1. Connecting Academics & Parents
Academic seminars to sharpen skills and build understanding in Fractions
Critical Point: Welcome parents to the session. This training was intended to take an hour, but can be adjusted to take more/less time as needed.
Step-by-Step Directions:
Welcome parents and introduce trainers.
Give purpose for training, which is to build the parent’s understanding of what their children are learning and strategies they will be using in the classroom, which align with the Math Florida Standards.
Explain that parents will also be leaving with “purposeful practice,” games and strategies to practice at home and will reinforce what they are learning in school.
Materials:
Fraction Tiles
Construction Paper cut into long strips (all the same size) of different colors (Sentence strips will work too) for make your own manipulatives activity
Blank copy paper for equivalent fractions paper folding activity
Equivalent Fractions Match-Up
Fraction War Cards – one of each set (same numerator and same denominator) for each pair of parents
Fractions War Record Sheet
Copies in packet: Fraction Match-Up Game, Fraction War (same denominator) and Fraction War (Same Numerator), Fractions Strips Page

2. Math may look different now.
There’s nothing better than seeing your kids SUCCEED
and there’s nothing worse than not being able to help them when they are struggling.
Share with parents that math may look different now. There’s nothing better than seeing your kids SUCCEED and there’s nothing worse than not being able to help them when they are struggling. This is research from Dr. Drew Westen, who is a professor at Emory University. Dr. Westen’s work was developed in collaboration with 100Kin 10.
Research from
Dr. Drew Westen, Emory professor,
and 100Kin10

3. Times change, technologies change, and knowledge changes about how to teach kids to apply what they know to real-life situations.
for joining in to learn more about how to help with math.
Thank you
Share that times change, technologies change, and knowledge changes too about how to teach kids to apply what they know to real-life situations. Thank parents for joining in to learn more about how to help with math.
Research from
Dr. Drew Westen, Emory professor,
and 100Kin10

4. Mathematics Florida Standards Focus
Grade 3
MAFS.3.NF.1.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. MAFS.3.NF.1.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. MAFS.3.NF.1.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. MAFS.3.G.1.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
Critical Point: Share the standards that are being learned throughout the Fractions Units.
Step-by-Step Directions:
Share the standards that will be covered.
Quickly share the standards that are involved with fractions in 3rd grade. Briefly highlight some of the important parts of the standards. This is more for your background knowledge, don’t spend a lot of time on this slide, because all of the standards are covered throughout the training.
If the parents want more information on the standards, encourage them to visit flstandards.org

5. Learning Progression: Fractions
Critical Point: To show where building understanding of fractions standards are and how they are connected between the different grade levels.
Step-by-Step Directions:
Share the standards briefly that address fractions.
Show how learning of fraction standards progresses from earlier grades to future grades.
You can point out that in prior years students only referred to fractions as half, thirds, or quarters. They never wrote fractions as we typically see fractions written. Third grade is the first grade where students need to write fractions as a fraction. This is important to let parents know.
Copyright 2009

6. 1 One Third Let’s Solve It!!!
Isaiah, Janai, and Jean want to share a Snickers bar fairly. How much will each student get? Use a model to justify your thinking.
How would you solve this problem?
How would a 3rd grader solve this problem?
Critical Point: To provide parents with an understanding of where 3rd grade students begin with their understanding of fractions and to introduce the variety of models that can be used to model fractions.
Step-by-Step Directions:
Pose the problem for parents to solve. Make sure they are creating a model to justify their thinking.
While they are solving, monitor and pose questions to get parents to think deeper about their solution. Also while you are monitoring find a couple different models/strategies for parents to share. Some questions for monitoring may include:
How does your model relate to the problem?
How do you know the candy bar was shared fairly?
Is there another way to represent this answer?
Click and the first question will appear, “How would you solve this problem?”
Invite a few parents to come up and share different solutions. Pose questions to have parents make connections.
Click and the second question will appear, “How would a 3rd grader solve this problem?” Discuss with parents how their solution strategy would not necessarily match what a 3rd grader would do when solving this problem.
Click again and you will see a rectangular area model, a circle area model, number line, followed by the word form. Let the parents know that since students did not learn how to write a fraction in 2nd grade that they will not begin with writing the fractions as fractions. First the concept will be discussed and understood before they begin writing fractions in fraction form with a numerator and denominator.
Trainer Notes: Parents should see a variety of models and know that their students will be using all these different models at different times throughout these units
One Third 1
Copyright 2009

