1. Connecting Academics & Parents
Academic seminars to sharpen skills and build understanding in
Addition & Subtraction
3rd Grade
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: Base ten blocks, Estimating Number Line Matching Game, Decks of Cards (optional to purchase for parents that attend)
Copies in packet: Paper base ten blocks, Estimating Number Line Matching Game, Representing Numbers Flexibly Matching Game, Addition/Subtraction problem sort, Card games directions sheet, Card games recording sheets, Powerpoint slide handout

2. Let’s get Started!!!!
Solve the problem by showing your thinking.
Be prepared to share your work.
It’s 302 miles to Disney World. We stopped for gas after traveling 183 miles. How many more miles do we still need to travel to get to Disney World?
Critical Point: To engage parents in a real-world problem that is similar to what students will be doing in the classroom.
Step-by-Step Directions:
Pose problem. Give parents 2 minutes to solve on their own using any strategy they choose.
As parents are solving, walk around and monitor different strategies being used. You will want to select 2 or 3 strategies to share. Pose questions to get parents to think deeper about their strategy and to justify their solution.
Select the parents that are sharing. (Consider some one that used a model, someone that used traditional place value algorithm and someone that solved it mentally but could justify their thinking to share).
Have parents share and make connections between the different strategies.
The purpose of this slide is for parents to get an idea of what kind of problem solving is expected in the classroom. It is also a chance for you as the trainer to highlight the importance of understanding and using different strategies for adding and subtracting. Explain that by the end of the training, they will be familiar with different strategies that help students understand addition and subtraction.
Also share that this is typically how your child’s math class is started. Depending on classrooms, students are expected to share thinking with words/pictures/or numbers to either a partner/group or the whole class.
Discuss that it’s important to think about the actions in the addition/subtraction problems, not the key words, “more than, more, total, difference, etc.” to determine which operation to use.
Trainer Note – Solving and sharing should take no longer than 5 minutes for this slide.

3. Mathematics Florida Standards Focus
Fluency is …
… quickly and efficiently computing accurately.
Grade 3
MAFS.3.NBT.1.1
Use place value understanding to round whole numbers to the nearest 10 or 100.
MAFS.3.NBT.1.2
add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Fluency is not …
… instant recall of basic facts.
Fluently
Critical Point: Share the standards that are being learned throughout the addition and subtraction fluency development.
Step-by-Step Directions:
Share the standards that will be covered.
Discuss that these are not the only addition/subtraction standards in 3rd grade, but these will be the focus of this training.
Click again and the definition for what fluency is will appear. Click a second time and the definition for what fluency is not will appear. Have a quick discussion on how students are expected to be fluently adding and subtracting within 1,000 by the end of 3rd grade.
If the parents want more information on the standards, encourage them to visit flstandards.org

