3^RD GRADE MATH Fractions PD - Feb. 2nd

enVision Topics 12 & 13 FRACTIONS!

debbie.waggoner@fayette.kyschools.us

“One Seventh”

Your chart will turn plaid after Clue #2.

Important Note:

If you can see this box, then the slide show is not playing and the reveal won’t work.

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Here is the solution:

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If you are using PowerPoint, click on Slide Show, then click on From Current Slide.

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If you are using Google Slides, click on View then Present.

www.stevewyborney.com

Steve Wyborney

Type your name and school in the chat.

As the clues appear, use the information to narrow the possibilities to a smaller set. After each clue, use estimation again to determine which of the remaining answers is the most reasonable.

How many beads are in the glass?

Write down your first estimate. After each clue, you’ll see if your estimate is still a possibility. After each clue, if it is no longer possible write down a new estimate – and be prepared to explain why you chose it.

www.stevewyborney.com

Steve Wyborney

Clue #1

Clue #2

Clue #3

Clue #4

Clue #1

The answer is an even

2-digit number.

Clue #2

The answer is not a multiple of 4.

Clue #3

The answer is a multiple of 7.

Clue #4

There are 4 possible numbers remaining. One of the numbers is one-seventh of another.

Eliminate both numbers.

www.stevewyborney.com

Steve Wyborney

After seeing the clues, you have narrowed the possibilities to a small set of numbers. Before you see the answer, select your final estimate. Write it down, and explain to someone why you chose that number.

www.stevewyborney.com

Steve Wyborney

70 beads

The Reveal

Click to see the answer.

Important Note:

If you can see this box, then the slide show is not playing and the reveal won’t work.

​

Here is the solution:

​

If you are using PowerPoint, click on Slide Show, then click on From Beginning.

​

If you are using Google Slides, click on View then Present.

www.stevewyborney.com

Steve Wyborney

80 Cube Conversations

Lessons

The Original

50 Splat! Lessons

The Original 20 Fraction Splat! Lessons

More Free, Downloadable Resources From Blog Posts

20 Days of Number Sense

& Rich Math Talk

The Original 40 Estimation Clipboard Sets

51 Esti-Mysteries

The Multiplication Course (a free course for students and teachers)

140 short videos arranged in playlists to help your students learn about multiplication

For more information read the blog post about The Multiplication Course here.

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To view the course on YouTube:

1. Click here to see the chapter playlists on my YouTube channel.
2. You’ll see all 12 chapters in the course.
3. Each chapter includes a sequence of lessons for students.

November 1 – January 8

January 11 – February 26

March 1 – April 16

April 19 – May 28

2020-2021 “New Esti-Mysteries and Number Sense Resources Every Day for the Rest of the School Year”

Click here to find

“More Estimation Clipboards.”

Click here to find

“150 New Esti-Mysteries.”

Splat!

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Set 3.1

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This set includes multiple splats.

Remember: Each splat (of the same color) must have the same number.

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You can download more free sets here.

Steve Wyborney

This is a custom version of Splat! designed to work in Google Slides.

Type your name and school in the chat.

More Splat slides: https://drive.google.com/drive/folders/1BUq11rrw2GxF9JREu0m8fKsS7pnt6Bk-?usp=sharing

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Steve Wyborney

www.stevewyborney.com

The total number of shapes is…

Splat!

How many shapes are under each splat? How do you know?

How else could you know?

Let’s look under the splats to see how many shapes are there.

What can we learn from this picture?

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Steve Wyborney

www.stevewyborney.com

The Fraction Splat! Series

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Set 11.1

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This set includes unit fractions and a single Splat!

You can download more free sets here.

Steve Wyborney

This is a custom version of Splat! designed to work in Google Slides.

More Splat slides: https://drive.google.com/drive/folders/1BUq11rrw2GxF9JREu0m8fKsS7pnt6Bk-?usp=sharing

4

Steve Wyborney

www.stevewyborney.com

What number does this represent?

Splat!

What is the total under the splat?

How do you know?

How else could you know?

Let’s look under the splat to see the total.

What can we learn from this picture?

5

Steve Wyborney

www.stevewyborney.com

3^RD GRADE

• In this grade, students learn about unit fractions with denominators of 2, 3, 4, 6, and 8, and begin to accumulate these to build more fractions of the same denominator. Students recognize and know the meaning of the symbol of a fraction.
• Students identify a unit fraction on the number line and iterate them to find values of other fractions, even fractions larger than 1.