7. Let’s Solve It!!!
Isaiah, Janai, and Jean want to share a Snickers bar fairly. How much will each student get?
1 3
Now try solving that same problem using math tools that your children will be using in the classroom.
Critical Point: Allow parents to problem solve using the same manipulatives that their students will be exposed to. You can have fraction tiles at each station for the parents or pass them out at the beginning of this slide.
Step-by-Step Directions:
Have parent get out the fraction tiles or pass out the fraction tiles so all parents have them.
Have parents solve the same problem as the previous slide but now using the same tool their children will accustomed to using in the classroom, fraction tiles.
Give a few minutes for the parents to get accustomed to how fraction tiles work and how they can use these tools to solve the given problem.
Click once and an animation of how this tool can be used to solve the problem.
Ask parents, “What are the benefits of using fraction tiles?”, and “How do your think these tools help your child to understand what a fraction is?”
Trainer Notes: Make sure to circulate the room to help parents who are not comfortable with manipulatives.
Copyright 2009

8. Let’s Make Our Own Math Manipulatives!!!
Take one 6 different color strips of paper.
Label the first strip “1 Whole.”
Fold the next strip of paper into 2 equal pieces. Label each piece
Continue to follow the same process to make thirds, fourths, sixths, and eighths.
Critical Point: Parents are going to make their own manipulatives that they can take home and use with their children. They can also make a set at home with their children. Prior to the training make sure to cut strips of construction paper. You can make them 1 inch by the width of the construction paper. Make sure all strips are the same size.
Step-by-Step Directions:
Have each parent take 6 strips of construction paper. (You can use sentence strips too.) Try to get all different colors if possible.
First parents will label the first strip with “1 Whole”.
Fold the next strip into two equal pieces. Stress the fact that both halves have to be the same size. Parents will need to line up the edges of the strips rather than just guessing where the middle of the page will be. Label each piece ½. Once it is labeled ask what parents they notice about two halves. They should see that two halves is equal to one whole. They can test this using the fraction strips they created.
Continue having parents now fold a strip into 4 equal pieces. You want to make sure that parents are not just guessing where ¼ should be but that are measuring by folding in half and then half again to get four equal pieces. Make sure you have extra strips of paper in case there are mistakes. Label each piece ¼. Continue to ask questions about how many fourths make a whole, etc…
Continue by have parents fold thirds, sixths, and eights. Thirds and sixths are challenging. They have to make sure that each piece is an equal size. Parents may need extra paper because their will be mistakes. I let parents play with it and to try and discover a plan before I give them any strategies to use. For thirds they can think of folding a letter or making an “S” shape and then flattening to make equal sized pieces. Sixths are just making thirds and then halving it. Eights are just taking half of half of half.
Once all strips are made you can ask questions such as:
How many sixths make a whole?
What is another fraction equal to ¾?
Tell me a fraction equal to ½. Are there any others?
How many fourths equals 6/8?
Etc…
Trainer Notes: You may want to have available and encourage parents to use rulers for thirds and sixths to make sure their pieces are equal.
Copyright 2009