4. MAFS Learning Progression: Addition & Subtraction Fluency
Critical Point: To show where addition/subtraction fluency standards are and how they are connected between the different grade levels.
Step-by-Step Directions:
Share the standards briefly that address addition/subtraction fluency.
Show how learning about addition & subtraction progresses from earlier grades to future grades.
Trainer Notes – Do not spend a lot of time on this (about 2 minutes max). Purpose is just to give them an idea where the fluency standards are before they get to 3rd and where they go after 3rd grade.
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5. Below are Common Misconceptions Students Have…
What mistakes did each child make?
Student A
Student B
Critical Point: To have parents think about common misconceptions children have when learning how to add and subtract with renaming/regrouping procedurally, without understanding.
Step-by-Step Directions:
Give parents about 2 minutes to discuss with their group what they think the misconceptions are.
Discuss as a whole group that Student A did not rename the tens or understand that ten tens make a hundred.
Discuss as a whole group that Student B did not use estimation to determine that their answer was not reasonable. They also did not regroup with understanding of place value. Also discuss that the traditional algorithm for Students B’s problem was not the most efficient and effective strategy to use. The student may have used flexible thinking or mental math strategies to count up or determine what number comes before 300, rather than using a procedure they don’t understand.
Trainer Notes – do this slide quickly. The purpose is for them to realize that their children learning procedurally is not the most effective way. This sets the tone for the strategies that will follow.
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6. Strategies to Build Understanding of Addition & Subtraction Fluency to 1,0000
Estimate Sums & Differences
Representing Numbers Flexibly
Break-Apart Strategy
Represent Addition & Subtraction
Place Value Strategies
Mental Math Strategies
Critical Point: This slide gives an overview of the different strategies that will be discussed in this training that help children learn addition/subtraction for understanding.
Step-by-Step Directions:
Quickly share that these are the strategies that will be discussed.
We will go into detail on each strategy and give suggestions for how to reinforce this at home.
Trainer Note – You do not need to read each strategy. Only spend about a minute.
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7. Estimate Sums and Differences
Estimation is a good tool to help students determine reasonableness of their solution.
Estimation needs to be done before they actually solve a problem.
Estimation & Rounding results in an easier number to do math with.
Estimate the difference of
What would the range of the number line be?
What would the middle number be?
Which number is it closest to?
Critical Point: To share with parents that estimation is a good strategy to determine reasonableness of solutions and should occur before you actually solve.
Step-by-Step Directions:
Share the details about estimating sums and differences.
Spend time highlighting that estimating occurs before you actually solve as a tool for determining reasonableness. Relate to Student B from the misconceptions slide. If Student B had used estimation, they would have easily recognized their solution was completely incorrect.
Share that a good tool to use is a number line to estimate the numbers before estimating sums and differences. Share the questions that could be used to guide using a number line.
Click and the two possible number lines will appear.
Share how to use the number lines to estimate the difference of Example dialogue could be, “To estimate 457, I would choose the number line with a range of is the middle number, 457 comes after so I would estimate/round to 500.” Go through same process with Then finish the estimate, “If you subtract 500 and 300, your estimate for would be 200.”
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8. Practice with Estimating Sums & Differences
Choose a card
Find the number line that can best be used to determine your estimate
Find the middle number
Find the location of the number on the number line
Estimate
Critical Point: To give parents a chance to use number lines to estimate sums and differences. Also to give them a tool to go home and reinforce with their children.
Step-by-Step Directions:
Pass out the number lines and problem cards.
Read the directions to the activity.
Have parents select problem cards and the corresponding number lines they would use to estimate by finding the middle number, where the number would be located and change to the estimated number.
Share how they can use this with their children in different ways.
Trainer Note – This should take a maximum of 5 minutes. The purpose is to just give them an idea of how the matching game works so they can implement it at home. More time can be spent on this activity if you have it available or your training is longer than an hour.
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9. How do these three different tools relate?
Representing Numbers Flexibly
= 1 unit
How do these three different tools relate?
= 10 units or a rod
= 100 units or a flat.
Critical Point: To give parents a chance to explore base ten blocks.
Step-by-Step Directions:
Pass out base ten blocks and share the vocabulary for each tool/what they represent.
Pose the question, “How do these three different tools relate?”
Give parents time to line up 10 units to make a ten, ten tens to make a flat, etc.
Share a few observations.
Discuss how there are paper versions of these tools in the packet, to use at home with their children.
Trainer Note – The purpose of this is to have them become familiar with the tools. Don’t spend more than 3 minutes on this task. They will use this information to help them represent numbers flexibly and represent addition/subtraction problems.

10. Represent 254 Is this still 254?
Critical Point: To show parents how to represent numbers with base ten blocks. Also to show to how to represent numbers flexibly, while keeping the same place value.
Step-by-Step Directions:
When the slide pops up it will say “represent 254.” Have parents represent 245 using base ten blocks. Give some time, then click and shows the model of 254.
Click the button and ask the question, “Is this still 254?” It will show a model of 2 hundreds, 4 tens and 14 ones. Have parents discuss and say whether they agree/disagree.
Discuss that it does still represent 254, just in a different way.
Click to the next slide to continue exploring flexible numbers.
Is this still 254?