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4^TH GRADE

• Students build on their prior knowledge of fractions to include unit fractions and accumulated fractions with these additional denominators: 2, 3, 4, 5, 6, 8, 10, 12, 100
• Students will write math sentences using fractions.
• Students compare fractions with different denominators by using equivalent fractions.
• Students also relate multiplication of whole numbers to multiplication of fractions by whole numbers.
• Use decimal notation for fractions with denominators of 10 and 100.

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5^TH GRADE & 6^TH GRADE

• Add and subtract fractions with unlike denominators by using what students know about equivalent fractions.
• Interpret a fraction as division of the numerator by the denominator.
• Multiply fractions by fractions
• Divide unit fractions by whole numbers or whole numbers by unit fractions.
• Divide fractions by fractions – 6^th grade

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THE RESULTS OF THE THIRD NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS (NAEP) SHOW AN APPARENT LACK OF UNDERSTANDING OF FRACTIONS BY 9-, 13-, AND 17-YEAR-OLDS

Estimate the answer: 12/13 + 7/8

A) 1

B) 2

C) 19

D) 21

E) I don’t know.

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ESTIMATE THE ANSWER: 12/13 + 7/8

• Only 24% of the 13-yr-olds responding chose the correct answer, “2”.

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• 55% selected 19 or 21
• These students seem to be operation on the fractions without any mental referents to aid their reasoning.

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MANIPULATIVE USE EMPHASIS

• Everything we teach in Math goes through 3 developmental stages (not all students at the same time):
• Concrete, Pictorial, Symbolic… so plan
• How will you get your students to…. ?

BUILD IT ! DRAW IT! WRITE IT!

…in every TOPIC!?!

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stephanie.gentry@garrard.kyschools.us

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Links on the Pacing Guide

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Topic 12 Review What You Know Prerequisite Skills

-Topics 12, 13 & 14 Vocabulary Cards -Fractions Sample Anchor Charts

Topic 13 Review What You Know Prerequisite Skills

Partitioning The Whole to Equal Shares Concept Card sort FAL

-Representing Fractions on a Number Line Concept FAL

-Understanding Fractions Concept Card sort FAL

-InterpretingFractions Concept Card sort FAL

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Google Slides for this 3rd grade fractions session: https://docs.google.com/presentation/d/1DS_pqv7ahj2dWLFPN6zLRLrtjfgJ5XNY1ZXWy2DhNcI/edit?usp=sharing

Google Folder for 3rd grade fractions session:

https://drive.google.com/drive/folders/1L9Zr4dssZmYVXCKjqPHswbX7cds5y4Le?usp=sharing

Topic 12 Review What You Know Prerequisite Skills

F1

G2

Concrete: Partition shapes into parts with equal areas using fraction pieces. Express the area of each part as a unit fraction

of the whole. Partitioned parts should be halves, thirds, fourths, sixths, eighths. For example a shape partitioned into 6

parts with equal area of each part 1/6 of the area of the shape.

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Pictorial: Understand a fraction 1/6 as the quantity formed by 1 part when a whole is partitioned into 6 equal parts;

understand a fraction 4/6 as a quantity formed by 4 parts of size 1/6. Describe the numerator and denominator using

visuals/pictures. 4/6 = 1/6 + 1/6 + 1/6 + 1/6

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Abstract: Understand a fraction 1/6 as the quantity formed by 1 part when a whole is partitioned into 6 equal parts;

understand a fraction 4/6 as a quantity formed by 4 parts of size 1/6. Describe the numerator and denominator using

numbers and words. 4/6 = 1/6 + 1/6 + 1/6 + 1/6

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AZ 3.NF.1 & 3.G.2

Page 1

Page 2

Concrete: Use fraction pieces to show equivalence of fractions and compare fractions by reasoning about their size. Show

two fractions as equivalent (equal) if they are the same size 1/2=2/4 . Use fraction pieces to generate simple equivalent fractions

1/2=3/6. Show whole numbers as fractions using fraction pieces 6/6=1, 6/1=6 . Use fraction pieces to compare fractions with the

same numerator (2/3 and 2/4 ) or the same denominator (2/3 and 3/3) by reasoning about their size, referring to the same whole.

Pictorial: Use visual pictures or number lines to show equivalence of fractions and compare fractions by reasoning about their size.

