PARCC Problem solving in math December 11 2014
PARCC & Problem solving in math December 11, 2014 Presented by: Charlotte Thompson & Taryn Miley
Jumping Right In… Real World Application – Grade 4
Real World Application – Grade 4 72 total
Take it a Step Further… • Explain your thinking • Molly believes 1 bus, 1 van, and 6 cars can hold all of the students. Explain why she is incorrect.
What Must Students Do When Solving Problems? • To solve even simple problems, students must: -understand the vocabulary and instructions contained within the problem -recall mathematical rules and formulas -recognize patterns -use sequential ordering to solve multi-step problems
Overall Learning Goals for Problem Solving During this session, participants will: • experience learning mathematics through problem solving • solve problems in different ways • develop strategies for teaching mathematics through problem solving 6
What is Problem Solving? • “Problem solving means engaging in a task for which the solution method is not known in advance. ” --Principles and Standards for School Mathematics • It encompasses exploring, reasoning, strategizing, estimating, conjecturing, testing, explaining, and proving.
What’s so great about problem solving? • Various strategies to solve the problems (pictures, numbers, equations, graphing) • Could have more than 1 solution • Encompasses multiple standards
Key Questions What Why Are you learning? Are you learning it? How Do you know? Did you get that answer?
What is a Problem? • A problem is a task that requires the learner to reason through a situation that will be challenging but not impossible. • Most often, the learner is working with a group of other students to meet the challenge. • Problems can generally be defined as an obstacle, that remains perplexing until solved.
Problem or Exercise? • An exercise is a set of number sentences intended for practice in the development of a skill. • A problem is what we commonly refer to as a “word problem. ” • But beware! Problems can become exercises!!
It’s More Than This… • I have read 134 of the 512 pages of my book. How many more pages must I read to reach the middle? • Word problems have their place in mathematics, but it’s not necessarily problem solving!
Problem Solving Strategies Two Methods You Can Use with Students
Four Phases • Students can learn to become better problem solvers. Polya’s (1957) “How to Solve It” book presented four phases or areas of problem-solving, which have become the framework often recommended for teaching and assessing problem-solving skills. The four steps are: • • 1. understanding the problem, 2. devising a plan to solve the problem, 3. implementing the plan (Solve), and 4. reflecting on the problem (Check).
UPS Strategy • Understand- what is the problem asking you to do? • Plan- how will you solve the problem? What strategy will you use? • Solve & Check- Solve the problem and Check your answer to make sure it makes sense
MY PROBLEM • I have 4 shirts one is red, one yellow, one white, and one blue. I have 2 pairs of pants that are black and khaki and one skirt that is dark blue. I can wear all these with all 4 shirts. How many different outfits do I have?
Step One- U • Understand what the problem is asking: How many different outfits do I have?
Look for Clues • Read the problem carefully. • Underline clue words. • Ask yourself if you've seen a problem similar to this one. If so, what is similar about it? • What did you need to do? • What facts are you given? • What do you need to find out?
Step Two- P • Plan how you will solve the problem. What strategy will you use? v. Draw a picture v. Use logical reasoning v. Guess and check v. Look for a pattern v. Choose an operation v. Use a formula v. Write an equation v. Solve a simpler problem v. Work backwards v. Make a list, table, graph, or diagram
Problem Solving Strategy • The method I have chosen to solve my problem is to draw a picture to show many different outfits I can make
Step Three- S • Solve and Check- Solve the problem and Check your answer to make sure it makes sense – 3 outfits with the red shirt – 3 outfits with the yellow shirt – 3 outfits with the blue shirt – 3 outfits with the white shirt – I have a total of 12 outfits with the clothes that I have in my closet.
Other Ways to Solve? • How else could you have solved this problem? v. Use logical reasoning v. Guess and check v. Choose an operation v. Write an equation v. Make a list, table, graph, or diagram
Practice • Problem solving requires practice! The more your practice, the better you get. Practice, practice.
CUBES Strategy • • • C- Circle the key numbers U- Underline the question B- Box in key words E- Evaluate and Eliminate S- Solve and Check
My Problem • Camden has a wall in his room that measures 13 feet long and 8 ½ feet high and is freshly painted. He wants to hang his favorite posters on the wall. Each poster measures 3 feet long and 2 feet high. What is the greatest number of posters that he can hang on the wall so that the posters do not overlap?
