exit slip: revisit essential question agenda: i do: review focus group materials we do we do: teach...

INTERMEDIATE MATHResources and Building Content

Knowledge

Education Transformation Office

Common Board Configuration (CBC)

Exit Slip:

•Revisit Essential Question

AGENDA:

I Do:•Review focus group materials

We Do:•Teach One/Learn One Activity •Math Content Training

They Do:•Map out how you’re going to teach the beginning of the year concepts.You Do:•Processing Time: Answer the essential question•Homework Instruction

Vocabulary: Pacing guide, Skills Sheets, Journal Entries , Scope and Sequence, Rubric, Essential Labs, NGSSS, Item Specs

ESSENTIAL QUESTION: How can exploring the math content and resources help me to be an effective teacher?

Objective: Today we will explore the math content and review resources to help implement best practices to teach the content effectively.

BENCHMARK: Math Resources and Content.

BELL RINGER:

DATE: August , 2013

Introductions: 3 – 2 - 1 Activity

3-2-1

Set 3 Goals for this school year

Write 2 actions that will assist you in

meeting your goals

Write 1 challenge that may

Encounter

ESSENTIAL QUESTION:

How can exploring the math content and resources help me to be an effective teacher?

What’s New and Continuing with ETO Elementary Math?

2013-2014 School Year

Full implementation of Common Core in the GO Math series.

Reflex math- Computer program for fluency

New Teacher Lead Center (TLC) packets Newly created bellringers by benchmark

infusing basic skills for practice New Think Central dash boards iReady

What’s NEW???

GO MATH 3rd Grade “Old vs. New”

GO MATH / ThinkCentral.com

Go Math textbooks are all correlated to Common Core.

Schools will receive updated Common Core Teacher’s Editions

You will continue to have access to the “Old GO MATH” with the NGSSS through thinkcentral.com

GO MATH Technology Correlations

Math Focus Group Created Materials

Pacing Guide Revisions Skills Sheets Independent Centers Binder Journal Entries Success Academy Lessons

Pacing Guide Revisions New Common Core Pacing Guides NGSSS Blended Curriculum New NBC Learn Video Links Lesson Combination Suggestions

Skills Sheets-Teacher Edition

Skills Sheets-Student Friendly

Independent Centers Binder

TEACH ONE, LEARN ONE

TEACH ONE, LEARN ONE

Use your popsicle stick to determine which group you are in.

Everyone will all be in groups of three. Every 3 minute segment, one person will be the

teacher, another person will be the student, and one could be the observer.› The teacher will teach the student a lesson on any

preferred subject. › The student will take notes. › The observer will watch the behaviors.

After three minutes you will switch roles. Continue to rotate until you have been all three roles.

Instructions of Collaborative Strategy

TEACH ONE, LEARN ONE What to do?

Wait until you’re told to begin. Once you get a signal to begin, you will write a response to a question for two minutes non-stop onto a sheet of paper.

TEACH ONE, LEARN ONE

What is Teaching?(Two Minutes)

TEACH ONE, LEARN ONE

What is Learning?(Two Minutes)

TEACH ONE, LEARN ONE

Now, discuss your answers with a shoulder partner.

You can revisit your two answers. Has your answer changed from the two question? If so, take two minutes to reflect and change your

answer.

DIGGING DEEPER INTO THE MATH

CONTENT 3rd Grade

TOPIC IAddition and Subtraction within 1,000

DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade

TOPIC I

Addition and Subtraction within 1,000

New Edition Common Core TextbookMACC.3.NBT.1.1, MACC.3.NBT.1.2, MACC.3.OA.4.8, Infusing the NGSSS MA.3.A.6.1 and MA.3.A.4.1

• Numbers1. Place Value2. Read3. Write4. Compare5. Order6. Inequalities symbols (<, >,

=, =)7. Real-World contexts

• Operations1. Addition2. Subtraction

• Estimation Strategies1. Rounding 2. Compatible Numbers3. Reasonableness4. Grouping 5. Decimals (context of money

that estimate to whole dollar

• Problem Solving (Rountine and Non-Routine)

1. Real-World content 2. Methods to determine

solutions1. Tables2. Charts3. Lists4. Searching for Patterns

3. Explain the method used to solve a problem

TOPIC I ESSENTIAL CONTENT INCLUDES:

Item Specs

Algebra –

Number, Operations, & Statistics

ITEM SPECS for MA.3.A.4.1

• Students may extend numeric or graphic patterns beyond the next step, or find one or more missing elements in a numeric or graphic pattern.

• Students will identify the rule for a pattern or the relationship between numbers.

BENCHMARK CLARIFICATIONWhat must students be able to do?

