Introduction

Students and Word Problems

Opening Activity: Mingle, Pair, Share Let’s get off our seats and mingle! Focus Question: What strategies do students use to solve word problems in your classroom? I will play music in the background, when it stops, you find the closest person to you (no running across the room to find your friend). Repeat the focus question One partner shares and the other listens. Partners switch roles. Repeat 1-6, 2x more Students mix around the room silently as music plays in the background. When the music stops, each student finds a partner closest to them (no running across the room to find your best friend!) and puts their hand together with their partner’s in a high five. When all students have found a partner, teacher poses a question and allows for some thinking time One partner shares and the other listens. Partners switch roles. After both partners have had a chance to speak (teacher will have to monitor this, based on the depth of the question), music starts again, students mingle, when music stops they find a new partner, teacher poses the same question. Repeat for each question.

Math Problem Solving Strategies Tree Map

Math Problem Solving with CGI Cognitively Guided Instruction By Maria Hernandez

What is CGI? Cognitively Guided Instruction (AKA as CGI math) is an approach to teaching mathematics that uses a student's own mathematical thinking as the basis for instruction. The method is the result of research conducted by Elizabeth Fennema and Thomas P. Carpenter from the University of Wisconsin - Madison

Why CGI? Studies have consistently demonstrated that Cognitively Guided Instruction (CGI) students show significant gains in problem solving.

Teacher’s Role To build from this prior knowledge so that students can eventually make connections between situational experiences and the abstract symbols typically found to represent them in mathematical equations (+, -, x and so forth.) This approach is quite different from the traditional method of teaching the symbolic computation first, and then expecting students to apply the concepts to problem solving situations.

Strategies

Classification of Word Problems Not all word problems are the same. What are some of the distinguishing factors that relate to the difficulty in solving various problems? Location of the unknown variable The types of actions or relationships described in the problem.

Addition and Subtraction Problem Types K-3rd

Join Problems (+) Result Unknown : Sum is unknown Change Unknown: 2nd number (addend) is unknown Start Unknown: 1st number (augend) is unknown

Result Unknown Change Unknown Start Unknown Robin had 5 toy cars. Her parents gave her 2 more toy cars for her birthday. How many toy cars did she have now? Strategy: Counting On Robin had 5 toy cars. Her parents gave her some more toy cars for her birthday. Then she had 7 toy cars. How many toy cars did Robin’s parents give her for her birthday? Strategy: Counting on to Robin had some toy cars. Her parents gave her 2 more toy cars for her birthday. Then she had 7 toy cars. How many toy cars did Robin have before her birthday? Strategy: Trial and Error

Result Unknown Change Unknown Start Unknown Strategies: Counting On Pictures Tallies Number Disks Break Down Bundling Expanded Place Value Pull Down Number Bonds Counting on to Magic Box Trial & Error

Let’s Create our Own Join Problems (+) Result Unknown : Sum is unknown Change Unknown: 2nd number (addend) is unknown Start Unknown: 1st number (augend) is unknown Partners: Sit and work with NEW a person who teaches the same grade level and create your own Math Word Problems. Think of what strategies will fit the word problems. Share Out!

Separate Problems (-) Result Unknown: Difference is unknown Change Unknown: 2nd number (subtrahend) is unknown Start Unknown: 1st number (minuend) is unknown.

Result Unknown Change Unknown Start Unknown Collen had 8 guppies. She gave 3 guppies to Roger. How many guppies does Colleen have left? Strategy: Counting Down Colleen had 8 guppies. She gave some guppies to Roger. Then she had 5 guppies left. How many guppies did Colleen give Roger? Strategy: Counting Down to Colleen had some guppies. She gave 3 guppies to Roger. Then she had 5 guppies left. How many guppies did Collen have to start with? Strategy: Trial and Error

Result Unknown Change Unknown Start Unknown Strategies: Counting Down Pictures Tallies Number Disks Break Down Unbundling Pull Down Counting down to Magic Box Trial & Error

Let’s Create our Own Separate Problems (-) Result Unknown: Difference is unknown Change Unknown: 2nd number (subtrahend) is unknown Start Unknown: 1st number (minuend) is unknown. Partners: Sit and work with a NEW person who teaches the same grade level and create your own Math Word Problems. Think of what strategies will fit the word problems. Share Out!