Show two fractions as equivalent (equal) if they are the same size 1/2=2/4 . Use visual pictures or number lines to generate simple

equivalent fractions 1/2=3/6. Show whole numbers as fractions using visuals 6/6=1, 6/1=6 . Use visuals to compare fractions with

the same numerator (2/3 and 2/4 ) or the same denominator (2/3 and 3/3) by reasoning about their size, referring to same whole.

Abstract: Explain equivalence of fractions and compare fractions by reasoning about their size. Show two fractions as equivalent

(equal) if they are the same size 1/2=2/4 . Explain how to generate simple equivalent fractions 1/2=3/6. Express whole numbers

as fractions 6/6=1, 6/1=6 . Compare fractions with the same numerator (2/3 and 2/4 ) or the same denominator (2/3 and 3/3)

by reasoning about their size, referring to same whole. Record results with >,<,= and justify the conclusions.

AZ 3.NF3

Page 3

Concrete: Use equal size fraction pieces in a straight line to draw equal intervals on a number line, 4 pieces to show 1/4s

from 0 to 1.

Pictorial: Represent a fraction ¼ (unit fraction) on a number line by defining the interval from 0 to 1 as the whole and

partitioning it into 4 equal parts, recognize each part has size ¼, and a unit fraction, ¼ is located ¼ of a whole unit from

0 on the number line. Represent a non-unit fraction ¾ on a number line by marking off lengths of ¼ (unit fractions) from 0.

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Abstract: Represent a non-unit fraction ¾ on a number line by marking off lengths of ¼ (unit fractions) from 0. Recognize

that the resulting interval has size ¾ and that its endpoint locates the non-unit fraction ¾ on the number line.

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AZ 3.NF.2

Page 4

Page 5

Breaking Down the Standard:

Select a statistical question of interest focused on numerical data.

Concrete: generate measurement data by measuring lengths using rulers marked

with halves and fourths of an inch

Pictorial: show the data by making a dot plot where he horizontal scale is marked off in

appropriate units – whole numbers, halves, or quarters

Abstract: make observations from the graph about the questions posed including

questions about the shape of the data and compare responses, analyze the data

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AZ 3.MD.4

Page 6

Page 11-14

Page 15-16

Page 17-20

Pages 21-23

Pages 21-23

Pages 24-27

Pages 24-27

Page 28 - 29

Page 32 - 34

Page 35-36

Page 37-39

Page 40-42

Page 43-44

Page 45-47

Marilyn Burns

⅓ green

⅔ blue

PAPER �FOLDING

Partitioning The Whole to Equal Shares Concept Card sort FAL

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CLOTHESLINE FRACTION WARM-UP

• Make the Clothesline fractions on your whiteboard:
• Where does it start? (0) Where does it end? (1) How do we find ½ ? (in the middle) How do we mark ¼? (in the middle of 0 and ½) How do we mark ¾? (in the middle of ½ and 1)
• Take your visual fraction card and decide where it will go on your number-line. If your card is mostly shaded where does it go? (near 1) If you card is not very shaded where does it go? (near 0) If your card is evenly shaded where does it go? (near ½)
• Check with the others at your table and see if they agree with where you placed your visual fraction, and let them know if you agree with where they placed theirs.
• When you are sure you have your visual fraction in the right place take turns at your table going up and placing your fractions on the clothesline.

Topic 13 Review What You Know Prerequisite Skills

Page 6

3c

3c

Pages 13 - 16

Pages 17-19

Pages 20-22

Pages 23-24

Pages 25-26

Pages 27-28

fourths

three-fourths

shaded

six-eighths

shaded

3/4 = 6/8

Pages 29-30

Page 31

-Understanding Fractions Concept Card sort FAL

-InterpretingFractions Concept Card sort FAL

Pages 32-33

Pages 39-40

Pages 34-38

Representing Fractions on a Number Line Concept FAL

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-Representing Fractions on a Number Line Concept FAL

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Waterfall Chat: Type but don’t press send until I say so: One way these are the SAME and/or

One way these are DIFFERENT

https://www.theresawills.com/

Math Workshop: Collaboration, Interaction & Student Voice

Whole class

Number Routine

Independent -> Partner

Activity

Small Group

Activity

Partner

Game

Independent + Small Group

Check for Understanding

Guided Group

Exploration

Independent + Small Group

Exploration

Whole class

Check for Understanding

https://www.theresawills.com/

Check out this video later of Theresa showing fraction learning stations in action 1 hour webinar.

A

B

C

D

A

C It’s the only one with an equal number of red faces

B

Equal number of each

B only had two faces, the rest had four.

