1. Connecting Academics & Parents
Addition & Subtraction Concepts
Critical Point: Welcome participants to the session. This training was intended to take one hour, but can be adjusted to take more/less time as needed. State that during the training, they will learn strategies to support their children in understanding addition and subtraction concepts. Additionally, they will receive real-world activities to take home and apply for extra support.
Step-by-Step Directions:
Welcome parents and introduce trainers.
Give purpose for training which is to build parents’ understanding of what their children are learning and strategies they will be using in the classroom, which align with the Mathematics 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 needed for training:
Counting manipulatives (color tiles, two-color tiles, counting bears, snap cubes etc.)
Participant packets
Deck of cards with Ace-10

2. Mathematics Florida Standards Focus
Kindergarten
MAFS.K.OA.1.a Use addition and subtraction within 10 to solve word problems involving both addends unknown, e.g., by using objects, drawings, and equations with symbols for the unknown numbers to represent the problem.
Critical Point: This training centers around the stated Mathematics Florida Standard. All activities within this training will be aligned with this standard.
Step-by-Step Directions:
In groups, have participants discuss and paraphrase their understanding of the standard.
Select participants to share.
Highlight and clarify vocabulary, “addend” and “equation” for participants. (Addends- two or more numbers added together to find a sum. Equations- two mathematical expressions joined with an equal sign)

3. Learning Progression: Addition & Subtraction Concepts
Critical Point: Show participants how addition and subtraction concepts progress from kindergarten to future grades. The addition and subtraction concepts learned in kindergarten are vital to students’ ability in applying the skills to greater values in successive grades.
Trainer Notes – Do not spend a lot of time on this (about 2 minutes max).
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4. Solve the following problem…
The principal was carrying a tray of 10 cupcakes to the Student of the Month celebration. The assistant principal bumped into her and some cupcakes fell off. How many cupcakes are still on the tray? How many are on the floor?
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 someone 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 their 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.
Trainer Note – Solving and sharing should take no longer than 5 minutes for this slide.
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5. Ways to solve… Act it Out Draw a Picture
The principal was carrying a tray of 10 cupcakes to the Student of the Month celebration. The assistant principal bumped into her and some cupcakes fell off. How many cupcakes are still on the tray? How many are on the floor?
Act it Out
Draw a Picture
Critical Point: Most students in kindergarten rely on the following problem solving strategies, “Act it Out” and “Draw a Picture.” These are concrete strategies to help students represent and solve various addition and subtraction word problems.
Step-to-Step Directions:
Discuss the strategy “Act it out.” As student’s make sense of the problem, they will select real items or math tools (counters) to represent the object in the problem. Students may model the action in the problem by either joining or separating math tools/actual items.
Discuss the strategy “Draw a Picture.” Some students may not need to use math tools. However, they may use models or drawings to represent the action in the word problem. Again, the focus should be on the action, either joining or separating.
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6. What’s the action?
Kindergarten students will develop an understanding of addition and subtraction concepts through the actions of joining and separating.
To develop conceptual understanding of the operations, research tells us to AVOID teaching students to use a key word strategy.
“When using this strategy, students often misinterpret words and shift from a focus on analyzing the problem and sense-making to a mechanical and potentially inappropriate reliance on key words.”
-Kenney et al. (2005)
Critical Point #1: As students begin to understand addition and subtraction, the focus should be on joining and separating situations. These situations should reflect students’ real-world experiences with joining and separating. “Contextual problems might derive from recent experiences in the classroom, a field trip, a discussion you have been having in art, science, or social studies, or from children’s literature” (Van de Walle, 2010). (i.e. There are 2 students sitting on the carpet. Three more joined them. How many students are now sitting on the carpet?)
Critical Point #2: In the past, instruction may have included the teaching of key words in mathematical word problems. However, there can be multiple key words in one scenario. (i.e. Christa had 3 containers of yogurt. How many more containers will she need to have enough yogurt for a 7 day week?) Teaching key words will lead to misconceptions and errors in solving problems. Instead, teaching students to rely on the action and understand the context of the problem is more effective.
