Dates:Tuesdays, Jan 7 – Feb 11

Time: 5:30 pm to 8:30 pm

Location: Victor Scott School

Tentative Course Timeline

Week/Content Topic Dates Pedagogy topic

Week 1Operational Strategies Jan 7

Introductory information, survey, pre-assessment

Teaching through Problem Solving Framework

Week 2Operational Strategies

& FractionsJan 14

Planning a Three-Part Lesson

Week 3Fractions Jan 21 Planning a Three-Part Lesson

Week 4Fractions & Algebra Jan 28 Formative Assessment

Teachers present planned lessons

Week 5Algebra Feb 4 Questioning

Week 6Algebra Feb 11 Post Test & Exit survey

Math and Science InstituteExploring Numbers and

Algebraic ThinkingToday’s Agenda

Recap on Fraction Concepts

Engaging in Operational Fractions Tasks

Planning an Effective Math Lesson

Plan a lesson for your year level

Facilitator: Rebeka Matthews Sousa – rsousa@moed.bmContent Specialist Teacher for Mathematics

5:30 pm

5:45 pm

6:45 pm

7:00 pm

Learning ObjectivesIn this session, Mathematicians will:OHave a deeper conceptual

understanding of fractionsOInvestigate various ways to

represent, compare, and operate with fractions

Exploring Fraction Concepts –Fraction Equivalents

Find fraction names for each shaded region. Explain how you saw each name you find.

Exploring Fraction Concepts –Fraction Equivalents

Using set models for equivalent fractions.Set out 24 counters – 16 red (apples) and 8 yellow (bananas)Your task: Group the counters into different fractional parts of the whole and use the parts to create fraction names for the fractions that are apples and the fractions that are bananas.

Exploring Fraction Concepts –Fraction Equivalents

Using set models for equivalent fractions.Set out 24 counters – 16 red (apples) and 8 yellow (bananas)Your task: Group the counters into different fractional parts of the whole and use the parts to create fraction names for the fractions that are apples and the fractions that are bananas.

Exploring Fraction Operations –Adding Fractions

Where and Why is it Wrong?A student adds these two fractions:

The answer is incorrect. Explain why it is incorrect. Is the answer reasonable?Using a strategy, other than using “like denominators” and following a rule for adding fractions, solve the problem.Explain using words or diagrams, how you would come to the correct answer.

Using Fraction Strips to show addition of fractions:

Models for Adding FractionsHave students develop algorithms rather than just memorizing them. Make sense out of what the algorithm means.Some may develop the understanding on their own from the models.

Models for Adding FractionsHave students develop algorithms rather than just memorizing them. Make sense out of what the algorithm means.Some may develop the understanding on their own from the models.

Models for Adding FractionsHave students develop algorithms rather than just memorizing them. Make sense out of what the algorithm means.Some may develop the understanding on their own from the models.

Models for Adding FractionsHave students develop algorithms rather than just memorizing them. Make sense out of what the algorithm means.Some may develop the understanding on their own from the models.

Models for Adding FractionsHave students develop algorithms rather than just memorizing them. Make sense out of what the algorithm means.Some may develop the understanding on their own from the models.

Models for Adding FractionsHave students develop algorithms rather than just memorizing them. Make sense out of what the algorithm means.Some may develop the understanding on their own from the models.

Exploring Fraction Operations –Adding/Subtracting Fractions

Can You Make it True?There are two missing values (in the numerators, or denominators, or one of each). Can you determine the digits that will make each problem true? You may not use digits already in the problemUse fraction benchmarks (0, ½, 1) to support thinking.

Exploring Fraction Operations –Adding/Subtracting Fractions

Jumps on the RulerUsing the ruler, find the results of these three problems without applying the common denominator algorithm,

Addressing Misconceptions for Adding/Subtracting Fractions

Assess students’ understanding and keep an eye on common misconceptions.1. Adding Both Numerators and

Denominators2. Failing to Find Common

Denominators3. Difficulty Finding Common Multiples4. Difficulty with Mixed Numbers

Commercial Break

Exploring Fraction Operations –Multiplying Fractions

Water, Walking, and WheelsHow would you work out the following problems, using a manipulative or drawing to figure out the answers to these three tasks.1. The walk from school to the public library takes

15 minutes. When Tatiana asked her mom how far they had gone, her mom said that they had gone of the way. How many minutes had they walked? (Assume constant walking rate)

2. There are 15 cars in Tiago’s matchbox car collection. Two-thirds of the cars are red. How many red cars does Michael have?

