1. Connecting Academics & Parents
Academic seminars to sharpen skills and build understanding in
MATHEMATICS: 4th grade Equivalent Fractions
TRAINING MATERIALS NEEDED:
Chart paper
Markers
Prepared sets of Equivalent Fraction Dominoes for parents to play
Fraction circles
Fraction bars
Cm grid paper
2 color counters
Rulers
Blank paper
Blank number lines
RESOURCES FOR PARTICPANT PACKETS:
Powerpoint
Full page learning progression
Slicing Squares
Equivalent Fraction Dominoes with directions and recording sheet
Online resources
CRITICAL POINT:
The purpose of this slide is to welcome parents and share that this session is about how to help their child have a better understanding of the 4th grade standard on equivalent fractions.
STEP-BY-STEP DIRECTIONS:
Welcome Parents and Guardians to the training.
Share that this training is about how they can help their child better understand the 4TH grade standard on finding equivalent fractions.
Explain that they will be engaged in some activities that will help them better understand the standard and help them support their child with developing their understanding.
The training will also include some purposeful practice tasks that they can do at home.
Only spend about 2 minutes on this slide.

2. How do you know that = ? Think of at least 2 explanations.
2 3
4 6
How do you know that = ?
Think of at least 2 explanations.
You can use any of the available tools to support your explanations.
CRITICAL POINT:
Engage parents with a task to set the stage for the training and assess their knowledge of equivalent fractions.
STEP-BY-STEP DIRECTIONS:
**Have a variety of tools available to parents to use (fraction circles, fraction bars, cm grid paper, blank open number lines, etc.)
**Prior to the training, have a t-chart without any headings prepared on chart paper.
Give parents 2 minutes to think on their own, and then 3-5 minutes to collaborate and share/compare their thinking with a partner.
While parents are sharing with each other, listen to their conversations and look for examples of the following possible explanations/models.
Record the examples you hear on chart paper with the Conceptually based explanations on the right, and the Procedurally based explanations on the left. At this point, you still should not have the headings on the top of the chart.(see next slide for example of completed t-chart).
“They are the same because you can reduce/simplify 4/6 and get 2/3.” (Procedural)
“If you have a set of 6 things (color counters) and you take 4 of them (flip four from red to yellow), that would be 4/6. But you can make the 6 (counters) into 3 groups of 2. The four yellow counters would now be two of those three groups. That means its 2/3.”(Conceptual)
“If you start with 2/3 and multiply the top and bottom number by 2, you will get 4/6…whatever you do to the bottom, you do to the top.”(Procedural)
“If you have 2/3 of a square/rectangle/circle shaded and you cut each of those shaded sections in half, you would end up with 4 parts shaded and 6 parts in all. That’s 4/6, and it would be the same amount shaded.” (Conceptual)
“If I use fraction bars/circles/number line to make 2/3 and also make 4/6, I can compare them and see they are the same.” (Conceptual)
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3. Why are the explanations sorted this way?
Conceptually Based
Procedurally Based =
“They are the same because you can reduce or simplify 4/6 and get 2/3.”
“If you start with 2/3 and multiply the top and bottom number by 2, you will get 4/6.”
“Whatever you do to the bottom, you do to the top.”
CRITICAL POINT:
To explain to parents the difference between conceptual explanations versus procedural explanations.
STEP-BY-STEP DIRECTIONS:
This slide should be shown along with the t-chart that was created based on the parents’ explanations.
Explain to the parents that these were some anticipated strategies that the parents would have used.
Share that all of these strategies are “correct”.
Ask the parents to analyze the explanations on the chart paper as well as those on the slide and think about why the explanations were sorted that way.
Have some parents share their thinking.
Click to advance the slide so that the headings of the t-chart appear.
Explain to parents that the strategies on the left (set model, fraction bars, number lines, area models (pictures with shading)) are conceptually based- they demonstrate a deep understanding of fractions, while the strategies on the right are procedural and more like rules that do not necessarily demonstrate an understanding of fractions.
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4. Mathematics Florida Standards Focus
Grade 4
MAFS.4.NF.1.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principal to recognize and generate equivalent fractions.
CRITICAL POINT:
Expose parents to the 4th grade standard and have them see that ultimately our goal is to have our 4th graders deepen their understanding of equivalent fractions and from that develop a conceptually based algorithm (rule/procedure).
STEP-BY-STEP DIRECTIONS:
This is the 4th grade standard.
Give parents time to read the standard.
Remind parents of the t-chart, and give them time to talk with a partner about how that t-chart relates to the standard.
Have some parents share out.
Clarify if needed that ultimately our goal is to have our 4th graders deepen their understanding of equivalent fractions and use that understanding to develop a conceptually based algorithm (rule/procedure).
Share that we don’t want to rush too quickly to the rules, because this can lead to student misconceptions.