11. Represent 254 Is this still 254?
Are there any other ways to represent 254?
Critical Point: To show parents how to represent numbers with base ten blocks. Also to show to how to represent numbers flexibly, while keeping the same place value.
Step-by-Step Directions:
When the slide pops up, it has the original representation of 254 with hundreds/tens/ones.
Click again and there is a new model with 1 hundred, 15 tens and 4 ones. Ask the question, “Is this still 254?”
Have parents discuss and come to the realization that it still represents 254.
Then click again and the question, “Are there any other ways to represent 254?” Give parents time to model and explore to find another way to represent 254.
Click again and ask the question, “Why is learning this important?” Discuss how it’s important because it helps students understand how to break-apart numbers in order to compute. Also, it will help with regrouping/renaming when adding/subtracting with understanding and using place value.
Trainer Notes – You can share that there is a matching game in the packet that parents can use to match different representations of the same number. They can use the base ten block models to explore. This could be done in the training if time permits and your training is longer than an hour.
Is this still 254?
Why is learning this important?

12. Representing the problem
Strategy Details:
Students use base ten blocks to represent, add and subtract numbers.
Students use what they know about representing numbers flexibly to model regrouping and renaming.
Students need to move from representing addition and subtraction problems with base ten blocks to drawing quick pics of the models.
Critical Point: Share with parents that a good way to begin solving addition/subtraction problems is by representing them with base ten blocks to model regrouping/renaming with understanding.
Step-by-Step Directions:
Go through the details of representing the problem.
Emphasize the third bullet, that kids need to move from representing with base ten blocks to drawing quick pictures of base ten blocks to model the problem. Click again and an example of how to draw the base ten blocks as a quick pic will appear. (May want to re-emphasize that the pics need to be “quick” and not detailed).
Trainer Notes - If time allows, have parents model quick pics.
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13. 354 + 78 Estimate. Then model to solve for the sum.
+ 78
Critical Point: To have parents represent an addition problem with base ten blocks.
Step-by-Step Directions:
Pose the problem. Have parents estimate and then model the problem to solve.
Monitor during solving and pose questions to get them thinking about representing numbers flexibly in order to rename and solve. Encourage parents to use precise vocabulary and place value when thinking/about and discussing the steps. Sample questions could be:
“What’s another way you could represent the 12 ones/units?”
“What does the 1 in the 12 represent?”
“How can you represent 13 tens another way?”
“What does the 1 above the 5 tens mean?”
When you click on the next slide it will show you a movie of renaming the addition problem.
Trainer Notes – This could be individual work or partner work. Make sure to encourage discussion about the steps.
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14. 354
+ 78 1 4 3 1 2
Critical Point: To show an example of what the addition with base ten blocks could look like.
Step-by-Step Directions:
When the slide appears, the problem and base ten models of each number will appear.
Click once to begin animation of the addition problem, including renaming.
Discuss how the actions with the base ten model relate to the actions in the numeric problem.
Click again and it will reveal the “break-apart strategy.” Don’t spend a lot of time discussing this now, it will be discussed later. Share how it is a strategy where you add the “place values” and how the base ten model is a direct representation of this strategy.
Trainer Notes – Only click once for the animation to begin. If needed, click “replay slide” to show the process again.
Replay Slide