MA.3.A.4.1

CONTENT LIMITSMA.3.A.4.1

• Items may use numeric patterns, graphic

patterns, function tables, or graphs. (bar graphs, picture graphs, or line plots only)

• Numeric patterns should be shown with 3 or more elements.

• Graphic patterns should be shown with 3 or more examples of the patterns repeated.

• Students should not be asked to extend the patterns more than 3 steps beyond what is given or to provide more than 3 missing elements.

What does it look like?MA.3.A.4.1

What does it look like?MA.3.A.4.1

LLook for a pattern or rule:

Rule: Multiply by 5

X 5 =

X 5 =

X 5 =

X 5 =

45

What are good strategies? MA.3.A.4.1

Read each problem carefully and know what’s being asked.

Students need to find a rule for the pattern.

Use the number pairs. Apply the pattern or rule to each relationship and think of an operation that will help find the missing number.

Students need to practice showing their work to avoid simple mistakes.

Activities… MA.3.A.4.1Chairs Around a Table:

Students will:

• Identify and extend a linear pattern involving the number of chairs that can be placed around a series of square tables.

• Describe linear patterns using words or symbols.

Materials: • Pattern Blocks (squares and triangles).

Using a context of chairs around square tables, students will be exposed to different linear patterns in this lesson. The patterns may vary slightly from situation to situation, where the students are allowed to determine a solution in multiple ways, in the end leading to an intuitive understanding of perimeter.

At Pal-a-Table, a new restaurant in town, there are 24 square tables. One chair is placed on each side of a table. How many customers can be seated at this restaurant? Show an arrangement of one table with four chairs. Draw a demonstration on the white board or tech board. Or use pattern blocks or other transparent manipulatives on the overhead projector.

Activities MA.3.A.4.1 cont…

Sample of 1 table with 4 chairs arrangement

When all students understand how chairs are placed, ask, "If there were 24 tables in a room, how many chairs would be needed?"

Have students make a table showing the pattern and finding the rule. Depending on students’ understanding of multiplication, they may immediately realize that the answer is 24 × 4 = 96.

Ask students to create a number sentence that will help solve for the missing number.

Activities MA.3.A.4.1 cont…

Activities MA.3.A.4.1 cont…

From the table, students should realize that the number of chairs is equal to four times the number of tables. Alternatively, they might recognize that each time a table is added, four chairs are added. This is a good opportunity to reinforce the connection between multiplication and repeated addition.

Teachers should ask students to explain their observations. "What is the pattern? How can you find the number of chairs for any number of tables?" [Multiply the number of tables by 4. If there are 24 tables, for instance, the number of chairs is 96. If there are n tables, the number of chairs is 4n.]

Item Specs

Algebra –

Number, Operations, & Statistics

ITEM SPECS for MA.3.A.6.1

BENCHMARK CLARIFICATIONWhat must students be able to do?

MA.3.A.6.1

• Students can use the

following estimation strategies when representing, comparing, and computing numbers through the hundred thousand:

› Clustering› Reasonableness› Chunking› Using a reference› Unitizing› Benchmarks› Compatible

numbers› Grouping› Rounding

What Are The Content Limits?MA.3.A.6.1

Numbers may be represented flexibly; for example 947 can be thought of as 9 hundreds, 4 tens, and 7 ones; 94 tens and 7 ones; or 8 hundreds 14 tens and 7 ones

Items may include the inequality symbols( >, <, =, =)

Items will not require the estimation strategy to be named

Front-end estimation will not be an acceptable estimation strategy

Decimals may be used in the context of money that estimate to a whole dollar

What does it look like?MA.3.A.6.1

What does it look like?MA.3.A.6.1

2,000

1,000

2,000

2,000+

7,000

Round to the nearest hundreds place value.

What Are Good Strategies?MA.3.A.6.1

Always have students draw the place value chart

When writing in expanded form, add the zeros after the place value

Use the “Dip” chant Use the rounding wrap (for example: 4

or less, let it rest. 5 or more raise the score)

In order for students to be successful with addition and subtraction, they need a firm comprehension of place value. In this lesson, students extend their understanding of place value to numbers through hundred thousands.

Activities… MA.3.A.6.1

Have the students pair up in twos. They can rotate and make their own Egyptians numbers and guess the value.