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7. JOINING What’s the action?
Rita had 5 Skittles. Lesley gave her 4 more. How many Skittles does Rita have now?
JOINING
Critical Point: “For the action of joining, there are three quantities involved: an initial or starting amount, a change amount (the part being added or joined), and the resulting amount (the total amount after the change takes place)” (Van de Walle et al., 2010).
Step-by-Step Directions:
Have participants read the problem-solving scenario and think about the action occurring. Note: Students are not expected to read the problems shown like they are on the PowerPoint because teachers will read problems and describe situations to students as they are learning to read.
Have participants share with a shoulder partner.
Come back together and discuss why this is a joining scenario.
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8. Rita has 9 Skittles Strategies to Solve
Rita had 5 Skittles. Lesley gave her 4 more. How many Skittles does Rita have now?
Critical Point: The standard way to fill a ten frame is to fill the top row first starting on the left. When the top is full, counters can be placed on the bottom row from the left. “For a while, many children will count every counter on their ten-frame. Some will take all counters off and begin each number from a blank frame. Others will soon learn to adjust numbers by adding on or taking off only what is required, often capitalizing on a row of five without counting” (Van De Wall et al., 2010).
Step-by-Step Directions
Explain that a ten-frame focuses on the relationship to ten as an anchor for numbers.
Have parents model the action of joining using ten-frame in participant packet and provided two-color counters.
Most parents will start with placing 5 Skittles on the ten-frame and then add 4 more. Highlight that they are starting with the first piece of information provided in the problem prior to moving to the next.
Rita has 9 Skittles
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9. SEPARATING What’s the action?
Layla was setting the table for dinner. She had 10 forks in her hand. She set one fork down at every seat. When she was done setting the table, she had 6 forks left in her hand. How many people are eating dinner?
SEPARATING
Critical Point: “… in separate problems, the initial amount is the whole or the largest amount, whereas in the ‘join’ problems, the result is the whole. In ‘separate’ problems the change is that an amount is being removed from the initial value” (Van de Walle, 2010).
Step-by-Step Directions:
Have participants read the problem-solving scenario and think about the action occurring. Note: Students are not expected to read the problems shown like they are on the PowerPoint because teachers will read problems and describe situations to students as they are learning to read.
Have participants share with a shoulder partner. As participants are sharing, circulate around the room and question. Ask them their thinking behind what makes this scenario a separating problem.
Come back together and discuss why this is a separating scenario.
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10. What’s the action? Layla has 6 forks in her hand
Layla was setting the table for dinner. She had 10 forks in her hand. She set 4 forks down on the table. How many forks are still in her hand?
Critical Point: Parents will use a ten-frame to solve separating problems.
Step-by-Step Directions:
Explain that a ten-frame focuses on the relationship to ten as an anchor for numbers.
Have parents model the action of separating using ten-frame in participant packet and provided two-color counters.
Ask how this ten-frame can be beneficial in problem-solving.
Layla has 6 forks in her hand
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11. Whole Part Part-Part-Whole
Critical Point: “Part-part-whole problems involve two parts that are combined into one whole. The combining may be a physical action, or it may be a mental combination where the parts are not physically combined” (Van de Walle, 2010).
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12. Part-Part-Whole
There are 4 small flowers and 2 large flowers in a garden. How many flowers are in the garden?
Critical Point: Participants will use tools, pictures etc. to solve addition and subtraction problems. Students may model part-part-whole with counters or pictures. These representations are more concrete and should lead to an abstract connection to representing with numbers.
Step-by-Step Directions:
Represent the 4 small flowers as one part.
Represent the 2 large flowers as the other part.
Combine both parts for the whole.
Connect visual representation to numbers. 6 4 2
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13. Part-Part-Whole Dominoes
Select one domino.
