Connecting Academics & Parents Academic seminars to sharpen skills and build understanding in Problem Solving Step by step directions: Introduce yourself. Share with parents that these workshops, CAP (Connecting Academics and Parents), were created based on feedback from parents wanting to learn more about the math concepts and how to help their children at home. Materials for training: Variety of counting manipulatives Technology Powerpoint packets

Mathematics Florida Standards Focus Grade 1 MAFS.1.OA.1.1 Use addition and subtraction within 20 to solve word problems1 involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem (1Students are not required to independently read the word problems.) Step by step directions: Read standard aloud. Highlight that all the problem structures will be briefly discussed, but more focus will be placed on comparing and unknowns in all positions. This workshop will also share different tools that help children make sense of problems and organize their thoughts.

Learning Progression: Problem Solving Step by step directions: Read each standard summary. Discuss how problem solving is used throughout this trajectory. Copyright 2009

Problem Solving Situations are Everywhere! Is the Math the same for each problem? How much money was in my account before I paid the mortgage? It takes 30 minutes to get to work…I was delayed by an accident and it took 45 minutes! I paid $25 more dollars a day at Disney than the $75 dollars I paid for Busch Gardens! There are 140 calories in regular Doritos! Baked chips have 20 less calories. For the birthday party we invited 12 girls and 11 boys! Step by step directions: Click to show title of the slide and read. Click and read each real world problem example. Ask parents to think “Where’s the Math?” Click again to remove and show next problem. Click to show question: Is the Math the same for each problem? Highlight that throughout this workshop we will take a closer look at the different types of problem structures that your children will be asked to solve. Copyright 2009

Problem Structure Chart   Result Unknown Change Unknown Start Unknown Add To Take From Put Together/Take Apart (Part/Part/Whole) Total Unknown   Addend Unknown Both Addends Unknown Compare  Difference Unknown Bigger Unknown  Smaller Unknown How much money was in my account before I paid the mortgage? It takes 30 minutes to get to work. I was delayed by an accident and it took 45 minutes! For the birthday party we invited 12 girls and 11 boys!   Step by step directions: Share that children are asked to look at problem structures that have different unknowns. Click to animate…in the first scenario the amount of money I started with is unknown. Click to animate…in the second scenario the amount of time I was delayed is unknown. Click to animate…in the third scenario the total number of kids invited to the party is unknown. Click to animate…in the fourth scenario the total amount of money paid for Disney is unknown. Click to animate…in the fifth scenario the amount of calories in baked chips is unknown. Highlight that because of all the varying structures, children need to understand and visualize what is happening in the problem. I paid $25 more dollars a day at Disney than the $75 dollars I paid for Busch Gardens!  There are 140 calories in regular Doritos! Baked chips have 20 less calories. Copyright 2009

Add To Two bunnies sat on the grass. 3 more bunnies hopped over to them. How many bunnies are on the grass now? How would you write an equation to represent this problem? At first glance these two problems are very similar to the initial problem, what are the similarities and differences between the problems? How would you write equations to represent these two problems? Two bunnies sat on the grass. Some more bunnies hopped over to them. Now there are 5 bunnies. How many bunnies hopped over to the first two? Some bunnies sat on the grass. 3 more bunnies hopped over to them. Now there are 5 bunnies. How many bunnies were on the grass before? Step By Step Directions: Explain to parents that you are going to briefly discuss the different Add To problem structures. Have them read and answer the initial problem. Click to show the question: How would you write an equation to represent this problem? Ask a parent to share their equation and explain that by the end of the year their children should be able to use equations with unknowns to represent problems. 2 + 3 = ? Click to bring up the 2 problems that represent change unknown and start unknown. Give parents a minute to read the two problems and think about how they would solve them. Click to bring up the question: At first glance these two problems are very similar to the initial problem, what are the similarities and differences between the problems? Give parents a minute or two to share thoughts with others in their group. Ask a few parents to share their ideas. Highlight any thoughts that relate to the change and starts being unknown: What they are being asked to find in each problem is different. Click to show the question: How would you write equations to represent these two problems? Ask a few to share their equations and discuss how they are different than the first equation because the unknown is in a different place. Possible equations for 1st example: 2 + ? = 5 or 5 – 2 = ? Possible equations for 2nd example: ? + 3 = 5 or 5 – 3 = ?

