1. Connecting Academics & Parents
Academic seminars to sharpen skills and build understanding in Modeling Addition and Subtraction
The purpose of this training:
Build understanding of modeling addition and subtraction through the use of manipulatives, quick pics, and representing numbers flexibly.
Options for differentiating this session
You may find that it takes longer than1 hour to deliver this workshop.
Options: Deliver over two sessions (maybe one for addition and one for subtraction) or Select slides/questions that would best fit the needs of your students/parents.
Materials-
Copies 1 per family
PowerPoint (optional)
CAP 2nd Grade Modeling Addition and Subtraction Handout
Learning Progression for Modeling Addition and Subtraction
2 digit shuffle grid
Cards for 2 digit shuffle
Base ten blocks- for each group
Place value chart
Paper, pencils, post-its available for parents to use

2. Mathematics Florida Standards Focus
Grade 2
MAFS.2.NBT.2.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Critical point-
We will be addressing this standard for modeling addition and subtraction within 1,000.
Step by step directions-
Share this standard with parents

3. Modeling addition and subtraction with regrouping
Learning Progression:
Modeling addition and subtraction with regrouping
Critical point
Show how learning about modeling addition and subtraction with regrouping progresses from earlier grades to future grades.
Students are using concrete models and drawings in second grade. Students need to add and subtract fluently by 4th grade.
Step by step directions-
Read 2.NBT.7 “Add and subtract within 1000, using concrete models or drawings and strategies based on place value” There is more information on each standard that is not displayed due to space. All standards can be found at
Share the progression starting with 1st through 4th grade. Let parents know, if their child is struggling with the current grade level content standard they can look at the previous learning for support.
A full size learning progression should be copy for each family. Point it out to parents as the slide may be difficult to read.
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4. Engage Do you think you could explain how you subtracted?
Critical point
We may think of the traditional algorithm as a set of steps or procedures that if done in the correct order will yield the correct solution instead of the abstract representation of a concrete process. Learning the procedures without connecting the base-ten system might foster misconceptions and common errors. The following slides will demonstrate common errors students make by learning “tricks” before understanding how to add and subtract conceptually.
Step by step directions
Give 1 minute for parents to solve the problem on the slide “ask parents to record their thinking on paper even if they used mental math” this will help you see the strategy they used when solving the problem.
Walk around to see how parents are solving the problem.
Inform parents that the majority of the audience used what we call “traditional algorithm” to solve the problem.
CLICK to show question: Do you think you could explain how you subtracted?
Give think thime.
Do not elicit responses at this time. Go to the next slide to see the solution to the problem and let parents check their work.
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5. Engage 124 - 78 4 6 Borrow Carry Knock on your neighbor’s door
Go get some sugar from you neighbor
Bigger bottom, better borrow!
You can’t take a bigger number from a smaller number 11
1 14
124 4 6
Critical Point:
Parents will see the regrouping process within the traditional algorithm and think about the phrases we may have learned to describe the regrouping process with subtraction. Familiarize parents with common phrases used to describe the regrouping process. Throughout this workshop parents should evaluate these phrases to determine the effectiveness of these terms to describe the regrouping process.
Step-by-Step Directions:
Click once to show the step by step procedure
Ask participants “think back to when you learned how to subtract, how you were taught subtraction?”
Click a few more time to see some words that we may have heard when we were taught how to subtract.
Do not address the use of these words at this time- they will be addressed later in the workshop
Ask participants “keep these words on hand throughout the workshop to evaluate their effectiveness to describe the regrouping process” (when you say these words is that really happening?)
Trainer Notes- when we were in school asking why or how was not necessarily accepted by teachers. A common approach to mathematics was follow the procedure correctly and you will get the correct answer. But not knowing why it works or how it works limits our understanding and our ability to apply this knowledge.
Trainer Notes – Only click once for the animation to begin. If needed, click “replay slide” to show the process again.