9. One Fourth Two Fourths Three Fourths Four Fourths
Let’s Count our Pieces
One Fourth
Two Fourths
Three Fourths
Four Fourths
Critical Point: In this slide parents will be learning how our students will be learn to name fractions. They will count pieces of a whole using the fraction as the unit. Just like if you were counting crayons. One crayon, two crayon, three crayon, etc… Now our unit will be fourths since that is the size of each piece. I have one fourth, two fourths, three fourths, etc…
Step-by-Step Directions:
Let parents know we are now going to look at naming fractions. On the slide there is one fourth. Since four pieces make a whole, my unit is fourths which is now represented as my denominator. I only have 1 out of those 4 equal pieces so my numerator is 1.
One piece out of four equal pieces makes 1/4 . Click once and another fourth will appear. Now I have two fourths. Two equal pieces out of four. Two fourths.
Click again and continue this process with three fourths and finally four fourths.
Ask questions such as, “What do you notice about four fourths?” or “What do you notice about the fraction equal to 1 whole?” Parents can model these with their fraction tiles or the fraction strips they made.
Trainer Notes: The next slide will look at the same topic but with fractions greater than one.
Copyright 2009

10. Number Lines
How many thirds make 2 wholes? Use a number line to prove it.
1 3
2 3
3 3
4 3
5 3
6 3 2 1
Critical Point: This slide is intended to give parents a little background on using a number line represent fractions, including fractions greater than 1 whole. The MAFS specifically call on students using number lines to model fractions so it is important that our students use them and our parents become comfortable with them.
Step-by-Step Directions:
Similar to the previous slide we will model how I can read and represent fractions on a number line.
Click on the line to model how you can count on a number line.
Make sure parents realize that each space on the number line is the same size. It takes 3 equal spaces to make one whole on our number line. As students begin to use number line they will not be able to draw very precise number lines where all iterations are evenly spaced. The importance is that they understand how to create a number line to display fractions and fractions greater than one whole.
Pose questions to get parents to think deeper about the number line model. Some questions may include:
What do you notice about the fractions on the number line?
What is the scale of our number line?
How does this number line relate to a number line with whole numbers?
Trainer Notes: One common misconception that students have is that the fraction is just the mark on the number line. To represent a fractions you have to understand that the fractions is represented by the space between the zero and the mark on the number line. When students count fractions on a number line it is important that they realize that they are counting the spaces between zero and the fraction not just counting marks on the line.
Copyright 2009

11. Let’s Count our Pieces 1 Whole How many fourths are equal one whole?
1 4
1 4
1 4
1 4
1 4
1 4
1 4
How many fourths are equal one whole?
4 4
What if we kept going?
Critical Point: To connect understanding of fractions to fractions greater than 1 whole by creating model representations.
Step-by-Step Directions:
Follow the same steps as slide 7. Explore what happens as we continue to count using fourths as our unit. After four fourths we will have five fourths, six fourths, etc…
After parents have explored fractions greater than one, Ask the following questions:
How many fourths are equal to one whole?
What do you notice about 7/4 when comparing it to one whole?
To introduce mixed numbers build off what parents discussed about four fourths equaling one whole. If you click again you will see how I could exchange four fourths for one whole and then continue on with the other three fourths, showing the equivalent value of 7/4 and 1 ¾.
Trainer Notes: Explain to parents that we used to call fractions such as 4/1 or even 7/4 improper fractions. Although that is acceptable we are moving towards calling these “fractions greater than one”. It is more descriptive and people always assume improper means not correct or in some way bad. Calling them “fractions greater than one” is what we want our students to be calling them.
7 4 > 1
What do you notice now?
7 4 = 1 3 4
Copyright 2009

12. Fractions Greater than One
(formerly known as improper fractions)
Sachi had of a pizza. Kerdell had of a pizza.
Did they have the same amount? Prove it with a picture.
1 Whole
1 4
1 4
4 1
1 Whole
Critical Point: This slide was put here to clear up a concept that many students have confusion with. They are able to understand what ¼ is but they do not understand that 4/1 is equal to four wholes.
Step-by-Step Directions:
Pose the questions and allow parents to discuss this with their groups. Ask each group to create one picture to prove or disprove their idea.
Ask parents the following questions.
What does the 1 in ¼ represents?
What does the 4 in ¼ represent?
How are they related?
What does the 4 in 4/1 represent?
What does the 1 in 4/1 represent?
How could you model this?
Click and you will see a model for each. Click again and you will see this modeled with a number line.
Trainer Notes: Explain to parents that we used to call fractions such as 4/1 or even 7/4 improper fractions. Although that is acceptable we are moving towards calling these “fractions greater than one”. It is more descriptive and people always assume improper means not correct or in some way bad. Calling them “fractions greater than one” is what we want our students to be calling them.
1 Whole
1 Whole
Copyright 2009

