whale.

How is 0.5 the same as ?

What relationship do 1, 2, 5, and 10 have?

A Blue whale is the same length as 3 school buses.

The length of each school bus is one part of the whole length of a Blue whale.

The whole length of a Blue whale was divided into three parts.

1 school bus3 school busses make a whole Blue whale.

The length of a school bus is 1 part of the whole length of a Blue whale.

This numerator is 1 because we are counting 1 school bus length.

The whole whale was divided into 3 parts

Sometimes a part does not evenly divide into tenths.

Remember, a decimal number represents numbers in groups of or 0.1

A school bus is or 0.333 the length of a Blue whale. The 3 can’t divide evenly into ten, so the 3 repeats forever.

How is 0.333 the same as ?

What relationship do 1, 3, and 10 have?

A Blue whale is the same length as 5 Great White sharks.

The length of each Great White shark is one part of the whole length of a Blue whale.

The whole length of a Blue whale was divided into five parts.

1 Great White shark5 Great White sharks make a whole Blue whale.

A Great White shark is 1 part of the whole length of a Blue whale.

What is the numerator?

What is the denominator?

What Decimal number represents how many Great White sharks make the length

of a whole Blue whale?

How many tenths? _____How do you know?What is the decimal? 0.___

What relationship do 1, 5, and 10 have?

Does knowing this relationship help you find the decimal?

A Blue whale is the same length as 1 Basketball court.

The length of a Basketball court is one part of the whole length of a Blue whale.

1 is 1 whole item. 2 is 1 whole item. Why?1 2

3 is also a whole item. 3Draw it out. How does that work?

After

Teacher will assist student to

•understand the problem more fully•think of ideas that will help them construct meaning of the problem in their lives•learn the material

• by •Reinforcing what has already been learned •Supporting their learning process individually •Developing their range of mathematical awareness

Everything is made of smaller parts.

How many parts make up your body?

What fraction is your head compared to your body?

Are you using length or total parts to make your whole number? Are you using something else? What is your whole?

Think think think…What fraction are your arms compared to your

body?

Does your fraction change if your count your fingers as parts? How?

The Blue Whale is the largest animal to have ever lived!

• It can be up to 100 feet long.• It eats krill which can be up to 2 inches long.• How can we find out what fraction of the

whole length of a whale the length of a krill is?

Length of a krill

Length of a Blue whale

Remember that there are 12 inches in every foot.

What decimal would that be?

Plankton is microscopic in size

A whole krill is very small yet, it can be divided into even smaller sections.

Plankton is smaller than the eye can see and it can still be divided into smaller sections.

How small is the smallest fraction?How big is the biggest fraction?

What do you think these dots are?

What fraction are they of the length of the krill?Think think thinkDo you have a guess to the fraction ofa Blue whale to the Pacific Ocean? Can you find out?

http://animals.nationalgeographic.com/animals/blue-whale-interactive/http://mathematicallysane.com/reform-mathematics-vs-the-basics/Van De Walle textbook

CCSS usedMathematics: Grade 3(2) Developing understanding of fractions, especially unit fractions (fractions with

numerator 1);• Students develop an understanding of fractions, beginning with unit fractions. • Students view fractions in general as being built out of unit fractions, and they

use fractions along with visual fraction models to represent parts of a whole. • Students understand that the size of a fractional part is relative to the size of

the whole.• Students are able to use fractions to represent numbers equal to, less than, and

greater than one.• They solve problems that involve comparing fractions by using visual fraction

models and strategies based on noticing equal numerators or denominators.

Citations

Tasks: Clearly describe the main task of the lesson. State what makes this a good problem or task, and how the problem or task will engage students in the important mathematical ideas you want to address in the lesson. In particular, for each task, think about numbers, context, and problem structures, and say why you are choosing

the numbers, contexts, and problem structures you decide upon.

This lesson was designed from chapter 15, 16, and 17 of the Van De Walle text to increase comprehension of previously learned fraction vocabulary and concept and build an increase in students understanding of fractions. The Before, During, and After phases are spoken of in several parts of the Van De Walle text along with his article about the math wars.