5. Learning Progression: Equivalent Fractions
3rd Grade
MAFS.3.NF.1.3
Explain equivalence of fractions using visual fraction models and number lines. Express whole numbers as fractions. Compare two fractions with the same numerator or same denominator by reasoning about their size.
4th Grade
MAFS.4.NF.1.1
Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principal to recognize and generate equivalent fractions.
CRITICAL POINT:
This slide shows how learning about equivalent fractions progresses from earlier grades to future grades. Parents should understand that the goal in 4th is for students to notice connections between the models and the fractions in the way that both the parts and wholes are counted and students should begin to generate the rule for writing equivalent fractions
STEP-BY-STEP DIRECTIONS:
Give parents time to look at the learning progression. They have a full page version in their packet that might be easier to look at.
Click to advance bring parents’ attention to the 3rd and 4th grade standards on equivalent fractions.
Ask parents what they notice about the progression from the 3rd grade standard to 4th grade.
Clarify to help parents see that both standards include the explanation of fraction equivalence through the use of models, but in 4th grade students should begin to notice connections between the models and the fractions in the way that both the parts and wholes are counted and students should begin to generate the rule for writing equivalent fractions.
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6. “Slicing Squares” 3 4 = 6 8 Shade in ¾ of each square.
Now, use horizontal “slices” to divide the fourths of each square into equal pieces.
Each square should use a different number of horizontal slices, and therefore have a different total number of equal sized pieces.
For each sliced square, write an equation showing the equivalent fraction.
CRITICAL POINT:
Parents will engage in the type of task that will be used to help students make a connection between visual models and the procedural rule for finding equivalent fractions.
STEP-BY-STEP DIRECTIONS:
Tell participants that they have already looked at examples of ways that students can use fraction bars, number lines, the set model and the area model.
Now, they will use the area model to make a connection between models of equivalent fractions and the way both the parts (numerators) and wholes (denominators) are counted to generate a rule.
Explain that students will use a variety of models as they work towards the generalization of the rule.
If participants are confused about what they are expected to do, you can click to advance the slide to show them the example of ¾ = 6/8.
You may need to reiterate that each square should have a different number of horizontal lines to divide the square, resulting in a different total number of equal pieces.
On chart paper, record all fractions equivalent to ¾ that were generated. =
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7. 3 4 = 6 8 3 4 = 9 12 3 4 = 12 16 3 4 = 15 20 What pattern do you see?
3 4 = 6 8
3 4 =
3 4 =
3 4 =
CRITICAL POINT:
Have parents see how the conceptually based exercise they just did supports that procedural rule
STEP-BY-STEP DIRECTIONS:
You can either use the chart paper of the equivalent fractions that you created during the previous slide, or you can click to show the anticipated equivalent fractions that the parents will find.
Ask parents to share any patterns that they see. They may say that they see doubles, multiples, etc….but ultimately we want parents to see that we now have evidence that supports the rule that they can generate equivalent fractions by multiplying the numerator and denominator by the same factor.
Have them turn and discuss how the conceptually based exercise they just did supports that procedural rule.

8. What is my new name? ?????? ?? 4 5 x 6 x 6 = 24 30 CRITICAL POINT:
The purpose of this exercise is to reinforce the connection to using multiplication to generate equivalent fractions.
STEP-BY-STEP DIRECTIONS:
First, explain to parents that we have a model of 4/5.
Click to show the next partly covered model.
Explain that this model is equivalent to the 4/5.
Give parents time to work with a partner to use the portion of the second model that they can see to figure out the new name of the equivalent fraction.
With the covered square, parents can see that there are four columns and six rows to the shaded part and five columns of six rows in the whole.
Share with parents that students’ experiences with arrays and area in 3rd grade will help them be successful with exercises similar to this one.
Therefore, the new name of the fraction can be found by multiplying the numerator and denominator by 6, because all of the fifths have been divided into 6 equal parts.
4 5
x 6 x 6 = ??

9. MAFS.4.NF.1.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principal to recognize and generate equivalent fractions.
Student Sample:
CRITICAL POINT:
The purpose of this slide is to show parents an example of how a student might show their understanding of this standard.
STEP-BY-STEP DIRECTIONS:
Draw parents’ attention back to the standard.
Share with them an example of a task that might be used to assess a student’s understanding of the standard.
Specifically, this task shows how a student might use a visual model to explain the procedure for finding equivalent fractions and also demonstrate how they can use that rule to generate equivalent fractions.
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10. 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.
“Equivalent Fractions Dominoes”
CRITICAL POINT:
Parents practice game they can play at home to reinforce the standard.
STEP-BY-STEP DIRECTIONS:
Refer parents to the “Equivalent Fractions Dominoes” directions, recording sheet and dominoes in their packet.
Give parents some time to play the game.
The amount of time that you give parents to play will depend on the amount of time left in the training.
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11. 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.
CRITICAL POINT:
Share with parents additional idea of how they can use recipes at home as a way to reinforce students’ understanding of finding equivalent fractions.
STEP-BY-STEP DIRECTIONS:
Share with parents this example of a recipe.
Ask parents what questions they could ask their child about recipes that connect to finding equivalent fractions. (Possible suggestions: What if you only have a 1/8 cup measuring cup?- rewrite the recipe so that the ingredients are all in eighths of a cup)
Ask parents to share some other real-world examples they think would be beneficial. (Possible suggestions: Time- quarter and half hour and how it connects to fractional part of an hour; ¼ = 15/60 ; money- 1 quarter is ¼ of a dollar and is equivalent to 25/100)
Note: This example was taken from the 4th grade Ready Teacher Toolbox.
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12. Equivalent Fraction Online Resources:
Fraction Track:
Equivalent Fraction Bingo:
Targeting Equivalent Fractions:
Equivalent Fractions Matching Game:
CRITICAL POINT:
Share with parents some online games that could help reinforce this standard.
STEP-BY-STEP DIRECTIONS:
If there is time and you have internet access, visit some of these websites.
Share with parents that they can use the same recording sheet from the equivalent fractions dominoes to have their child keep track of their thinking when they are playing the games and hold them accountable while they are playing. There is a copy of these resources in the participant packet.
Address any additional questions parents may have.
Thank parents for coming.
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