Education Transformation Office

Education Transformation Office
INTERMEDIATE MATH Resources and Building Content Knowledge Education Transformation Office

Common Board Configuration (CBC)
DATE: August , 2013 Introductions: 3 – Activity Vocabulary: Pacing guide, Skills Sheets, Journal Entries , Scope and Sequence, Rubric, Essential Labs, NGSSS, Item Specs Exit Slip: Revisit Essential Question BELL RINGER: BENCHMARK: Math Resources and Content. 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 Objective: Today we will explore the math content and review resources to help implement best practices to teach the content effectively. ESSENTIAL QUESTION: How can exploring the math content and resources help me to be an effective teacher?

Write 2 actions that will assist you in meeting your goals
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?
4/13/2017 8:58 PM What’s New and Continuing with ETO Elementary Math? School Year © 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

What’s NEW??? 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

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
This binder has ideas and Activities for the Independent Center. The math Coach has this binder.

TEACH ONE, LEARN ONE

Instructions of Collaborative Strategy
TEACH ONE, LEARN ONE Instructions of Collaborative Strategy 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.

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 I Addition and Subtraction within 1,000

TOPIC I DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade Addition and Subtraction within 1,000 New Edition Common Core Textbook MACC.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

TOPIC I ESSENTIAL CONTENT INCLUDES:
Numbers Place Value Read Write Compare Order Inequalities symbols (<, >, =, =) Real-World contexts Operations Addition Subtraction Estimation Strategies Rounding Compatible Numbers Reasonableness Grouping Decimals (context of money that estimate to whole dollar Problem Solving (Rountine and Non-Routine) Real-World content Methods to determine solutions Tables Charts Lists Searching for Patterns Explain the method used to solve a problem

Item Specs Algebra – Number, Operations, & Statistics
ITEM SPECS for MA.3.A.4.1 Item Specs Algebra – Number, Operations, & Statistics

BENCHMARK CLARIFICATION What must students be able to do?
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.

CONTENT LIMITS MA.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

LLook for a pattern or rule: X 5 = Rule: Multiply by 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.4.1 Chairs 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).

Activities MA.3.A.4.1 cont… 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. Sample of 1 table with 4 chairs arrangement

Activities MA.3.A.4.1 cont… 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… 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 Item Specs Algebra – Number, Operations, & Statistics

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

Round to the nearest hundreds place value. 2,000 1,000 2,000 + 2,000 7,000

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 II Numbers through 100, 000

TOPIC II DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade Numbers through 100,000 Old 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.4.8 Infusing the NGSSS MA.3.A.6.1 and MA.3.A.6.2

TOPIC II Essential Content Includes:
Numbers Place Value Read Write Compare Order Inequality symbols (<, >, =, =) Real-World contexts Operations Addition Subtraction Estimation Strategies Rounding Compatible Numbers Reasonableness Grouping Decimals (context of money that estimate to whole dollar Problem Solving (Rountine and Non-Routine) Real-World content Methods to determine solutions Tables Charts Lists Searching for Patterns Explain the method used to solve a problem

Item Specs Algebra – Numbers through 100,000
ITEM SPECS for MA.3.A.6.2 Item Specs Algebra – Numbers through 100,000

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 LIMITS MA.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? in red
Erin Charles 3 (students circled) Gayle Paco Charles Erin 2 (students circled) Gayle Paco Charles Gayle 1(students circled) Erin Paco Charles Paco + 0 (students circled) Erin Gayle 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.

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

Mathematical Practices

OELCS 2005 Math Module 3 Speaker Notes
Standards for 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.” Mathematically literate students are able to analyze, reason, and communicate ideas effectively as they pose, formulate, solve and interpret mathematical problems in a variety of situations. ~ Bill McCallum

OELCS 2005 Math Module 3 Speaker Notes
Mathematical Practices Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning Make Sense, Persevere, Reason abstractly and quantitatively, construct viable arguments, critique others reasoning, Model with mathematics , use tools strategically while attending to precision, structure and repeated reasoning

Topic I and II Mathematical 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 II Mathematical 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 Podcast MP 6 and 7 Let’s Watch one together!
How did you see the practice being implemented?

TOPIC II Collect and Analyze Data

TOPIC III DIGGING DEEPER INTO THE MATH CONTENT 3rd Grade Collect and Analyze Data New Edition Common Core Textbook MACC.3.MD.2.3, MACC.3.MD.2.4 Infusing the NGSSS MA.3.S.7.1

TOPIC III Essential Content Includes:
Picture Graph (Pictographs) Sample size (No more than 200) Parts of a graph Keys (Scale of 1, 2, 5, 10) Interpreting and comparing information Generating Questions Colleting responses Displaying data (interpret, create, and explain) Real-World / mathematical contexts Bar Graphs Sample size (No more than 1,000) Scale (units of 1, 2, 5, 10, 50, or 100) Interpreting, create, and comparing information Generating questions Collecting responses Display data (interpret, create, and explain) Frequency Tables – Sample size (no more than 200) Line Plots – Sample size (no more than 200) Problem Solving (Routine and Non-Routine) Real-World content Methods to determine solutions Tables Charts Lists Searching for Patterns Explain the method used to solve a problem

Item Specs Sample question Data Analysis-
ITEM SPECS for MA.3.S.7.1 Item Specs Sample question Data Analysis-

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.

CONTENT LIMITS MA.3.S.7.1 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 LIMITS cont… MA.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.

What does it look like? Frequency Table Bar Graph

Show students how to use process of elimination
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 6 4 10 10 8 4 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.

What does it look like? Frequency Table Pictograph

Pay attention to the half symbols.
In this case, students will use a frequency table to match up the correct pictograph. Make a routine for students to write the corresponding number next to each activity. Have them write the total. 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. EXAMPLE: 10 10 4 * 2 10 5 5 10 4 8 10

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?

The most X’s 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

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 Podcast MP 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 III Multiplication

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.

Left Side of Interactive Student Notebook (ISN)
Essential Question: Left Side of Interactive Student Notebook (ISN) How can exploring the math and science content and resources help me to be an effective teacher?

ETO Elementary Collaboration Website
You can find this presentation in addition to all curricular resources on our very own ETO Collaboration Website Please visit us at: Build, Sustain, Accelerate

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