Step One- C Circle Key Numbers • Camden has a wall in his room that measures 13 feet long and 8 ½ feet high and is freshly painted. He wants to hang his favorite posters on the wall. Each poster measures 3 feet long and 2 feet high. What is the greatest number of posters that he can hang on the wall so that the posters do not overlap?
Step Two- U Underline the Question • Camden has a wall in his room that measures 13 feet long and 8 ½ feet high and is freshly painted. He wants to hang his favorite posters on the wall. Each poster measures 3 feet long and 2 feet high. What is the greatest number of posters that he can hang on the wall so that the posters do not overlap?
Step Three- B Box in Key Terms • Camden has a wall in his room that measures 13 feet long and 8 ½ feet high and is freshly painted. He wants to hang his favorite posters on the wall. Each poster measures 3 feet long and 2 feet high. What is the greatest number of posters that he can hang on the wall so that the posters do not overlap?
Step Four- E Evaluate and Eliminate • Wall = 13 ft. x 8 ½ ft. • Poster = 3 ft. x 2 ft. Question: What is the greatest number of posters that he can hang on the wall so that the posters do not overlap? What strategy could I use to solve?
Step Five- S Solve and Check • Explain your thinking- How do you know your answer is correct?
Try It Out… • 4 hungry teachers want to order burritos for lunch on Friday. Each burrito costs $4. 12. The 4 teachers have $20 total. Will there be enough to buy 4 burritos? • Show your answer two different ways. THINK—PAIR--SHARE
Problem Solving Strategies What About Students with Disabilities
Concrete-Representational-Abstract (C-R-A) Phase of Instruction • Instructional method incorporates hands-on materials and pictorial representations. • Students first represent the problem with objects manipulatives. • Then advance to semi-concrete or representational phase and draw or use pictorial representations of the quantities • Abstract phase of instruction involves numeric representations, instead of pictorial displays.
Interventions Found Effective for Students with Disabilities Reinforcement and corrective feedback for fluency Concrete-Representational-Abstract (C-R-A) Instruction Direct/Explicit Instruction Demonstration/Modeling Verbalization while problem solving Big Ideas Metacognitive strategies: Self-monitoring, Self-Instruction • Computer-Assisted Instruction • Monitoring student progress • Teaching skills to mastery • •
Common Characteristics of a Good Problem • It should be challenging to the learner. • It should hold the learner’s interest. • The learner should be able to connect the problem to her life and/or to other math problems or subjects. • It should contain a range of challenges. • It should be able to be solved in several ways.
Classroom Application Amping up the Rigor
Create Different Question Formats: Middle School • • M/C - one right answer (traditional format) M/C - more than one right answer (at least A-F) Short Answer - fill-in-the blank Open Ended - compare/contrast; explain/defend; how do you know?
Choosing Problem-Solving Tasks • The problem must be meaningful to the students. • The teacher must sometimes adapt the problem to make it more meaningful. • The teacher must work the problem to anticipate mathematical ideas and possible questions that problem might raise.
Presenting the Problem • It must be interesting and engaging. • It must be presented so that all children believe that it’s possible to solve the problem, but that they will be challenged. • The teacher has to decide whether students will work individually or in groups.
Group Work or Individual Work? • In groups, students don’t give up as quickly. • Students have greater confidence in their abilities to solve problems when working in groups. • When in a group, students hear a broad range of strategies from others. • Kids enjoy working in groups! • Students remember what they learn better when they assist each other. • If students are less productive, arrangements can be made for them to work alone. • There will be a heightened noise level—but conversation is an important part of the learning process.
Once the Kids Are Working… • Allow students to “wrestle” with the problem without just telling them the answer! • If we are just telling them what to do, the students are not engaged in the process. • Finally, teachers have to determine how to assess what the students are learning and what they need to learn next.
Learning Mathematics through Problem Solving • Students learn to apply the mathematics as they are learning it. • They can make connections within mathematics and to other areas of the curriculum. • Students can understand what they have learned. • Students can explain their thinking to others
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