Part-Part-Whole Problems Whole Unknown : Finding the size of the whole Part Unknown: Have one of the parts and the whole; and asks the solver to find the size of the other part.

Whole Unknown Part Unknown 6 boys and 4 girls were playing soccer. How many children were playing soccer? Strategy: Counting On 10 children were playing soccer. 6 were boys and the rest were girls. How many girls were playing soccer? Strategy: Magic Box

Whole Unknown Part Unknown Strategies: Counting on Pictures Tallies Number Disks Break Down Bundling Expanded Place Value Pull Down Number Bonds Magic Box Unbundling

Let’s Create our Own Part-Part-Whole Problems Whole Unknown : Finding the size of the whole Part Unknown: Have one of the parts and the whole; and asks the solver to find the size of the other part. Partners: Sit and work with a NEW person who teaches the same grade level and create your own Math Word Problems. Think of what strategies will fit the word problems. Share Out!

Compare Problems Difference Unknown: Answer (difference) is unknown Compared Set Unknown: A number of a compared set is unknown. Referent Unknown: The referred set is unknown.

Difference Unknown Compared Set Unknown Referent Unknown Mark has 3 mice. Joy has 7 mice. Joy has how many more mice mice than Mark? Strategy: Unbundling Mark has 3 mice. Joy has 4 more mice than Mark. How many mice does Joy have? Magic Box Joy has 7 mice. She has 4 more mice than Mark. How many mice does Mark have?

Difference Unknown Compared Set Unknown Referent Unknown Strategies: Pictures Number Disks Unbundling Magic Box Tallies

Let’s Create our Own Compare Problems Difference Unknown: Answer (difference) is unknown Compared Set Unknown: A number of a compared set is unknown. Referent Unknown: The referred set is unknown. Partners: Sit and work with a NEW person who teaches the same grade level and create your own Math Word Problems. Think of what strategies will fit the word problems. Share Out!

Common Core and CGI Mathematical Practice #1: Students will make sense of problems and persevere in solving them. The connection here is obvious….that is the premise of CGI. Mathematical Practice #2: Students will reason abstractly and quantitatively. When students are involved in problem solving they are seeing numbers in context and they are required to attend to the meaning of quantities. Mathematical Practice #3: Students will construct viable arguments and critique the reasoning of others. This occurs on a daily basis in a CGI classroom as students share their solution strategies and their answers to problems. If disagreements occur, student are encouraged to engage in discourse with their classmates. Mathematical Practice #4: Modeling with Mathematics. In CGI classrooms, students are encouraged to represent their mathematical thinking with different representations. This varies from using tools, to drawing pictures but eventually leads to equations.

Common Core and CGI Mathematical Practice #5: Using Appropriate Tools Strategically. CGI students will do this naturally. When presented a word problem, CGI students choose any method and tool that makes sense to them. Mathematical Practice #6: Attend to Precision. CGI students are required to communicate their mathematical reasoning precisely. They are asked to attend to units and labels and use vocabulary and symbols accurately. Mathematical Practice #7: Look for and make use of structure. CGI students naturally pay attention to the structure of a problem. They follow the sequence of the word problem and by using tools that make sense to them, they are able to solve complex problems. Many of these problem types are ones teachers might not believe young children are capable of understanding. Mathematical Practice #8: Look for and express regularity in repeated reasoning. Students in these classrooms look for patterns, and through discussion teachers can encourage all the known solution methods and help students look for shortcuts. Children are also encouraged to continually check for reasonableness. Although there might be a few concepts in elementary mathematics that do not lend themselves to word problems, most concepts do. This is why CGI is a natural fit with the Common Core State Standards.

Problem Solving Manipulatives

Success of CGI For CGI math to be successful, teachers must have a thorough understanding of the grade-level curriculum and the distinctions between different problem types within that curriculum. They must also have a working knowledge of the processes that are typically used to solve these problems, and the various stages that students go through in developing their own concrete knowledge. The End

They can do it!

Closing Activity Fill out the Math Strategies Reference Sheet in 1min. No Cheat Sheets! Person with the most will get raffle tickets for every box correctly filled.