Activities MA.3.A.6.1 cont…

Let’s take a look at Lesson 1.4

Mental Math Strategies for Addition

TOPIC IINumbers through 100, 000

DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade

TOPIC II

Numbers through 100,000Old Edition Next Generation Sunshine State Standards Textbook (ONLY)MACC.3.NBT.1.1, MACC.3.NBT.1.2, MACC.3.NBT.1.3, MACC.OA.4.8Infusing the NGSSS MA.3.A.6.1 and MA.3.A.6.2

• Numbers1. Place Value2. Read3. Write4. Compare5. Order6. Inequality symbols (<, >, =,

=)7. Real-World contexts

• Operations1. Addition2. Subtraction

• Estimation Strategies1. Rounding 2. Compatible Numbers3. Reasonableness4. Grouping 5. Decimals (context of money

that estimate to whole dollar

• Problem Solving (Rountine and Non-Routine)

1. Real-World content 2. Methods to determine

solutions1. Tables2. Charts3. Lists4. Searching for Patterns

3. Explain the method used to solve a problem

TOPIC II Essential Content Includes:

Item Specs

Algebra –

Numbers through 100,000

ITEM SPECS for MA.3.A.6.2

BENCHMARK CLARIFICATIONWhat must students be able to do?

MA.3.A.6.2

• Students will solve non-routine problems in situations where tables, charts, lists, and patterns could be used to find the solutions.

CONTENT LIMITSMA.3.A.6.2

• Items should require students to solve non-

routine problems and not align with the clarifications of MA.3.A.4.1 (extending a graphic pattern or identifying a simple relationship [rule] for a pattern).

What does it look like?MA.3.A.6.2

What does it look like?in red

Charles

Erin

Gayle

Paco

Erin

Erin

Erin

Gayle

Gayle

Gayle

Paco

Paco

Paco

Charles

Charles

Charles

3 (students

circled)

2 (students circled)

1(students circled)

+ 0 (students

circled)

6 different pairs of two students can be made

What are good strategies?MA.3.A.6.2

Always have students draw a chart or make an organized list

Make sure students are using a strategy that they understand and can demonstrate and verbalize on their conclusion.

Students need to check if answer make sense.

ACTIVITIES… MA.3.A.6.2 Students may work in small groups

Example: A frog in a pit tries to go out. He jumps 3 steps up and then slides 1 step down. If the height of the pit is 21 steps, how many jumps does the frog need to make?  

Example: Show 5 different combinations of US coins that total 53¢.  

Example: The 24 chairs in the classroom are arranged in rows with the same number of chairs in each row. List all of the possible ways the chairs can be arranged.  

revise

Mathematical Practices

“The Standards for Mathematical Practice are unique in that they describe how teachers need to teach to ensure their students become mathematically proficient. We were purposeful in calling them standards because then they won’t be ignored.”

~ Bill McCallum

Standards for Mathematical Practices

Mathematical Practices

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Topic I and IIMathematical Practices

MP 6: Attend to precision

Mathematically proficient students can…

use clear definitions and mathematical vocabulary to communicate their own reasoning

careful about specifying units of measure and labels to clarify the correspondence with quantities in a problem

Topic I and IIMathematical Practices

MP 7: Look for and make use of structure

Mathematically proficient students can…

look closely to determine possible patterns and structure (properties) within a problem

analyze patterns and apply them in appropriate mathematical context

Professional Development PodcastMP 6 and 7

Let’s Watch one together!

How did you see the practice being implemented?

TOPIC IICollect and Analyze Data

DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade

TOPIC III

Collect and Analyze Data

New Edition Common Core TextbookMACC.3.MD.2.3, MACC.3.MD.2.4Infusing the NGSSS MA.3.S.7.1

• Picture Graph (Pictographs)1. Sample size (No more than 200)

2. Parts of a graph3. Keys (Scale of 1, 2, 5, 10)4. Interpreting and comparing

information5. Generating Questions6. Colleting responses7. Displaying data (interpret, create,

and explain) 8. Real-World / mathematical contexts

• Bar Graphs1. Sample size (No more than 1,000)2. Parts of a graph 3. Scale (units of 1, 2, 5, 10, 50, or

100)4. Interpreting, create, and

comparing information5. Generating questions6. Collecting responses 7. Display data (interpret, create, and

explain) 8. Real-World / mathematical contexts

• Frequency Tables – Sample size (no more than 200)

• Line Plots – Sample size (no more than 200)

• Problem Solving (Routine and Non-Routine)

1. Real-World content 2. Methods to determine

solutions1. Tables2. Charts3. Lists4. Searching for Patterns

3. Explain the method used to solve a problem

TOPIC III Essential Content Includes:

Item Specs

Sample question

Data Analysis-

ITEM SPECS for MA.3.S.7.1

BENCHMARK CLARIFICATIONWhat must students be able to do?

MA.3.S.7.1

• Students will construct, analyze, and draw conclusions from frequency tables, bar graphs, picture graphs, and line plots.

