1. Connecting Academics & Parents
Compare Numbers
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 comparing numbers. 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:
Snap cubes
Two-color counters
Decks of cards
Participant Packets
Paperclips

2. Mathematics Florida Standards Focus
Kindergarten
MAFS.K.CC.3.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. MAFS.K.CC.3.7 Compare two numbers between 1 and 10 presented as written numerals.
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.
Although students are not expected to use symbols, they will be expected to use the vocabulary of “greater than”, “less than”, and “equal to” in order to make comparisons.

3. Learning Progression: Compare Numbers
Critical Point: Show participants how comparing numbers progresses from kindergarten to future grades. The 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. Which tray has more cookies?
Mr. Frost and Mr. Roper each had a tray of cookies. Who had more cookies?
Mr. Roper
Mr. Frost
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. This is such a simplistic problem that parents will most likely solve it quickly in their head (5-3=2) and not think about how they solved it. Share with parents that while they may know this information quickly, kindergarten students are in a learning stage and need to think about the actions in the problem and how to communicate them. If parents are sitting still not showing their thinking, the trainer might need to have some questions to prompt them like "Did you think about the 3 cookies on one tray and how many more cookies are on the other tray?"
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 comparing numbers. Explain that by the end of the training, they will be familiar with different strategies that help children understand this concept.
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. More Than Less Than More than? Less than?
Almost any child entering kindergarten can choose the set that is more if presented with two sets that are quite obviously different in number.
More Than
The word less proves to be more difficult for children than more. A possible explanation is that children have many opportunities to use the word more but have limited exposure to the word less.
Less Than
Critical Point:
The concepts of “more,” “less,” and “same” are basic relationships contributing to the overall concept of number. Children begin to develop relational ideas before they begin school. For all three concepts, children should construct sets using counters as well as make comparisons or choices between two given sets.
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6. 2 8 Which is bigger? Misconceptions Critical Point:
Standard for Mathematical Practice (SMP) 6 states students and teachers should attend to precision. This includes vocabulary and precise language when discussing mathematical concepts.
Step-by-Step Directions:
Ask participants which number is “bigger”. Do not ask participants how they know 8 is bigger. Just say, “What I hear you say is that 8 is bigger.”
You are modeling this as a non-example. The next slide will reveal a misconception that students will have if we as teachers are using the word bigger rather than greater.
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7. 2 8 Which is bigger? Misconceptions Critical Point:
Explain to participants that when we use the word “bigger than” rather than “greater than” it builds a misconception in students. Bigger/smaller does not refer to quantity, but rather size. Greater/less/fewer is what we should be using for quantity. Greater does not mean the size of a number, rather the magnitude of a number. We can avoid building misconceptions like this in our students by using the appropriate language as well as showing examples like the above, where 2 is much bigger than 8, however 8 is still greater than 2.
Step-by-Step Directions:
Now ask participants, which is number is bigger? Most participants will still say 8. If everyone says 8, ask them what do they think a student would say if they were asked which is bigger. Most will agree that students would say the number 2 because of the size.
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8. The alligator is “eating” the greater number. Is this okay?
Misconceptions
The alligator is “eating” the greater number. Is this okay? 2 8
Critical Point:
This is not okay. Alligators do not eat numbers. This is just a trick. There are other strategies that are more effective and precise for teaching the inequality symbols, but these will not be introduced until 1st grade. Inequality Symbols < > are not part of kindergarten standard. Not only are the symbols not part of the kindergarten standards, but we want to avoid being imprecise as we use “tricks” to remember meanings of symbols. Children who think the gator eats "smaller" numbers vs. "larger" numbers not only forget how the story goes and then don't use the symbol correctly but they also build more of that misconception of smaller = lesser/ bigger or larger= greater. Remember, no alligator is going to physically eat a greater number.
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9. Using Models to Compare Numbers: Snap Cubes
Critical Point:
There are many strategies students can use to compare numbers. One strategy includes using snap cubes to build and compare quantities. Students can match up objects in the set to determine which set is greater than, less than, or equal to.
Step-by-Step Directions:
Instruct participants to turn to spinners in packet and distribute paperclips (one to each pair of participants)
Player one spins and builds a snap cube tower with that number of cubes.
Player two repeats.
Players compare towers and identify who has the greater value (rules can be modified to include the lesser value)
Player one spins and builds a snap cube tower with that number of cubes.
Player two spins and builds.
Players compare towers.
Three is the same as three. The two towers are equal.
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10. Which tray has more cookies?
Critical Point:
Show example of how the snap cube strategy can be applied to a problem-solving scenario to compare numbers.
Step-by-Step Directions:
Participants will build the amount on the first tray using snap cubes.
Participants will build the amount on the second tray using snap cubes.
Participants will compare quantities to determine which tray has more cookies.
5 is greater than 3.
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11. 6 9 Using Models to Compare Numbers: Ten-Frames
Each student selects a number card and builds their set on a ten frame.
Players take off one counter each at the same time.
Players continue taking off one counter each until one player has no counters left.
The red player has more counters than the yellow player.
Nine is greater than six.
Critical Point:
There are many strategies students can use to compare numbers. One strategy includes using ten-frames to build and compare quantities. Students can match up objects in the set to determine which set is greater than, less than, or equal to.
Step-by-Step Directions:
Direct participants to turn to the ten-frame
Use animations on PowerPoint to guide directions to participants
When finished with the examples, have participants complete the activity two times