Draw the domino pips on your recording sheet.
Write the total number of pips in your “whole” box.
Write the number of pips in each part in the “part” boxes. 6
Critical Point: An option for applying part-part-whole strategy is to use dominoes.
Step-by-Step Directions:
1. Select one domino.
2. Draw the domino pips on your recording sheet.
3. Write the total number of pips in your “whole” box.
4. Write the number of pips in each part in the “part” boxes.
Trainer Note – This should take a maximum of 5 minutes. The purpose is to just give them an idea of how Part-Part-Whole Dominoes work 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. 5 1
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14. Decomposing with Number Bonds
whole
part
Critical Point: Part-Part-Whole has a direct connection to the strategy of number bonds. This is an example of decomposition. In the progression of understanding, this step will move the students into building understanding of a method by recording their decompositions using number bonds. The purpose of the number bonds is for the students to have a physical model to record and build understanding of joining the two sets (or eventually the separating of the whole into two sets).
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15. Decomposing with Number Bonds
Dakota has some crayons. Seven crayons are yellow. Two crayons are green. How many crayons does Dakota have? 9 7 2
Critical Point: Participants will create a number bond using a problem-solving scenario. In this scenario, participants will combine both sets to make a whole. Essentially, the action models joining the parts to form a whole or sum. The concepts of composition and decomposition are crucial in order to build a solid foundation for addition and subtraction.
Step-by-Step Directions:
Pose problem. Give participants one minute to solve. Note: Students are not expected to read the problems shown like they are on the PowerPoint because teachers will read problems and describe situations to students as they are learning to read.
Make connections to the Part-Part-Whole strategy.
Dakota has 9 crayons
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16. Decomposing with Number Bonds
Dakota has 9 crayons. Seven crayons are yellow. The rest are green. How many crayons are green? 9 7 2
Critical Point: Participants will create a number bond using a problem-solving scenario. In this scenario, participants will find the missing part by separating the whole into two sets.
Step-by-Step Directions:
Pose problem. Give participants one minute to solve. Note: Students are not expected to read the problems shown like they are on the PowerPoint because teachers will read problems and describe situations to students as they are learning to read.
Make connections to the Part-Part-Whole strategy.
2 crayons are green
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17. Make a Ten Game Use the Ace through 10 cards from a deck of cards.
The Ace will represent “1.”
Shuffle the cards and turn nine cards face up in a 3x3 grid on the table.
Player 1 takes any pairs that make a ten (or single 10 cards)
Player 2 fills in the empty spaces with new cards (face up) and takes pairs that have a sum of ten (or single 10 cards).
Play continues alternating between Player 1 and Player 2 until all cards are gone.
The player with the most cards “wins.”
Critical Point: Participants will use tools, pictures etc. to solve addition and subtraction problems.
Step-by-Step Directions:
Explain the rules of “Make a Ten” game
Use the Ace through 9 (or 10) cards from a deck of cards.
The Ace will represent “1.”
Shuffle the cards and turn nine cards face up in a 3x3 grid on the table.
Player 1 takes any pairs that make a ten (or single 10 cards)
Player 2 fills in the empty spaces with new cards (face up) and takes pairs that have a sum of ten (or single 10 cards).
Play continues alternating between Player 1 and Player 2 until all cards are gone.
The player with the most cards “wins.”
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18. Make a Ten Game Critical Point:
Make a ten and add the extra is an addition strategy taught in first and second grade. Knowing the combinations that make ten is taught in kindergarten.
Step-by-Step Directions:
1. Bring to attention the decomposition modeled and how it makes addition easier to compute.

19. 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.
Identifying Problem-Solving Actions Part-Part-Whole Dominoes Make a Ten Game
Critical Point: Give parents purposeful practice and resources to use at home to reinforce addition and subtraction concepts.
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 funding allows, may want to purchase a deck of cards for each parent that attends the training.
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20. 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.

21. 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.