elementary mathematics fourth and fifth grade level... · elementary mathematics fourth and fifth...

Quarter Four Concept Lesson Professional Development HO # 0 Deconstructing the TTLP

Los Angeles Unified School District

Elementary Mathematics

Fourth and Fifth Grade

Deconstructing the TTLP


Outcomes

Understand how concept lessons can translate into everyday practices and how the concept lessons link to the Thinking Through a Lesson Protocol (TTLP)

Engage in the Quarter 4 Concept Lesson

as teachers by Generating Possible Solutions Anticipating Student Misconceptions and

Questions to Address Them Sequencing Student Solutions and

Designing Questions that Facilitate a Mathematically Productive Discussion

Identify the instructional strategies

embedded in concept lessons and how the needs of diverse learners (ELs, SELs, GATE students and other students with special needs) are addressed


Thinking Through a Lesson Protocol The main purpose of the Thinking Through a Lesson Protocol is to prompt you in thinking deeply about a specific lesson

that you will be teaching that is based on a cognitively challenging mathematical task.

SET-UP Selecting and setting up a mathematical task

EXPLORE Supporting students’ exploration of the task

SHARE, DISCUSS, AND ANALYZE Sharing and discussing the task

What are your mathematical goals for the lesson (i.e., what is it that you want students to know and understand about mathematics as a result of this lesson)?

In what ways does the task build on students’

previous knowledge? What definitions, concepts, or ideas do students need to know in order to begin to work on the task?

What are all the ways the task can be solved?

- Which of these methods do you think your students will use?

- What misconceptions might students have? - What errors might students make? What are your expectations for students as they

work on and complete this task?

- What resources or tools will students have to use in their work?

- How will the students work – independently, in small groups, or in pairs – to explore this task?

- How long will they work individually or in small groups/pairs? Will students be partnered in a specific way? If so, in what way?

- How will students record and report their work?

How will you introduce students to the activity so

as not to reduce the demands of the task? What will you hear that lets you know students

understand the task?

As students are working independently or in small groups:

- What questions will you ask to focus their thinking?

- What will you see or hear that lets you know how students are thinking about the mathematical ideas?

- What questions will you ask to assess students’ understanding of key mathematical ideas, problem solving strategies, or the representations?

- What questions will you ask to advance students’ understanding of the mathematical ideas?

- What questions will you ask to encourage students to share their thinking with others or to assess their understanding of their peer’s ideas?

How will you ensure that students remain engaged

in the task?

- What will you do if a student does not know how to begin to solve the task?

- What will you do if a student finishes the task almost immediately and becomes bored or disruptive?

- What will you do if students focus on non-mathematical aspects of the activity (e.g., spend most of their time making beautiful poster of their work)?

How will you orchestrate the class discussion so that you accomplish your mathematical goals? Specifically:

- Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?

- In what ways will the order in which solutions are presented help develop students’ understanding of the mathematical ideas that are the focus of your lesson?

- What specific questions will you ask so that students will:

make sense of the mathematical ideas that you want them to learn?

expand on, debate, and question the solutions being shared?

make connections between the different strategies that are presented?

look for patterns?

begin to form generalizations? What will you see or hear that lets you know that

students in the class understand the mathematical ideas that you intended for them to learn?

What will you do tomorrow that will build on this

lesson?


Set Up What mathematical concepts will be developed in the implementation of this

task?

What are the possible solutions to the task?


Set Up What mathematical concepts will be developed in the implementation of this task?

Where will this task be situated in the instructional guide? What experiences have come before and what experiences will come after this task to support the building of conceptual understanding? How does this task address ELs, SELs, GATE students, and students with special needs?


Explore What do you expect your students to do as they engage in the lesson?

What misconceptions or errors are surfacing?


Question Types Found in Quarter 4 Concept Lesson

Questioning and Student Engagement

To focus thinking To assess thinking To advance thinking


Question Types

Types and Purpose of Questions

Focusing Thinking Assessing Thinking Advancing Thinking

What it does

Talks about issues outside of math in order to enable links to be made with mathematics.

Helps students to focus on key elements or aspects of the situation in order to enable problem-solving.

Ask students to articulate, elaborate, or clarify ideas.

Enables correct mathematical language to be used to talk about them

Rehearses known facts/ procedures. Enables students to state facts/procedures.

Requires immediate answer.

Extends the situation under discussion to other situations where similar ideas may be used.

Makes links between mathematical ideas and representations.

Points to relationships among mathematical ideas and mathematics and other areas of study/life.

Points to underlying mathematical relationships and meanings.

What it sounds

like

What is the problem asking you?

What is important about this?

What games have you played where you used…?

What is a…? (reference to context of problem)

How could you record what you just told me?

How could you use a … to help you record what is happening?

How did you get your answer?

How do you know you are correct?

What is this called? How would you use

an equation to record what you just told me?

How would this work with other numbers?

How do you know whether or not this pattern always works?

In what other situations could you apply this?

How are … and … related?

What other patterns do you see?

Where else have we used this?


Explore What additional questions can you ask as students are engaged in the lesson?