12. Which tray has more cookies?
Critical Point:
Show example of how the ten-frame strategy can be applied to a problem-solving scenario to compare numbers.
Step-by-Step Directions:
Participants will model the amount on the first tray using counters and a ten-frame.
Participants will repeat for the amount of the second tray.
Participants will compare quantities by removing one counter from each ten-frame until only one ten-frame has counters remaining. The ten-frame with the remaining counters has the greater amount of cookies.
5 is greater than 3.
Five is two more than three.
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13. 8 4 Using Models to Compare Numbers: Number Lines
Students each select a number card and place a counter on the number line to match their number card.
Compare the numbers. Which number is more? Which number is less?
For students that need enrichment, have them figure out how many more or less one number is than the other. 8 4
Critical Point:
“A number line has several advantages. First, it shows the distance from 0. In addition, it is an excellent tool for modeling the operations. Jumps can be shown in the same way as with whole numbers and fractions” (Van de Walle, 2010). On a number line, as you move to the right, the values increase. Conversely, when you move to the left, values decrease. Knowing this, students can make comparisons of values using a number line. Students will use number lines to compare fractions and decimals in successive grades.
Step-by-Step Directions:
Ask participants, “Why is it important to have students compare numbers on a number line?” and “How would doing this be beneficial in classrooms?”
To compare two or more numbers, participants will identify and circle the points on the number line.
Lead a discussion about the placement of a number and its relative magnitude (i.e. the farther right on the number line, the greater the value).

14. Which tray has more cookies?
Critical Point:
Show example of how a number line can be applied to a problem-solving scenario to compare numbers.
Step-by-Step Directions:
Participants will model the amount on the first tray by circling “5” on the number line.
Participants will repeat for the amount of the second tray.
Participants will compare quantities by their locations on the number line.
Also, they may “jump” the distance between the two quantities to find how much “more” or how much “less”.
5 is greater than 3.
Five is two more than three.
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15. Making Sets
Show students a set of counters. Students will create three sets allowing them to demonstrate understanding of comparisons
Sets should include less than, equal to, and more than the shown set
Less than
Equal to
More than
Critical Point:
This activity gives participants an opportunity to reflect on the sets of counters and create sets that are “less than”, “more than”, and “equal to.” “For all three concepts (more, less, and same), children should construct sets using counters as well as making comparisons or choices between two given sets” (Van de Walle, 2010). During this activity, questions should be asked such as, “Why do you think this set has less?”
Step-by-Step Directions:
Have participants turn to the “Making Sets” mat in their Participant Packet.
Participants will identify the quantity in the provided set. In this example, the set is equal to 8.
Then, they will create three sets. One each for less than, equal to, and more than.
Shoulder partners should then compare their sets in order to recognize that sets “less than” and “more than” may differ from person to person.
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16. * Rules can be modified so the lesser number wins.
Comparing Numbers War
Using only number cards (Ace-10, Ace represents 1) deal the cards equally among all players.
Simultaneously, players will turn their top card face up to display a number.
The player with the greatest number collects all cards played. Players can justify their thinking using counters (beans, cereal, etc.)
The player with the most cards at the conclusion of the game wins!
* Rules can be modified so the lesser number wins.
Critical Point:
A key component of this training is providing games/activities for participants to take home for practical application. Comparing Numbers War is a quick game that can be played to help students understand this specific concept.
Step-by-Step Directions:
Using only number cards (Ace-10, Ace represents 1) deal the cards equally among all players.
Simultaneously, players will turn their top card face up to display a number.
The player with the greatest number collects all cards played. Players can justify their thinking using counters (beans, cereal, etc.)
The player with the most cards at the conclusion of the game wins! (Rules can be modified so the lesser number wins.)

17. 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.
Comparing Numbers War
Deck of Cards
Dominoes
Spinners to Compare Numbers
Making Sets with Counters
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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18. 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.

19. 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.