The ActivInspire software for the Promethean board allows the students to interact with the presentation and become active in their learning. I believe this activity/ instruction uses concrete and conceptual information to help 3rd graders gain a deeper understanding of fractions.

Van De Walle discusses the need to introduce fractions and decimals together throughout chapter 17. On page 287, he discusses building on whole number concepts, which is also a feature of this lesson plan.

One thing this lesson plan only does at the beginning is address breaking a whole apart specifically; ex the parts of a sandwich are separated. In the bulk of this lesson we are using the “unit” of a Blue whale. I felt it would be a) inappropriate to actually split a whale, and b) that is assumed to have been discussed in the sandwich lesson they have already had.

I believe this lesson fully addresses the CCSS for 3rd grade fractions.

I chose to use the imagery I did because many of the items used are familiar, some of them are not, and it can be very engaging to see the size of a vaguely familiar animal against objects that are more well known. I used specific vocabulary and tried to emphasize vocabulary based on Van De Walle’s discussion of “Fraction Language” begun on page 293. I also used “iterating” with the repeated slide formats (pg 294).

Assessment: Describe/show how you will assess student learning during and/or after the lesson. In most cases, this will be some kind of informal assessment measure. In addition to stating HOW you will assess student

learning (through oral discussion, through reviewing student work, through individual journal entries, etc.) clearly state WHAT you will be looking for in student responses. What will count as evidence of student understanding?

Most of the assessment of this lesson is informal and performed throughout the lesson. I will assess their understanding by listening to their discussions, having students go to the Promethean board and demonstrate their thinking to the class and me, and reading their white board dialogues. I will also assess their understanding with their answers to the Think think think questions sent home.

I am trying to discover if they have a clear understanding, as demonstrated by their findings throughout the lesson, of unit fractions, that a fraction is relative to the size of the whole, what the numerator/ denominator is, what it stands for, and what it means as amounts vary.

I am also looking to see if they are able to find the equivalent decimal and discover what their strategy for doing that is.

The responses to the homework will be the “evidence” of student understanding.

Adaptations: Describe how you will adapt the lesson to meet the needs of diverse learners in your classroom. Select TWO groups of students (e.g., English Language Learners, inclusion students, gifted students) and describe how you will adapt the lesson, as appropriate, to meet their needs. Be specific. Include specific

examples of how you will adapt the lesson.

Math is wonderfully adaptable to English Language Learners as measurement doesn’t have a language barrier. My adaptations would be geared towards vocabulary that varies between their home language and English. This lesson is very vocabulary heavy and ELL students may need extra help with learning the vocabulary through several modalities such as collaborative grouping or self made flash cards (I believe they will have greater retention if they create the flashcards themselves).

I would give inclusion students worksheets with more fraction pictures. I prefer “real life” pictures because I feel that it helps create a better bridge to understanding. I would also adapt their homework to finding patterns and fractions around their home and for them to bring in examples either written, photos, drawn etc but explainable depending on the severity of the disability.

For both sets of students, if there was further need, I would use pictures and 3- dimensional numbers and first have students use these manipulatives to depict various fraction pictures while using the vocabulary with them. I would have them progress to writing various fractions while using the vocabulary until they were comfortable with the mathematical language. By beginning with the manipulatives, children can use concrete materials to help scaffold into more abstract ideas.

Collaboration: Describe how you collaborated with your colleagues to develop a unit. What worked? What didn’t work? What was it like to link to your colleagues’ lesson?

I worked some of this out with my Master teacher as she showed me how the ActivInspire software works with the Promethean board. I found that bouncing ideas off of her was very helpful and I wish I would have had more time with her for this. We worked together for about 20 minutes as she walked me through putting a lesson “flipchart” together using PowerPoint as the base. I have seen the students interact with these lessons and believe that they really absorb more because they are more engaged in the learning process.

Kersti, I know you dislike Power Point, and if I knew another way to use the ActivInspire software I would, but I don’t….please don’t hate on my Power Point, it’s really an ActivInspire Flipchart – Mari