Focusing Assessing Advancing


Share, Discuss, and Analyze What will you see or hear that lets you know students are developing understanding of

the concept? What questions will you need to ask to build mathematical understanding?

What questions will you ask to connect solutions and strategies?

What might you hear your students say to summarize the mathematical ideas of the lesson?

What instructional strategies will meet the needs of ELs, SELs, Gate students and other students with special needs?


Addressing Diverse Learners

What instructional strategies are embedded in the concept lessons and how are the needs of diverse learners (ELs, SELs, GATE students and other students with special needs) addressed?


Concept Lesson

Standard(s)

Mathematical Task

Set Up Explore

Consider all possible solutions

Focus, Assess and Advance

Student Exploration

Build on prior knowledge

Set context for task

Address Misconceptions

through Questioning

Select Student Work for Sharing

Consider Mathematical Goals

Share, Discuss and Analyze

Share Student Work in an Order that Builds

Conceptual Understanding

Orchestrate Discussion through Questioning and

Talk Moves

Summarize Key Mathematical Ideas; Make

a Link to Algorithm or Formula

What Shape Are You In?

Grade 4 Quarter 4 Mathematics Professional Development Handout # 1 “Geometry”

9 -9

8 -8

7 -7

6 -6

5 -5

4 -4

3 -3

2 -2

1 -1

10 -10

Students might think that 24 is the area, instead of the perimeter

Students might think that play pens with the same perimeter have the same area

Students might think that a square is not a rectangle

Students might think that there is only 1 solution to the task

If using color tiles, students might count out 24 tiles and use all 24 to build the perimeter of the pen. But, o students might build the rectangle

with “flushed” corners, instead of having the 2 tiles at each of the corners only meet at one of their vertices, so this could result in a rectangle that has a perimeter of 28 and not 24 units.

2

10

10

2

If using color tiles, students might count out 24 tiles and use all 24 to build the perimeter of the pen. But, o students might consider the area

of the play pen to be only the space on the inside of the “perimeter” built by the tiles. So, in the above example, students might think that the area of that rectangle is 16 square units.

Students might add absolute values of numbers

Students might think that negative numbers that have an absolute value greater than a positive number might be larger (i.e. they may think -7 is greater than 4)

When using a number line students might think than when you add you always move to the right of your starting point.

Students might think that the sum of 2 numbers is always greater than the two addends, so 6+-2 being the same as 4 might be a little disconcerting since 4 is less than the addend 6.

Students might figure out that a negative sign means subtraction but not know how to subtract a larger number from a smaller number. So, for example, they might figure out that Jeremy’s roll has a sum of 4 (6-2), but for Eva’s roll they may think the sum is 2 (1-3).

Puppy Playpen

1. Your friend has 24 feet of fencing. How would you place the fence so that the puppy has the biggest rectangular playpen possible?

Explain how you know. Represent your solution in as many ways as possible.

Your friend just got a new puppy. He asks you to help him build a playpen for the puppy. The playpen will be in the shape of a rectangle and have a fence around it.

LAUSD Mathematics Program 2006 - 2007

Elementary Instructional Guide Concept Lesson, Grade 4

Quarter 4

Puppy Playpen

2. When your friend’s grandfather finds out about the puppy, he gives your friend another 16 feet of fencing. How would you place the total amount of fencing so that the puppy has the biggest rectangular playpen possible?

Explain how you know. Show your solution in as many ways as possible.

3. Another friend also got a puppy. Her parents’ gave her some fencing to make a rectangular puppy playpen. Explain to her how to place the fence so that her puppy has the biggest rectangular playpen possible and how you know it will be the biggest playpen.



Quarter 4



Quarter 4

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Quarter 4

The Game of Chips

5th

Grade Lesson

Quarter 4

.

In the game of Chips, each yellow chip represents a value of positive one and each red chip represents a value of negative one.

Each player takes a turn and rolls 2 dice – one white and one red. The player receives the number of chips that match with the numbers they rolled and then finds the sum. For example, if you rolled a 4 on the white die and a 2 on the red die you would receive 4 yellow chips and 2 red chips. You would then find the sum. The winner is the player who has the highest score after 2 turns.

Following is what your friends, Jamal and Eva, rolled:

1st turn Jamal: red 2, yellow 6 Eva: red 3, yellow 1 2nd turn Jamal: red 3, yellow 3 Eva: red 6, yellow 1

1. What is each player’s sum for the 1st turn? Show how you found your answer and write a number sentence for each.

2. What is each player’s sum for the 2nd turn? Show how you found your answer and write a

number sentence for each.



Quarter 4

The Game of Chips

5th

Grade Lesson

Quarter 4

3. Eva says she won the game because she has the largest sum after 2 turns. Is she correct? Explain how you know.

4. How could you use a number line to show each of the number sentences?



Quarter 4

The Game of Chips

Jamal Eva

1st

turn 1st

turn

2nd

turn 2nd

turn

Final score Final score



Quarter 4

Jamal Eva

1st

turn

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

2nd

turn

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Final score

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7



Quarter 4

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