13. Fractions Greater Than One
(formerly known as improper fractions)
Tanya has pumpkin pies left over from Thanksgiving. How many fourths of pumpkin pie does she have? Prove it with a model.
Terrie baked several pies for Thanksgiving. Each pie was cut into 4 slices. She counted 21 slices of pie left after her party. How could she record the pie she had left over as a mixed number? Prove it with a model.
Who has more pie left over?
Critical Point: Now we engage our parents with renaming fractions greater than one into mixed numbers and vice versa. They will then explore comparing fractions.
Step-by-Step Directions:
Pose both problems for parents and give them independent time to solve. You want to encourage them to use models, such as: fraction tiles, pictures, or a number line to justify their thinking. As parents are working independently monitor and pose questions to get them to think deeper about the problem. Some questions may include:
How do the two problems compare?
Are you using the same strategy for the first problem and the second problem? Why or why not?
Is there another way you could prove your thinking?
After a few minutes, give parents time to share with a partner/group their model and solution.
Select and sequence a few parents to share their models to the whole group. You want to look for parents that were able to convert 4 ¾ into a fraction greater than one and convert 21/4 into a mixed number with various models/strategies.
Trainer Notes: Explain to parents that we used to call fractions such as 4/1 or even 7/4 improper fractions. Although that is acceptable we are moving towards calling these “fractions greater than one”. It is more descriptive and people always assume improper means not correct or in some way bad. Calling them “fractions greater than one” is what we want our students to be calling them.
Copyright 2009

14. Equivalent Fractions Start with one whole sheet of paper.
Fold the paper into two equal pieces.
Shade in of the paper.
Now fold the same paper into four equal pieces.
What fraction can now describe the shaded region?
Fold the paper one more time so we have 8 equal pieces.
What fraction is now represented?
What do you notice about , and 1 2 ?
Critical Point: To have parents explore and understand equivalent fractions by using a paper-folding model.
Step-by-Step Directions:
Pass out one blank sheet of paper to each participant. Let every parent know that they received “one whole sheet of paper.”
Ask parents to fold the paper in half and shade in one out of the two equal parts. Then pose the question, “What fraction of your paper did you shade?” Parents should understand that they shaded in ½ of the whole paper.
Now have parents fold the paper in half again going in the other direction. Ask parents the following questions:
How many sections is your paper divided into now?
How many are shaded?
Did the space that was shaded change or did it stay the same?
What fraction of the paper is now shaded?
Fold the paper in half again (making 8 equal pieces). Ask parents the following questions:
What do you notice?
Did the space that was shaded change?
What fraction is now shaded?
What do you notice about the three fractions created, ½, 2/4, and 4/8? Parents should realize that they have created equal or equivalent fractions.
Trainer Notes: The one big point you want to get across is that this hands-on experience is important when having children develop the understanding of equivalent fractions. Also share that the denominators are limited to 1, 2, 3, 4, 6, and 8.
Copyright 2009

15. Equivalent Fractions Melanie had 2 3 of her coloring book finished.
Timothy had of his coloring book finished.
Melanie said they had the same amount of the coloring book finished.
Timothy said he had more of his coloring book finished.
Who do you think is right?
Use a picture to prove your thinking.
Critical Point: Pose this problem for parents to work on to apply what they have learned on the previous slide. Allow them to use fractions tiles, the fraction strips they made, or any picture or number lines to prove their work.
Step-by-Step Directions:
Pose the problem and have parents work independently or with a partner to solve. Encourage the use of the tools they have been practicing with, i.e. fraction tiles, fraction strips, drawings, number lines, etc…
Select one or two parents to share their strategies. Ask parents, “How can you prove you are correct?” “Can you use another strategy to prove you are correct?”
Trainer Notes: Share with parents that this is a type of question that children are familiar with. They are asked to agree/disagree regularly within the classrooms and to prove/explain their thinking. Also share with parents that part of exploring equivalent fractions is with fractions greater than a whole and mixed numbers as well.
Copyright 2009