6. Common errors Critical point
Students need to understand that a number can be partitioned in different ways. In the first example 65 can be broken into or Any way they partition it the value will remain the same (65). Modeling the regrouping process will develop understanding of thinking of numbers flexibly.
Step by step directions
Ask parents “What mistake do you think this students made?”
Allow parents to have a conversation with their neighbors about the error made within the problem
Click to show second problem
Ask parents to raise their hand if they have ever heard “for subtraction you always start with the bigger number and subtract the smaller number?”
Ask parents “how could the statement “for subtraction you always start with the bigger number and subtract the smaller number?” result in this error?
Ask for volunteers.
Common error- without understanding of place value students may not think about the calculation as a whole and treat each column as separate subtraction. In each scenario students started with the bigger number and subtract the smaller number. They may have ignored that 5 is apart of 65 and 7 apart of 27 switching the order would change the difference.
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7. Tools for understanding
When using these to represent whole numbers, what is the value of each?
How do these blocks relate to one another?
Critical point
Base ten blocks are an important tool for understanding place value. Your students may refer to these manipulatives as units, rods or longs, flats, and cube.
They are named this way because in future grade levels they will be assigned different values.
Step by step direction-
Ask parents “What is the value of each?”
The value of units- 1
The value of rod-10
The value of flat- 100
The value of large cube-1,000
Ask parents “How do these blocks relate to one another?”
It takes 10 units to make a rod
10 rods to make a flat
10 flats to make a large cube
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8. Use base-ten blocks to solve this problem.
Emily had 27 pieces of candy. Linda gave her 35 more. How many pieces of candy does Emily have now?
Critical point
Students are often introduced to the standard algorithm before they made sense with regrouping using base-ten blocks. Before they jump straight to the algorithm, they should understand the connection between the actions with the base ten blocks and the numbers written in the standard algorithm. If they do not we may see the common error = 512.
Step by step directions
Have participants use base-ten blocks to solve the problem
Circulate around the room to see different ways participants solved the problems (2 minutes)
Ask parents “Is their solution reasonable?”
Click slide to show animation of 27+35=512 and ask parents “Is 512 reasonable?” “If 512 not reasonably how might a students get that solution?”
Ask parents “Think about how you solved this problem when watching this video. Was there anything the teacher did differently?”
During the debrief conversation make the point that modeling with regrouping will strengthen children’s conceptual and procedural understanding of 2-digit subtraction.
Parents need to keep the base-ten blocks with their solution for the next activity.
Trainer hint- open the youtube video’s before you start the training. Many times access to youtube is allowed after you override the permissions.
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9. I carried the 3 Critical point-
When adding with regrouping students need a strong foundation in place value. With the first example is equal to 13 ones or 1 ten and 3 ones.
Step by step directions
Ask parents “What mistake do you think this students made?”
Allow parents to have a conversation with their neighbors about the error made within the problem
Click to show second problem
Ask for volunteers.
This is an example of where a student may ignore place value and use the word carry “I carried the 3”
Using a phrase like “I traded 10 ones for 1 ten” would better describe the correct regrouping process
Common error- When adding with regrouping students may reverse the digits when they regroup.
I carried the 3
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10. Use Quick pics to solve this problem.
Emily had 27 pieces of candy. Linda gave her 35 more. How many pieces of candy does Emily have now?
Critical point-
A way to still develop understanding at home without base-ten blocks is using quick pictures or (quick pics). Representing the base-ten blocks builds connections between the concrete and the abstract representations.
Step by step directions
Have participants use those same base-ten blocks and create a quick pick that would represent the action in the problem. (Give parents 1-2 minutes to draw a quick pick)
Ask parents to consider this question while watching the video “how could drawing quick pics help students avoid common errors?”
Click the video to play
Ask for volunteers to answer “how could drawing quick pics help students avoid common errors?”
Possible answer
When creating quick pick students represent each part of the problem using representations. Modeling the action (the math) using these quick picks help students conceptualize the mathematics and prevent many common errors.
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11. How would you model this problem?
Model-N-Record!
This is a 2 player game
Chose who will be partner A and partner B.
Partner A will be modeling the problem and explaining the process to partner B.
Partner B will record each action step as it happens in number form.
There were 403 coins in Linda’s piggy bank of the coins were dimes. How many of the coins were not dimes?
Critical point-
Physical models for base-ten concepts can play a key role in helping children develop the idea of “a ten” as both a single entity and as a se of ten units (Van De Walle, 2010)
This can also develop the understanding of decomposing numbers. If a child understands they can compose 10 tens to 1 hundred then the same would be true as the inverse 1 hundred equals 10 tens.
Step by step directions
For this activity parents will work in groups of 2.
Parents chose who will be partner A and partner B.
Partner A will be modeling the problem and explaining the process to partner B.
Partner B will record each action step as it happens in number form.
What aha’s did you have when playing this game? How might this activity be helpful for your child? Could you play with your child?
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12. 124 - 78 4 6 1 14 Partner A 11 Replay Slide Partner B Critical Point:
1 14
124 4 6
Critical Point:
To show an example of what subtraction with base ten blocks could look like as it relates to the standard algorithm
This is just an example of what partner A and B would be doing during the activity.
Step-by-Step Directions:
This is an example of what partner A and partner B should be doing in the previous slide
If your participants don’t need further clarification of the directions you can skip this slide.
Trainer Notes – Only click once for the animation to begin. If needed, click “replay slide” to show the process again.
Replay Slide