Take From There are 5 apples on the table. I ate 2 of them. How many apples are on the table now? How would you write an equation to represent this problem? At first glance these two problems are very similar to the initial problem, what are the similarities and differences between the problems? How would you write equations to represent these two problems? There are 5 apples on the table. I ate some of them. Now there are 3 apples on the table. How many apples did I eat? Some apples were on the table. I ate 2 of them. Now there are 3 apples. How many apples were on the table before? Step By Step Directions: Explain to parents that you are going to briefly discuss the different Take From problem structures. Have them read and answer the initial problem. Click to show the question: How would you write an equation to represent this problem? Ask a parent to share their equation and explain that by the end of the year their children should be able to use equations with unknowns to represent problems. 5 – 2 = ? Click to bring up the 2 problems that represent change unknown and start unknown. Give parents a minute to read the two problems and think about how they would solve them. Click to bring up the question: At first glance these two problems are very similar to the initial problem, what are the similarities and differences between the problems? Give parents a minute or two to share thoughts with others in their group. Ask a few parents to share their ideas. Highlight any thoughts that relate to the change and starts being unknown: What they are being asked to find in each problem is different. Click to show the question: How would you write equations to represent these two problems? Ask a few to share their equations and discuss how they are different than the first equation because the unknown is in a different place. Possible equations for 1st example: 5 - ? = 3 or 3 + ? = 5 Possible equations for 2nd example: ? – 2 = 3 or 3 + 2 = ?

Problem Solving Tool Actions and Direct Modeling Use manipulatives or drawings to directly model what is happening in the problem… There are 5 airplanes at the airport. 4 airplanes just landed. How many airplanes are at the airport now? There are 9 airplanes at the airport. 5 of them took off. How many airplanes are at the airport now? Step By Step Directions: Explain to parents that you are going to share a problem solving tool that can be used to model different problem structures. Ask the parents to solve these problems by using manipulatives and modeling what is happening in the problem. Click to show 1st problem; Give parents a few minutes to solve. Click to show the animation of how to model the problem. Share with parents that it is important for their children to identify the actions of the story and be able to identify what their manipulative is representing from the story. For example, the first 5 tiles represent the airplanes at the airport and the second 4 tiles represent the airplanes that just landed. Click to show 2nd problem; Give parents a few minutes to solve. Ask parents: How was modeling this problem different from the 1st problem? Possible responses: subtraction; removing tiles rather than adding tiles Copyright 2009

Key Words: Howard County 1. Key words are misleading. Some key words typically mean addition or subtraction. But not always. Consider: There were 4 jackets left on the playground on Monday and 5 jackets left on the playground on Tuesday. How many jackets were left on the playground? "Left" in this problem does not mean subtract. 2. Many problems have no key words. For example, How many legs do 7 elephants have? does not have a key word. However, any 1st grader should be able to solve the problem by thinking and drawing a picture or building a model. 3. It sends a bad message. The most important strategy when solving a problem is to make sense of the problem and to think. Key words encourage students to ignore meaning and look for a formula. Mathematics is about meaning (Van de Walle, 2012). Step by step directions: Share key word slide. Highlight that key words are misleading and lead children to ignore meaning in a problem solving situation. Howard County Copyright 2009

Put Together/Take Apart 3 red apples and 2 green apples are on the table. How many apples are on the table? How does this problem structure compare to the airplane problems? How are these 2 problems similar and different? 5 apples are on the table. 3 are red and the rest are green. How many apples are green? Grandma has 5 apples. How many are red and how many are green? Step By Step Directions: Explain to parents that you are going to briefly discuss the different put together and take apart problem structures. Have them read and answer the initial problem. Click to show the question: How does this problem structure compare to the airplane problems? Possible responses: no action, just two sets of objects on a table Click to bring up the 2 problems that represent one part/addend unknown and both parts/addends unknown. Give parents a minute to read the two problems and think about how they would solve them. Click to bring up the question: How are these 2 problems similar and different? Give parents a minute or two to share thoughts with others in their group. Ask a few parents to share their ideas. Possible response: in both problems we know the total/whole; first one is missing one part and the second one is missing both parts; second problem is open-ended; more than one answer for the second problem Highlight that in these types of problem there is no action taking place.