15. 124 - 78 Estimate. Then model to solve for the difference.
Critical Point: To have parents represent an subtraction problem with base ten blocks.
Step-by-Step Directions:
Pose the problem. Have parents estimate and then model the problem to solve.
Monitor during solving and pose questions to get them thinking about representing numbers flexibly in order to rename and solve. Encourage parents to use precise vocabulary and place value when thinking/about and discussing the steps. Sample questions could be:
“How can you take 8 ones from 4 ones?”
“How did the 4 ones become 14 ones?”
“How did the 1 ten become 11 tens?”
“How did you use what you know about 1 hundred and 1 ten to make it 11 tens?”
“How does your model relate to the problem?”
Pose the question, “How was represent the subtraction problem different than representing the addition problem?” You want to get parents to understand that in the subtraction problem they are only building one number and taking the amount from that number. This is a common misconception students have.
When you click on the next slide it will show you a movie of regrouping the subtraction problem.
Trainer Notes – This could be individual work or partner work. Make sure to encourage discussion about the steps.
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16. 11
1 14
124 4 6
Critical Point: To show an example of what subtraction with base ten blocks could look like.
Step-by-Step Directions:
When the slide appears, the problem and base ten models of the number will appear.
Click once to begin animation of the subtraction problem, including regrouping.
Discuss how relating the base ten model to the numeric problem is essential for when students are solving without a model. We want them to have a good understanding of how place value is involved. Modeling these problems will help them eventually describe the steps without a model. This will be discussed again on slides
Trainer Notes – Only click once for the animation to begin. If needed, click “replay slide” to show the process again.
Replay Slide

17. Break Apart Strategies to Add/Subtract
Strategy Details:
Find the expanded form of each number.
Add each place to find the total.
Combine all the totals to find the sum of the original number.
May need to model with base ten blocks or quick pictures.
Critical Point: To share another strategy for adding using place value and the expanded form.
Step-by-Step Directions:
Share the details of the break apart strategy and the example problem.
Discuss that since students already have an understanding on different ways to represent and decompose numbers, they can break apart based on place values in order to add/subtract.
Make connections to models created in the previous problems.
Trainer Notes – Just share this strategy. Only 3 minutes is allotted for this slide. If time permits, you could have parents practice this strategy with another problem.
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18. Using Place Value to Add/Subtract
Strategy Details:
Visualize and think about actions in the problem, not key words, to determine if you are adding or subtracting.
Use place value language to discuss steps for adding/subtracting with regrouping or renaming (May still want to use a place value mat and base ten blocks to help guide using place value language to describe the steps).
Record equations to show the actions in the problem and solution.
Critical Point: To share the next strategy of using place value to add/subtract.
Step-by-Step Directions:
Share the strategies for adding/subtracting using the place value strategy (also known as traditional algorithm). Focusing on bullet 1, that their children will explore problems using real-world scenarios. The focus on this training was more on strategies for adding/subtracting up to 1,000 but their children will see it mostly in context. It’s important to make connections to real-world at home whenever possible.
Share that the focus of this strategy is on using the correct vocabulary to discuss steps for adding/subtracting with regrouping/renaming.
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19. 354 + 78 4 1 1 3 2 Add your ones. 4 ones plus 8 ones equals 12 ones.
+ 78
12 ones is the same as 1 ten and 2 ones, so I can add 1 to the tens’ column.
Now I can add my tens. I have 13 tens. 4 1 1 3 2
13 tens is the same as 1 hundred and 3 tens, so I can add 1 to the hundred’s place.
Critical Point: To show an example of using precise place value vocabulary when adding.
Step-by-Step Directions:
When the slide appears the problem will be there.
Click again and a description for adding the ones will appear.
Click again and a description for regrouping the ones will appear.
Click again and a description for adding the tens will appear.
Click again and a description for regrouping the tens will appear.
Click again and a description for adding the hundreds and answer will appear.
Discuss with parents that sometimes it’s important to go back to creating a model and then describing the steps could be useful. It’s important that students are able to describe these steps with the place value language, not a procedure.
I now have 4 hundreds giving me 432.