3. Marie filled 15 glasses with cup of milk in each row. How much milk did Wilma use?

Modeling Multiplication Problems

How would you explain each solution?

Exploring Fraction Operations –Multiplying Fractions

How much?

How much is of How would you work this problem without using standard algorithm?

How much is of How would you work this problem without using standard algorithm? How can you use this problem to explain the standard algorithm?

Exploring Fraction Operations –Multiplying Fractions

Possible solutions

Exploring Fraction Operations –Multiplying Fractions

Possible solutions

Addressing Misconceptions for Multiplying Fractions

Assess students’ understanding and keep an eye on common misconceptions.1. Treating the Denominator the Same

as in Addition and Subtraction Problems

2. Inability to Estimate the Approximate Size to the Answer

3. Matching Multiplication Situations with Multiplication (and Not Division)

Exploring Fraction Operations –Multiplying Fractions

Divided upDetermine your answers using a non-standard algorithm

a. 1 ¼ hours to do three chores. How much time for each?

Exploring Fraction Operations –DividingFractions

How would you explain these two models of divisions?

Exploring Fraction

Operations –DividingFracti

ons

How would you explain these two models of divisions?

Addressing Misconceptions for Dividing Fractions

Assess students’ understanding and keep an eye on common misconceptions.1. Thinking the Answer Should Be

Smaller2. Connecting the Illustration with the

Answer3. Writing Remainders

Effective Teaching Process for Fraction Operations

p.120-121 of J. Van de Walle et al.Understanding Fraction Operations“Students must be able to compute with fractions flexibly and accurately. Success with fractions, in particular computation, is closely related to success in Algebra. If students enter formal algebra with a weak understanding of fraction computation (in other words, they have memorized the four procedures but do not understand them), they are at risk for struggling, which in turn can limit college and career opportunities. Deeper understanding and flexibility take time! This is recognized by research…”

O Read p.121-122 Effective Teaching ProcessO Read p.140 Teaching Considerations for Teaching

Fractions

Planning a LessonKeep in mind the planning criteria and rubric for teachingThe lesson should be a condensed lesson (20 mins)And a lesson appropriate for the level that you teach.

P3 P4 P5 P6 Middle

DeniseAngela

KamalJanine

UneakaChantal

VivienneDesmond

ChantelRenee

Key to planning

How will you know that your students know it?

Planning Learning TasksAsking yourself the following questions will help you plan effective learning tasks:OWhat are the concepts I want my students

to learn from the task I plan?OHow will I determine my students’ prior

knowledge?OHow ill I design lesson (learning tasks) to

help student explore and learn these concepts?

OHow will I assess student learning?

…The Three-Part Lesson

Criteria for Effective Mathematics Tasks

A good instructional task captures students’ interest and imagination and satisfies the following criteria:• The solution is not immediately obvious• The problem provides a learning situation related to a key

concept or big idea• The task is aligned with the Cambridge Objective(s)• The context of the problem is meaningful to students.• There may be more than one solution.• The problem promotes the use of one or more problem

solving strategies• The situation requires decision making above and beyond the

choosing of a mathematical operation.• The solution time is reasonable.• The situation may encourage collaboration in seeking

solutions.

Checklist for Planning Effective Mathematics TasksThe Lesson Has a balance of skills: mental math, conceptual understanding, problem solving, and

computational skills May include the Three-Part Lesson as a vehicle to Teach Through Problem-solving:

(Activate Thinking, Working on it, Reflect and Connect) A good instructional task captures students’ interests and imagination and

also satisfies the following criteria.The Task(s) Are aligned with the Cambridge Objective(s). Provides a learning situation related to key concept or big ideas. Or problem is meaningful relevant and interesting to students. Cognitively demanding (solution is not immediately obvious) and there may be more

than one solution) Or problem promotes the use of one or more problem solving strategies (multiple entry

or exit points) Differentiated Requires decision making above and beyond the choosing of a mathematical operation. May encourage collaboration in seeking solutions. Resources, materials, manipulatives prepared in advanced.Assessment Variety of assessment tools to access students throughout the lessonQuestioning Questions are prepared in advance to encourage mathematical thinking and

communication of mathematical reasoning.

What types of questions will I ask students to promote thinking and

to assess?Teachers promote the sharing of ideas by asking the following kinds of questions:O What did you do to find out…?O How could you show that…?O Can you explain why…?O How do you know that…?O How do you know that your idea is correct?O Can someone explain a different strategy?

Formative Assessment

Example

Always, sometimes or Never True

Teacher Reflection & Homework

OHave I including all of the necessary requirements of my lesson?

OWhat will I need to bring or prepare for the next session?