MATH JOURNEYS TEACHING THROUGH PROBLEM-SOLVING. THE PROBLEM-SOLVING CYCLE 1.Review the table. What do you find interesting or puzzling? 2.In what way.

Slides:

Advertisements

Similar presentations

What is a fraction? 1 A simple fraction has two parts:

Advertisements

Students use models to compare fractions.

Chapter 6: Percents Section 3 Finding a Percent of a Number.

Sense Making and Perseverance Learning goal: Explore strategies teachers can use to encourage students to make sense of problems and persevere in solving.

Fractions Choose three pieces of paper of the same colour. Choose a pen that will write on them. Take a seat. Have a chat. How can we fairly share the.

Equivalent Fractions Raising and Reducing.

Placing and Identifying Fractions on The Number Line

Equivalent Fractions Raising and Reducing.

Multiplication of Fractions: Thinking More Deeply Steve Klass 48th Annual Fall Conference of the California Mathematics Council - South Palm Springs, CA,

Lesson 25 Objective: Divide a whole number by a unit fraction

The GCF of two numbers is 5 and the LCM of the numbers is 280

Vista Middle School’s Garden Las Cruces, New Mexico A Lesson Study On Perimeter and Area in the 7 th Grade.

Division of Fractions: Thinking More Deeply Division of Fractions: Thinking More Deeply Steve Klass National Council of Teachers of Mathematics Kansas.

Created by Susan Price Finding a fraction of a whole number involves using the math operations of division and multiplication. Janie scored 2/3 of her.

Grade 4 – Module 5 Module Focus Session

Unit 5 Unit 5. KEY WORDS Student outcome: I know what a fraction is A fraction is a number that stands for part of something. Usually a fraction represents.

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi 2007 Over.

Everyday Math Grade 4 – Lesson 7.9 Comparing and Ordering Fractions

Understanding and Reasoning about Multiplication of Fractions.

Strategies to support student learning of fractions

LESSON How do you compare and order rational numbers? Comparing and Ordering Rational Numbers 2.3.

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi Building.

BASIC MATH SKILLS LESSON 3: RENAMING FRACTIONS IN SIMPLEST FORM P. 59.

Warm Up Find the GCF of these sets 1) 10, 122) 14, 213) 24, 40 Answers: 1) 2 2) 7 3) 8.

Creative Data handling Understand the process and progression of data handling cycle Develop creative strategies for promoting the different stages of.

5-2 6 th grade math Adding and Subtracting with Like Denominators.

Equivalent Fractions Raising and Reducing

Fractions Part of a whole 1 3 numerator denominator Out of Divided by.

Making Equivalent Fractions.

Bell Work. Today you will think about how to find a mystery number based on information given to you as part of a game. In the game, you will practice.

Long and Short Term Goals To develop a responsible and positive attitude we chose Respect for Self, Others and Learning for the long term goal. Our students.

Math 5 Unit Review Instructor: Mrs. Tew Turner. In this lesson we will review for the unit assessment and learn test taking strategies.

NETW10RK Maths investigations.

Everyday Math Grade 4 – Lesson 7.2 Fraction of a Number

Unit 4 6 th Grade Math Multipying and Dividing Fractions Review.

MU15L2D21 Measuring to the Nearest Tenth Unit 15, Lesson 2, Day 2.

Create a 5 Whys. Think about the purpose of maths and what type of mathematical learners you wish to create in the classroom.

Developing subject knowledge and practice in fractions. To identify some of the difficulties and misconceptions which children have & implications for.

Compare Fractions SWBAT compare fractions with like denominators and fractions with unlike denominators.

Understanding Student Thinking in Algebra Relational Thinking.

Lesson 3 Comparing Fractions. Rule for Comparing Two Fractions To compare two fractions, both fractions must have the same denominator. (The same denominator.

Adding & Subtracting Fractions With Like Denominators.

Write a fraction for a whole. 1. How to count parts of a group.

In this lesson you are going to learn how to divide fractions by multiplying by the reciprocal.

1 Math CAMPPP 2012 Plenary 1 Why students struggle with fractions.

Comparing and Ordering Rational Numbers

For example, what is ?.

Fractions(5) LO: Compare the value of unit fraction.

Multiplying and Dividing

Intoduction to Fractions

On page, write each fraction in simplest form.

GCF Problem Solving How can you tell if a word problem requires you to use Greatest Common Factor?

How are Science and Math Used in Engineering?

Adding and subtracting rational expressions

Building Math in the classroom - Teaching Through Problem-Solving -

For example, what is ?.

Section 3.1 Study Materials

Adding and subtracting rational expressions

Equivalent Fractions Raising and Reducing.

For example, what is ?.

6th grade Math Miss Quimby’s Class

Year 6 (National Numeracy Strategy) (Based on DFEE Sample Lessons)

Multiplying and Dividing Rational Expressions

Year 6 (National Numeracy Strategy) (Based on DFEE Sample Lessons)

Review The circle is divided into（）equal parts,

Which is bigger 3 5

Section 3.5 Study Materials

For example, what is − ?.

Decimals: Connections to the Common Core and the IES Practice Guide

Presentation transcript:

MATH JOURNEYS TEACHING THROUGH PROBLEM-SOLVING

THE PROBLEM-SOLVING CYCLE 1.Review the table. What do you find interesting or puzzling? 2.In what way are the phases of a problem-solving lesson like your current practice? 3.In what way are they different? 4.What seems especially challenging? 5.Identify individually (or as a team) one or more aspects of TTPS that you would like to work on during Math Journeys and during your team’s lesson study cycle? 6. Note this in the goals section of the lesson plan template.

INVESTIGATE FRACTIONS TASKS There’s something weird about fractions. If the numerator, which is the top, is the same, the bigger the denominator the smaller the fraction. JORDAN, grade 5

TRY THIS: Problem 1: Estimate the answer to 12/13 +7/8. You will not have time to solve the problem using paper and pencil.

STUDENT RESULTS Student ResponsesPercent Responding Age Don’t know14

TRY THIS: Problem 2: Find two fractions between ½ and 1. Write these on your paper.

STUDENT WORK Look at the 6 examples of student work Three are from students who learned fractions in a measurement context (Measure Up curriculum) Three are from students who used a basal textbook

TRY THIS: Problem 3: Jim has ¾ of a yard of string which he wishes to divide into pieces, each 1/8 of a yard long. How many pieces will he have?

DISCUSSION Now that you have solved three different fraction tasks and discussed student solutions: Briefly summarize as a group your insights into the question “What is difficult for students about fractions?”

WHAT IS THE STUDENT THINKING? Researcher: Which fraction is smaller? 6/4 or 6/5 Chris: 6/4. Because 4 takes longer to get to 6 than 5 does.

MODELS OF THE FRACTION ¾ Each model has different strengths and shortcomings for building student understanding, and there is one single “best” model. Ultimately, students will need to understand that ¾ can represent several very different situations. What are the different situations?

“MYSTERY STRIP” ACTIVITY In this packet are a meter-length strip of paper tape and a mystery- length strip of paper tape. Individually try to solve the following problem and then discuss your solutions as a group. Without using standard measuring devices, express the length of the mystery piece (a fractional part of a meter) in meters. After you do the work individually, share your ideas about how students might solve the problem and what they might find challenging. What understandings of fractions would help students solve the problem?

VIDEO LESSON: DR. AKIHIKO TAKAHASHI Review the lesson in teams. Watch the lesson. Take notes. What are students understanding? What are their strategies? Are they interested in the lesson? Write down the questions he asks students?