20. Let start with the ones. I cannot take 8 ones from 4 ones so I need to regroup.11 1 14
124
- 78
I will trade 1 of my tens for 10 ones, so I now have 1 ten and 10 more ones giving me 14 ones.
14 ones minus 8 equals 6.
Now let’s look at our tens. I cannot take 7 tens from 1 ten, so I need to regroup. 4 6
Critical Point: To share the next strategy of using place value to subtract with regrouping, using place value language.
Step-by-Step Directions:
When the slide appears, the problem is there.
Click and the steps for regrouping with the ones place will occur.
Click again and the steps for subtracting and regrouping with the tens and hundreds place will occur.
Discuss with parents that sometimes it’s important to go back to creating a model and then describing the steps could be useful. It’s important that students are able to describe these steps with the place value language, not a procedure.
Encourage them that when they are helping their child with addition/subtraction to encourage this language to develop understanding of place value and how it relates to subtraction/addition.
Discuss that after the process of moving through concrete (manipulatives) – pictoral (drawing pictures) – abstract (traditional algorithm/place value), you want to encourage children to use invented strategies and mental math to solve problems flexibly.
Trainer Notes – You may want to refer back to slide 5 where the student that subtracted went through a procedure they didn’t understand instead of just counting back 1.
I will trade my 1 hundred for 10 tens. Now I have 11 tens.
11 tens minus 7 tens is 4 tens.
124 – 78 equals 46.

21. Let’s Practice!!!
Estimate. Then solve the problem. Record the equation that represents the problem.
The table shows how many people were in line for different rides at Disney World at 9 A.M.
How many people were in line for Big Thunder Mountain Railroad and Space Mountain at 9 A.M.?
How many more people were in line for The Seven Dwarfs Mine Ride than Big Thunder Mountain Railroad?
Critical Point: To have parents apply the different strategies they learned for addition/subtraction.
Step-by-Step Directions:
Pose the problems and have parents estimate and then solve, encouraging them to focus on strategies such as: break-apart, representing with base ten blocks or a quick picture and place value.
As parents are solving, walk around and monitor different strategies being used. You will want to select 2 or 3 strategies to share. Pose questions to get parents to think deeper about their strategy and to justify their solution. Possible HOT questions:
“What actions told you what operation to use?”
“Is there another way you could solve that problem?”
“How does your strategy relate to place value?”
“Could you have chosen a more efficient strategy?”
Select the parents that are sharing. Consider having parents share that used: base ten blocks, quick pictures, break-apart strategy and place value. Have parents share and make connections between the different strategies.
The purpose of this slide is for parents to get an idea of what kind of problem solving is expected in the classroom. It is also a chance for you as the trainer to highlight the importance of understanding and using different strategies for adding and subtracting.
Re-discuss the importance of real-world connections to math and how using activities/places you go frequently and developing problems could be engaging and help students see the importance in math.
Pose the question, “How do the strategies we discussed help students achieve fluency with addition/subtraction to 1,000?” Discuss how the understanding of the strategies helps and fluency once again is not just basic recall – it’s have an efficient strategy that gets you to a correct solution quickly.
Trainer Notes – This slide should take about 8-10 minutes.
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22. 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.
Purposeful Practice:
Number Lines for Estimating Sums and Differences
Addition/Subtraction Problem Sort
Representing Numbers Flexibly Matching Game
Here are games to reinforce the concepts in this training. All you would need is a deck of cards!!!
Close to 500
Race to 0
Race to 1,000
Sum War
Difference War
The Shopping Challenge
Critical Point: To give parents purposeful practice and resources to use at home to reinforce addition/subtraction to 1,000.
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. There are directions for each one in the packet.
Encourage them to try it at home and use those as a guide to develop their own meaningful problems and tasks.
Trainer Notes – If time permits, you may want to play one of the games in the training. Also if funding allows, may want to purchase a deck of cards for each parent that attends the training.
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23. 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
Critical Point: This slide is only shared at Train the Trainer session for delivery model options.
Step-by-Step Directions:
1. Share slide to help teachers/trainers think through implementation of this training.

24. 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
Critical Point: This slide is only shared at Train the Trainer session for delivery model options.
Step-by-Step Directions:
1. Share slide to help teachers/trainers think through implementation of this training.