16. Equivalent Fractions Match-Up
Critical Point: To give parents a game/some type of way to apply understanding of equivalent fractions with their child at home.
Step-by-Step Directions:
Let parents know that this game is in their hand-outs.
Pass out the pre-cut cards for each set of parents/group.
Have the parents work together to find the two equivalent fractions. Create a model to prove that they are equivalent.
Take turns with your partner. The player with the most matches wins.
Ask parents what other ways they could implement this game at home, such as concentration.
Trainer Notes: Only play this game if you have enough time to do so, if not just reference it in their hand-out packet. If you do play, don’t spend more than 3-5 minutes.
Copyright 2009

17. Comparing Fractions
Parker and Emily both started with the same amount of Halloween candy. Parker finished of his candy and Emily finished of hers. Who finished more of their candy? Use a picture or number line to prove your thinking.
𝟑 𝟔 > 𝟏 𝟔
Both fractions have the same denominator so the size of each piece is the same. 3 pieces is greater than 1 piece.
Critical Point: To explore strategies for comparing fractions with the same size pieces. (Same denominator).
Step-by-Step Directions:
Pose the following problem and ask parents to solve it and prove their thinking with a model.
Click and you will see the model of both fractions.
Parents should see that since both fractions are divided into sixths they have the same size pieces. If the pieces are the same then the greater number of those same size pieces will be the greater fraction.
Trainer Notes: The next slide looks at this with a number line.

18. Comparing Fractions
Parker and Emily both started with the same amount of Halloween candy. Parker finished of his candy and Emily finished of hers. Who finished more of their candy? Use a picture or number line to prove your thinking.
>
Both fractions have the same denominator so the size of each piece is the same. 3 pieces is greater than 1 piece.
Students might also notice that is equal to the benchmark fraction They can then see that if is equal to one half and is less than one half, must be greater than
3 6
Critical Point: To explore strategy of a number line for comparing fractions with the same size pieces. (Same denominator).
Step-by-Step Directions:
This slide is the same problem as the previous slide. Now we will explore using a number line to solve it.
Click and the number line example will show.
Click again and a message will pop-up regarding using benchmark fractions. Parents may begin to see that 3/6 is equal to half and also note that since 1/6 is less than a half, so the comparison could be done through reasoning about benchmark fractions. This is not a standard for 3rd grade but is the kind of logical thinking we want to encourage.
1 6 1

19. 3 4 > 3 8 Comparing Fractions
Michael promised me of his sandwich. Carl said I could have of his sandwich. Both sandwiches were the same size. Who offered me more of their sandwich?
>
You have 3 pieces of both models, but the pieces that make the fourths are larger than the pieces that make the eighths, so 3 4 >
Critical Point: To explore strategies for comparing fractions that have the same number of pieces (same numerator).
Step-by-Step Directions:
Pose the following problem and ask parents to solve it and prove their thinking with a model.
Click and you will see the model of both fractions. Since both fractions have the same number of pieces we have to look at the size of the pieces in order to compare them. Fourths are larger than eighths so ¾ would be greater than 3/8.
Trainer Notes: The next slide looks at this with a number line.

20. 3 4 > 3 8 Comparing Fractions
Michael promised me of his sandwich. Carl said I could have of his sandwich. Both sandwiches were the same size. Who offered me more of their sandwich?
>
You have 3 pieces of both models, but the pieces that make the fourths are larger than the pieces that make the eighths, so 3 4 >
Students might notice that is greater than one half and that is less than one half, therefore is greater than
3 4 1
Critical Point: To explore using a number line to compare fractions that have the same number of pieces (same numerator).
Step by Step Instructions:
This slide is the same problem as the previous slide. Now we will explore using a number line to solve it.
Click and the number line example will show. Notice that since the denominators are different I need two different number lines to model it.
Click again and a message will pop-up regarding using benchmark fractions. Parents may begin to see that 3/4 is greater than half and that 3/8 is less than a half, so ¾ must be greater than 3/8. Using benchmarks to compare fractions is not a standard for 3rd grade but is the kind of logical thinking we want to encourage.
3 8