13. How would you model this problem?
There were 403 coins in Linda’s piggy bank of the coins were dimes. How many of the coins were not dimes?
Critical point-
Physical models for base-ten concepts can play a key role in helping children develop the idea of “a ten” as both a single entity and as a set of ten units (Van De Walle, 2010)
This can also develop the understanding of decomposing numbers. If a child understands they can compose 10 tens to make 1 hundred then the inverse would also be true, 1 hundred can be decomposed to equal 10 tens.
Step by step directions
Ask parents how the vocabulary in this video compared to you and your partners description of the subtraction process.
Watch the video
Debrief with parents about the similar vocabulary used when subtracting with regrouping.
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14. Go get some sugar from your neighbor?
Common errors
Go get some sugar from your neighbor?
Critical point
These examples demonstrate why it is so important not to rush into abstract recording of the column method for subtraction. Students need experience regrouping using concrete models before they are exposed to an abstract method of subtraction.
Step by step directions
Have parents look at each of the subtraction problems to look for the mistake that the students have made.
Ask parents “What error do you see in this subtraction problem? What do you think they did incorrectly when solving this problem?”
Allow parents to have a conversation with their neighbors about the error made within the problem
Click to show second problem
Ask for volunteers.
Common error- students may try to record the regrouping process in the written form without understanding what the process represents conceptually. In the first problem students remembered they needed to “take something from a number” but did not understand that they needed to regroup (keeping the value the same) from the tens place (6 tens and 12 ones)
In the second problem they “gave the ones place more” but did not regroup from the tens place (6 tens and 12 ones).
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15. How could you use a quick pic to help you solve a 3-digit subtraction problem?
A baby beluga whale weighs 162 lbs. a baby hippopotamus weighs 126 lbs. How much more does the baby beluga weigh than the baby hippopotamus?
Critical point-
A way to still develop understanding at home without base-ten blocks is using quick pictures or (quick pics). Representing the base-ten blocks builds connections between the concrete and the abstract representations.
Step by step directions
Ask parents to solve this problem using quick pictures
Give parents a suggestion “think about how you solved the previous problem using base-ten blocks when solving this problem”
Circulate around the room to check understanding
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16. Where do we want to go? Critical point
The goal of this slide is to demonstrate that our ultimate goal is for students to use the most efficient strategy and representation to solve any problem.
Step by step directions-
Using models and recording what they show will strengthen children’s conceptual and procedural understanding of addition and subtraction.

17. Regroup Exchange Trade
The Replacements
Instead of …
We can say …
Borrow
Carry
Knock on your neighbor’s door
Go get some sugar from you neighbor
Bigger bottom, better borrow!
You can’t take a bigger number from a smaller number
Regroup
Exchange
Trade
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18. 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.
2-Digit Shuffle
Materials – number cards and grid (attached), Pennies or other coins. Player 1-Heads and Player 2-Tails
Directions- Shuffle the number cards and place them face down in a pile.
Take two cards. Say the sum of the two numbers. Your partner checks your sum.
If your sum is correct, place a counter on a square on your grid. If you regrouped to solve, place a coin on another square. Take turns.
Cover all the squares. The player with more counters on the board wins.
Model-N-Record: Played earlier in the training. See hand out for directions.
Critical Point:
Activities for parents to play at home to reinforce concepts of modeling addition and subtraction.
Both of these activities are listed on the CAP handout
Step by Step Directions
Have parents pair up and play 2-digit shuffle (if time)
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19. 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.

20. 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.