12 8 ? ? 4 8 Problem Solving Tool Part-Part-Whole or Bar Model There were 12 cars in the school parking lot. 8 of them were minivans. How many cars in the parking lot were not minivans? There were 4 trucks and 8 cars driving on the highway. How many vehicles were on the highway? 12 Whole/Total 8 Part ?  ? Whole/Total  4 Part  8 Step By Step Directions: Explain to parents that you are going to share a problem solving tool that can be used to organize different problem structures. Read the problem and share the part/part/whole box. Discuss how each box represents a part of the problem. Ask parents what operation is used to solve this problem? Possible response: addition; put the 2 numbers together Click to show the 2nd question: Have parents sketch out what a part/part/whole box would look like to represent this problem. Click to show part/part/whole box. Whole group discussion: How is this box different from the previous example? Possible responses: total is given; one of the parts is missing; use subtraction or add-up to solve Why is this a beneficial tool for children? Possible responses: helps children organize their thinking; helps identifying missing part or whole; helps children visualize the problem Copyright 2009

Compare Joey has 9 stickers. Tyler has 13 stickers. How many more stickers does Tyler have than Joey? How would you solve this problem? Tyler has 4 more stickers than Joey. Joey has 9 stickers. How many stickers does Tyler have? How is this problem different than the previous problem? Step By Step Directions: Explain to parents that the last problem structure that you are going to discuss is compare. This is a more difficult problem structure for children. Click to bring up the first problem. Students can usually tell you who has more or who has less, but they tend to have a more difficult time determining how many more or less. Ask parents to solve and think about what the model of this problem would look like. Trainer should look for parents that used a picture or manipulative that shows a representation of the 7 and the 9 next to each other…do not click to show examples until a parent has shared or nobody uses this model. Click to show student work samples. Highlight how student modeled both numbers and matched up the pictures and found the difference in the first example and in the second example student modeled the problem the same way but included an equation. Ask parents: How is this model useful when solving comparison problems? Possible responses: helps to visualize problem; easier to see how many more or less; focus is on comparing numbers so that you could use addition or subtraction to solve (9+ ? = 13 or 13 – 9 = ?)  Click to show 2nd problem and have them read…click again to show question: How is this problem different than the previous problem? Possible responses: does not have more or less in the text; both numbers in the problem will not be modeled side by side Click to show question: How would you solve this problem? Give parents a few minutes to solve and build a model. Trainer should look for parents that modeled 9 and added 4 more. Highlight that children will work through a variety of comparing problems throughout the year. Depending on when this workshop is being delivered, children may or may not have had exposure to this type of problem structure. Drawing a model or using tools can help children make sense of the problem and solve. Copyright 2009

Step by step directions: Determining how many more or less is a more difficult concept for children, this game was included to give children additional practice in building models to compare (find the difference between) numbers. Share the Rules of the Game: Cover the board with any type of marker. Each person takes off 2 markers and builds/draws a model of the 2 numbers. Solve to find the difference. Keep playing until all markers have been removed. Give parents about 5 minutes to play the Comparison Game. Bring them back together to debrief about modifications that could be made at home: Possible responses: use additional basic fact strategies; create story problems based on the numbers; keep score by tracking the differences

Take it Home and Try It! TRY THIS AT HOME! Warning: Implementing this engaging activity will result in an increase in motivation and long-lasting learning. Questions to Ask When Problem Solving What is happening in this problem? Tell me in your own words. What are you trying to find out? What will your answer be (Yes or No, a person’s name, a number, etc.)? How will you go about solving this problem? What is your plan? What do the numbers in the problem represent (7 is number of tables, 21 is the number of chairs, etc.)? How could a model help you solve this problem? What does each part of your model represent from the story? Can you write an expression or equation to help you solve the problem? What does the number in your solution represent? Step by step directions: Share the questions on the slide with the parents and let them know that a larger copy of the questions can be found in their packet. These questions can be used to help their child get “unstuck” when doing homework or when discussing math encountered in daily life. Copyright 2009

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.

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.