B is an equal amount of both happy and sad whereas the others had a majority of happy or sad faces

Less than 4 faces

D

It’s the only one with more than half green.

The only one with majority green

Independent-to-Partner/Group Activities

Read independent-to-partner/group activities (pp. 185-186) and independent-to-Partner Learning Station (pp. 195-196).

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How are students accountable for independent work BEFORE moving to partner work?

https://www.theresawills.com/

Check out this quick video of Theresa showing Independent & Partner groups in action.

Try it! 1) Independently pull some of the toys into the circle based on a rule.

Then, when both partners have completed their slide, swap slides and try to guess the rule.

Small Group Activities

Read small-group activities (pp. 186-187) and Small-Group Activities (pp. 196-198).

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How do students show multiple correct solutions?

https://www.theresawills.com/

Check out this quick video of Theresa showing small group fractions resizing in action.

Pull this square and resize it on top of the whole

Try it! Find the fraction (based on the entire image as the whole) and show it with the resizable square

Pull this square and resize it on top of the whole

.

Create duplicate slides for each possible way of finding the fraction.

Try it! Find the fraction (based on the entire image as the whole) and show it with the resizable square.C

Pull this square and resize it on top of the whole

Try it! Find the fraction (based on the entire image as the whole) and show it with the resizable square

Pull this square and resize it on top of the whole

Try it! Find the fraction (based on the entire image as the whole) and show it with the resizable square

Pull this square and resize it on top of the whole

Try it! Find the fraction (based on the entire image as the whole) and show it with the resizable square

Pull this square and resize it on top of the whole

Try it! Find the fraction (based on the entire image as the whole) and show it with the resizable square

Partner Games

Read Partner Games (p. 187) and Partner Game (p. 198).

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How is each and every student valued in the partnership?

https://www.theresawills.com/

Check out this short video of Theresa showing the Partner Games in action.

Pull out the turquoise cards

Pull out the turquoise cards

Independent-to-Small-Group Check for Understanding

Read Independent-to-Small-Group Check for Understanding (pp. 188-189) and Independent-to-Small-Group Check for Understanding (pp. 200-201).

How does this task value independent response and group discussion?

https://www.theresawills.com/

I know these are in order because

I know these are in order because

I know these are in order because

I know these are in order because

Guided Group Exploration

Read Guided Group Exploration (p. 188) and Guided Group Exploration (pp. 194-195).

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When would you want to work on a mini-lesson with a specific group of students?

https://www.theresawills.com/

is of .

5

1

2

is of .

3

is of .

is of .

is of .

Create a challenge slide for your peers, use the virtual manipulative link: https://www.mathplayground.com/mathbars.html

Group 1

Group 3

Group 2

Group 4

Group 1

Group 3

Group 2

Group 4

Make your own: https://www.mathplayground.com/mathbars.html

Make your own: https://www.mathplayground.com/mathbars.html

Independent-to-Small Group Exploration

Read Independent-to-Small Group Exploration (p. 188) and Independent-to-Small Group Exploration (pp. 198-199).

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How is each student responsible for independent thinking and small group discussion?

https://www.theresawills.com/

Check out this short video of Theresa showing small group pattern blocks in action.

1

1

Try it! Each person in the group is responsible for 1 column on the slide. Complete the next 4 slides.

1

1

Try it! Each person in the group is responsible for 1 column on the slide. Complete the next 4 slides.

1

1

Try it! Each person in the group is responsible for 1 column on the slide. Complete the next 4 slides.

1

1

Try it! Each person in the group is responsible for 1 column on the slide. Complete the next 4 slides.

Whole-Class Exit Ticket

Read End with Whole-Class Check for Understanding (pp. 190-191) and Whole-Class Exit Ticket (pp. 201-202).

Why is this whole-class activity used at the end of the learning stations class?

https://www.theresawills.com/

How do you know that 1/99 is larger than 1/100?

When you have a common top number then you have to think about the bottom number. Smaller numbers are bigger.

I would rather have a slide of pizza when it is shared with 99 people than 100 people. But they are almost the same size.

Because 100 is bigger than 99

If you made a common denominator, 1/99 is bigger

I think of 1/9 and 1/10 and I get more if I only have to share with 9 friends instead of 10

If you have less slices of pizza then the slices are bigger

100 is bigger than 99, so 1/99 is bigger than 1/100

1/100 is closer to zero.

99 is less than 100

Own a space is a technique where you give students a place to type. Students will naturally summarize their idea if the space is smaller.