21. Find the Error
Judy ate of the pizza and Bill ate of the pizza. Who ate more pizza? Willy said Judy ate more and then he proved it with a picture. Do you agree with Willy?
What mistake did Willy make?
𝟏 𝟒
𝟏 𝟑
Critical Point: The whole must be the same size in order to compare fractions. This is a common misconception among students.
Step-by-Step Directions:
Pose the question to parents and have them discuss with their groups. “What misconception does Willy have?
In order to compare fractions the whole must be the same size. In the example pictured here the two wholes are not the same size. 1/3 is in fact greater than ¼ but you cannot compare fractions if the whole is not the same/
Copyright 2009

22. Fractions War – Same Denominator
𝟐 𝟔
<
𝟓 𝟔
Critical Point: To show parents how they could apply the strategies for comparing fractions in a game format.
Step-by-Step Directions:
Click through the PowerPoint to see how to play Fractions War. This game came directly from the GCGs and Cpalms,.
Notice that all the cards have a denominator of 6. With a partner, divide the cards in half.
Each player flips over the top card in their pile.
Both cards are compared and the player with the greater value keeps both cards.
The comparison statement must be written on the record sheet. Students must also draw a model proving their comparison.
Trainer Notes: Participants do not need to play the next version of Fractions War but can see the game on the following slide. In this game all fractions have a common numerator, 1. They are all unit fractions. In this version they compare their fractions using a rectangular model.
𝟗 𝟔
𝟒 𝟔
> 1

23. Fractions War – Same Numerator
𝟏 𝟑
𝟏 𝟖
>
Critical Point: To share with parents the fraction war game to apply understanding of comparing fractions with the same numerator.
Step-by-Step Directions:
Click through the PowerPoint to see how to play Fractions War. This game came directly from the GCGs and Cpalms,.
Notice that all the cards have a numerator of 1.
Trainer Notes: Participants do not need to play this game, just share how it compares to the previous fraction war cards.

24. Take it Home and Try It! DO TRY THIS AT HOME!
Warning: Implementing this engaging activity will result in an increase in motivation and long-lasting learning.
Find examples of fractions in the real world. Look in magazines and newspapers. Write equivalent fractions for the fraction you find.
Make your own math manipulatives with your child.
Play fractions games like Fractions War and Fraction Match-up to compare and determine equivalent fractions.
When you order pizza or bake brownies, discuss what fraction of the whole you ate. Make predictions about who will eat more and then check your predictions.
Critical Point: To give parents purposeful practice and resources to use at home to reinforce understanding of fractions.
Step-by-Step Directions:
When the slide appears, there are “purposeful practice” tasks. Go through the different details and encourage parents to look in their packet at the resources.
Encourage them to try it at home and use those as a guide to develop their own meaningful problems and tasks.
Trainer Notes: Have at least one “Take home and try it” activity for the parent to do with their child.
Copyright 2009

25. Possible Delivery Models for CAP Sessions:
School Parent night K-5
Teacher’s or grade level’s own workshop
School invites parents to a curriculum night
Break-out sessions offered by grade level and content area
Teachers who attended TTT or watched voiceover TTT video deliver sessions
Teachers who attended TTT or watched voiceover TTT video deliver sessions to their own class of parents
Grade level can organize a workshop on needed content and have own parent night
Only shared at Train the Trainer session for delivery model options.

26. Tips for Success in Organizing CAP sessions:
Find a team of people to help with organizing the event
Send home bright colored half-sheet flyers and use parent link calls to notify parents
Have parents rsvp
Look for sponsorships from business partners/PTA to have snacks or a full meal for the parents
Consider baby-sitting options on-site
Consider time frames that meet the needs of your parents.
Morning session, at dismissal, evenings
Only shared at Train the Trainer session for delivery model options.