• Students will analyze data to supply missing data in frequency tables, bar graphs, picture graphs, and line plots.

Students may be required to choose the most appropriate data from observations, surveys, and/or experiments

Items may assess identifying parts of a correct graph and recognizing the appropriate scale

The increments on the scale are limited to units of 1, 2, 5, 10, 20, 25, 50, or 100

CONTENT LIMITSMA.3.S.7.1

Pictographs can use keys containing a scale of 1, 2, 5 , 10

The data presented in graphs should represent no more than five categories

The total sample size for bar graphs should be no more than 1, 000

The total sample size should be no more than 200 for frequency tables, pictographs, and line plots.

Addition, subtraction, or multiplication of whole numbers may be used within the item.

CONTENT LIMITS cont…MA.3.S.7.1

What does it look like?

Frequency Table

Bar Graph

Show students how to use process of elimination. Since there were 4 scones sold, then we could eliminate A and D.

And there are 8 brownies sold. Answer choice B shows that.

Then we verify if Muffin showed 2 sold and Cookies shows 10 sold.

8

4

4

108

6

10

8

What are some good strategies to consider:

Extracting data from a Bar Graph:

• Read the title first and then the scale to know what and how much the increments are.

• Write the corresponding value next to or on top of each bar.

• Pay attention to what is being asked to answer.

Frequency Table

Pictograph

What does it look like?

Extracting data from a pictograph:

It is very IMPORTANT that students read the title first and then the key so they know what and how many the symbols represent.

Make a routine for students to write the corresponding number next to each activity. Have them write the total.

In this case, students will use a frequency table to match up the correct pictograph.

EXAMPLE:

104

10

102

5

104

10

58

*

Pay attention to the half symbols.

What are some good strategies to consider:

Extracting data from a Pictograph:

• It is very IMPORTANT that students read the title first and then the key so they know what and how much the symbols represent.

• Write the value next to each symbol and then find the total for each row of symbols.

• Pay attention to what is being asked to answer.

What does it look like?

Line plots may be confusing to some students. It is easy to mix up the numbers below the number line and the X’s above it.

Students need to remember that the numbers below the number line are like the categories in a pictograph or a bar graph. In a line plot, these categories are numerical. The number of X’s above each number on the number line tells how many times this number or category occurs.

Answer: C

The most X’s

What are some good strategies to consider:Extracting data from a Line Plot:• Remember that the numbers

below the number line are like the categories in a pictograph or a bar graph. In a line plot, these categories are numerical.

• The number of X’s tells how many times the number or category occurs.

• Pay attention to what is being asked to answer.

Topic III Mathematical Practices

MP 1: Make sense of problems and persevere in solving them.

Mathematically proficient students can…

explain the meaning of the problem

monitor and evaluate their progress “Does this make sense?”

use a variety of strategies to solve problems

Topic III Mathematical Practices

MP 4: Model with mathematics.

Mathematically proficient students can…

apply mathematics to solve problems that arise in everyday life

reflect on their attempt to solve problems and make revisions to improve their model as necessary

Professional Development PodcastMP 1 and 4

Let’s Watch one together!

How did you see the practice being implemented?

Activities for Data Analysis You could have the kids survey others in the class for selected

questions - do you have pets, favorite food, type of ice cream etc. From the info collected, create a bar graph. You could give the kids suggested topics but let them pick their own questions.

You can also have them build individual graphs by rolling dice. Make dice that fit with your theme. Give each student a blank graph and let them label the columns (or you can do this part). I use this at a center and the kids roll a die and record the roll on the graph. This week we are studying jobs that people do. I have a graph with pictures of a doctor, police officer, firefighter, teacher, and a postal worker. The die is labeled with these pictures also. The students take turns rolling the die until everyone has rolled and recorded 10 times on their own graph. They should all different.

TOPIC IIIMultiplication

What must students be able to do?

Model multiplication, including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations, measurement and partitioning.

What are the benchmark clarifications?

What does it look like?

What does it look like?

3 groups of 2

+ +

2 + + 2 2

What are good strategies?

Combinations-Make a tree diagram to show every combination

Use the finger multiplication trick for 9s and 6s-10s

Circle key words to help indicate the operation used.

Essential Question:

How can exploring the math and science content and resources help me to be an effective teacher?

Left Side of Interactive

Student Notebook (ISN)

ETO Elementary Collaboration Website

Build, Sustain, Accelerate

You can find this presentation in addition to all curricular resources on our very

own ETO Collaboration WebsitePlease visit us at:

http://www.etomiami.com/

QUESTIONS/CONCERNS