Math Workshop: Collaboration, Interaction & Student Voice

Whole class

Number Routine

Independent -> Partner

Activity

Small Group

Activity

Partner

Game

Independent + Small Group

Check for Understanding

Guided Group

Exploration

Independent + Small Group

Exploration

Whole class

Check for Understanding

https://www.theresawills.com/

https://mikewiernicki.com/olympic-display/

Act 1

Show the Olympic Cola Display Picture

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Ask students what they notice about the picture.  Write down their observations.

Ask students what they wonder or what they are curious about.  Record their curiosities and questions.

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Possible questions:

How many 12-packs of soda are there in the display?

How many cans of soda are in the display?

Write an estimate.

Write an estimate that you know is too high.  Write an estimate that you know is too low.

Metric Olympics Packet pages 36-40

Act 2

Give students a copy of the student version of the display:

Act 3

Share solutions and strategies.  Compare strategies and results.

How reasonable was your estimate?

What might you do differently next time?

What worked well for you this time?

Metric Olympics Packet pages 36-40

https://youtu.be/or_X0y7WRAo

From beginning of video to 4:15

Highlights:

• Shows students reflecting on their student work from Solve and Share
• Then reflecting on the student work samples from enVisions
• Students use red/green response boards
• Sentence frames to reflect on class data in pictograph

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https://youtu.be/or_X0y7WRAo

From 4:15 to 9:06

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Highlights:

• Kagan strategies – review what you know, why is it important with a partner
• Teacher counts down time remaining in groups as a visual signal, claps to get attention
• Gives time to work on whiteboards alone before sharing with a partner
• What’s a great question to ask your partner?
• Gives exit question to do on whiteboard – successful students go to independent work
• Students who need more help become the small group for the day with manipulatives

https://youtu.be/or_X0y7WRAo

From 9:06 to 14:17

Highlights:

• Refers to benchmark fractions verbally and with a number line
• Students chorally answer questions for emphasis
• Students talk to partner to share answers and tell why their answer is correct
• Class praises student for good thinking

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Grade 3: https://hcpss.instructure.com/courses/97/pages/routines

Howard County Math ROUTINES

NUMBER LINE�ROUTINE

Standards: 2.MD.6, 3.NF.2, 3.NF.3d, 4.NF.2, 4.NF.6, 4.NF.7, 5.NBT.3b Mathematical Practice #1, 2, and 6

This routine helps students to understand relationships between numbers (including fractions and decimals-4th/5th only) and the relative magnitude of numbers. Students are asked to determine numbers that could be placed on a given number line. The teacher should vary the endpoints. Students should be expected to explain their thinking.

Present a number line with the endpoints labeled. Ensure that number choices are within the scope of the grade level curriculum.

https://vimeo.com/131918013

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• What number would be located at the pointer? Why do you think so?
• What number would be the halfway point on this number line? About where would it be located?
• List 3 other numbers that would be located on this number line, about where would they be located? How do you know?
• What is an example of a number that would not be located on this number line? Why?

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• Where would the fraction ½ be located on this number line?
• What number would be the halfway point on this number line? About where would it be located?
• List 3 other numbers that would be located on this number line, about where would they be located? How do you know?
• What is an example of a number that would not be located on this number line? Why?

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NUMBER LINE ROUTINE

Additional Suggestions:

• Given a number line with endpoints labeled, have students generate five numbers would fall between the endpoints. Ask students to estimate the location of one of the numbers and justify their thinking.
• Students may use sticky notes for numbers to place them with a follow up discussion as to whether or not any sticky notes placed should be adjusted either left or right. Discuss rationale for adjustment.
• Have students identify the halfway point. Take all responses and allow students to defend or debate.
• Place an arrow and ask what is a reasonable value for the point at which the arrow is pointing?
• As an alternative, place a labeled point on a number line and ask students to generate possible endpoints.
• What is an example of a number that would NOT be placed on this number line? Why?
• Change one of the endpoints and ask students if the placement of a given number will change? Explain.
• Select one of the endpoints and ask students to identify numbers close to that point

NUMBER LINE ONLINE�HTTPS://APPS.MATHLEARNINGCENTER.ORG/NUMBER-LINE/�

WHICH ONE DOESN’T BELONG?

https://wodb.ca

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3^RD GRADE MATH Fractions PD - Feb. 2nd

enVision Topics 12 & 13 FRACTIONS!

debbie.waggoner@fayette.kyschools.us

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